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Scheme of a SingleQuantum-Dot System:

Gate

QuantumDot

Source Drain

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ε(

(a) (b)

(c)

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scaled by s = 0.7

--

e

e

Electrodes

e+

q21

q2q

1

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occupied states

T= 0 K

=

(δ)(c)

(α)

(b)(a)

unoccupied states

qD

qS

qD

qS

q =0

q =0

q =0

q =e

q =+e

q =0

(γ)

εFεF(S)

e2CΣ

2

CE =

εF

εF

VDS IDS

Source Drain

Island

Tunnel Barriers

εF(S)

VDS IDS

CE

εF

εF(I)

(q=+e)

εF

εFεF

(S)

εF(S)

Metal

εF

εGroundstate

x

εF

Ve DS

εF(D)

εF

iε εf

C

ε

ε

Source

x

(D)

Island

Charging Threshold (I)(q = +e)

Charging Threshold(I)

(q = -e)

Energy-Level Scheme:

∆ε

Source

Tunnel Barrier

Drain

Excitation +e Charging

(I)(q=-e)

Restoration-e ChargingExcitation

(I)(q=0)

(I)(q=0)

(β)

Restoration

electro-

ε Excited State

x

∆ε

ε(S)

Elastic Tunneling

electro-staticshift

staticshift

E

Drain

DrainSource

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Regime of(c)

(b)

(a) Regime of DSV > 0V = 0DS

VG1,S

VG2,S

VG2,S

VG1,S

Slope

∆

∆∆

∆

∆∆

∆

∆∆ 1 -

1 -

∆

Single-Electron

Common Path

TunnelingCoulomb Blockade

N+1

NN-1

VDS

N

N-1N

N+1

e2

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E∆ I D

E∆ S IeVDS

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CG*

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∆

N+2

∆

N∆

N-1

∆

f (S)

f (S)

f (D)

f (D)

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∆N

∆N

∆N+1

∆N+1

∆N

N

∆ N0

∆N+1

∆N

CG1

e

CG2

N-1

∆

N+2

∆

N+1

∆

N+3

∆

N∆

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∆ N

E∆ D I

E∆ I S

Source DrainIsland+1

0

E∆ S I

∆

E∆ I DE∆ I S

D IE

V*GS∆

eVDS

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µelchi

µchi

= µelchi

(a)

µchj

cj

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(c)

ij V

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i j

ci

ji

= µelchj

Reference

PotentialElectrochemical

Reference

Reference

x

x

ε

ε

+ -

++

--

With External Voltage Applied:

In Electric Contact:

Uncharged and Isolated:

W

ε

W

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∆. 021

# . c021 -D%<$<zyO2^

v> "

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∆.021 # [ 3C^ [ 0 . c321

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CD

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(b)

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(c)=∆VGS

GS

1

0

same metal:

(e)V = 0 GSV = 0

NC

different metal:

(d)

C−∆VGS = VGS

VDSC

∆

−

0VDS

VDS

VDS

e2

CΣ

e2

CΣ

VDS

VDS

VGS

VGS

Source Drain

Gate

Tunnel Barriers

Source Drain

Gate

Island

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VGS

ε

Source Drain

εN +1C

Source Drain

GateVGS

IDS

Source Drain

Gate

IDS

IDS

IDS

IDS

different metal

different metal

∆

different four

metals

all same metal

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v\N " [ ∆ c OID^O2b<$K_>Ya

∆ c OIKC [ 3 . c3 [ 1 . c1 [ 0 . c0 % O]

" OIKC [ \ . c0 % O] :

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. c1 . c3

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∆. 021 # [ 3 .

c3 [ 1 . c1

[ 0 . c0

[ 0

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Substrate

Glass Tipwith SET

(a)

SET,SubstrateV

fix pointvoltage

Dec

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the

dist

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T a

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ubst

rate

SET,SubstrateV

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DrainSource

TunnelJunctions

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GaAs/AlGaAs-Heterostructure

Unoccupied

at donorselectron states

GS=V

+

+++

+

z

yx

2DES

VDS

Alloyed Contacts

Mag

netic

Fie

ld

IDS

2DES,SV

(Gate)

Single-Electron Transistor

GaAs Buffer

GaAs

AlGaAs : Si

GaAs

AlGaAs

GaAs Substrate

55 nm

0.5 mm

++

+ ++

++

+++

+ ++

0.9 µm

10 nm

20 nm

1.0 µm

2DES

85 nm

GaAs/AlGaAsSuperlattice

0.25 µm

++++

+

++

ε

GaAsAlGaAs : Si AlGaAs

2DES

z

Conduction Band Minimum

ID

S

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-2

-1

0

1

2

1 1.5 2 2.5 3

2DE

S,S

0

ε

B

ε εε

Magnetic Field B

V

(m

V)

(b)

(a)

Magnetic Field (T)

µch2DES

C0ε

Conduction

(Β)

Band

2DES

0 0 0

Landau Levels

D( ,B)ε

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[nm]

GaAs

# !,M # g ! +"/ £¤ ©« ! #;)! Y+ # °+! ! #"9+ $ 3± ° ® ± , ")!&H+)!+, " !" +#"/ ' )% °)& Q% ± ° ® v±0 '"9+)(o± § ¨ o*r## ® ')"&H)!"+)!g³,=, )!) ® ;+)! ! ,, !#"-; !/. 0 + !'+#"/1;+ °+±0 ° !g³ ; &/0&(8d) = &<&(l#$A, F PQ a c .)A3 + &B# = & &>3e F H l N c PQ e SU 2| [ R ! = d d e U e SU ; * 4 # = & &(3-/0&>,) * 8 c &^l#$A! +t~ + ):!c&>!*&(3G4 A3 4 ) #') = !$ &D#'&>60&>!#*4G)A! + &&0&58 +t & = A4+4 e SU "!$# &D# &>,&(8 3 88d)A!4 "! b )A3 F H e SU F e U + & 3+A!$4 )A! )'8>8*3?4 | R ! = & -)A! ) = 84+8>A,& )2 ):! &>! + ):!$", 6*3+)]8>&(4+4 !9 &(8 !*)A,)0WA,,) 4 )W4 3$8 *3+& = &(3 ",4G)A!+ & *!$#'3+&(#D!"!*) = & &(3 48(",& b )A3C4$8 ,A3:&E4'4 & = 4$c4 = A,, &b &(8 +t & = A4+4 4k3+&(l# 3&5# ) &`/0) + &(!*&>30 4+8>A,&54 ! &@4+ = &@3?"!9:& i $& ) & 4 = ",,&0&58 +t & = :44 !43k < 4 e SU F | [ | l p d e U A!$# + &<# &>,&(8 3 8k8d):!$4 "! FIH l#$A! = #*) 4]4 & = 4@3&5", t~ &(# !53k < 476 < ,83k < 4 & &>3+):4 3$8 *3&54G) &>3 & 3+A!$4 + ):! A/) | ! = :9 ; &>3+&d.):3&B4$8 l#$A! = #') 4 + # = & &(3.3+) = 4& &>3?", $!$#'3+&(#*4 )a.& &(!$4f)".$!"!*) = & &(3+4 r & A8(8d&(4+4 ) ! &54 + & & ! &(36*, c/0& j &>&>!D4 !9:,&> &(,&58 3):!8 A3 !9G&>!$&>30 "!#4 !ªA,&b>t6$"3 8d,&^l#$A! >~ + ):!&>!$&>30@)A!D"!&>!*&(3@4+8>A,&^)". | |*H = &; )G.& = &; ; )G4*6*6$3&544 &>3><>= ,#)!) /%,# %+1 ! !#?+,,+±@/M ² ,+ !)!)=)#" ² ` ¢ £¤;¥¦§ ¨ª© «g¬#±A/ .#"9+ $ CBY ± !#ED F ¦ £¤HGJILK ( « ( ¬ ¥¦§ ¨M G ¬ = N# g !+#"/j,g)!+)! O £¤ G ¥0¦§ ¨+P ¦ ¬ G ¬ . ! g' ) @ +"/; ! ++j ! +)!+,#M ± !1#+ ® ¯ !" $+Q/ M Gg¥0¦8IK ( « ( ® ¬ ³BY ;++ °%/)*` ¯ D F .9 ³ ³.Hv0RL,Q 0S ¯ * ³ = Q !/)@° M+1 ! *+,+g± ! T?0g³UL.0 !o #)±1;O+QM#" +1 ! ³

¯ !#"%$'&(*)!+,.-/01+ = ",]S$8 $ + ):!$4',) & = 6&(3+ *3+&(4 ]6 8(",,t/&(,) | H &(, ] ! "3+&a3+&(l# 3&5#* 8 "3+& :8>8>&(4+4 /*,& ! 8d) =@= &(3+8 A,,r< ,A/*,& x &> &b># ,t )A!@3&>.3 A&(3+ ):3+4 !#"$ %&'(*)+%,"$- ./"0,12"34-5(67 8 :9;"< =9>@?A $%CB@7 3"DE< $4-F4%,"$G $A! = #*) 4]4 & = 4 .)A3&(,&58 3 8>", 3+A!$46):3 = &(:4*3+& = &(! 4 &k/0&>&(!T3&5",t>r~ &5# !T# &>3+&>! '4.)A3 !$4 A!$8d&I / 4 A6 !9`/ª*,t = &>3 ",4%, :&IH , 8d)A!/ & 8 * !ªGA!$#&(! A!$8d&5# ,)]8(", )21 >#* + ):! o A " r1I /E& = /0&(#$# !ª<4 = ",,'6$A3 + 8>,&54 !@ +* !JH Y2K = & = /*3?"!*& * 8 G 4 8>)A! :8 &5# !Dc4 = A,, A3&5<.3+) = /) 4 #'&54/ = & A, &>,&(8 3+)]#*&(4Eo :g r1I /k4&>,.> .)A3 = )A!B#9*3 !9^&>6 "1 A,#:3) + )".$, 8d&> = 4 = 8 &(# mmm > ; 4& = >8d):!$#;$8 )A3 = &>3 A,4Eo 0l r I / = ):,&58b*,"3 /0&( = &>6 "1c)A. mmm > ; = &>3 A,4 ):!`6*3&(6$ &(3!*&5#4*/$4 3? &o p# 0 r I / #'&>60):4 + !ª 4& = 8d)A!#;$8 )A3D8d,r$4 &>3?4.3) = 8d):,,) #*4 /& j &(&>! = & A,E&>,&(8g> 3+)'#'&(4Eo ML r1I /a"3+3?"!9 !9 4 !9:,&98("3+/):!^!"!*) */0& o L | L H r1 2ON c >t/9$8+]/$",,4 oqp L r = ):,&58b*,&(4)A3< ) = 8d,r$4 &>3?4E/0& j &>&(! = & ",-&>,&(8 3+)]#*&(4k)A3 = &58 "! 8(", /*3+&(0P$!$8 + ):!$4)A3I /4 38 $3 !9 3k < 476 < ,83k < 4 & &(3)4 38 $3&54 H 3$8 *3 !9 3k < 4/6 < , 3k < 4 & &(3)4 3$8 *3+&(4 4E &>3 $4$A,9"6*6*3+)::8 ).):3 = &>,,>#'&:$!*&(# R i l#$A! = #*) 4 FRQSUTgFRVW *!$A/*,&W6$A3+ = & &(3+4DA!$# 4 &>3+&d.)A3+&$4&(# ! ",, & &d1'6&(3 = &>! 46*3+&(4&>! &5# ! $ 4 )A3 X A4& 43k < 4/6 < , K Y Y 3k Y < 4> & &(3)4 38 $3& * 8 8>)A! !$4@ j )># = &(!$4 )A!", &>,&(8g> 3):!4]4 & = R i&Z H M ; & R i&Z H 4 ,)'8> &5# & &>3 3k < 4/6 < , 3k < 4 & &>3+)>P*!8 )A!)A3 ! < , 3k < 4/63k < 476 < ,83k < 49l#$"! = &>,,$/0&>,) &^4$37. :8d& 4&>&b j M H$8 3k < 4/6 < ,83k < 4 & &>3+):4 3$8 *3+&(4 ) &>3 4& &>3?", A# A! :&(4(sI 3k < 4 < , < 4k"!# < , K Y Y 3k Y < 4kA,,)'4C8>A! /0&':3) ! ", = ):4 !*), 7 8d&= 4 = 8 = ):!*)A, A&(3 / = )A!*):, :&>3 = )A,&(8b$,A3C/0&( = &(6 n1; \[XOZ .)A3 = !9c@8d3'4 ", I ; & &(!*&>3A& 8 60):4 + ):! )A. & 8d):!$#;$8 )A! /"!$# = ! = = 4 *!"/*,& / "3 !9 &`4 )'8 * ) = & 3/& j &(&>! 3k "!# < , =] ) &>! ",_4 &>6$4C)A3 &>,,4C"3+&&(:4 ,tc):/ !$&(# /"/*3*6 ,t8 "!9 !ª + &<4 )'8 * ) = & 3 I i $& ) & * :3) + l", c"!# & = )]#9*, )A!;>#'):6&5# &(8 ! l#*& j )0># = &(!$4 ):!$",-&>,&(8 3):! 4]4 & = 4 R iZ H "3+&8d3+&( &5# A4G8d)A!#;$8 + ):! /$A!$# !48 & &>3+):4 3$8 *3+&C)00&(3 !9@ = &(A!.3+&>&^6$ .)A3 &>,&(8 3+)A!$4 ) /& !948( &>3+&(# .)A3& &>!7*6 ) H|0|_^ = & = 60&>3? *3&54 /&(,) I ; & R i&Z HD, A&>3 4 ]6 8>A,,r H| ! = $ 8+ A!$#T, &54 g ) R g | ! = /0&>,) &4$37. :8d& ; &T8d):!$8d&(! 3? )A! 4 $4$",,r ! &D3?"!9:&)A. g d H| K ) g d H| K 9

Q-/01+ ° v()!+, !g) &;, g,+ °+ (a)

(b)

AlGaAs : Si+

++ +

+++

AlGaAs : Si+

++ +

+++

AlGaAs

AlGaAs

GaAs

AlGaAs : Si

GaAs

AlGaAs

+++

+

+

+++

+

++

AlGaAs

GaAs Buffer

GaAs

AlGaAs : Si

GaAs

AlGaAs

GaAs Substrate

++

+ ++

++

+++

+

+

+++

+

++

z

++

++

++

z


++++

+

++

ε

GaAsAlGaAs : Si AlGaAs

z

2DES2DES

2DES

AlGaAs/GaAsSuperlattice

+

AlGaAs

z

++

GaAsAlGaAs

+++

ε

AlGaAs : Si


GaAs Buffer

GaAs Substrate

SuperlatticeAlGaAs/GaAs

2DES

35 nm ...250 nm

[100]

250 nm35 nm ...

~ 10 nm

~ 10 nm

J (:?# #)!+=% RL,1& ,Q)RL, 1,#0+o+ !#" ! & ±0 ! °+#, !#)+)!+,j1/01+ ° ¦ ¬ ## . ¦ ¬ # ! +)!)`³ !" ;, " ) /e,)$ g±%,, ° !,, °+)!+,3 ° !#,+; " ! ! %S, 1,)+/o,/+#+³ = )b, ; !±3 !'gS± + !' !o; ³ # ³&>,&(8 3+)A!$4 60&>3 = & ! c4l#$A3&k)". H|0| ! = /# H|| ! = + &>3+&BA3&E"/0)0 g ) g | &(,&58 3):!$4 I ; &D&>,&(8 3+)A! 8d):!$8d&(! 3+ )A! ! & R iZ H 8>A! &5A4 ,r /0& A3 &(# ,)]8(",,t /#"6$6*,t !9 ):, A&54 ) = & A, &>,&(8 3+)]#*&(4 )A! + &<4$37. :8d&

I !#"%$'&(*)!+,.-/01+ I ; &k8d)A!#;$8 + ):!/$A!$# &(,&58 3):!$4 "3+&a#'&548>3 /&5# &>,, +* !D"!&b &(8 r & = :44"6*6$3)21 = )A! ; &&b &(8 +t & = A4+4 4<,) "!$# + 4k. )*3+4kD,"3A& b &(3 = &>,&>!9 "!$# &(3&>.)A3+&El"! = 8d)A!9:$! !9@&b &(8 4 ; )3+&(", r~ &Bl"! = #*) 4'4 & = ! 4$8 & &>3+):4 3$8 *3+&(4 + &<.):,,) !ªA6*6*3+):A8 &(4 A3&%8>) =@= )A!E.):3h# t] # !ª & R i&Z Hk, &(3+A,,r !`# &>3+&>! .`$!$8 + ):!$",3+& ):!$4 4&>& b 7$ sI X $4 !9E&(,&58 3):!;> /0&( = , + )0:3+A6 0n4 38 $3&5# = & ",$&>,&(8 3)'#'&54 n #'&>!*) &5#A4 T ?@E!FRVSA VE+G V BD TDo L:g r n "3+&G#'&(6)4 &5# ):! )A6 )A. +* 4 & &(3)4 38 $3& H$8 !# )A. 4 3$8 *3+&(4 &>3+& &:3+4 .)A3B4 #; !9 2

)*,) = /9> /*,)'8+nA#'&G&d.>.&(8 4 !Dl#$A! = #') 4]4 & = 4 4&>& * 4 )A3 8^3+& ] & / [ A4 !$&>3Eo Ll r Mª< !&d1* = 6*,& 4 r &(! ! b 7 m ! $ 4@8>:47& &D476$, >1: & &>,&(8 3)'#'&54`8>)A!;>4 4 4^)".-4 1 &>,&(8 3)'#'&54 n 3+&>&G)A! &(:8 4 #'&:s j ) )0 &>3k&>,&(8 3+)'#'&(4k"!# )A!$& !$!*&>3a&>,&(8 3)'#'& A6*6*,r !9!*& r & )A, 0A&54 ) + &(4& &B&>,&(8 3)'#'&54 &G&>,&(8 3+)A!$4^"3+&G&>,&(8 3)4 + 8(",,tD#'&>6$,& &(# /0&>,) &(:8 : &As ; & R iZ H 4# r #'&5# ! ) 4 = A,,_3& )A!D/0& j &>&>! &': &%:$!9:&>3?4 n + &`l#$A! = #') n"!$# j ) ,"3A&@"3+&(:4C)A. R i&Z H :8 + !9T:4^4)0$3+8>&@A!$# #'3+ ! &>,&(8 3+)'#'& ) &l#$"! = #') ; & & 4BA!$# # 4B)A. + &VW3QQbECABgBgFbB6T7AB VW3Q@A0CE/ & ):, A&cA6*6*, &5# ) & )0 &>3° &c&(,&58 3)'#'&54 ; & !$!*&>3 &c&>,&(8g> 3+)'#'&(4f4 )0*,#B4+8d3+&>&(! + & 8d3+):4+4_:8 + !9^)". & ) &(3 &>,&(8 3)'#'&54f"!$#À8 :4 &&>,&(8 3+)]#*&(4-.)A3 + &<l#$"! = #') I m ! A! "!*) &(3Â6*6*3+)::8 + & R i&Z H 4a# t] #'&(# /#T& 8 * !9A3+)) &(4 ! ) & & &>3+):4 3$8 *3+& $ 8 A3&#'&:$!*&(# /#`&>,&(8 3+)A!;>t/&5 = , )A3?"6 < !c&d1* = >6*,& 4c4 ) ! ! b $ / ; & # t &>3?47& 3& )A!$4@:8 A4@4)0*3?8d&f#*3+ !o &&>,&(8 3+)]#*&(4E"!# + & l#$"! = #') H !$8>& ",, &547& 8>) = 6):!*&>! 4<"3+&`3+&(A, r~ &5# ! &<4 = &k6*,"!$&0*4$8 A! A33?"!ªA& = &(! 4#*&>!*) &(#D:4 FRQ=Sr?@EtA Q A VIT VB WªG SV W;B o L p(r @< a &`8d)A!4 3 8 + ):!T/& j &(&>! j )c& 8 &(#:3)]) &54 *!*!*&(,_/$A33 &>3?4"3+&<.):3 = &(# #;*& )D&(,&58 3+):4 8`#*&>6*,& + ):! "3+)0$!$# + &A3+)) &(4 * 8 4Â,> '4a6*3+&(4&>! #;*& )D!*&: +t &G4*3. A8>&@8 "3A&(4 3?"6$6&5# ):! + &G.3&(&@4*3. A8>&)".3k < 4 "!$# < ,83k < 4 ; &a&(,&58 3)4 8 #'&(6*,& )A!,&(!9 + 4 ]6 8>A,,r | H )| R ^ = .)A3C4$8 R iZ H3&5#;$8 !9 + &<A8 $A,,r4 t~ &k)". &E&(,&58 3+)A!D4]4 & = ! &El#$A! = #') 3&54760&(8 r &>,r m ! * 4 3+&(", r~ + ):! + &k/$"3+3 &>3?4 "3+&Â,4) *!;>"/*,&E/ + & &B&>,&(8 3)'#'&54 ; &<6*3+&(4&>! #'&54 A!T ) #*46*3+)A/*,& = 4)A. &("3+, &(3, :)0 4 o L0 r1 &(3& & : & &>,&(8 3+)'#'&(4A) 6$"3 ",,tG#'&>6$,& &(# + !*&: +t &: & )A, 0A&54 I m !$4 &(:# )".f& 8 $ !9S$G.)'8b$4&(# 3k> )A! /0&( = bYm X :4 /&(&>!$4&(# ) # 4 )A3 ,)'8(",,t & R iZ H^,&(:# !ª ) !$4*, + !9C, !*&(4 * 8 # r #'& & R iZ H !B# 0&(3>&>! 3& )A!$4 A8 !9cA4 4)0*3?8d&]#*3+ !)A3: &k&>,&(8 3+)]#*&(4]A!$# A4 &El#$A! =#') o LML r ; & &(8 ! l#*& A4EA,4)D/&(&>!W8d) = / !*&(# & 46*, > & &(8 >! l$& o H|| r 4 4 4 !9A,& )A!4 = 6*,A! &(# / & bYm X "3+& 3?"6$6&5# ! &E3+& ):!)A. &<l"! = #') 8($4 !9G# 4 *3+/0&(#D8d):!;:$! !9@6) &(! + A,4 I m 47):, !9 , !$&(4 ! & R i&Z H "3+& A,4) ):/ !*&5# / .)'8$47&5# ,A4&>3/&5 = !#;$8 !96;>t#*)A6$A! # ]$4 ):!T.3+) = 4*37. :8d&<, A&(3 ! ) + & & &(3)4 38 $3& < 4 !9:,&> &(,&58 3+)A! 3?"!$4 4 ):3 A4/0&>&(!T#'&b:$!$&(#/# * 4 &(8 ! l#*&co H|*H r

Q-/01+ ° v()!+, !g) &;, g,+ °+

(b)

(a)

Gate 1

Gate 2

QDDrain Source

2DES

Gate 12DES

2DESGate 2

2DES

QD

VDS

Gi,SV

Gi,SV

In-Plane-Gate Technique:

2DES depleted

SEM-Image:

TunnelBarriers

Drain Source

2.0 µm

HeterostructureGaAs/AlGaAs-

VDS

SourceVG2,S

Drain

Gate 1

VG1,S

IDS

Etched Structure

Gate 2

SEM-Image:

IDS


Source

Drain

Split-Gate Technique:

TunnelBarriers

SourceDrain2DES 2DES

0.6 µm

In Planeof 2DES:

ElectrodesSplitgate

2DES depleted

( ? #)!+@%#)b) ¯ ±0 1/01+ ° ¦ ¬ ¯ [±]±# ##g±/ , )Q+)!+,1 !.±07#)! ! ¯ (Y- ! &#)! ,&H" b+)!+,±0++³Q ¯ ( -K !)!gg±b RL,1& ,)RL,Q 1# !7@RL,Q ! +)!) ¦ r ³-0 ° ± ¯ %t ³7+ ! I ¯ ¬ ¦ ¬ ) ±S1/01+ A/± $ ± !#" ¯ ( -/ !#""%$++³ = /# !g);±##)! ! )!+#" = g±%"%$Q ! ; ! + 0³°0³ ¯ .g±0#+ !"e , + 0## ± +&; $ +) /³ ¦ t ³ +)!)! L%r = ³j !) +)! I ¬

!#"%$'&(*)!+,.-/01+ I &(8>&>! ,r 4+8>"!$! !ª 6*3+)A/0&(4 = 8>3)48>)A60&(4 &/&(&>! $47&5# ) = )'# .` ,)'8(",,t & & &>3+):4 3$8 *3+&B/T48>3+ 8 * !9 ):3C)21 # t~( !9 &@4$37. :8d& ; & R iZ HD/0&b>8d) = &54E#'&>6$,& &(# /&(,) & = )'# :$&5# 4*3. A8>&0 A,,) !ª ) # r] #'& & R i&Z H ! )@4 !9A,&b>t&>,&(8 3+)A! 3+A!$4 4 )A3A33?"!9:& = &>! 4ao H| R H| r ; & &(8 ! l#*&E",4)",,) 4 )@8>) = / !$& !;>t6*,"!*& 46*, >1: & &58 ! l#*& G &(4& &(8 ! l#*&54"l#$A! = #') 4 & /0&>&>!@3+&(A, r~ &5# ]6 8>",*# = >& &>3^/0& j &>&>! | H ) HA^ = ; &`,&(:#*4k"3+&B, &>3?",,tT"3+3?"!9:&(# ) &Gl#$A! =#') & &(,&58 3 8>", 3+A!$4760)A3 ^ :&(4^6*,A8>& ! 6"3?",,&(, ) &@6*,"!*&G)". & & >&(3)4 3$8 *3+&%, A&(3+4 ; 4 <4$8 3&5", t~ + ):!$4_A3& #'&(!*) &(#GA4EtA V BAE WªA QSVW D V T T V_T ;Z ,&(8 3+)A! 3?"!$460)A3 C A4 ) )'8(8b*3 + &B&5#;A&<3+& ):!D)". &l#$A! = #') ;< !DA# "! A& 4 & !;>4 *!"/ , c)". & *!$!*&>, /$A33 &>3?4# 4+A# "! A& 4 %+ &(4& *!*!*&(, /$"3+3 &>3?49A3&a,):!9 ! & 3 46$ + A,&>1 &>!4 )A!$4A!$# 4 ",,) ! &>!$&>3A& + 8(", & : N ; &@, 7 &(3<",47) 3+&(4 3 8 4 & = 0A! $#*&)A. #'3? !;>47)*3?8d& )A, 0A& * 8 8("!@/0&C"6*6$, &(# &(8>&>! ,r0 2 )A3:kA!$#@8d) )A3A&>3?4o H| r &#*& = )A!$4 3? &(# 4 !9A,&b>t&>,&(8 3+)A! 3+A!$4760)A3 ):! 476*, >1: &l#$A! =#') 4'4 & = &>3+& + & ) A,9&>,&(8 3+)A! ! = /0&>3 ! + &l#$A! = #*) 8>)0*,#W/& *!*&(#D4 A3 + !9 "! & = 6 #')

&5", t~ )A!4 )". B VFHG+AE WªA Q=V W 0D V_T T V _T &(3& &>,&(8 3):! 3?"!$460)A3 )'8>8*3?4 6&(360&>!$# 8*,A3,r ) + &96*,"!*& )A. & & &(3)4 38 $3& , A&(3+4 A!$# &(3&>.)A3+&] + & ):,&E"3+&(`)". & R i l#$"! = #') "3+&k4A& 8 &5# ! b j$qg sI ; &`4 3$8 *3+&B)A. b 7$qg A4C6*3&547&(! &(# ! H L0 / [ &(&(# A!$# 8d) )A3#>&>3?4co H| g r "!$# .`*3 &(3`#'& &(,):6&5# / [ ; & )A3?# "!$#W8>) ):3:&>3?4 X^ H A!$#8d) )A3A&(3+4 ; H'8 = #<A!$#<8d) )A3A&(3+4 47&(&%3+&d.&>3+&>!8d&(4 !o H| l r M b 3?4 ,tE & >&>3+):4 3$8 *3+& 4:3) ! l#$A! = &(,, & = /0&(#*#*&(#T/0& j &>&(! j ) * ,t#')A60&(#D, A&(3+4 $ 8 A3&<4&>6$A3+ &5#/ * ! , A&>3?4A8 !9 A4 *!$!*&>,_/$"3+3 &>3?4 m ! + &<4&(8d):!$# 4 &>6TG6 ,,"3 4& 8 &(#)0 )A. + & & &>3+):4 3$8 *3+& I H ; "3$8 ª iB 3 +< $4 !9A!$# ; )A!$#$To H| p(r &E&>1 &>!#'&(# + &`4 3$8 *3+& ! $ 3?# 4 &>6 /# = & A, &>,&(8 3+)]#*&D4*3+3)*!$# !9 & l#$A! = #') 4&>&b j$qg / d ; $ 4 :4CA! = 60)A3 A! 4 &>6 .):3C&>1]6$,):3 !9 + &B&(!*&>30D4760&(8 3 =)".f ) = > , :&El"! = #') 4 I b j$qg 84 ) 49<l#$A! = >#') /0)21$47&5#@/ E< 4 )])A3 "!#c8d) )A3A&>3?4 o H| r.)A3h8>"6A8 A!$8d&-4760&(8 3+):4+8d)A6 s ; &-l#$"! = #') h 4 .)A3 = &(#E/ = &("!4 )A.$ ):6: &E&>,&(8 3+)'#'&B6*3+)'#;$8 !9 A! &>,&(8 3+):4 8E#'&>6*,& + ):! &d1*8>&>6 ^ ! 4 = ",,_A3&5#;*& ) G,"3A&(3 # 4 "!8d&k)". &% & = & ", ) &<l#$A! = &>,, ; *!*!$&>, !9 4 ):!*,r 6)44 /*,&k/0& j &>&(!Dl#$A! = #') "!# 4*/$4 3? & H8 &>3 8>A,fl#$A! = #') 4'4 & = 4E) &>3E&(!*&>3A& 8>A,,r * $!*!*&>,%/$"3+3 &>3?4 ; & A3&#'&b:$!$&(# / & 8d):!$#;$8 )A! /$A!$# )0 4& )A. &A3+) ! , :&>3?4 * 8 :4 & #*3+ /$:8+T)". !*) /0& !9 !;>4 $!$"/*,& ) & &(3 4 !$8d& B 4<&(A4 )4 A3 "!@& = 6 Gl#$A! = #*) /`8 ))4 !9 &3 $ 8+]!*&544 )A. + & , A&(3 '. +,EL;, 7.* '##) b, °+" ! $,/,+, ! $ 3 )!g); )b !#M)!g±0 !#")!g) ;+ )$)!)/ ".M# + !#) ± ', !+ e )! "% !g)!)!/ ±# ##g± ± I . L`³

Q-/01+ ° v()!+, !g) &;, g,+ °+

n+ GaAs

GaAs or InGaAs

n+ GaAs

(a)

(b)

GaAs

n+ GaAs

GaAs(c)

GSV

Metal

AlGaAs

Tunnel Barrier

Tunnel BarrierQuantum Well

Quantum Dot

AlGaAsVDS

IDS

Source

Drain

Source

Drain

Metal GateVDS

IDS

GSVAlGaAs

AlGaAs

Source

Top Gate Electrode

(:? #)!MY $, !g) ¯ y±1/01+ ° ¦ K,+)! ¬ ¦ ¬ = ## ±0°1/01+ ±# ##g±4/ !" # !)!) 0%% 1,#0 ! ¯ ( -K+ ;g±#±0g± ; ! ++ ! ±0# !" )+/+³ = ±0M !M)!g±N/##+)b, ,+#±°±0 ª³ ¦ ¬ #)!)#, !")!&H+)!+, ,#, !1 , °)#" b+)!+,± b±K ±0 )!)! ! M #" ?0g±±0 0&H,+$ ) " # ; M+)!+,#'+ #+± ! ±g³ ¦ ¬ # %&± , ")!&+)!+,1; ? = ! OE#, !; ! ++ ## ±±3L "+)!+,±0 # ##+)! !#"³ = o" o),±)!)! ! r*)! ± !#" ) ± /#+)! "t ,#1,, ³-0 e1,# ;++'#,g±Erg% !#+&;+,,+/³8>)A! ! !9 &Dl#$"! = #') /&5 + .`$,&d1'6&(3 = &>! 4G8d)*,# /0&D#*)A!*&Wo H| g r$ 8 #'& = ):!$4 3+ &El#$"! = #') 4 6*3+)A60&>3 &(4 3+& = !$# !9@)A! 3&5", ) = 4 G $A! = #') 4a)". "3 )$4^4 A6& &B/&(&>! 6$3&547&(! &(# n .):3 !$4 "!8d&0 8 3>8*,"3Co H| p(r &>,, 6 + 8(",ho H| L r1:3 !9>t, A&<o 0l H:H| r1A!$# 33+&*,A3 o H:HAH r !$&a4 )0*,# &c", '4 ! = !# B ! 3 !$4 8c60) &>! ",ª$8 $ )A!$4`#;*& ) #')A!$)A3B# 4> 3 /9 + ):!$4 = : /*3+&(0 "! 4 =@= & 3 ! &(!$#'&5# / + &@, )A3?"6 o LA LA r ; &c,A3:&>3 &#'& ] 8d&0 &c,"3A&(3 &c3 4 )A. !9 &(4& # 4 $3/0&(# 8>)A!;:$!9> !9 6) &(! + A,4 ; * 4 4^!*) *!$4$", s i & ] 8>&(4^)A3 !",,t ! &>!$#'&5# :4al#$A! = 3+&(4E/*3+&(0*6 ! ) 47& &>3?", A,,&'4B:8 + !9 A4< 4&>3 &(4E)A.4 3+)A!ªA,r )A3 &5],r8>)0*6$,&5# l#$A! = #') 4To HAH R r G $"! = #') 4c"3+&.)*!$# /0&>,) &7:$!9A&(3@)".476$, >1: &`4 3$8 *3+&o HAH r )A3 ! &@#'&>6$,& )A! 3+& ):!T)".-476$, >1: &`#*&b:$!*&5#l#$A! = 60) ! 8d):! A8 o HAH r ; & 8 A3+:8 &(3 4 8 = & &(!G8 "!9:& &5A8 "3 = !ª>1*6 "!$#8d)])A, !9>#') ! 8b'8>,& ; &>3+&d.)A3+&0]l#$"! = #') 4]4 & = 3&5l# 3+&&>1 &>!4 r &k8 "3?A8 &(3 r~ )A! = &(:4$3& = &(! 4 / $! !ª 47& &>3?", 6$A3+ = & &(3+4(s

!#"%$'&(*)!+,.-/01+ < , )9 6*3+&>6"3+&(# ! &4+ = & 0_l"! = #') 4BA3& !$# r] #9$",4# 4 !$8 = ):3&^)A3 ,&(4+4 ! & 3 6*3+)A60&>3 &(4 #;*& ) "3 )A!4 ! &E8d):!;>:$! !9c6) &(! + A, 2) =@= )A! )".k",, = &>! )A!*&5# l"! = #') 4 3$8 *3&54 4 + . A3 )0$4 = > &>3 A,4k"3+&@8d) = / !*&(# A!$# = & A, &>,&(8 3)'#'&54E"!$# 8 A3:&(4^"3+&`6*3+&(4&>! k ) .):3 =+ &El"! = #') ; &E# r &>3?4&a3+& ):!$4 )".h4& = 8d):!$#;$8 )A3 & &(3)4 38 $3&54%/0&b> &*!$#'&(3<&d1'60&>3 = &>! ",98d):!$# )A!$4 & ,) & = 60&>3? *3+&0 & &>3 = & ",t>C)A3 !$4*, ):3>t, A& ni ):!*)A3?49"!#G:8>8>&>6 )A3?4 "3+&:*1'&(# ! + & 3%8 A3:&4 & ; &(3&>.)A3+&+ &# t &>3?47&-3& )A!$4f8("!B/0& 3+&( &(#`& &>3 A4 = & A,'&>,&(8 3+)]#*&-):3f:4f^# &(,&58 3 8 .:$1]&5# 8 "3A&`# 4 3 /ª )A! ; ) #*& &(3 = !*& &c8>)A!;:$! !9 60) &(! ",f.)A3+ &&(,&58 3):!$4 ! &Tl#$"! = #') &547& !9A3+&(# &>! 4 & ) /0& 0A&>! ! ):8>8d)*! b !# !ª@A! :#'&(l#$ &E#'&548>3 6 )A! 4A):A, )". + &^.)A,,) !9JH]&(8 )A!$4 )A.+* 4 2 "6 &>3

7B&& DE4A7( )+%,"$- ./"? '%&M"3%," %"3 9;"$% D 4 D< 4 = 6*,& = )]#*&>, :4E6*3+)A60):4&(# "!# &>,"/0)A3? &(# ! H LML H /W# &>3+&>! 0 )A3?4o R HAH g HAH l r ; ) 0A& ! )GA8(8d)0$! - &kl#$"! +t~ )A!c)A. & !*& + 8C&>!*&(3G):!+ &&>,&(8 3+)A! 4,A!$# + & 4 !9:,&> &(,&58 3):!B&>!$&>3 &(4 J p #;*& ) & !*& + 8 &(!*&>30E)A.+ &k&>,&(8 3):!$4 !D"3+&^:#*#'&5# ) + &k&>,&(8 3)4 + 8a&>!*&(3 &>3 = R R L: #'&(3 r &5#c.)A3+ & = & A, 47,"!# A33?"!ªA& = &(! ; &E&>!$&>3 &(4 J p "3+& = &(:4*3+&(# 3+&(46&58 )+ &k/) 7 ) = )". &<8>)A!;:! !ª`60) &>! ", D 4 &E8d):!$#;$8 )A! /$"!# = ! = =J c &(3& J c 4 t &>! 3&(, r & ) 8d) =G= ):! 3+&d.&>3+&>!8d& .):3 &W8>:47& )".`A!&(,&58 3 8>",,rc!*& 3+A, /9*,r = &>3 A, ; $ 4 &>,#*4 & ) ", &(!*&>30

^ p F! " p$#K w J p J c z&% ∆ d('")#

K c L ) c d ^ ) ∆ R0 c L &(3& ∆ F % c &>3+&0 c #*&>!*) &(4 + & ) A, ! = /0&>3c)A. 8>)A!$#9$8 + ):!/$A!$# &>,&(8 3):!$4C.)A3 &G&>,&(8 3 8(",*$!$8 "3A&5#Tl#$"! = #') & c &>,&(8 3+)A!$4)A. + & ) A, ! = /0&>3 A3&E8d) = 6&(!$4 &5# ! & 3 !*& +t &k8 "3A&k/60):4 +t &/$:8+A3+)0*!$#^8 A3:&(4>"!$# ∆ 4 &(3&>.)A3+& &%! = /0&>3h)".*:#*# )A!$A,A&>,&(8 3+)A!$4 +*

, = ² ,+ ° !+#±#)## ±0g² r##±% !3)! b *0;±01± ² ±*;+ !" g)! +g± t ¦ + ; ¬ , ° ±0# !" t)²³- '/.102. Y), ;+ ! ,+ ! ∆$ ;+ !#"7)t+g±+/ $N. =)#+)!+, 0 %&

;g³ = ! , °Mb"# " ! ¦ $ M ¬ Gg¥¯43 «65 $ ¦ $87 ¬ M G+¥¯43 «65 ! M+,+#b ³,QQ# g.,+0r e±0 ,#,, !K ! -+ ! I ³ ³ ¯ .Jv#0 #)! ! !1; ! ++ Q+)!+,#o !' ±0/. $ ¦ $97 ¬ M G+¥¯43 «65 ! °1rg, #)!³Y g, %#+ / +)!+,±0+7.Y !& ! ! !±0#+g± " "+ /$ ° ; %O +7 !K+# ! ! ,++ 7$ + /7 1°+)!+, .* ³ ³.YK±7;+#±++ ¦ $ M ¬ G+¥¯+3 «65 ° " +;++ °#)#, #)!L.) #" ##?g³

I ³ ]L#) ±+) % j = #1] ! ±0+) ¦ ¬

r0

-εc

εi

V0e0

Reference

Quantum Dot

) (*"/, + ° r "!#$ -0 !#")&),7&" !+&%' °g,g±')tb $ +) /% ;, M ## !#"@;+ ) ! ! ! *;, (% )« * M+#±# N##±ª³ = ;, ! ! * *;, % + #& " ; )Y ! 'rg±Q/ 7 M*) « ! %+)!+,1 ! ;+ ) ) « o e ,)±.! ! ±07;+#±M7 +)!+, # @;e$ #± +)!+,1 !1;+ )!e%Q ,,±0 "e+)!+,±++³; &a&(!*&>30@4760&(8 3 = #'&548>3 /0&(4 &^6)44 /*,&^&>!$&>30@,& &(,4%.)A3 &a&(,&58 3+)A!4 !A!&0&58 +t &k8>)A!;:! !ªc6) &>! + A, S !*&E4 )0$,# !*) &As; & 4 !9A,&b>t&>,&(8 3+)A!k&>!$&>3 &(4 J p J c A3& A4+4 = &5# )^/& &(8 &(#B!*& &>3/ + &^&>,&(8 3):!c! = /0&>3 !*)A3 / + &^&>,&(8 3)4 + 860) &>! ", 8 A!9A&549)A! &E&(,&58 3)'#'&54 b )A3`8 "3 !9 &l#$"! = #') G + & H &(,&58 3+)A! .3) = 3&>.>&(3&(!$8d&@&(,&58 3+)'#'& W+ & &>,&(8 3+)'8 & = 8>", 60) &>! ", ~ &(3)S !*) ):!*,r & &>,&(8b> 3)4 + 8k8 A3 !9`&>!*&(3 43&5l# 3+&(#/9 A,4) &E&(!*&>30 .)A3A& 7+ !9 ! ) &:3+4 *!*)'8(8b*6 &(#4 !9A,&b>t6$A3 + 8>,& 4 & &>!*&(3 J + K ; &>3+&d.):3& &a&>!*&(3# &>3+&>!$8>& ∆ H ^ p $ 8 "!D&(,&58 3+)A! .&(&>,4/& j &(&>!D/0& !9 ,)]8( &(#):! & l#$A! = #') A!$# /& !9 ,)'8> &5# ):! & 3+&d.&(3&(!$8d&@&(,&58 3+)'#'& W &&(,&58 3)'8 & = 8>A, 6) &>! + A, &(l#$", ~ &>3+)ª 4 r &(!/

∆ H ^ p F H ^ p % ^ p6 F J

+K J c % '")#

K c L ) c d ^ ) , % c K- c [ $ H| ; &-8 A3 !9&(!*&>30 4 = )'# :$&(#E/ J + K J c !`8>) = 6$A3 47):! ) H H g:M 2 "!90> !9 + & &>!*&(3 # &>3+&>!$8>& $ H| #'&b:!*&(4&>!*&(3 ,& &>,4c.):3 8 "3 !9 &l#$A! = #') 4 = ,"3 ) - A4o47&5# ! 2 "6 &>3 H + ) + &>3 ):3+#$4>s ; &2):!$4 "! m ! &>3?A8 )A! [ )'#'&>, ++ &<"!4 ~ L = 6*, &54

I T4 !9:,&> &(,&58 3):!W460&(8 3 = &>1 4 4 $ 8 4<!*) &(8 &5#W/# &! = /0&>3B)".&>,&(8 3+)A!$4 ! &<l#$A! = #*) $[ )A3+&>) &(3

!#"%$'&(*)!+,.-/01+ I & ! &(3+:8 + ):! /0& j &>&(! 8 "3A&54"3+&E)A!*,r#*&(4+8d3 /0&(#D/D8>"6A8 A!$8d&54 * 8 "3+& !$#*&>60&>!$#'&(! )". &<&>,&(8 3+)A!D! = /0&>3 ):! &`l"! = #') ; * 4 .)*!$#*4 &E! = & m 2 ):!$4 "! m ! &>3?A8 )A! [ )'#'&>, 2 m [ m X ) + A3&°A9DG A4+4 = 6 )A!$4=$4$A,,rE!*) o ", # < = ):3& A8(8b*3? & #*&(4+8d3 6 + ):! 4E#'& &>,)A60&(# ! + &@.)A,,) !9 < 8>) = 6$A3 47):! /0& j &>&(! + & 2 )A!4 "! m ! &>3?A8b>+ ):! [ )'#'&>, A!$# & :&>!*&(3+A,0#'&548>3 6 + ):! ! &(3 = 4-)"._A! ! &>3?A8 + !ª >t&>,&(8 3+)A!4'4 & = 4<#'):!*& !H'&(8 + ):! $ "!$# ! 2 "6 &>3 g* ; &(3& &4760&(8 3+):4+8d):6#T)A.&(!*&>30W,& &(,4`)".k l#$A! = #') G 4c#'&548>3 /&5# ] 4 /$,& ! &>,&(8 3 8(", 3?"!$460)A3 &>1]60&>3 = &(! 4 D !8d3+&(A4 !9G#*3+ !;>4)0*3?8d& )A, 0A& \ 8 49;"3 $,M"3#"$9! 7( 2"$9 )+%,"$- ./"$ 8 :9;"< % 8 -@ % % % ,- 74%4 %C"3 $B&9./4 :9;"< =9 DE - " 7 %&5% 0 $ $,% O1 DE"< 8 49;"3 $4< 496*3+&(4&>! &5# ! H]&(8 )A! R ABl#$A! = #') 4$4",,t@#'&b:!*&(# !4& = 8d)A!#;$8g> )A3 = &>3 A,4k/ & 8 * !ªª / &>,&(8 3)4 + 8@#'&(6*,& )A! #;$& ) )A, 0A&(4kA6*6*, &5# ) &G&>,&(8 3+)'#'&(4 /#T,)'8>A,f#*)A6 !9D"!$# 6n)A3^/ 8 "!9 !ª &@4 )'8 * ) = & 3 )A.+ &T8d) = 60)0*!# 4& = 8d):!$#;$8 )A3 = &>3 A, ; ) :$!$# = )A3+&6*3+)A60&>3 #*&(4+8d3 6 + ):!)A.C l#$"! = #*) 8d)A!9:$! !9 8>)A!$#;8 )A!9> /$A!$# &(,&58 3+)A!4 & & :3+4 B )8>)A!$4 #*&>3 &k6 '4 8>A, &>,& = &>! 4 & &^&(,&58 3)4 8CA33?"!ªA& = &(! = )'#'&>,, !9+ & T6T Q=VFHAE T3D A.B+AE WªA Q=V W D V ; &(3&5n. &(3 &E"3+&k"/*,& )c#'&>3 r & ! $ 4H]&58 + ):! &>1'6*3&544 )A!$4-.)A3 &<&(,&58 3)4 8^6) &(! + A,_A!$# &B8>,:44 8>", 60) &>! ",&(!*&>30 )A. &`&>,&(8 3):!T4'4 & = !*&>&5#'&(# ) &(4 A/*, 4 T !H]&58 + ):! $ l &

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& 4%8d):!$4 #'&(39.):3 & = ) = &>! 4$8 B4'4 & = 8>)A! ! !9E!*) /9 % H&(,&58 3):!$4 ; !9T)A!$& &>,&(8 3+)A! .3) = T3+&d.&(3&(!$8d&c&(,&58 3)'#'& &(,&58 3+):4 860) &>! ", ~ &(3) "!$# 6ª 7+ !9 B ) 6)4 )A! _ * ,& A&(&>6 !9 + &&(,&58 3+):4 860) &>! ",4 ^ p )A. + &T&>,&(8 3+)]#*&(4 :*1'&(# ):3 A4 )W/0&T6&(37.):3 = &5# s K c ; &&(,&58 3):!a.&(&>,4_A,):!9 4 + &%&(,&58 3 8=:$&(,# %& ' " Y K H_0 (8>0$4&(#k/ + & % H &(,&58 3):!$4CA,3+&(:#;D6*3&547&(! 0/# + & ):! 8 "3A&`# 4 3 /9 )A! `_ A!$# / & &C&>,&(8 3+)'#'&C60) &>! ",4 ^ p ; & :$!$A,,r 8d):! 3 /9 &a/ % " Y K `_d ) &60) &>! ",:&>!*&(3a)A. &-&>,&(8 3+)A! 6)4 )A! _n ) & &>3 + &%&(,&58 3+)A! !$#;8d&(4 4 ) ! = :&D8 "3A&(4@):! &T&(,&58 3+)'#'&(4",47) 8d):! 3 /9 !9 ) 4c60) &>! ",&(!*&>30 A& a A4C#')A!*&<.)A3 ):/ ! !9 + &B&(,&58 3)4 8k&>!$&>30)A. &B8 "3A& c )A!E = & A, 47,"!# 47&(& R R L:7 &96) &(! + A,"&>!$&>30 ∆

`_ )". &9&>,&(8 3+)A!^ 60):4 + ):! _ 4 )A/ !*&5#c/ ! &A3? + !9 &k# 0&(3&(! + A, &>,&(8 3)4 + 8C&>!*&(38>)A! 3 /9 )A!4 " Y K `_0 H_ 4 _ d #<.3+) = F| ) F % ',&5A# !9 )∆ `_ F Y U

c " Y

K `_ d H_ 4 _ # F % " YK H_ K H_ 4 _0 [$ R p « = 1/01+ v) #)!)° b"'+, $b ! .* ³ ³. ') " % '1/01+ !##"9+g±J.#, !++&;+ $ ! " "+ !±0#++±'' +)!+,±++³

!#"%$'&(*)!+,.-/01+ !*& 4 )0*,#E!*) &0 &%.):3+8>& `_ .&(, / + & &>,&(8 3):! 6)4 )A! _ 4h):/ !*&5#.3+) = + &°A3?A# &(! )". ∆

`_0 !D6)4 )A!* `_ F %&(' ∆ `_ F & ' " YK `_0 % K &(' `_ 4 _0 4 $ R * 8 @ 4-# 0&(3&(! % ) % d `_ &>3+& `_ 4 & &>,&(8 3 8:$&(,# ! &C"3+3+A!9A&>= &>! 60):4 )A! _ r &>!/ R l:

% `_ F & ' " H_0 F & ' " YK H_0 % & ' `_ 4 _ [ $ R L

2) = 6"3 !9 + &`4&(8>)A!$# &>3 = )". R : )A. $ R L #'& ] &54 / &6*3+&d. :8 )A3 K 4 !8d& * 4G.)A3?8d& 8d)A! 3 /9 + ):! 4 !$#;$8>&(# / + &D&>,&(8 3+)A! 8 A3:& 4&>,. K+K; &G6) &(! + A,f&>!*&(3 .):3^ ) A,h)A. &(,&58 3):!$4 ! &@"3+3+A!9A&>= &>! 4-.)*!$# /cA#$# !ª`):!*&C&(,&58 3+)A! n. &>3 &k) + &>3-.3+) = &a3+&d.&(3&(!$8d&a&>,&(8g> 3)'#'& ) 4f60):4 + ):!$4 ! ) & 4'4 & = * ,&A&>&(6 !9 + &&>,&(8 3+):4 8%60) &>! ",)A.h",, &>,&(8 3+)'#'&(48>)A!$4 A! s F "

#K

∆ H_+M F "

#K % " Y

K `_> K `_+ 4 _M [ $ | m !$4&>3 !9," Y

K H_d .3) = &>1]6$3&544 ):! $ R gA &>,#*4k.)A3 + & 60) &>! ",9&(!*&>30T)A. &>,&(8 3+)A!$48>)A!;:$!$&(# ! &<l"! = #') F "

#K Y K"

#K `_+ 4 _ K `_+ 4 _d

% `_ H_ 4 _ # x _ % '" p #K p H_ ^ pF K " # K "

#K

# `_+ 4 _ K "

#K `_ 4 _M

% " #K `_ H_ 4 _d # x _ % " #

K'" p #K p H_d ^ p [ $ H ; &3:$3?4 a &>3 = )". $ H 3&(6*3+&(4&>! 4 & bE G V BD T V,A V FHG bE G V BD Q=S bE+G VBD Q QbB + & 47&58d):!$# V E+G V BD T6V,A V FHGT bE 6S Q B D V bE+G VBD Q$T .):3 & t &>!G&>,&(8 3+)]#*&A33?"!9:& = &>! "!# &G# &(,&58 3 8 = 3 1 =X ) + "3+&<#'& &>3 = !*&5#T/ + &13^3+&>&(! m 4.`*!8 )A! ; & +* 3?# &(3 = 0A&(4 ! ) :8>8d)*! &KFHD QjGªAB B# 4 3 /ª )A! &.)*3 +W &(3 = & E+G V BD3?ªD V Q=VFHAE T Y< ,4) + & 3`8>)A! 3 /ª )A!$4`"3+& &d1'6*3+&(4+4&(#/ + & 3^3&(&>! m 4 .`*!$8 )A! = v G 3 Q,++#±3 ¦8I ³ ¯ ¬ ! )!,@r##±' !' r+ ; ! +' ! "g± +±0# ! g#+ ,#"+ °+/.3±e °g,S³

I ³ j(),1b RQ+S² ## Er-;+ t) , ,#"+ °+

8 :9;"< 2"<#"$9 $:%\%&9;"3% ( 0 B@49! $% 74-F4%,"$; &&>,&(8 3)4 + 8 3^3+&>&>! m 4h.`*!8 )A! A4 #*&b:$!*&5#@/ H :d b )A39 ) = )0:&>!*&()0$4 4) 3+)A6 8^# &>,&(8 3 8 = &(# = + )0 A!c&>,&(8 3)'#'&54 + & 3^3+&>&>! m 4 .`*!8 )A! 4

H_ 4 _ F H N c f _ % _ f [ $ R [ *, + 6$,t !9 ++ &k&>,&(8 3+)A!D8 "3A& % &(,#*4 + & &(,,t>1!$) ! 2 )0$,) = / 6)0> &>! ", _ 8($4&(#/"! &>,&(8 3+)A!D 6)4 )A! _ m . &k69 G4&(8>)A!$#&>,&(8 3+)A! 60):4 + ):! _ F _ & 3^3&(&>! m 4G.`*!$8 )A! R #'&(4+8d3 /0&(4c 69$3& 2 )0$,) = / ! &(3+:8 )A! /0& j &>&(! /0) &>,&(8 3+)A!$4 8d) = 6$"3+& :$3?4 ` &(3 = ! H M m ! 6*3+&(4>&(!$8d&E)A.h&(,&58 3)'#'&54 )A3 "! ! ) = )A&(!*&>)$4# &>,&(8 3 8 = 3 1 `_ 4 _ #*& ] &54.3+) = $ R !9 ! ) A8>8>)0*! c+ & !#;$8d&5# = :&T8 "3A&54 ; &T&(,&58 3+)A!9>&(,&58 3):! ! &(3+:8 )A! 4 + &>3+&d.):3&c3+&(#;8d&(# / & 6$3&547&(!$8d& )A. & = & ",-&>,&(8b> 3)'#'&54 ! 8d) = 6"3 4)A! ) &69*3+& 2 )0$,) = / ! &>3?A8 + ):! ; $ 4 4'*!$#'&(3+4 )])'#/ G4 = 6*,&^&>1* = 6*,& 47&(& b 7 L 8 s ; )G&>,&(8 3):!$4 "3+&^8>)A!;:$!$&(# ! & `h 4 i >6$,A!*&C/0& j &>&(! j )B6$"3?",,&(, = & ", 6*, &C&>,&(8 3+)'#'&(4- # 4 A!$8d&54 K A!$# 47&(&b j L 8 3 M ; &(4&B"3+&0'.):3 !$4 "!$8>&0&>,&(8 3):!$4)A. R i l#$A! = #') /0&b>j &>&(!T6$"3?",,&>, &(,&58 3+)'#'&(4 ; &E3^3&(&>! m 4.`$!$8 + ):!T.)A3 & = ):3&3A&>!$&>3?", 8(A4&E)".+* 4%"3+3?"!9:& = &>! 4&>& b 7 L 8 ,&>. 7 :49/0&>&(! #'&>3 t &(# H L2L0l /

",, = & 4A!$# [ 0]4 = oqp r <Z 1'6*3+&(4+47&5#@/ + &a60) ! % )<6) ! 47&(6$"3? + ):!A6*3+) Pj&58 &(# ! )+ & `h 4 i >t6*,"!*& F _ % _ &>3+& _ _ #'&>!$) & + & !;> 6$,A!*& 8d) = 60)A!$&>! )A. _ )A3 _ 3+&(46&58 +t &>,r0 A!$# & k "!# k 8d)])A3?# !$ &(4E)A. + &(4& 60) ! 4 &4)A,r + ):!.):3 b 7 L 8 ,&>. 3+&(:#*4 ! j )># = &(!$4 )A!", b )0*3 &(3 3+&>6*3+&(4&>! )A!:4 `_+ 4 _ F k 4 k F V HR N Z k 4 k &>1'6 # $ A + & b )*3 &>3 3+A!$4j.):3 = k 4 k .)A3 t &>! k k

k 4 k F

4 ! w d K % k z 4 ! w k z c 4 ! w d K z . | k! k 4 ! w k z 4 ! w d K % k z c 4 ! w d K z . k k K [$ "]"$# XU0TL9RU0L&%X'% P)(*,+.-0/1+324I ; &^&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3?A8 )A! !DB6*,"!$&^6"3?",,&(, ) + &k&>,&(8 3)'#'&54 k Fk F K $4&>& b 7 L 8 3 4 + &>3+&d.):3&E#'& &>3 = !$&(# /

K 4 K F H N c HR N 65 &d1'6 , - # $ :g:

!#"%$'&(*)!+,.-/01+

Metal Electrode

Metal Electrode

rs

2d

d1

Metal Electrode

rs rs’

rs rs’ rs rs’

(b)

ρ-e

-e

rs’

Two parallel electrodes:

One plane electrode:Free space:

Dielectric interface:

(a)

(c)

(d)

-e -e

Dielectric Medium 2

Dielectric Medium 1

Origin

Origin

Origin

-e

-e

-e

-e

-e

-e

z’

z

0

:J (*)!+,1 !M+)!+,&H+)!+, ! ! ¦ ¬ Et+&+L.# !& !; ! ++% ! +)!+,# )!gg± b ± !Y±+ ;g±+/M RQ+S² r## ª ! ## Q&#+. `³ ³.00#0 #)! !ª³ ¦ ¬ = >0+,++Q%] °)+)!+&,± ,+# Q),0&), ! !S³ ¦ ¬ #t Y ! 0)!));+)!+,±7. @RQ++ª² v# !K ! O# ! ¦ ,+ ¦8I ³ I ¬,¬ ³9H+ !#) ! ° Q +,+ ¦ ¬ #±¦ ¬ ³ ¦ ¬ !" (*)!+,#o+1, !+±3°*#) ; ! ++3 ),±+, ! #)! ' += ±+, 0 ! ¦ ,+ ¦8I ³ ¬,¬ ³ ¦ ± ¬ = +)!+,&H+)!+, ! !Y)!,e "9+g±+/e ;) gb !. !&++; ! ++ °+± %± '"9+±0 ), !M#1+³ + 5 F R 4 ! w K z 4 ! w z4 ! w d K z [ $ 0lI b ):3 ,"3A&a&>,&(8 3+)A!;>t6*, &^47&(6$"3? + ):!$4 K

"!# 5 /0&(8>) = &(4*! "!# $ :g: 3+&(#9$8d&54 ) &E6ª*3& 2 )*,) = / ! &>3?A8 + ):!60) &>! ",

I ³ ° !)!# '*$ ()!+, ##g±3 +)! !1 M##

I b ):3%):!*,t@):!*&C6*, &a&(,&58 3)'#'&^8d,):4&b>t/# & 5 K 5 3+&(#;$8>&(4 ) 5 2H % &>1]6 % R K h,&5A# !9 ) &&>,&(8 3)4 + 8@&(,&58 3+)A!9> &(,&58 3+)A! ! &>3?A8 )A!oqp r `_ 4 _+ F H N c Hf f H % V H K

f f Z YK [ $ p b ):3_4 = ",,A&>,&(8 3+)A!;>t&>,&(8 3+)A!E# 4 "!$8>&(4 f f K & ! &(3+:8 + ):!k.)A,,) 4 H f f &(3&5A4G.)A3 f f 5 K & 48>3&(&>! !9 / & 6$, & &(,&58 3+)'#'& ,&(:#*4 ) "! ! &>3?A8 )A! .):,,) !ª H f f x s ; ) &>,&(8 3+)A!$4@ # 4 "!$8>& ! .3):! )".k6*,"!*& = & ",f&>,&(8 3+)]#*&<.&>&(,9 ,A3:&`# 4 "!8d&(4 f _ % _ f 5 D/0& j &>&(! + & =)A!$,t &@# 60)A,&B.):3 = &5# / "! &>,&(8 3):! "!# 4 = 0A&@8 "3A&<):! + & = & ",&>,&(8 3+)'#'& ; &# 4+8b$4+47&5#E&d1* = 6$,&54h4 ) 4h8d,&(A3,r _+ & &>,&(8 3+)]#*& A33?"!9:& = &>! 4 #'&> &>3 = !*&54 + & &>,&(8 3):!;>t&>,&(8 3):! ! &>3?A8 + ):! ; $ 4 4hA,4) 3*&-.)A3 & 4&>,.> &(!*&>30:) &(3!*&5#T/ `_ 4 _M * 8 t &(4k# r &(3:&>! &(!*&>30 8>)A! 3 /9 )A!4 ) & &>3+ &<4&>,.> &(!*&>30 &>3 = ! H 8>A!*!*) P4 /0&<&d1*8>,t$#*&(#.3) = + &B4 = 4 !8d& 8>)A! !4 + &B8>)A! 3 /ª )A!$4 )A. + &E&>,&(8 3+)A! +D 4 = 0A&<8 A3:&(4 !$#9$8d&5#D)A!+ & &(,&58 3+)'#'&(4 b ):3%<8>)A! !*)0$4 8 "3A&# 4 3 /9 + ):! &(8 ! l#*&(4%"3+&!$) ! )) &>3?8d) = & + &a4&>,.> &(!*&>30G# r &>3A&(!$8b H !$8d&a, &(3l"! = = &(8 "! 8>A,$&d1'60&(8b> + ):! ",r*&(4 A3& 8>A,8*, &5#BA!$# + &&>,&(8 3+)A!$4h"3+& 3&(6*3&547&(! &(#B/Ba8>)A! !*)04 &>.`*!$8 )A! !W476$:8d& + & 4&>,.> &(!*&>30 # r &(3:&>!$8D!*&>&5# !$) /&c8("!$8>&>,,&5# .):3+ &`.)A,,) !9 ]< # 4+8b44 ):! ) I )&>1*8d,r$#'& +* 4E47&(, .> ! &>3?A8 + ):! &(3 = a+* 44 0A& 4C#')A!*&k/

",, = & 4A!$# [ '4 = o p r -F "3%& % 7( 8 49;"3 $% % % % 2"$9)+%,"$- . " &8d):!$4 #'&(3fa3+&(", 4 + 8 l#$"! = #') nA4 # 48$4+47&5# ! H]&58 + ):! "!$#`48 & = > 8>A,,r #'&(6 8 &5# ! b j$ p98>)A! ! !9 8d):!$#;$8 )A! /$"!$# &>,&(8 3):!$4 ; & = , )A! "! .)A3 &547&W&>,&(8 3+)A!$4 4):/ !$&(# / :#*# !9 + & !*& 8 &>!*&(3 #K R"e SU J c H_d ) & 60) &>! ",&(!*&>30 )A. $ H dX 3+&>6$,:8 !9 + & = ) = &>! ° &58 )A3 A!$# &c60):4 + ):! &(8 )A3 _ )". &@&(,&58 3+)A!4/ + & 3@3&54760&(8 r &):6&(3+ ):3+4# "!$#N &

= , )A! )A60&>3? )A3 .)A3 & &(,&58 3):! 4'4 & = :$1]&5#T&>,&(8 3+):4 8E6) &(! + A,_ ",,h&>,&(8 3)'#'&54C8("!T/0& 3 7 &(! !T8d)])A3?# !$ &k3&(6*3&547&(! + ):! N F _+M A4 ^ p6 F " #K # R"e SU % " `_ HR "

#K " #K

# `_ 4 _ $ 0

+ & 2V bB Q]AE_)A3 /$"3+&E8d):!;:$! !9@6) &(! + A,"/ `_ F " `_ % K `_ 4 _ "/. `_0 % J c H_0

g !#"%$'&(*)!+,.-/01+ F `_ H_ 4 _0 # x _ % K `_ 4 _ '" p$#K p `_ ^ p % J c H_0 [ $ ML

Z !*&>3A& 8>",0# 0&(3&(!$8d&54 ! &k8d):!$#;$8 )A!;>t/$"!# = ! = `/& j &(&>! &k# 0&(3&(! = &>3 A,4 &C/&(&>! A&(! ! )`:8>8d)*! / &^6)4 )A!9>t#'&(6&(!$#'&(!$8d&a)". J c `_ Mb )A3 8>)A!$4 #*&>3 !9,)'8>A, "3 )A!k)". &9&b &(8 r & = A4+4 #;$& ) + &9,)'8>", "3 )A!)A. & = &(3 ", & !*& 8%&(!*&>30^)A60&>3? )A3 A4 )^/& = )'# :&(# 47&(&aoqp r M H8 A&(!*&>3?", 3+&( = &>! k !$8>,t# !ª/$A!$# 4 3$8 *3+&G&b &(8 4 4k/0&:)A!$# &@48>)A60&`)A. 4 )0$,#c/0&k# 4+8b44&(# &>3+& & $4 !*) &aB8>,)47&(3%,)])0 ) &k# 0&(3&(! &>3 = 4 )A. + & = , )A! "!T#'&(3 r &5#

+ -.- RX#U0\NP@V RX#U0\NP@VV]\X#NL9U\THP@V; &W&(,&58 3+)A!9> &(,&58 3+)A! ! &(3+:8 + ):! ! + & l#$"! = #') D 4T#'&548>3 /&5# ! & = , ):!):6&(3+ ):3 $ 0 / + & &(3 =

L F HR "

#K " #K

# `_ 4 _ A!$# 4 + &>3+&d.):3& # 3&58 ,ry t &>! / & &(,&58 3)4 8 3^3&(&>! m 4 .`*!$8 )A! .)A3+ &' t &>! &(,&58 3)'#'&@"3+3+A!9A& = &>! "!# # &>,&(8 3 8 = 3 1 &>!$8>&0 &G&>,&(8 3+)A!;>&(,&58 3+)A! ! &>3?A8 )A! 4 3+&(#;$8>&(# / + & 6*3+&(4&>!8d& )A. + & = & ",a&>,&(8 3)'#'&54 !8>) = 6$"3 47):! ) + & 69$3& 2 )*,) = / ! &>3?A8 )A! H f _ % _ f /0& j &>&(! j )k60) ! 8 A3:&(4 :4 A4C&d1'6*, !*&(# ! H'&(8 + ):! $qg' ; ^ 4 &G&>,&(8 3+)]#*&`"3+3?"!9:& = &>! #'& &(3 = !*&(4 + &c&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &(3+:8 )A! ; $ 4 = )'# :8> )A! 4<&(46&58 ",,t = 6):3 "! G ! 8>A4&(4 &(3& & # = & &(3@)". + &Tl#$"! = #') c 4c8d) = 6"3?"/*,& ) # 4 "!$8>&(4 ) = & A,>t, A&&>,&(8 3+)]#*&(4oqp r m ! &>3 8>A,-l#$"! = #') 4'4 & = 46*3+&(4&>! &(# ! b $qg + &a4)0*3?8d& A!$#@#'3? !c,&5A#*49A3&C)A!*,r`4&>6$A3+ &5#`/ *!$!*&>,/$A33 &>3?4 )".'.& W &>!4 )A.*!$"!*) = & &(3+4 &>3+&(:4 + & l#$A! = #') # = & &>3 4 ! &3?"!9:&)". *!$#*3&5#c!$"!$) = & &>3?4 ; &>3+&d.):3& !4$8 4 3$8 *3+&0 + &a8>,)47&> /G,&5A#*4= 4+8d3+&>&(! K &@&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3?A8 )A! ! &G& = /&5#*#'&5# l#$A! =#') K x< ,4) "! ! ) = )0:&>!*&()0$4 # &>,&(8 3 8 = 3 1 )A3 c# &>,&(8 3 8 = 4 = 8 8($4&(4= )'# :8> )A!$4@)A.EW6ª*3& 2 )*,) = / ! &>3?A8 )A! b )A3 !$4 "!8d&0 48 # &(,&58 3 8= 4 = 8 D 4 .)0*!$#T &B4$37. :8d&E)".9A! & 8 &5#T4 38 $3& + & ! &(37. :8d&(4 )A. & &(3)4 3$8 *3+&(4ao p r1* 47& = 8d):!$#;$8 ):3/6 !$4*, )A3 ! &(37. :8d&(4-)A3 + &^4*3. A8>&)A.-8d):,,) #*",,rT6*3&(6$"3+&(# 47& = 8d):!$#;$8 ):3k8>,t4 &>3?4 ):3"! 8B4*3. A8d&G6$:44 t >+ ):! o H:H L r ; &(4& = )'# :8> )A!$4`"3+&",4) 0A&>! ! ) A8>8>)0*! / & 3^3+&>&(! m 4 G )@+)!+,±0+ ± !+)!+, ! . ),0&), ! !S³ '?+± ! b"+Q±e# ,++ *v+)!+, !g)@ "+³ = ,#)!) / +)!+#)b #M#v !"' °T?; °#, !#" +,°1,#+M,, °@ #)! ' ! ! ±L0 !#" ±0 ), !+1( ±° Q+ "+"/3e #?; ! °+);+,#) +³

I ³ ° !)!# '*$ ()!+, ##g±3 +)! !1 M## g.`$!$8 + ):! H : #'&(4+8d3 / !ª &@8>) = 6*,& &`&(,&58 3+):4 8BA33?"!9:& = &>! &58d&(! ,t ! R |0|*H 3+,A!$# "!$# 8>) ):3:&>3?4 o H R | r 8>A,8*, &5# 476 &>3 8(",0l"! = #') 4 +G3?A# ", # &>,&(8 3 8 = 4 = 8 ; &k3+&(46&58 r &-3^3+&>&(! m 4 .`$!$8 + ):! 4 .)0$!$# &(3& b )A3B l"! = #') & = /&5#*#'&(# ! = 3 1W)".,) &(3B# &>,&(8 3 8 8>)A!$4 A! &&(,&58 3):!;> &(,&58 3):! ! &(3+:8 + ):! 4^&(! "!8d&(# A!$# A,4) + & = A!>t&>,&(8 3+)A! 4 &54 ! & l#$A! = #') A3& = )]# :$&5# 8d) = 6"3+&(# ) & 8(A4& + )0 # &(,&58 3 8= 4 = 8 + -.- \X#N VYL9R'PSV W=V TV JMPS\XV]\THL9R; & 2V bB Q]AEoG+D QQªFRQ °?ªD V QV FHAE "/ `_ .):3 + &B&(,&58 3+)A!4 * 8 #'&>60&>!#*4^)A!+ &@"3+3+A!9A& = &(! /9 !*) )A! + &G&>,&(8 3):! ! = /0&>3 4 r &>! /# $ ML:d ; &8>)A! 3 /9 )A!4 A3& ! &>3+6*3+& &(# ! &k.)A,,) !9ª'A!$#D4:& 8 &(# ! b j$ H| sH ; &':$3+4 k &(3 = " `_ #'&548>3 /0&(4 &@&(,&58 3+):4 8<60) &>! ", 8d):! 3 /9 )A!8>0$47&5#c/ & :*1'&(#8 "3A&a# 4 3 /9 )A! `_ . + &k&>,&(8 3)4 + 860) &>!;> ",4E)". + & &>,&(8 3+)'#'&(4EA3& 4& E ) ~ &>3+) m = 0A&c8 A3:&(4k)". $ 4 ):!W8 "3A&# 4 3 /9 + ):! !$#;$8>&(#`)A! + & &>,&(8 3)'#'&54_A!$#<4&>&(!B/ & &>,&(8 3+)A!$4h"3+& :&>! ! ) A8>8>)0*! / & 3^3&(&>! m 4 .`*!$8 )A! `_ 4 _ k b $ H| MR ; &a4&(8>)A!$# &>3 = %

K d `_ 4 _ 8d):! !$4 + & ! &(3+:8 + ):!c)". &C&>,&(8 3+)A! 6)4 )A! _ FRV T D Q F A °G 9AB T ):!@A,, & &>,&(8 3+)'#'&(4 ; * 4 &(3 = :4%A,3+&(:#; = &>! + ):!*&(#c 9 &a&>!$# )".4H]&(8 )A! g* ; &C.)A,,) !9E&d1* = 6$,&54= ,,t4 3+ & 4 = 6):3 "!$8>&As < ! &>,&(8 3+)A! ! .3):! )". = & ",f&>,&(8 3+)'#'& b 7 H| / 4c 7 3+:8 &5# / 4 = 0A&8 "3A&(4 & 4@&>,&(8 3)4 + 86)0> &(! + A, "3 &(4 46)4 )A! _ 3+&>, +t & ) & = & A,C&(,&58 3+)'#'& m 4 &k):3 !.)A3 !$4 "!$8>&0])". &IH'8 ) 7 #c&0&58 )".h,) &>3+&(# /$"3+3 &>3?4 !:$&>,#& = 44 ):!T#'& ] 8d&(4 m 8>)A! 3 /9 &54 ) + &<&>1 &>3+!$", 8>)A!;:! !ªc6) &>! + A,_4 !$8>& #')]&(4`!*) #'&(6&(!$# ):! & 6)4 )A! )". &) &(3B&>,&(8 3+)A!$4 ):!*,r ):! &6)4 )A!D)A. + &E&>,&(8 3+)A! 47&(, . ! + &<"3+3?"!9:& = &>! ;< ,4) ! &(37. :8d&54; t] !9D,)'8(",%8 A!9A& ! &# &(,&58 3 8@6*3+)A60&>3 &(4 8d3+&( & T8d):! 3 /9 + ):! ) &8d):!;:$! !9 60) &>! ", ] `_ 4 _ o p r Y< ! &d1* = 6$,& 4' r &(! ! b $ H| / 3^)A,#')A! ):4+4 "!$# [ )A, !$A3 o H R H rh6*3):6)47&5# $4 !9 + &`# &(,&58 3 8<8d):!;:$!*&>= &>! .):3-&(! A!$8 !9B&>1*8 )A!/ !# !ªB&>!$&>3 &(4 !!"!*)4 3$8 *3+&(4 < # &>,&(8b> 3 8 = 4 = 8 8>"! /0&E& &(3C 3?A8 +t &a):33&(69*,4 r &a.)A3 + &E&>,&(8 3+)A!$4 * ; & $ 3?# &>3 = "/. `_ ! 2L: #'&(6&(!$#*4, !$&("3+,rc)A! &k&(,&58 3+):4 8^6)0> &(! + A,4 ^ p )". + &c&>,&(8 3+)'#'&(4(s ; &c&>,&(8 3+):4 + 8`60) &(! ",98 A!9A&G)". "!&>,&(8 3+)A! 60):4 )A! _ #;*& ) 8 "!9:& ! &&>,&(8 3+):4 8`60) &>! ", ^ p)".h&>,&(8 3)'#'& 4 6*3+)A60)A3 )A!$A, ) &^.3?A8 + ):!)A. = 0A&E8 A3:& p `_0k 47&(& R:R 7 !$#;$8>&(# / + &E&>,&(8 3+)A!):! &E&(,&58 3+)'#'& " `_0 p `_0 d ^ p [ $ | ; * 4 3&$&(8 4 &^&>,&(8 3+):4 8C3+&(8 6*3+)'8 4&>&k# 4+8b44 ):! ) $ RAR M ; )A, >:&(4k"6*6$, &(# )7: &@&>,&(8 3+)'#'&(4k8>A! /0&$4&(# ! &(! )A!$A,,r )T8 A!9A& &/$"3+&E8d):!;:$! !9@6) &(! + A, )". &<l#$A! = #') o HAHAH H| L r

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ε((( (r)

Metal Electrodes

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ε((( (1)

ε((( (2)

Metal Electrode

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Dielectric Medium 1

Dielectric Medium 2

ε((( (r)

(r)

(r)Φion

G(r,r)e2-

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ε0C

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(d)

(b)

Mat

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l 2

Mat

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l 2

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l 1r

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0

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) , # !# M#?) + "-;+ ) %Y y± ¦ ¬ , ?0g± " ± !1, #0 ! % ! "' "++³ ¦ ¬ = ' ! " b"'°, ")!M+)!+,K !±0#+g±K °)@),±³,)!, * #+)± !±+g± ;)tb ! ! !&v+*; ! ++.±0 ), !e °g±0 t%% ± '"9+Q+)!+, ! #1,,Q +)!+, 7 . !& ' ( ( G 37;+)!3 +)!+, r !&v+ '@( ( G ³ ¦ ¬ = +)!+,1 !N;+ )±0 "9+#+1; ! ++j K),±+±# ##'+)!+,1 ! ;+ ) )#±,g%;³ ¦ ± ¬ = 1$ ! Q '+#±# &±' ° ! # ±% t) $,/0 !#" ! ;, !ª³ ; &9,A4 &(3 = J c `_ #'&(4+8d3 /&54 60):4 + ):!k#*&>60&>!$#'&(! 8d):!$#;$8 )A!;>t/$A!$# = !;> = = #;*& )D# 0&(3&(! = &>3 A,4a 6)4 )A!4a)A. &Gl#$A! = #') m ^ !;>8d,r$#'&(4".):3 !$4 "!8d&0 &a8d)A!#;$8 + ):!;>t/$"!$#@)0 4& % & &(3)MP*!$8 + ):!$4 ):3 &4 &>&>6c8>)A!;:$!$& = &>! 6*3+&(4&>! & 8 &5#G4*3. A8>&(4 #;*& ) & 3?"!$4 + ):! ) A8g>9 = 47&(& b j H| # d H*3. A8d&D8 A3:&(4'$4",,t 6*3+&(4&>! )A! 4$8 4*37. :8d&54"!$# 3&(6&(,, !ª &G&(,&58 3):!$4 .3+) = 4$8 4*3. A8>&(4^"3+& = )'#'&>,,&5# / & :$3?4 &>3 = ! 2L: `_ M

(*"/ -;,# %* g± ()!+, -/01+ g; ) & = 6 A4 r~ &0 + &&>1 &>3+!$A, 8>)A!;:$! !9 60) &(! ", " `_0 4 Q]D V`&(l#$", ) &&(,&58 3)4 8k60) &(! ",h6*3)0:$,& + !*)&(,&58 3):!$46*3+&(4&>! C ! &`l#$"! = #*) ; & , &(3 !*&:,&58 4 & 4&(8>)A!$# &(3 = %K d `_ 4 _ #'&(4+8d3 / !ª + & 8d):! 3 /9 )A!#9*& ) &a) ! = :&a8 A3:&(4 # !*&a4 )*,#",47)</0&k A3&)A. %+ &a&>1 &>3+!$A,8>)A!;:! !ª<6) &(! + A, 4%# &>3+&>! % ) &a&b &(8 r &C8>)A!;:$! !9B6) &>! + A,04&>&(!c/# &4 !9A,&k&>,&(8 3):!$4 !T

A3 3&(&b>9):3 "3 3+&>&> b )]8+#>t, A&^"!$4+ ~

8 %4 1 0 B@49;"3 - % 2"3:"3 8 9! "3 0,"3#"34% "3% 0 B@49;"3 - 7( % 8 49;"3 $% 0,12"34- '% % % )+%,"3&- . 7"i *& ) + & #'& A3 & ^)".$A33?"!ªA& = &(! 4 .)A3f l#$A! = #') + &%&>1*A8 47):,t )A!)A. & H'8 3):# !9:&>3 &5l )A! .)A3 &>,&(8 3):!$4 ! l"! = #') 8("!*!$) !:&>!*&(3+A,$/0&% r &>! m ! * 4 H]&(8 )A!#:$3?4 ,t B!*) + ):! 4 ! 3+)'#;$8d&5#c,"/0&>, !9 & > &(,&58 3+)A! 4 &54`4 A3 + !ª .3+) = + &7A3+)0*!$#$4 &)". + & >t&>,&(8 3):! 4]4 & = ; &>!c47) = & A6*6*3+)21 = + ):!$4_.)A3 3&5 + !9 ! &>3?A8 !9k&>,&(8 3):!$4 ! ^l#$A! =#*) A3& /$3 &bª = &>! + ):!*&(# ; &>3+&(". &(3 & ) ",0&>!*&(3`46&58 3+B)". <6$A3+A/):, 8R i l#$A! = #') _ ):!*&0 j )a"!$# + 3+&>&%&(,&58 3):!$4 A3&96$3&547&(! &(# )C& = 6 A4 t~ &+ & = 60)A3 A!$8d& )". ",r !ª ! &>3 = 4@)".C.& ):3 = A!##>t&>,&(8 3+)A! 4 &(4 !$4 &5A#)A.94 !9A,&b>t&>,&(8 3+)A!T4 &(4 &>! # 4+8b44 !ª !A&>!$&>3?", + &B&(,&58 3+)A! 8E6$3):6&(3 + &54)A.Bl#$"! = #*) 4 b !$A,,r &W8d):!$8d&(6 4 FRV FHD Q0? +G VB W "!# GFRV1A VFHD Q0? +G VB W "3+&^# 4 !90 4 &(# + -$-LªU\ " PSR*\THP@V P (\ X eRHXU\NPSV " U*NP TV@X#N YL;\THP@V; &&>!*&(3<4760&(8 3 = )A. + &Cl#$"! = #') :$,,&(# &>,&(8 3):!$4 4 ):/ !$&(#/4)A, ] !ª + & >t&>,&(8 3):! H*8 3)# !9A&(3-&5l )A! ^ p 4"! ^ p6$# F 4"! ^ p d 4"! ^ p%# [ $ H 4&! ^ p #'&(!*) &(4 + & ) A, &(!*&>30 )A. &<4 & f 4"! ^ p ' )". + & &>,&(8b> 3):!$4 ! + &Gl#$A! = #') ; &B! = /&(3 ! 4 "!$#*4 .)A3k = $, + 6*,& )".%l#$A! =! = /&(3+4 * 8 &B/0&c8 ):4&>! 6$3):6&(3,r .)A3E8 "3?A8 &(3 r~> !9 + &G4 &54a)A. & > &(,&58 3+)A!G4'4 & = 3^))'#cl#$A! = ! = /&(3+4%"3+&-.)*!$#`.)A3-l"! = #') 4 60):4>4&(4+4 !98d&>3 ! 4 =@= & 3 &(40,&(:# !9 ) ! &:3+A,4C)". = ) )A! , A&@"!9*,"3 = )0>= &(! = /9 A,4)@) &>3 l#$"! + + &54, A& + & ) A, 46 !D):3 &B46 !D6*3)MPj&(8 )A!8 "3?A8 &>3 t~ & & >t&>,&(8 3):! 4'4 & = A4Bl#$A! = ! = /&(3+4 m 3+3&0*,"3G4 "60&(#l#$A! = #') 44$A,,r@#')<!*) ) &>3 ! &A3?",4 )A. = ) )A!$4 K & &>3 &(,&544f.):3%&5A8 4& )". 6$A3+ = & &(3+4 A!$# ^ p6 4 )*,#@/&a6)44 /$,& )B#'&(!*) & + & >t&>,&(8 3+)A!4 &54c#'&b:$! &>,r ; ) ) # &d1'6*, 8 l#$A! = ! = /&(3+4 ! &D.):,,) !ªª &4 &549"3+& ,"/0&>,&(#@/ ! F| 4 H 4 R 4 ddd ]4 "3 !9k.3+) = ! F | .):3 &A3+)0*!#*4 &)".+ & > &(,&58 3):! 4'4 & = ! + &kl"! = #*) ; &^&d1*8 &(# 4 &(4 A3&a!# = /0&>3+&(#$!$ = / *)047,r !$8>3&5A4 !ªE&>!*&(30 & 4&! ^ p 4"! H ^ p

g I !#"%$'&(*)!+,.-/01+ A,,) !ªkA,4)^.)A3%#*&A&(!*&>3?A8B#;*& ) + &C46$ + A,$4 =@= & 3`)". &al"! = #') ):3 #9*& ) + &<476 !].):3 !4 "!$8>& K ):!*& A4k4)A, &(# & >t&>,&(8 3+)A! 4'4 & = .)A3k"3+/ 3?"3T8d)A!9:$! !960) &>! ",A!$#&(,&58 3):!;> &(,&58 3):! ! &>3?A8 )A! ; &E6 '4 8(4 )". l"! = #') 4 43 8 I #;*& ) & "3 & D)". + &@&d1 &(3!",f8d)A!9:$! !960) &>! ", n .):3 !$4 A!$8d& +)A3 ) A&() = & 3 8>A, 4 =@= & 30I #;*& ) + & "3 )A!$4 !T48>3&(&>! !9 &E&(,&58 3+)A!9> &(,&58 3+)A! ! &>3?A8 + ):!*"!#I #;*& )E# &>3+&>! 3&(, r & = 0A! #'& )".0l#$A! r~ + ):!B&(!*&>30E/B8>)A!;:$! !9EA!$#&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3?A8 )A! &>!*&(3 ; &H*8 3)# !9A&(3 &(l#$ + ):! $ H 8d) &(3+4 !c)A!$&, = = & ",4 ! + & ) &(39, = 4 !ªA,& ) = 4 ; & ! &(3&54 + !ªT6 ]4 8>4 ! & ! &(36$, /0& j &>&(! 8d)A!9:$!*& = &(! A!$#k&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3?A8 + ):!E,&5A# !9 )a8>)A3+3&(, )A!$4 /0& j &>&(! &%&>,&(8 3+)A!$4 4 .)0*!#/0& j &>&(!D/) , = 4 + -$- # # NP THZ[L;\TPSV %(1PªNQNX#L9\THV eRHXU\NPSV %3TV[L YL9V]\ Z Pª\[ )'#'&(,4C.)A3kl#$"! = #') 4 &B/0&>&(! ! &(4 : &5#T"!$# "6*6*, &(# ) 8>&>3 ! &>1#>60&>3 = &(! 4 @< = )A3+&<8d) = 6$,& &<6*3+&(4&>! )A!D)A. + &B,"3A&< = )0*! )". + &>):3& 8>", )A3 $ 8 < A4_/&(&>!`#*)A!*& 4 .)0$!$# ! + & 8>)A,,&58 + ):!<)".$# r &(3+4&%3+& ] & 4-o p; l r &>3+& &k& = 6 :4 r~ &k):!*,t8d&>3 !DA460&(8 4

I 4$",,r T/0)21> , :& o H RAR r )A3`6$"3?"/0)A, 8@8>)A!;:$! !9 6) &>! + A,ao H R H R r 4B:4>4 = &5# .):3 #'&(4+8d3 / !ª + &T4 A6&D)A. + &D&d1 &(3!$A,8d)A!9:$! !9W6) &>! + A, ; &, 7 &>3 t &(4 :3+4 "6$6*3)21 = )A! )c,)'8(", = ! = = ! 6) &>! + A, ,"!$#>48("60&k)". + & 3*&E&>1 &>3+!$", 8>)A!;:! !ªG60) &>! ", I + .& &>,&(8 3+)A!$4 ! 4$8 <4'4 & = ,&(4+4 + &>! H| & = , + ):! A!c)". & ! &>3?A8 + ):! &>,&(8 3+)A!$48>"! /& &d1*A8 ,r 4)A, &5# ! = &>3 8(",,t + 3+&(A4)A!"/*,&&b )A3 < 4 + & /$:47&D.):3 & .& >t&>,&(8 3+)A! &d.`$!$8 + ):! & 4$6&(360):4 + ):!)".@H], &(3 #'& &>3 = !$A! 4 + 4 !9A,&b>t&>,&(8 3+)A! 4 &54 : 7+ !9 ) &T&>1 &>3+!$",8d):!;:$! !960) &(! ",AA3&o$4&(#kA!$# &

= , )A! "! ! & = 3 1^6*3+&(4&>! )A!)". * 4/$:47& 4 !# = &(3 8>A,,r# :)A!$A, r~ &5# 47&(&0'.):3 !$4 A!$8d& o H RAR r MI b ):3 * &>,&(8 3):!@!# = /0&>3?4 "6*6*3+)21 = )A!$4 & )E/&a#')A!*& n $4$A,,rB/$:47&5#)A!"3 3+&>&G)A3

A3 3&(&b> b )'8+#> , :&<4 &(4 ]< ! &0&58 +t &G8>)A!;:$! !96) &(! + A, 4)A/ !*&(# .)A3 &c4 !ªA,&`&(,&58 3+)A!4 H !9A,&b>t&>,&(8 3+)A! 4 &(4kA3&`)A/ !*&(# +& A&(!*&>!*&(3 &54 J p ; &(4& = /0& = )A3+&A#'&5l & )^/0&$4&(# ! + & 2 )A!$4 A! m ! &>3?A8 )A! [ )]#*&>, A! + ):4&a&(,&58 3):! 8a4 &(4 "!$#4 !9:,&> &(,&58 3+)A!&>!*&(3 &54.)0*!# .):3 &E&>1 &>3+!$A, 8>)A!;:! !ªG60) &>! ", I b ):3 * &>,&(8 3+)A! ! = /&(3+4 + & ; ) = :4> b &(3 = "6*6*3+)21 = )A! :4/0&>&(!$4&(# 8d) = / !*&(# + ] ) 44)A!&(l#$ + ):! o H R g r I 4$",,r .):3 & #'&(4+8d3 6 )A! )A. l"! = #') f H f _ % _ f ! &>3?A8 + ):! 4A4+4 = &5# 4&>&_.):3 !$4 A!$8d& o H R:R H R H R H R l r d=< 4G6) ! &5# )0 * 4 4&(l#$A, ) + &-3^3&(&>! m 49.`$!$8 + ):!)A. & !;:$! &E46$A8>&:$,,&(#/#c ) = )A&>!$&>)04# &>,&(8 3 8 = &(# =

(*"/ -;,# %* g± ()!+, -/01+ g I m . & ] ) 4+4)A!C&5l#$ + ):!kA!$#@H'8 3):# !9:&>3 &(l#$ )A!E"3+& 47):, &(#k4&>,.>t8>)A!$4 4 &(! ,ro H R p>r .):3G r &>! &>,&(8 3)4 + 8 4*3+3)*!$# !9S = 0A& 8 "3A&54<"3+& A&(! ! )A8(8d)*! /# + &/0)0*!#*"3 8>)A!$# + ):!$4E.):3 & ) A,-&(,&58 3+):4 8@6) &(! + A, ; &547&B8(",8b*, + ):!$4CA3&3$4",,tD/$:47&5#D)A!

"3 3+&>&> , A&E)A3^ "3 3+&>&b> b )'8+#>, :& "!4 ~ 2 )A3+3&(, )A! &b &(8 4 /0& j &>&>! & &>,&(8 3+)A!$4 /0&(4 #'&54 &d1*8 "!ªA& ! &>3?A8 )A! A3&B&d1*8d,r$#'&5#T/ 4$8 A! "!$4+ ~ 4 !$8>& ):4&`"3+&<!*) #'&548>3 /0&(#/c4 !ªA,&E6*3)'#;8 A!$4 ~ )A. 4 !9A,&b>t6$"3 8d,&E4 &(4 .)A3 !$4 A!$8d&*/ 4 !9>A,&OH', &>3h#'& &>3 = !$A! M b *!$8 + ):!$",]#'&(!$4 = & + )'#*4_A3&Q$4&(#k.):3 = 6*3) ] !9 &(3&co H R r I H]6 &>3 8(",-4 =@= & 3 ! + & /$"3+&8d):!;:$! !9 6) &>! + A, A!$# ! & 2 )0$,) = / ! &>3?A8 )A!k,&5A#*4 )CC4 &(,,t>t, A&94 3$8 *3+& ! &9&(!*&>30k46&58 3 = = ! = t~( !ª &`&(!*&>30 .)A3kA#$# !ª"! &>,&(8 3+)A! ) + &Gl#$A! = #') .):3^8>&>3 ! m = 8 m! = /0&>3?4 m 3+& = !$#*4 ):! & A3 + ):!k)". & ):! 4 )A!k&>!*&(3 ! &%60&>3 )'# 84]4 & = )".%3+&(A,h ) = 4 *!$# m 4^3$,& 4C.)0$!$# &(,,=]!*) !T.):3a3+&(A,h ) = 4 ]<A&(!*&>3?", r~ &(#

*!$# m 4-3*,&k8>"!/&^#'&>3 t &(#@.):3 4$8 l#$A! = #') 4 ! = 0A!*& 8:$&(,#*4Eo H R L r I 2)A3+3+&>, )A!4 ! &%476 ",A6)4 )A!E)A. + &9&(,&58 3+)A!4 "3+&h.)0*!$#^.):3 ,) #*&>!$4 l#$"! = #') 4$4 !$8>& &E&(,&58 3+)A!4 6*3&>.&>3 #;$& ) &E&>,&(8 3)4 + 8 2 )0$,) = / ! &>3?A8 )A!8>&>3 !D8d):!;:ª0$3+ )A!$4 /0& j &>&>! 60) ! 8 "3A&(4 I ; & = )'# :8> )A!$4 )". &9.& >t&>,&(8 3+)A!E4 &(4 !B R i l#$A! = #') /^4+8d3+&>&(!;> !9 + &k&>,&(8 3):!;>t&>,&(8 3):! ! &>3?A8 + ):!c/c6$"3?",,&(,6$, &^&>,&(8 3)'#'&54 A4 ! &(4> : &5#/

",, = "!#8>) ):3:&>3?4Coqp r I b ):3B"!W&(,&58 3+)A!9> &(,&58 3+)A! ! &>3?A8 )A! &(3 = .)A,,) !9 H f _ % _ f !$4 &(:# )".`69*3+&2)*,) = / ! &>3?A8 + ):!]& &>!A!$",r 8>A, 4)A,r + ):!$4 &^/&(&>!.)0*!# .):36$A3+A/):, 8 8d):!;:$! !9C60) &>! ",4%oqp5r H$8 A!<"!$4+ ~ = = 8+]4h4+8d3+&>&>! !9)A. #*&3?"!9:&

2)*,) = / ! &>3?A8 + ):! I b ):3 ,A3:& l#$A! = #') 4 )". 3+3+&0$,A3h4 "60&0 & 2 ):!$4 "! > m ! &(3+:8 + ):! [ )'#'&>, :4/&(&>! A6*6*, &5# ) &d1 3+:8 4 !9:,&> 6"3 8d,&^&(!*&>30,& &>,_476$:8 !9:4C"!$#D8d) = >6$A3& 4 4 + 8(",,t + "!$#') = [ 3 1 ; &>):3 .)A3 3+& ] & s o H:H r MI < 4]4 & = 8k8d) = 6"3 4)A! /& j &(&>! 2 m [ = )]#*&>, A!$# &d1'6&(3 = &>! A, #* :46*3+&(4&>! &5#@/ )0 &>! ) &>!* iB 3 < $4 + !ª`"!# H ; "3$8 co g r0.)A3 &>3 8>A,l#$"! = #') 4'4 & = 4A#'&(!*) &(#GA49 ) = >t, A& l#$"! = #') 4 &>3+& + & l#$"!9>r~ )A!T&(!*&>30 #;*& )8d):!;:$! !9 P$4 #*) = ! &54 ) &>3 + &<&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3?A8 )A! H]) = & 3$&(4 /ª A,4) , = )A!$4_)". + & 2 m [ "3+&96*3+&(4&>! &5# [ )]#;> :8> )A!$4 #;*& )@&>,&(8 3):!&>1'8 "!9:& ! &>3?A8 )A!D"!$# 8d):33+&>, + ):!$4 & )@/0& 0A&(! ! )cA8(8d)0$! .):3 `6$3):6&(3 #'&(4+8 6 )A! )". &E&d1'6&(3 = &>! A, #*

< 6*6*,r !9 A MQ V FHG bE = )'# :$&(4 &c&(,&58 3):! 8c4 &54E)". & l#$A! =#*) ; h 4 & = A!$& 8:$&>,# 4f"! = 6):3 "! h *! !9k6$A3+ = & &(3 )^,&("3+!= ):3& A/) < & 3&5", t~ &(# l#$A! = #') A!$# &8d):!;:$!*&5# ! &(3+:8 + !9D.& >a):3= A!##>t&>,&(8 3+)A!D4'4 & = ; &<&b &(8 C 4C4 3+)A!9:&>3 .)A3^l#$"! = #') 4 A!D.)A3 3+&(A, ) = 4E4 !$8d& + & = A!$& 8c8d):!;:$!*& = &>! n &d1'6*3+&(4+47&5# / + & 8b'8>,) 3+)A! &>!*&(3PQ a F e SU n !$8d3+&(:47&54 H p = &; 60&>3 ; &(4, .):3 + &@&b &(8 r & = :44 !3k < 4 & :&d1*8d&(&(#*4- .& ; &547, + & ]6 8>",0l#$"! r~ )A!c&(!*&>30 PQ a c r &(!c/#@6"3?"/0)A, 8^&>,&(8 3+):4 8E8d)A!9:$! !9 ; &0&(& = "!D&>!$&>30 F ^ 4C4 = ",,

g !#"%$'&(*)!+,.-/01+ | A = &;+6 ; 4 !$8d& + & "!#& > . A8 ):3B.):3C3k < 4 4c):!*,t F % | [ A ; &.):,,) !ª`3+& = "3'4 )cl#$"! = #') 4 ! = 0A!*& 8M:&>,#*4>sI ; &`4 !9A,&b>t6$"3 8d,&`4 &54C)A.- R i l#$A! = #') ^ 6$A3+A/):, 8E&>1 &>3+!$",8d):!;:$! !9 60) &>! ",f"3+&B#'&548>3 /&5# ! 60&>3+6&(!$# 8b*,"3 = :!*& + 8%:&>,# / 4)>8>A,,&(# b )'8+#> i "3 !4 &(4Eo H | H H r I +D & :$3+4 &d1'60&>3 = &(! 4 ! H LML H ):! R i l#$A! = #') 4 ! $ = 0A!*& 8:$&>,#*4 & ; ) = :4> b &(3 = A6*6*3+)21 = + ):! A4C/&(&>! "6*6*, &(# o H R g rh,&(:# !9 )47)0>t8(",,&5#k8d) = 6*3+&(4+4 /*,&9"!# !8d) = 6*3+&(4+4 /*,& 3+& )A!49o H R r ! & l#$"! = #') m G A4 + &K:3+4 #*& = )A!$4 3? + ):! + G & 2 m [ = )'#'&(, 4G!*) `+ &TA#'&5l#$ &#'&(4+8d3 6 )A!.)A3 4$8 Gl#$A! = #') 4]4 & = I [ ):4 )". &<8(",8b*, + ):!):!.& > &(,&58 3+)A!Dl#$"! = #') 4 .)'8b$4 )A!D8 "!9:&(4 ! &C&>!*&(3B4760&(8 3 = + "6*6*,r !ª = 0A!*& 8:$&>,# H !8d&CA! !;>4 *!$A/*,&6$"3? = & &>3 ",,) 4 ) 3& &5",n8d):33+&>, + ):!a&0&58 4 n , :&0M.):3 !4 "!$8>&0>4 !ªA,& > 3 6$,& 3+A!$4 + ):! !$#;$8>&(# / = :!*& + 8 :$&(,#Wo H : r + -$-/ RXU\NP@V %TV YL9V]\ Z PS\ TH\ JML9N L9OPSRTHU 'P@V*W=V TVJ Pª\X#V]\THL9RL9V J N X 3PYRHP@ZO RXU\NP@V RXU\NP@V bV]\X#NL9U\THP@V 4 YXPª\L9R VYX#N "$# XU\N Z; ) #'& = ):!$4 3+ & + &B8>) = 6*,&d1 )".9A! ! &(3+:8 + !9 &(,&58 3):!D4'4 & = ",3&5A#; !TG4 = 6$,&E&>1' = 6*,& & ) ", &(!*&>30 46&58 3+cA3&k4 ) ! ! b $ HAH .)A3):!*&0j ) "!$# + 3+&>& &(,&58 3):!$4 ! R i l#$"! = #') 6$"3?"/0)A, 8T8>)A!;:! !ª60) &>! ", sI < 4 !9A,&&(,&58 3+)A! ! &Dl#$"! = #') @ :4GA3+)0*!#*4 &&>!$&>30 FH 4&! F | F PQ a c "!$#cA!@&d1*8 )A! 46&58 3 = 3& &5", !9EA!G&5l# # 4 A! ,:#*#'&>3)".h&>!*&(3 ,& &(,4 I b ):3 j ) &>,&(8 3+)A!$4 ! + &`4'4 & = & ) ",_&>!*&(3 F R 4"! F | .)A3 &A3+)0*!#*4 & !$8>,t#'&(4 & !*& 8 &(!*&>30`)". /0) &>,&(8 3):!$4%A!$# &C&>,&(8 3+)A!;>&>,&(8 3+)A! ! &>3?A8 )A! m = 6):3 "! ) 3+&(", r~ &0 &G&d1*8 )A! 460&(8 3 = )". $ 4j )0> &(,&58 3):!4'4 & = #')]&(4 !$) 3+&b$&58 4 = 6*,r &E&d1*8 )A! )". + &E&>,&(8 3+)A!$4 ! * &(3 4 !9:,&> 6$A3 + 8>,&k4 &(4 8d):!$4 "! &>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3?A8 )A! m 4 = ):3&E8d) = 6*,&>1 I + + 3&(&&(,&58 3+)A!4 & &d1*8 )A! 460&(8 3 = /0&(8>) = &(4G",3+&(A#9 #'&(!$4& ,) &d1*8 )A!D&>!*&(3 &54 & $/&(,) &<8>)A!;:$! !9cl#$A! +t~ + ):!&(!*&>30 PQ a c ; )%A&>&(6 + & # 48$4+4 )A!B.)A3 &>,&(8 3 8(", 3+A!$4760)A3 h 3+)09 l#$A! = #') 4=A&>!$&>3?", 4$8 "!D&>!*&(346&58 3 = A4'4 ) A,t)". Sf):3 A Q S E+G V BD QT V1A V TE)A! &l#$A! = #') !4 &(A#)". 4 !9:,&> &(,&58 3):!4 &(4 + -$- + TH\THP@V "3# X#U0\N YZ L9V UT`\L;\TPSV "$# XU\NYZ P (L YL9V]\ YZ Pª\; ) #*&(4+8d3 /0& &@3+&("3+3?"!9:& = &>! )A.-&>,&(8 3+)A!$4^/0& j &>&(! l#$A! = #') A!$# &>,&(8g> 3)'#'&54 ^ 4E8d):! &>! &>! a ) ! 3+)'#;$8>& + & = ! = = &>!*&(3 * 8 4^3+&(l# 3&5#

(*"/ -;,# %* g± ()!+, -/01+ g

0

5

10

15

20

25

30

tota

l ene

rgy

(meV

)

E a1

E a2

aE

tota

l ene

rgy

(meV

)

3

2e 3e1e

30

20

10

0

µ(N=3)

µ(N=2)

µ(N=1)

N=1 N=3N=2

Tot

al E

nerg

y E

(N,l)

[

meV

]

Excited States’ Energies

Groundstates’ Energies

E(N,l=0)

µ(N) = E(N,l=0) - E(N-1,l=0)

Addition Energy:

)°+#"/ &;+,# '#. ! ± +)!+,# ! &± ! °+#, !)0#;)! + ## !#" ;+ ) ,, ° " £¤ © « ¯ °± #0 #)! @j+)!+,&H+)!+, !ª³ = Cb °' § ¨ § ¨ ±( ¯ I )!g± !#"%°#"9+ $± ° ¦8I ³ ¬ vQ ±Q% ® I M# ³= =+)!+,&H+)!+,° ! !+; ! ++M ! +)!+,Y±0 ° !b+] # g !+#"/ £¤ © « ³ = Q1/1 ! #+)!+, ;+3±+g± o !#. ! ! K+)!+,# $ @.*± ! + +)!+,# ¦ ±g±r ³ vO# ± -9³ = ))! 7 I ¬ ³ )BA#$# &a!*&d1 &(,&58 3+)[email protected]+) = E3+&d.&(3&(!$8d& &(,&58 3)'#'& ) &al#$"! = #*) % &(!A,3+&(:#; &(,&58 3):!$4A3&T6*3+&(4&>! + &>3+& ! + & 3K:3)*!$#*4 & ; * 4 A FRV FHD Q Q B ^ H ^ p 4E#'&b:!*&(# / & # &>3+&>!$8>&@/& j &(&>! & :3)*!$#*4 &&(!*&>30 H 4"! F | ^ p )A. H &>,&(8 3):!$4 ! &al#$"! = #*) A!$# &:3)*!$#*4 &^&>!*&(3 4"! F | ^ p )". &>,&(8 3):!$4 ! + &<l#$"! = #')

^ H ^ p H 4"! F | ^ p6 % 4&! F| ^ p6 [ $ R m _ 4_47) = & = &(4 #'&(!*) &(#E:4 & bE+G VBD S0G FHG+AE?ªD V Q=VFHAE;D 7V WªA Q=V W 0D V H "3 !9 + &>,&(8 3+)A!$4 ! + &El#$"! = #') A!$#:#*# !9 &k!*&>1 &(,&58 3+)A!*+* 4 &>!$&>30 4 &G"!$A,)A)04 )". & A QªFRV )A.93&5", ) = 4 ; &B) + &>3a6*3+)]8>&(4+4n 4 A3 + !ª + &>,&(8 3):!$4 ! &KA3+)0*!$#$4 & A!$# 0 !9T)0 ):!*&c&>,&(8 3+)A! ) &3&>.&>3+&>!$8>&c&>,&(8 3+)]#*& + &>,&(8 3)'8 & = 8(",960) &>! ", ^ n 3&$&(8 4`"!FHD QªF TA V FHD Q 6*3+)'8d&544)". & l#$"! = #*) A!$# 3+&(l# 3&54 & = ! = = &>!*&(3^ % H 4"! F| ^ p % 4&! F| ^ p F^ % ^ ^ p M

g !#"%$'&(*)!+,.-/01+ ; &T&(!*&>3 &(4 ^ ^ p6 F | 4 H 4 R 4 ddd "3+&D#*&b:$! !9 A! &(!*&>30,A#*#*&>3 * 8 ,,f/0&'$4&(# ! &`!*&d1 2 "6 &>3 g )D#'&548>3 /& & 3+&(4 ):,#*4.):3 4 !9:,&> &(,&58 3+)A! 3+A!$4760)A3 3)9 l#$A! = #') "!$#%:&>!*&(3+A, r~ & + &%&(!*&>30,A#*#*&>3 ! 3)'#;$8>&(# ! 2 A6 &(3 H ;9A3 + ):!$4 ! &,& &>,*# 4 A!$8d& )". $ 4 &(!*&>30,A#*#*&>3 K ∆ F ^ H ^ p % ^ ^ p $ : + F ddd % H 4 4 H dddA3&T3+&d.&(33+&(# :4 A FRV FHD Q T ?G V B W )A. & l"! = #') "!# 4 )0*,# !*) /&= 1]&5# *6 +@ & GbFRV,A V FHD Q T ? +G VB W )". &al"! = #') )A. e:$1]&5#G&>,&(8 3):!! = /&(3

∆

F 4&! F| ^ p % 4 | ^ p $ A] F ddd % H 4 4 H ddd [; &547&El#$A! + + &54"3+& !$# 8( &5# ! &E&(!*&>304760&(8 3 = #'&(6 8 &5# ! b H:H

+ -$- 3P@RHRXU\TSX U0TH\L;\THP@V % L9V " THV SRX +JML;N \THU0RX UT`\L;\TPSV %m E 4 ):3 +]* ,& )T& = 6 A4 t~ & + # &>3+&>! !$# )A.-&d1*8 )A!4 = &>1 4 ! l#$A! = #') 4>sI Z 1*8 !9E"!G&>,&(8 3+)A!G.3+) = E4 !ªA,&b>t6$"3 8d,& 4 & )<^4 !9A,&b>t6$"3 8d,&4 & )A.* &(3_&(!*&>30E"!# &>3+&>/<8d3+&( !9a )A,& ,) &>3h&>!*&(3 4f#'&>!$) &5#JTgFRQ 0E S?9AB VFHGE GFRV1A VFHD Q 4&>& b $ H R d ; &(4&a"3+& + &^)A!*,rc&d1*8 )A!$4 #'&548>3 /&5# ! & 2 )A!$4 A! > m ! &>3?A8 + ):! [ )'#'&(, I Z ,&(8 3+)A! 4]4 & = 4 ! l#$"! = #') 4 6$"3?"/0)A, 8 8d):!;:$! !9 60) &>! ",8 "3?A8 &(3 r~ &5# / PQ a c "!$# /$A3& 2 )*,) = / ! &>3?A8 )A!D)A/0& & ) ! m 4 + &b>)A3+& = o H g r * 8 ",,) 4 )@4&>6"3? &k/0& j &>&(! + &<8d&(! &>3>t)".> = :44 = ) + ):!)A. & ):,&a&>,&(8 3):!4]4 & = "!$# &^3+&>, r & = ) )A!)". + &a&(,&58 3):!$4 b A3 !;>.3+A3&5#D4760&(8 3+):4+8d)A6 )A! R i l#$A! = #') 4`o H l rh3+& &(A,4 +* 4^8>&>! &(3>t)".> = A4+4= ) )A! A4cW8>)A,,&58 r &D&>1'8 + ):! )A. &T&>,&(8 3):! 4'4 & = m 4 l#$"! r~ &5# ! PQ a c !$#*&>60&>!$#'&(! ,r )". &c! = /&(3 )". 8d)A!9:$!*&(# &>,&(8 3+)A!$4 < 6*6$,t !9T= A!$& 8:$&>,# 47)0>t8(",,&5# A MQ V1D Sr?@EtA TD Q$T "3+& .)0*!# A4 8>)A,,&58 r &D&>1'8 > )A!$4 o H l r ; ):4& 8>A! 4 + ,,%/0&c.)0$!$# . T4, ,t "! A3 = ):! 8G60) &>! ",8d):! 3 /9 + ):! 4 ! 3)'#;8d&(# o H p5r I < 4 !$# 8> &5# ! b 7$ H R / A,4) ] /*3? + ):!$",f):3E3) + ):!$",98>)A,,&58 +t &G&>1*8 > )A!$4 = /0&a):/$4&>3 A/*,& ; ):4& &C/0&>&>!6*3+&(# 8 &(#c.):3-&(,&58 3):!4'4 & = 4 ! l#$A! = #*) 4#') = !$ &(# / 2

)0$,) = / ! &>3?A8 + ):! b ):3c,A3:&D&>,&(8 3):!! = /0&>3?4* '#'3+)]#9! = 8(", = )'#'&>, = /&<A6*6*, 8("/*,&co H 0 H ML r °)! b o ² ±#±0 °+#"/9² !Y)!, ,g±e±+o !/ ¦ ) ' ¬ 7 *¦ ) ' ¬ 1g±%@,,+ b ! *¦ ) ' ¬ ³ BY ±0# # ! ,³

(*"/ -;,# %* g± ()!+, -/01+ g

Excited StatesGroundstate

etc.

(c) Excitations in Spin Texture:

Single-Particle Excitations:(a)

εDifferentOrbital States

(b) Excitations in Collective Motion:

N-Electron ’Cloud’

RotationCenter of

Mass Motion BreathingVibration

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N,m N’,m’and

Spatial Extension of

(a) Arbitrary Electrode Arrangement:

Metal Electrodes

Different fractions of image charge are induced.

N’,m’

Spherical or Cylindrical Electrode Arrangement:(b)

Parallel Plane Electrode Arrangement:(c)

2D Spatial Extensions of

(α) (β)

Same fraction of image charge are induced.

Metal Electrode 2

Metal Electrode 1

d

d

Plane of a

Metal Electrode 2

Metal Electrode 1

1

2

2D Quantum Dot

Same fraction of image charge are induced.

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m ! & 6$3& )04 2 "6 &>3 + & &>,&(8 3):!G4'4 & = 8>)A!;:$!$&(# !c^l"! = #') :4/0&>&(!#'&548>3 /0&(# :4-A! ! &>3?A8 !9 >t&>,&(8 3+)A! 4'4 & = ;< 4 B8>)A!$4&(l#*&(! 8d):! + !9> )A!*]4 !9A,&b>t&>,&(8 3+)A! 3?"!4760)A3 -+ 3+)09 48 Gl"! = #') 4 # 4+8b$4+47&5# !+* 4 2 "6 &>3%/#'$4 !9 + &A&(!*&>3?",*#*&(4+8d3 6 + ):! ! &(3 = 4f)A. > &(,&58 3+)A!G4 &(4 !+ &al#$A! = #') ; &a46&58 3)48>)A6B)A.A3+)0*!$#;>h"!#c&d1*8 &5# 4 &(4%)". & .& > ) = A!>t&>,&(8 3+)A!@4'4 & = ! + &Cl#$"! = #') 9 4 # 4+8b$4+4&(#G/<&>!*&(3B8d):!$4&>3 >+ ):!T"30 = &>! 4 .)A33+&("3+3?"!9 !9G"!D&>,&(8 3+)A!D/0& j &>&>!Tl#$A! = #*) "!#,&(:#*4A!$#^/ ] $, m 4 &>1*8d,r$4 )A!k6*3 !$8 6*,& ; &-A8>8>&(4+4 )&>1'8 &(#E4 &(4 ,&5A#*4 4$A,,r )A! !$8d3+&(:47& /ª 4) = & = &54-A,4) )G`#'&(8>3&5A4& )". 8*33+&>! + !$8d3+&(:4 !9 = 0>! $#'& )A. + &C#'3? !;>47)*3?8d& ):, A& ; &C#;]!$ = 8(49,&(A# !9 ) $ 4%/& ] )*3 4# 4+8b$4+4&(# * ! = A4 &>3-&(l#$ )A!A6*6*3+):A8 ; &^8d) = 6*,&d1 @)". &^#;]!$ = > 8>4 + )A60&>! !9 8 "!$!*&>,4 )&d1*8 &(# 4 &(4C)A!T& = 7 &>3 A QD)A! 8>)A,,&58 )A3a4 #'&= 0A&(4 # 8b*, C ) #'&(#9$8d&E.3+) = 4 !9:,&*,+ ^ + 8*3 & !*.)A3 = )A!T"/0)0 + &%&(!*&>30E46&58 3 = )A. & l#$"! = #') f + )0 .`*3 &(3 A4+4 = 6 + ):!$4 m !B8(A4&)A. 8>)A3+3&(, )A!$4 ! &G&(,&58 3):! 4]4 & = )". &cl#$A! = #') lA4 >t4&>,&(8 )A!3*,&(4 &>1 4 4 & * !9 3?"!4 )A!$4 /& j &(&>! >-A!$# H >t&>,&(8 3+)A!D4 &(4 .):3:#*# !9@)A3 0 !9@)0 "! &>,&(8 3+)A! .- DE4< $ ', ,- 0/ 921# 43+<9! #"$ %& 7( )+%,"$- . " 0O1 2"34-m ! b ?g' H 9 &&d1'6&(3 = &>! A,%4& $6 )". l#$A! = #') ` 4`4 ) ! $ 8 ,,/0&j$4&(# ! +* 4 2 "6 &>3 ) #'& = )A!4 3+ & 47) = & )A. + & &>,&(8 3 8(", 3?"!4760)A3 6$3):6&(3 + &54a)A. l#$A! = #') 4 ; & l#$A! = #*) 4]4 & = 4<#'&b:!*&(# / 6$A3 + A,&(,&58 3)4 8c#'&(6*,& )A! )A.C j )0>t# = &>!4 )A!$A, &>,&(8 3+)A! 4]4 & = R iZ H K ! 3k < 4/6 < , c65 xx 3k c65 N < 4 & &(3)4 38 $3& 4&>&9A,4) b 7$ &3k < 476 < ,83k < 4 & &(3)MP*!$8 )A! ! &>3. A8d& l ! = /0&>,) &4*3. A8>&As [ & A,, 8476*, >1: &(4 &>3+&#*&>60):4 &(# ):! )A6 )".C = &54T3+& = !*&5# n. &>3`6$"3 ",,t & 8 * !9 + &4*3. A8d&)".+ & & &(3)4 3$8 *3+& ; &C# = & &>39)A. + &CA3&5a/0& j &>&(! & 6$49)A. + & &54 4A/) :g | ! = m !@A#$# + ):! ) &547& )A69 &54" = & ",, 8 /$A8+ & &>,&(8 3+)'#'& )A!+ &C3+& &>3?47&a4 #'&C)A. & *!#')A60&(# 4*/$4 3? & | qg =@= * 8+ A4$4&(#*V,D GªA Q (*)!+, ±#, / 87 I P + < 9 G .S), °# !)! !/ ;: G M + ;b%=< I ¯ ³

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(a)

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2

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σ (µ

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Gi,SV

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IDS

VDS

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SD

S

Source

VBS

Splitgate Electrodes

Drain

Backgate


86 nm

GaAs Buffer

AlGaAs Buffer

GaAs

AlGaAs : Si

GaAs

AlGaAs

GaAs Substrate

51 nm

0.5 mm

++

+ ++

++

+++

+

+++

+

++

1.9 m

2.0 m

0.3 m

10 nm

25 nm

µ

µ

µ

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2DES

Backgate

Con

duct

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µS]

Backgate-Souce Voltage [V]VBS

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= °±/# ° !g) #, ± ! ° Q-/01+ ¯ V E+G V BD T V,A V FHG?ªD V QV FHAE D @V WªA Q=V W 0D V K ) & + + &<"6$6*, 8> )A! )". /A8+: &E&>!4*3+&(4 ^ & T ªA?@)". &`&d1 &(3!$A,h8>)A!;:! !ª60) &(! ",h3& = !4A, = )4 *!$ &(8 &5# ; &>3+&d.):3& ) & = 6 :4 r~ & * 4k6*3+)A60&>3 0 & * &>3 ) $47&5# &b>47)*3+8>& )A, 0A& ^ 4B!*) 46&58 :$&(# ) /0& &/$:8+# &b>47)*3+8>& )A, 0A&^ ; &C4+ = 6*,& A4 = )0$! &(# ! x & 6 &a# ,r + ):! 3&>.3 A&(3+ ):3 </$A4& & = 60&>3? $3&k)". RAR = m ! b g* H /: ]6 8(",08b*3 &)A. 8d)A!#;$8 "!$8>& * + ^ + &>3?44 &a/$A8+ &>4)0$3+8>& ):, A& ^ .):3 4 = ",,k#*3+ !;>4)0*3?8d& )A, 0A& ^ + 4D4 ) ! < 4&>3 &54)A.k8>)A!$#9$8 "!$8>& 6&5'4 4 ):/$47&(3 &(# * 8 4 ! &(36$3& &(# ! &T.)A,,) !9 :4 D W;EtD CEtDG A OTGbFEErA V FHD Q$T 2OXkM m !I8d):! 3+A3 ) + & 8 A3+:8 &(3 4 8>44 ) ! .)A3^ = & ",f4 !9A,&b>t&>,&(8 3+)A! 3?"!4 4 )A3 47&(& b H p"8 &`6&5 & 4A3&T VBD Q 0E D W;EtA V < 6$6*,t !9 !@A#$# + ):!G = :!*& + 8Q:$&(,# 4&>& b ?g' R

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-15

0

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1

2

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15

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VDS

VBSBackgate Voltage [V]

VBSBackgate Voltage [V]

Mag

netic

Fie

ld B

[T

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DSI

Mag

netic

Fie

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[T

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1

0

[µS]

(b)

B

VDS 0

J ¦ ¬ ±+ ¥ ) #" # ±0 1/01+ b ) S ev# !K= " ! #+)±y#)! !g±C#))!+)' @)t#%%Y ¯ (Y-;³ ¦ ¬ - °±#be ¦ ¬ 0+,+g± ! e"/0,g)!*)!g³ ¦ ±g± r ' ILI ¬

= °±/# ° !g) #, ± ! ° Q-/01+ ¯ ; &@l#*&(4 )A! "3 4&(4(s * 8 ! = /0&>3 )A.%&>,&(8 3+)A!$4 ,, /0&B.)*!$# 4'.>:08 &>! ,) & = 6&(3+ *3+& ! &Gl"! = #') ! + &>3 = )'#;]!$ = 8k&(l# , /*3 = ; &<6*3+)A/$A/ , 4"! ^ p )".=:$!$# !9 &<&(,&58 3):! 4'4 & = ! &Bl#$A! =#*) % ! &a4 & f 4"! ^ p6' 4 t &>!c/ &+3 /*/4 m # 4 3 /9 + ):!@.`*!$8 )A! o HAH g r 4&! ^ p F Y

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^ ^ p 4 | ^ p % % H 4 | ^ p + ddd % H 4 4 H 4 ddd g* + &<8d):!$# )A!$4^ H ^ p % ^ 5 4 "!$#

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(α) (β) (γ)

Source

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N+1

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N-1

Drain

ε N+2

N+1

N

N+2

N+1

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± :

° !#± !g+±ª³ ±/.S +#"/3)±#±0 *¦ ) ' ¬ ±0# g± / ¦ ³ ¬ ),g±' 'r !#"e)tb $ +) / : ! $b,/0 " / +)!+,1 !-;+ ) ) '1³ª K"+)8.@± !1++ ; ! ++K+"/K)!7$ +)! !' )t±#±0Q#/)³ ! b +g' 3+&>, +t & ) &c&>,&(8 3)'8 & = 8(", 60) &(! ", ^ )". & 47)*3+8>&@&>,&(8g> 3)'#'& < 4 = ,"3%&(!*&>30@4+8 & = & A49A,3+&(:#;G6*3&547&(! &(# ! 2 A6 &(3 H .):3 = & ",4 !ªA,&b>t&>,&(8 3):!8 A3 !9@#'& 8d&54 ; & &>!*&(3W/$"3+3 &>3?4k.):3@8 "!9 !9 &D! = /0&>3G)".a&>,&(8 3):!$4 ! &Dl#$"!;> = #') 4 = n1 = ", . ^ , &54 ! & = #*#',& /& j &(&>! ^ H ^ p A!$# ^ ^ p A4D#'&(6 8 &5# ! b g* < 8>&>3 ! ",r*&54D)". ^ p &>3+&^ H ^ p6 F ^ & ! = /&(3c)".C&(,&58 3):!$4 ! &Tl#$A! = #') ª$8g> $ &(4 /0& j &>&>! "!$# H & &>!T ,) &(4 & = 60&>3? $3& 4&>& b +g* Mb ):3 &>,&(8 3 8(", 3?"!4760)A3 h ! &54 + )A!4 & l"! = #') :4 )E/0& 8d)0$6*,&5# )@c4&(8>)A!$#3+&(4&>3 ) 3 ++ &E&>,&(8 3+)'8 & = 8>", 60) &>! ", ^ + $i &>60&>!$# !9 ):!+ &a4 :!)A. &k"6*6$, &(# #*3+ !;>4)0*3?8d& )A, 0A& ^ + * 8 #'&b:!*&(4 &a# 0&(3&(!$8d&^ % ^ + F ^ + & &(,&58 3):!$4Y$) .3+) = &a47)*3+8>& ) & #'3+ !@3+&(4&>3 ) 3):3 ] 8d& &(3+4+ ; )@8d) &>3 /) 8>:47&54 $ ! )A!*&k# 48$4+4 )A! ! + &^.)A,,) !9 &3+&(4&>3 ) 3 @ & * &(39&>,&(8 3+)]8 & = 8(",*60) &>! ", ,,$/0&C#'&(!*) &(#c:4 FRVVBZ &E3+&(4&>3 ) 3 +D &E,) &>3 &>,&(8 3+)]8 & = 8(", 60) &>! ", :4 GDEE+G V,DB 2a ; &3+&(46&58 +t &a&(,&58 3+)'8 & = 8>A, 6) &>! + A,4A3&

^ . = n1 ^ 4 ^

+ A!$# ^ = ! ^ 4 ^

+ [i *& ) ] 0*, m 4k&d1*8d,r$4 ):!W6*3 !$8 6*,&0_ ,) & = 6&(3+ *3+&0 + & &(,&58 3+)'8 & = 8>A,60) &>! ",4 ^ . A!$# ^ 4&>6$A3+ & & )'8>8*6 &(#B.3) = &*!*)'8(8b*6 &(#G4 &(4 !+ & & = 7 &>3 "!$# 8>)A,,&58 )A393+&(4&>3 ) 3n3&54760&(8 r &(,t H !$8d& ^ . ^ A&>,&(8 3+)A!$4 $ &>3-&>!*&(3`"3+&C ,"/*,& ! &a& = 7 &(3 &(3&5A4o*!$)]8(8b*6 &5# 4 &(49)A.,) &54 &>!$&>30A3&k ,A/*,& ! + &<8d):,,&(8 ):3 b !# !ª + & l"! = #') f ! &Q:3)*!$#*4 & f 4 | ^ p ' )". & >t&>,&(8 3+)A!4'4 & = 4 !ªA,&b>t&>,&(8 3):! 3?"!$460)A3 3+)09 T &`l#$"! = #') ^ 4C/*,)'8+:&(# . &

= °±/# ° !g) #, ± ! ° Q-/01+ ¯ = ! = A, &>!*&(3∆ . + F ^ H ^ p % ^ . 4.):3 & H + &>,&(8 3):!@/& !9<:#*#'&5#G.3) = & = 7 &>3 ) &al"! = #') :A!$#+ & = ! = ", &(!*&>30∆ + F/^ % ^ ^ p 4.):3 & &>,&(8 3+)A!G/& !9 :&>!G) + &Cl#$"! = #') ) & 8d)A,,&(8 )A3A3+&( ,r&>1*8d&>&5#*4 & + &>3 = ",]&>!*&(3 H = ,A3 &>!*&(3k# &>3+&>!$8>&(4h.):3h3+&(8 "3 !9 &&(,&58 3):! 4,"!$# &(3&e r &(!c.)A3 & = & ", 4 !9A,&b>t&>,&(8 3+)A! 3?"!4 4 )A3 ! 2 A6 &(3H ; $4"A!`&(,&58 3):! 3+A!$4760)A3 6*3+)]8>&(4+4_.3) = & = 7 &(3 )<8>)A,,&58 )A328 "!9 !9 &! = /&(3<)". &>,&(8 3+)A!$4 ! &l"! = #') < ! & = &5"! = &0 4B4*6*6$3&544&(# .+ &E3+&>, )A!

^ H ^ p ^ . ^ ^ ^ p g* g: )A,#*4 ; & 8d):!$# )A! g'qgA 4f4A& 8 &5# ! b g' $ d ; & l"! = #*) 4'4 & = 4 ! + & D W;EtD C3CEtDG A B 0F 2 "!9 !9 &^&>,&(8 3+):4 + 8 6) &>! + A,0)A. &E&>,&(8 3)'#'& .)A3 )*3C4+ = 6*,& &B/$A8+: &k&>,&(8 3+)'#'& &<&>!*&(3/$A33 &>3 4) &>3?8d) = &<A!$#T&(,&58 3+)A! 3?"!$46):3 C 3+)09 T &`l#$"! = #') )'8>8b$3+4 . ^ H ^ p , &(4f/0& j &>&(! ^ . A!$# ^ Z ,&(8 3+)A! 3+A!$46):3 f "6$6&(!$4 #;*& )_TgFRQ E&(,&58 3):!$4 6$A4+4 !9 &<l"! = #') ):!*&En. &(3 &E) &(3 .^ R ^ p ^ . ^ H ^ p6 ^ ^ ^ p [; $ 4 4 )A! 4 4A& 8 &5# ! b +g' m 4 + &a3+& = &^)".TgFRQ 0E S bE G V BD Q VW3QSQbEFRQ &(3& &a&(,&58 3+)A!!# = /0&>3 )A! &kl#$"! = #') ª$8 $ &(4 /0& j &>&(! A!$# H m !$8>3&5A4 !9 & &>t4)0$3+8>& ):, A&%.`*3 &(3 & ! = /&(3f)".$&(,&58 3+)A!4/0&(8>) = &(4:$1]&5# ) H '/&58>47&

^ R ^ p ^ . ^ ^ H ^ p 4*6*6$3&544&(4 &eª$8 $ )A!$4 /c)A!$&C)A3 = )A3+&a&(,&58 3):!8 "3A&54 47&(& b +g* 7d; &(3&>.)A3+&0 &(! !8d3+&(A4 !9 &. &b>47)*3+8>& )A, 0A&c "! 4 * !9A,r 4 = ",,/ :4 /0& j &>&>! ^ . "!# ^ n 4&>3 &54 )A.$8d)A!#;$8 "!$8>&%60&(0]4h"3+&9):/$47&(3 A/*,&-4 = > ,"3 ) = & ",_4 !9A,&b>t&>,&(8 3+)A! 3?"!$4 4 ):3 n & D W;EtD CCbEtDG 0A D TGFEEtA V FHD QT 47&(& b ?g' H / d9< 8d):!$#;$8 "!8d&k6&5 4):/$47&(3 &(# ^ ) L .^ . 2 ^ ^ ) L 2 ^ [ g* l; &%3+&(4)A!$A!$8d& 8d)A!# + ):!E.)A3 &Q2V8d)A!#;$8 "!$8>&-60&(0E",)A!9 &: & )A, 0A&"1 4 ^ ) L 4CA8 * & &(# ^ ) L ∆

^ )L .

-0,, %+±0##+' ° " %#°#?0 !1+v +,)tbg± #) &H+)!+, #0&#+)! !#"40++,,+ ! ! " ), @;° ! ± #) /$ !,#)!) / ' I `³ = ! ! !)!);±0 !,+#,,g±' 0 0³

¯ ³ #&;,-;+,,+L/' % ^ . 2 ^ H ^ ) L ∆

^ )L 2 ^ [ g* p

!*& 4 )0*,#<!$) & + 8 "!9 !9^M &-&(,&58 3+)'#'& 6) &>! + A, !':&>!*&(3+A, &8>)A!;:$! !9^60) &(! ",.)A3 & &(,&58 3):!`4]4 & = ! & l#$A! = #') h 4 &(8 &5# & $4f,)])0<8>,)47&(3 ) * 4 6*3+)A/*,& = s b )A394 = A,,'8 A!9A&54h)". & &>,&(8 3+):4 8%60) &>! ",^ ) + & ) A,9&>!$&>30 4&! ^ p6 )A. &>,&(8 3):!$4 ! & 4 & f 4"! ^ p ' 44 * . &(# , !$&("3+,r + ^ ) $ 8 8>A! /0&<#'&548>3 /&5#/ 4"! ^ ) ^ )

F %) wgf 4"! ^ p2 ' z d 4 &(3& ) f 4"! ^ p ' #'&(!*) &(4 & .3?A8 )A! )A. = A&D8 A3:& !$#;$8>&(# ! &&(,&58 3+)'#'& /# &8d):!;:$!*&5# > &(,&58 3):!W4'4 & = ! + &4 & f 4"! ^ p6' 4&>&H]&58 + ):! s

) wf 4&! ^ p ' z YKd 4"! ^ p

" #K ) H_d 4"! ^ p [

< 4@6) ! &5# )0 ! 2 "6 &>3 o*!$#'&(38d&(3 ! 8>)A!$# + ):!$4 &D.3?A8 )A! = :/0&(8>) = & !$#*&>60&>!$#'&(! )". & >t&>,&(8 3+)A!4 &$47) + &E8>"!DA4+4 = & +

) wgf 4"! ^ p ' z F ) w+f H 4&! ^ p ' z

) g* 4 A, #T) &(3a #'&(3a3?"!ªA&k.)A3 &' &>t4)0$3+8>& )A, 0A& ^ ) L "!$# + &G&>,&(8 3):!! = /&(3 ; &&(!*&>30 ,:#*#'&(3 ^ ^ p ddd % H 4 4 H 4 ddd #'&(6 8 &5# ! b ?g' 4!P$4 4 * . &(# , !*&(A3,r @+ &a8 "!9:&)". & : &b>47)*3?8d& )A, :& ^ ) L &E):/ !^ ^ ) L ∆

^ )L F^ ^ ) L % ) d ∆ ^ ) L [ g* L

H$/$4 3+:8 + !9 g' l: .3) = g' p "!$# !9 ! )C:8>8>)0*! g' L: + &-# 4 "!8d& ∆^ )L/0& j &>&(! :# P7A8>&>! 8d)A!#;$8 "!$8>&k6&5'4 4C#'&>3 t &(# )

) d ∆ ^ )L F/^ H ^ p % ^ ^ p [ g' H| ; )B& = 6 A4 t~ &0.)A3 )A/ ! !9 g' H| &eA&() = & 3 8CA33?"!ªA& = &(! /& j &(&>!K &&(,&58 3+)'#'& &(3& + & &(,&58 3+):4 8@6) &(! + A, 4<8 A!9A&5# "!# l"! = #') :4 ) /&c8 )47&(! ! . )*3^)". + & ", # T)". g* M* ! ):!*& "!$# + &G. A8 )A3

) r &54 &B.3?A8 )A! )A. = :&`8 A3:&E6*3+&(4&>! ):! &>,&(8 3+)]#*& !#;$8d&5# / &8 A3:& ! &@l#$"! = #') ! &G) + &>3 A!$# A4 r &>! /#D3+&>, + ):! g* H| 8d):! &>3 4C8 "!9:&(4 ∆^ )L ) + &<3+&(A, &>!$&>304 * . )A. &Bl#$A! = #') b )A3^= & ",, 8k4 !9:,&> &(,&58 3+)A! 3?"!$4 4 ):3 )A3 +* ! + & 2 )A!$4 A! m ! &(3+:8 + ):! [ )'#'&(,

) 4* r &>!k/ & 8>"6A8 A!$8d& 3? + ) c L ) c b ):3 = & ",:4'4 & = & # 4 "!$8>&∆^ )L 4%6&(3 )'# 80 ∆

^ )L F c

L) 47&(& 2 A6 &(3 H M b )A3 Bl#$A! = #') 4'4 & = n ! A&(!*&>3?", n #'& ] )A!$4a.3+) = $ 4^60&>3 )'# 8 "3+&B&>1]60&(8 &5# :4a8("! /0&c47&(&>!.):3 !4 "!$8>&0".3+) = &a8>A,8*, &5#@&>!*&(3`46&58 3 = 4 ) ! ! b 7$ HAH H2 ,&5"3+,t

³ "& -%# !)! !/ +" !# % ! ¦ ) F . ) ¬ )t# ¯ ):/$4&>3 A/*,&-"3+& &547& ! + & = A!$& 8:$&>,#@#'&>60&>!$#*&>! = &5A4*3+& = &>! 4h6*3+&(4&>! &(# ! b g' H 8 &>3+& &-# 4 A!$8d& /0& j &>&(! j ) :# P7A8>&>! 8>)A!$#;8 A!$8d& 60&(0'4 "3 &54 = 0A!*& 8Y:$&>,# $ ! + &9.3? = & ):3)A. + & 2 ):!$4 "! m ! &(3+:8 + ):! [ )'#'&(,+ &<# 4 "!$8>&k/& j &(&>! j )c8d):!$#;$8 A!$8d&k60&('4 4 #'&548>3 /&5#/ cL) c d ∆ ^ )

L F J + K % J c 4 & 0!$) 6&(3 )'# 8 . + &@&>!*&(3 &54 J )". + &c4 !9A,&b>t6$A3 + 8>,&`& A&>!4 &54k"3+&B!*) #*&A&(!*&>3? &0 & J + K F J .):3 F ddd % H 4 4 H ddd

7 20,"3 & " 1 , %&7( )+%,"3&- . " % " %m ! 2 A6 &(3 H & &E# 48$44&(# + &<)'8>8*33+&>!8d&k)". 8 "3A&>t4 A/ , c3& )A!$4 !+ & ^ ^ + 6*,"!$& n + & 2 )0*,) = / /*,)]8+n:#'& 3+& )A!4 &(3&)A!*,rW)A!*&D#'&b:ª>! & ! = /0&>3 )A. &(,&58 3):!$4E&d1 4 4E)A! + & 47,"!# *< # P7A8d&(! < ) + &(4& "3+& &4 !9A,&b>t&>,&(8 3+)A! 3?"!$460)A3 3& )A!$4 &>3+& j )B#'&:$! &^!# = /0&>3?4 A!$# H )".&(,&58 3):!B8 "3A&54 A3& ",,) &(#<)A! + & = & A, 4,A!$# n"!#°:$!$A,,rE3+& )A!4 & &>!= ):3&60):4+4 /*,&C8 A3:& 4 &54 & ! &(4 : & ! * 4OH'&(8 + ):! &^8d):33+&(46):!$# !93+& ):!$4 ! & ^ ^ + 6*,"!*&^.)A3 @l#$A! = #*) $-/.-'L1%TU # X#NTHZ XV]\m ! b ?g' + &* + ^ + 8 A3+:8 &>3 4 8>4 = &(A4*3+&(# )A! + &`l#$A! = #') 4'4> & = #'&>6 8 &(# ! b +g' H 9 A3& 4 ) ! .)A3 # 4 !$8 /$:8+: &b>47)*3?8d& )A, 0A& A,t*&54 ^ 2 ,&5"3+,t & 2 )*,) = /9> /*,)'8+nA#'&3& )A!$4G"3+& ] 4 /*,& m ! :#*# )A!m 4 &>69> , :& m* !$8>3&5A4&(4 ! &`8b*3+3&(! "3+&E)A/$4&>3 &5# H]) = &*,+ ^ + 8 "3?A8 &>3 4>+ 8(44 ) & &>!DG#*&(8d3+&(:47& !*,+ D !$8d3+&(:4 !9 f ^ + f ; )@/0& &>33+&(4)A, & &8 "!9:&(4 ! * + + & # 0&(3&(! ",98d):!$#;$8 A!$8d&@#2* + # ^ + 4k6*3+&d.&(3&5# .):3^6$3&>4&>! )A!`/&58>0$47& 8 A!9A&54 ! &* + ^ + "3+&-&(! "!8d&(# n a4 &(6;> , A& !8d3+&(A4&/0&(8>) = &(4G60&(0 !T#2* + # ^ + + &E3&54760&(8 r & ",r*&E)". ^ + m ! b 2g'qg & # 0&(3&(! + A,:8>)A!$#;8 A!$8d&-#2* + # ^ + 4_4 ) ! ! :3&]4+8>A,& :4 .`*!$8 )A!B)A. & /$:8+# & ):, A& ^ .)A3 & # &>3+&>! / A4 )A, :&(4 ^ + 9 < A! 4 * !9A,r@4 = ",, ^ + & 2 )0*,) = /c/*,)'8+nA#*& ):4+8 ,, + ):!$49A3& ):/$4&>3 &(#@:4%#'&>4+8d3 /&5# ! & 6*3+& ] )0$4H]&(8 )A! K ) & + & # &>3+&>! + A,]8>)A!$#9$8 "!$8>&-#2* + # ^ + ^ + F| 4_&(l#$A, ) & 8>)A!$#;8 A!$8d&* + ^ + .)A3f4 = ",, f ^ + f X !$8d3+&(:4 !9+ &CA/$47):,t & ",r*&)". ^ + + & 3?"!9:& !c/$:8+: & )A, 0A& ^ &>3+& 3?"!4760)A3 < = °±0 '"9+ )+#±+ #" +# ± ! °g,g± / #, !".M)! O& !+ @r7+#/ %7 >#± T"9+ $ MM±0 !&H,0+$ ) "M M³ ±± !% MM,+& ± ! $ )!" ¦ ¬ .;°±0 $ ) ") ! Q#" [+)±1;#)! !g±ª³

/ ³ #&;,-;+,,+L/' % + 3)9 &Bl#$"! = #') )]8(8b*3?4 4/*3+):A#*&>!*&5#, !*&(A3,r f ^ + f ; &547&E3+&b> ):!$4 )A. 3?"!$460)A3 &>!8d,):4&-", = ):4 3 ) = / 8>",,rk4 A6&5# N 3& )A!$4 /& j &(&>! + & = &(3& 3?"!4760)A3 f 3+)09 <+ & l#$"! = #') 4f/*,)]8+:&(# n & 2 )0$,) = /G/*,)'8+nA#*&3+& = &(4 $-/.- 3P@Z # L;NT %PSV T`\ # XU0\L;\THP@V %( NPSZ VYX#N 'P@V %T YX#N L9\THP@V %m ! b ?g' l k 4+8 & = & 4 r &(! .)A3 & # 0&(3&(! 3?"!4760)A3 3+& = &(4 ! & ^ ^ + 6*,"!$&0*#'&(3 r &5# .3+) = &(!*&>308d)A!4 #'&>3? + ):!$4(sI m ! & D W;EtD CCbEtDG 0A B0F + &<! = /&(3 )".f&>,&(8 3+)A!$4):! &<l#$A! =#') 4:*1'&(#].)A3 !$4 "!$8>& ) $4 !$8d&

^ H ^ p ^ . ^ ^ ^ p [ g' HAH + !8d3+&(A4 !9 f ^ + f & &>!*&(3 ,A#*#'&(3 ^ ^ p 4B4 * . &5# #;*& ) &8>A6$A8 +t & 8>)0*6$, !9 ) + &C#'3? !@&>,&(8 3+)]#*& 0< 8>&>3 !@6)4 r & A!$#@!*&: +t &^ + + 3+&(4 )A,# ",r*&(4 + & 2 )*,) = /T/*,)'8+nA#'& 4 ) &>3?8d) = &EA!$# &B! = /0&>3)". &>,&(8 3+)A!$4k):! + &l#$A! = #*) 8>A!W&>!*&(3:& 8>A,,rª8 & .):3 !4 "!$8>&/& j &(&>! "!$# H .

^ . ^ H ^ p ^ [ g' H R m ! b ?g' l *4$8 G3+& ):! 4 = "3A&(#/ 8 * !9 I ; &k,A3:&>3 &E/ :4 f ^ + f & = )A3+&k8 "3A&k4 &(4 .)A3 + &<l#$"! = #') /0&b>8d) = &-6)44 /*,& ; &MB0F TD ,T+FRQ E S E+G V BD QJV W3Q=Q E!FRQ 0 &>3+&%&>!$&>3A& + 8(",,t &C&>,&(8 3):!c! = /0&>3 4%)A!*,rGA,,) &(# )°S$8 $ &C/0& j &>&>! A!$# H :"3+&#'&b:!*&(# / &<8d)A!# + ):!

^ R ^ p ^ . ^ H ^ p ^ ^ ^ p [ g' H ; &B60):4+4 /*,& ^ ^ + ",r*&(4C.`*,t:$,, !9 g' H "3+&<3+&(4 3 8 &(# ) + &B3 ) = >/ 8>",,r 4 "60&(# 3+& ):!$4TA# P7:8d&(! T ) & 2)0*,) = / /*,)'8+nA#*& 3& = &(4 4&>&b g' l:dI i $& ) g' H R + &B/0)0$!$#*"3 &(4 ^ ^ + "!$# ^ + ^ + ! + & ^ ^ + 6*,"!*&'/& j &(&>! * 8 &^&(,&58 3):!! = /&(3+4 "!$# H )A! &El#$A! =#') A3&k&>!$&>3A& + 8(",,tc60):4+4 /*,&0*A3&E#'&:$!*&5#/ + &<8d):!$# )A!$4

^ F ^ H ^ 4 ^ + "!# ^ + F^ H ^ + 4 ^ + 4 &(3& ^ % ^ + F ^ + [ g' H ]; &(4& /):3+#'&(3, !*&(4@"3+& 6*,) 7 &(# ! b g' l*o< 4 ] 4 /*,& ! &D&>1]60&>3 = &(! ",#* )A. b ?g'qg &547&G/):3+#*&>3+, !*&(4 ^ "!$# ^ + #*&>60&>!$# , !*&(A3,rD)A! ^ + m &>,,4 _ !$#'&(&(# ! $ 4_&d1'60&>3 = &>! + &%&(!*&>30^,A#*#'&(3 ^ ^ p 4_4 * . &5#

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J '"9 )o+#±## ± ¥ ± ) #" 1# ±%1/01+ ! ! !"³ ³+. °g,g±7%1r## Q±0 !&H,0+-$ ) " ) ¦ ; ! +7 ±*Q !e³= 1## ¬ ±0 O" b $ ) " ) F ³ )! g"/0,g)!#)!/. ! +" !#3+,+&;± ± ¥ ± ) ;+)! ! 7 - ±) O #+ ± ¥ ± ) ; $ ¯ -;³ ], $ ;gOM ! 3± '"9+ )=±0##+ !±0 !g'17&H)! O * g,o ¦ ) ¬ b !1 !+* *&;+ $ =" $ ) " $)) F .9#+" $ ;gO317&H)! O e±0+g,% !K e+0,+g³9 0 !#"° + !" ;gO Q± '"9 )ª±0##+Q± ¥ ± ) .# Y*;g#r#) = + !" ±7;± ! +,+*17° t !% ¦ ) F . ) ¬ )t#³ % o#?,+ °og,. b 17 ! +, 'r)! °1 #))!+)S ) %?0 !7.9± ¥ ± ) !%)! °1++. ³ ³. , )!)!% ,)!L; ± ) F ¥ ± ) . , ))! + !" !± ¥ ± ) ³ ¦ ±0L+±Er ³ 7+ ! )`³' I . I ¬

³ "& -%# !)! !/ +" !# % ! ¦ ) F . ) ¬ )t# /, !*&5"3+,t + 8 "!ª !9 &B&>,&(8 3)4 + 8k60) &>! ", ^ )A. + &B/A8+: &k&>,&(8b> 3+)'#'&B/ ^ A!$# + &`&(,&58 3)4 8E60) &>! ", ^ + )". + &G#*3+ ! &(,&58 3)'#'&`/#^ + s=^ ^ p

^ + F % + A!$# =^ ^ p ^ F % [ g' H g:

&(3& #'&>!$) &54 + &T.3?A8 + ):! )". = 0A& 8 A3:& !$#;$8>&(# ):! & /A8+: &&>,&(8 3+)'#'&k/# &E&(,&58 3):!D8 "3A&(4 ! &<l#$A! = #*) "!# + &k.3?A8 )A! !$#;$8>&(4 )A! &<#'3+ ! &>,&(8 3+)'#'& ; & j )c47,)A60&(4# ^ # ^ + $8 A3+:8 &(3 r~> !9 &E/):3+#'&(3, !*&(4 ^ "!$# ^ +

A3&k)A/ !*&5#/ # &>3+&>! + !9 g' H ] +3+&(46&58 ) ^ + A!$# ) ^ "!$# 0 !9 ! )cA8(8d)0$! g' H gA s# ^ # ^ + F % +

"!$# # ^ + # ^ + F H % + [ g' H l

m !<8>:47&%)". & 2 )A!4 "! m ! &(3+:8 )A! [ )'#'&(,:):3_ = & ",]4 !9:,&> &(,&58 3):! 3+A!$4 4> ):3 &^47,)A60&(4-"3+& r &>!c/ % c + c "!$# c % c + c A3+&(46&58 r &(,t 4&>&EA,4) b H :MI < 8d&(3 ! ^ 4 ^ + ",r*&54 + &E3&(, )A!$4^ . F/^ H ^ 4 ^ + "!# ^ F/^ ^ 4 ^ + g' H p "3+&G.`*,t:$,,&(# < & 4 = & + = & ; & 3+&(460&(8 +t &@&>!*&(3 48 & = & 4`4 ) ! !b g' l* m ",,) 4 )G)A/ ! + &^# &>3+&>!$8>& ^ H ^ p % ^ ^ p &# 4 "!$8>& ! & &(!*&>30 ,:#*#'&(3 # 3+&(8 ,r .3+) = & 3&54760&(8 r & #*3+ !;>4)0*3?8d& ):, :& ^ + s

^ H ^ p % ^ ^ p F d ^ +

[ g' H m ! + & l#$"! = #') *!$#*&>3 ! &(4 : + ):! & # 4 "!8d& 4DA/) H = &; A3 + ):!$4 ! &T)A3?#'&>3@)". H| .)A3 # 0&(3&(! m ! 2 A6 &(3 H .):3 = & ",k4 !9A,&b>t&>,&(8 3+)A! 3?"!4 4 )A3 ^ H ^ p % ^ ^ p F c A4 $47&5# b ):3^ l#$"! = #*) k +* ! & 2 ):!$4 "! m ! &>3?A8 )A! [ )'#'&(, &)A/ ! ^ H ^ p6 % ^ ^ p6 F J + K % J c m !A&>!$&>3?", & "3 )A!$4 ! ^ H ^ p % ^ ^ p &@/0&>&>! #*&>!*) &(# :4KA FRV FHD QT ? +G VB W )". &El#$"! = #') 4&>&IH]&58 )A! p ]MI ; & +BA0G VFHD Q[D 'F A KGªAB T p D QV bE G V BD T F X i H 8("! A,4)/0&<#'& &>3 = !*&5# .3+) = &E&>1]60&>3 = &(! ", #$ $s2) = 6$A3 !9 g* H : + g' H| '):!*&k)A/ !$4 &E6$3):6):3 + ):!$", @. :8 )A3

F ^ + ∆ ^ [ g' H L; $4 + & 4+8>A, !9C. A8 )A3h/& j &(&>!GC8 A!9A&-)". ^ A!$# + & 4 * . )". + & &>!*&(3,A#*#'&(33+&>, +t &>,r ) & b &>3 = ,& &>,k)". + & 47)*3?8d& &(,&58 3)'#'& 4D):/ !$&(#/ 8d) = 6$A3 !9 &W# 4 "!$8>& ∆

^ ! : & )A, 0A& /0& j &>&(! j ) :# P7A8>&>!

/ I ³ #&;,-;+,,+L/' %

V(S)BS DS V( )

DS V

−µ(N)

(n,V ,V )BS DS

N+2

N+1

N

N+1

N

Regimes of Coulomb Blockade

( )V(D)BS

N+1

N

(N+1)µ

Selch

elch

D

DS

Regimes of Single-Electron TunnelingVBS

VDS

αB

µ

Slope:

N+2

N+1

NN+1

N+2

N

N+1

N-1

N+2N+1

N+1

N+1

N-1N

NN+1

N-1N

N

N-1

Slope: αB

αD

Dα1-

0

µµ

eV

ε

#&;,Q+" !#% *## ±0Q1/01+ ³ = M, °M !Q, ° !)Q #@+,+g± v ' °)*, !")!&H+)!+, ,, 1M !"³/³ .@#?0+# b !"+)ª , + #)! #)! O±+" #$b !+ ! M), # ;g³= g± " !° b O0 ! = o+)!+, # @;$ ±e$ = ° " ; r±ª³-0 !#")!&H+)!+,.,&;,/.;+1, !+± ,, ##) / ; ! + %± +)!+&,*e ## ±0/. :r##±+/ #" !g)#, ±0 !Y !e = # !g)) / %;g±'+" #±1+e #)! #)! O±+" !. ± ),+³-0 +" !#Q±#+± o+" ! °+ %, ")!&H+)!+,##+)! !#"0³8d):!$#;$8 "!8d&B60&(0'4a ^ + F | A!$# + & = "1 = = 3+&(4 )A,# ",r*& ^ +)". &c3+&(460&(8 +t & 2 )0*,) = / /$,)'8+nA#'&@3+& ):! s F ^ +

∆ ^ F [ g| [ R H| Y A ; )& = 6 A4 t~ &G0: !0/0&(4 #'&54 &c4+8>A, !9 . :8 )A3 t &(4 &.3+:8 + ):!B)". = :& 8 "3A&%):! + & /$A8+ &-&>,&(8 3+)]#*& !$#;$8>&(#`/ & &>,&(8 3+)A!$4 ! &<l"! = #') 47&(&k&>,&(8 3)4 + 8^3+&(8 6*3+)'8 0 b 7$ :db 3+) = + &47,)A60&(4 ! b ?g'qg A!$# + & 3&(, )A! g' H l & .3+:8 )A! + )". = :&8 "3A& !#;$8d&5# )A! &<#*3+ ! ,&5A# 4 ):/ ! ) + F | [ | | [ | R X 3+&(#') !ª & = &(A4*3+& = &>! 4)". b +g* g /#D8 )]):4 !9 &`#'3? ! !4 &(A#D)A. &G47)*3?8d&B8>)A! :8 :4 + &B3+&d.&(3&(!$8d&E.):3^A,,f"6$6*, &(# )A, 0A&54 ) &@4'4 & =

-;,,+/'%RQ± ±'( ?0+ g± -+ %] ## / &G3+&>, + ):!$4k#'&>3 r &(# "/0) &`3& = ! ", # / &>1'8 "!9 !9 & !$#'&>1 H +i` ; &>! 4):/ !*&5# !$4 &5A#)". + &(3& F | [ R H | [ | R M; &4 = +

F | [ g H | [ | 4B,&(4+4 + "![*! 0f4 !$8d&.`*3 &(3 = 0A&G8 "3A&54aA3& !$#9$8d&5# ):! + &c476*, >1: &B&(,&58 3+)'#'&(4^):! ):6 )A. & & >&>3+):4 3$8 *3+&E#'&b:$! !9 &Gl#$"! = #') ; * 4 4C6*3+) &(!D/#D#'& &>3 = !$& & 3 p )+%,"$ "3#"$ ?_ %&CB@7 3"/0 B@49;"3 $<9>7BO1 ( % % 8 9! "3 0,"3#"347( " )5%"$&- . "m ! + & 6*3+& ] )0$4,H]&(8 )A! &a3& = &54 )". 2 )0$,) = /c/*,)'8+2:#'& "!#c4 !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9 &E/&(&>! #'&>! + :$&5# +* ! &<6"3? = & &>3 46$A8>& ^ ^ + /# &>!9>&(3 8>)A!$4 #'&>3? + ):!$4CA!$# A3&G48 & = 8>A,,r7 r &(! ! b +g' l* m ! &>1'6&(3 = &>! A,#$ D)A. b fg'qg oFRV FRQ &3& = &54E)". 4 !ªA,&b>t&>,&(8 3):! *!*!$&>, !9S_:#*# )A!$A,60&(0'4 ! + &# &>3+&>! ", 8d)A!#;$8 "!$8>& #2* + # ^ + )]8(8b*3 .):3 = !9 7A3 #> , A&4 3$8 *3+& ! & ^ ^ + 6*,"!*& ; & !# 8( & A#*# )A!", 3?"!4760)A3 8 "!*!*&(,4 3+)09 D &Gl#$"! = #') /0&(8>) = &B ,A/*,& ! + &B3+& ):!D)".94 !9:,&>&(,&58 3):! $!*!*&>, !9ªn,&(:# !ªa&5A8 <+ = & )E^4 &>6;>t, :& !$8d3+&(:47&-)". &8b$33+&>! * + @ !$8d3+&(:4 !9 f ^ + f H;$8 A#*# )A!", 3+A!$4760)A3 8 "!$!*&>,4 &/0&>&(!@3&(6):3 &(#A!$# ! &(36*3+& &(# ! H L2L R / 4& &>3?",A3+)0*6$4 o H g | HAH H g H H r m = 6*3&544 r &3+&(4*, 4cA3&D)A/ !*&5# , &>[email protected]+) = &>3 8>A, l#$A! = #') 4 o g r H !$8>& ! 4$8 4 !9A,&b>t&>,&(8 3+)A! *!*!$&>, !9 3& = & + & ! = /&(3 )".E&>,&(8 3+)A!$4c8("! &(!*&>3A& 8>",,rS$8 $ &^):!*,r /& j &(&>!

A!$# H ddd % H 4 4 H ddd &(4&:#*# )A!$A, 4 !9:,&> &(,&58 3):! *!*!*&(, !9 8 "!*!$&>, &E/0&>&>! 7 3 /9 &(# ) &d1*8 &5#4 &54 )". &<l#$A! = #*) /0& !9 $4&(# / &>,&(8 3+)A!$4 *!*!*&(, !9 ! ) "!$# ) )".+ &Cl#$A! = #') b ):,,) !9o H H CL H g R r1 &(3& & ,,# 48$4+4 $ 4 ! &>3 = 4)A.

> &(,&58 3+)A!c4 &(4 + )0 3&54 3 8 + !ª &C#*&(4+8d3 6 + ):! )BE460&(8 :8 = )'#'&(,*.):3+ &<l#$"! = #') < 4 4 /*,& ! & &>1]60&>3 = &(! ",'#* C)". b ?g'qg & 60&('4 ! + &# &>3+&>! + A,8>)A!$#9$8 "!$8>&D#8* + # ^ + 4 $ . & + &>3c6"3?",,&(, ) &T/0)A3?#'&(3, !$& ^ )A3 &/0)A3?#'&(3, !$& ^ +

)". & 3& )A!@)". 4 !9:,&> &(,&58 3):! *!*!*&(, !9 ; * 4 !$# 8> &(4 !$& 8 A!*!*&(,4@"3+&& + &>3@):6&(!*&(# ! 3&547):!$"!8d& & b &>3 = ,& &>, ^ )".4)0$3+8>&G):3 & b &(3 = ,& &>, ^ + )". #'3? ! b )A3 ^ + | &47)*3?8d&c&>,&(8 3+)'#'&:8 4EA4 + &c& = 7 &(3 .)A3 ^ + | A4 & 8>)A,,&58 ):3 .):3 &#'3? ! &(,&58 3+)'#'& 4 ] 8>& &(3+4+ "6*6$, &(# / A4 ^ + *&(,&58 3+)A!4 .3) = &B& = &(3C"3+&a&(! &>3 !9+ &kl"! = #*) 'A!$# &(,&58 3+)A!4-A3&a,&5 !9 &kl#$"! = #') ) &E8>)A,,&58 ):34 #'& m 4 &(3&>.)A3+&^! $3+A, )c# 4 !9 4 /& j &(&>!DA#*# )A!", 8 A!*!*&>,4 /& !ª):6&(!*&(# )A! + & & = 7 &>3T4 #'& "!$# A#*# )A!",a8 "!*!*&(,4/0& !9 ):6&(!*&(# ):! &8>)A,,&58 )A34 #'&

/ ³ #&;,-;+,,+L/' % $- + - " TV@RHX eRHXU0\NPSV VYV XRTHV X STZ XP ( L9V * &2eRHXU\NPSV %4 TH\TPSVYL9R YL9VYV XR% P@V \ YX eZ T`\\X#N " T X YX\P U0TH\X " \L;\X'% P (\ YX * &2 RXU\NP@V " $%\XZm ! b +g* p;( 4 !9A,&b>t&>,&(8 3+)A! *!$!*&>, !ª 3& = & 4h4+8 & = + 8(",,t^4 ) ! ! * 8 + &k!# = /0&>3 )". &(,&58 3):!$4 8>"!Kª$8 $ &k/& j &(&>! A!$# H S !*&kA#$# + ):!$", 3+A!$4760)A3 8 A!*!*&>,)". + ):4& )A/47&(3 &(# ! b +g'qg 4-#'&>6 8 &(# + 4%/0)A3?#'&(3, !$& #') &(#, !*& 6$A3+A,,&>, ) &^/0)A3?#'&>3+, !*& ) & 2 )0*,) = / /*,)'8+2:#'&C3+& = & + &(,&58 3):!$4 & )A60&>!$4 ! 3&547):!$"!8d& ) & b &(3 = ,& &(,$)A. & FRVVB ; )&>1]6$, ! &9)A3 !*M,& $4 8>)A!$4 #'&>3 A6*6&(!$4 :$! &9/ :4 ^ + ° A3 !9+ &: & )A, 0A& ^ ",)A!ª &a6$ +c !$# 8( &5#c/ + &a#$A4 &(#@, !$& ! b ?g' pn i *& ) + &%:*1'&(# ^ + &E&(,&58 3)'8 & = 8>A, 6) &>! + A, # &>3+&>!8d&E/0& j &>&>!D#'3? !A!$# 47)*3+8>& 4.:*1'&(# + 8 "!9 !ª ^ & &>,&(8 3+):4 + 8D60) &>! ",C)". &l#$A! = #*) 9 494 $ . &(# b )A394) = & ^ ",r*&(4 = "3A&5# ! b g' pn^/ "!# J &k3+&(46&58 +t &^&(!*&>30 4+8 & = &54 "3+& t &>! ! b +g' p2/ & $4# 4+8b$4+4 ! + &a.)A,,) !9 + &k&>,&(8 3+)A! 8 6*3+)A60&>3 &(4-)". + &El#$"! = #') .)A3 .)0*3)A. &(4& ^ ^ + A,t$&(4(sI # X#NL;\THP@V # PSTV]\ 4 m ! + & 2 )*,) = /@/*,)'8+2:#'& 3+& = & ^ &C! = /0&>3)".h&>,&(8 3):!$4 ! + &<l#$"! = #') 4:*1'&5# ) $4 !$8>&

^ H ^ 4 ^ + ^ . ^ ^ ^ 4 ^ + 44 ) ! ! b +g' p2/ M] !T):!*& A!$# + &B&(,&58 3+)A!4 .3) = + & b &(3 = ,& &>, )A. && = &>3-#')k!*) &(! &>3 + & l#$"! = #') 4 !$8d& .):3 & = + &&>!*&(3E/$"3+3 &(3^ H ^ 4 ^ + % ^ . &>1 4 4 ; ! &^) + &>3 "!# :!$)B&>,&(8 3+)A!8("! ,&( & &kl#$"! = #') 4 !8d&k/ 4 "3 !9<.3+) = + &%A3+)0*!$#$4 &a)". & >t&>,&(8 3+)A!4'4 & = "!D&>,&(8 3+)A! )*,# !D = n1 = = + &E&>!$&>30 ^ ^ 4 ^ + F 4 | ^ 4 ^ + % % H 4 | ^ 4 ^ + * 8 4 ,&(4+4 A! ^ & &&>!*&(3 )@3+&(A8 "! *!*)'8(8b*6 &(#D4 & ! + &<8d):,,&(8 )A3 I # X#NL;\THP@V # P@THV]\ L9V 4 X !$8d3+&(:4 !9 &B/$:8+# & )A, 0A& ^ &&>!*&(3D,:#*#'&>3 ^ ^ 4 ^ + 4^4 * . &5# #*) ! 3&(, r &(,t ) ^ . "!$# ^ , )!))@ ) F r ) .± b)!)!+)S ) F r ) 0³

JJ ¦ " " ¬ ¦ ¬ -O ,#&;,+" !0; ! ++. #)! #)! O±'" !3%$ ± ¦ $ ¬ ),'b± + ) ! ¦ ) F . ) ¬#)³,Q ±#±0 )Q, !#")!&H+)!+, ,#&;, #+) ¦ ;, ! #± !gbg±/' ±,+±) ! ¬ ;+# ! !.%, !#")!&H+)!+,.##+)! !#"e+" ! .J#))!+)S ;±0)! #)! #)! O± " ! °$ +)!+,#+³ ¦ ¬ (#"/, + °+ ¦ ) F . ) ¬ $)!#+ !#± !g+±K ! ¦ ¬ ! ¦ ¬ ¦ % ¬ ³9.g,%% ¦ ¬ .ª±#±0 ) #+)ª !Q;+#g± vQ+)!+,#Q+ !#"e ## ±0/3 #±+ !#" ,#, ! #?0+ g±1b $ % ¦ $ ¬ &),1/01+ ³ = !° !°±0# ¦ ,+¦ ¬,¬ + / 1b, !#"r y M"±1b $ % $'&H+)!+,.1/1 y>/1, !#" t #?0+ g±71b $ '$3&), 1/01+ ³ = 3)tb, ;eg g±N/ @++g± !#"1++,7.vM 1+L. / ##+)! !#"10++,M= ¦ $ ¬ +)!+, %+)!)/.;)!g/$ !#"+; !± #?0+ g±'1 $ ³

-;,,+/'%RQ± ±'( ?0+ g± -+ %] ## /

∆DS V( )V

(D)BS

Groundstate

-e

-e

-e

-e

Transition

E(N+1,k)

E(N+1,0)

E(N,0)

Groundstate

E(N+1,0)

E(N+1,k)

Transition

E(N,m)E(N,0)

(b)

Coulomb Blockade

disabled

(a)

Quantum Dot Charging:

(c)

Excited State

Transition

opened

opened

Transition

closed

Transition to

µ

V(S)BS DS V( )

N,0 N+1,0

N+1,0 N,0

N+1,k

N+1,k

(α)

(β)

(γ)

(δ)

(ε)

(β)(α)

(ε)

(γ)(δ)

Region of Coulomb Blockade

µ(n,V ,V )

µ

Additional Energy Level

Region of Single-Electron Tunneling

due to Excited State

Additional Channel on Emitter Side by Reaching Excited Statewith Charging

VBS

VDSVBS

Celch

N+1

N+2

N

N+1

N+2

N+1

N

N+1

N+2

N+1

N

N+1N

N+1

N

N+1N

0

Eelch

BS DS

eVDS

N+1

N+2

N+2

N+1

N

/ ³ #&;,-;+,,+L/' % < ^ &(3&

^ . FE^ H ^ 4 ^ + 4"! &(,&58 3):[email protected]) = + & b &>3 = ,& &>,0)". + &a& = &>3 :49&(!*)09 &>!$&>30 )@",,) + &>! &(3 !9D 3+A!$4 + ):! .3+) = + & A3+)0$!$#*4 &@)". + & ) & A3+)0*!$#;>4 & )". & H >t&>,&(8 3+)A!c4'4 & = ! &al#$"! = #*) 47&(& b +g* pn/ M; * 4 4 + & 3?"!$4 + ):! ,) &(4 6)44 /*,&`&>!*&(3 &>! 4 A3 + !ª .3+) = &A3+)0*!#*4 &c)". + & &(,&58 3):! 4'4 & = H !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9 3+& = !$46)44 /*,& * ! &° & )A, 0A& ! &(3 A, ^ ^ ^ 4 !$8>& + &>3+&^ . ^ H ^ 4 ^ + ^ [ g' R | ; &3 : 4 #'&)". 3&(, )A! g* R | &>!4*3+&(4 4 "3 !9k.3) = + &A3+)0$!$#*4 &)". + & H >t&>,&(8 3+)A!4'4 & = ! &^l#$A! = #') & H &>,&(8 3):!,&5 ] !9 + &kl"! = #') :$!#*4 4%&(!*&>30 ^ H ^ 4 ^ + A!.*!*)'8g>8b*6 &5#B4 & ! + & 8>)A,,&58 )A3 ; * 4h/&58d) = &54 /*,)'8+A&5#< ^ 4&>& b g' p2/ 7 + &>! &(3 !9 & 2 )*,) = / /*,)]8+n:#'&k3& = &k)A. H &(,&58 3):!$4 I # X#NL;\THP@V # PSTV]\ 4 < ^ * ! & & )A, :& ! &>3 ",9#'&:$!*&5# / g* R | "E4 &(6;>t, A& !$8d3+&(:47& ! &C8*3+3&(! )'8>8*3?4 !$# 8> &(#@/Gk6&5 ! &# 0&(3&(! + A,8>)A!$#;8 A!$8d&a %+ 6)4 )A! s Z ,&58 3+)A!4f.3) = + & b &>3 = ,& &>,$)A. &k& = 7 &>3 4&>& = 4 ) &k"!DA#*# + ):!$", 8 A!*!*&>, .):3&>! &(3 !9 &El#$A! =#') #'&:$!*&54a4$8 c,& &>,_:4 !$# 8> &(# ! b g* pn/ H "3 !9c.3+) = &°:3)*!$#*4 & f 4 | ^ 4 ^ + ' )A. + & >t&>,&(8 3+)A!D4'4 & = ! &<l#$A! =#') A!BA#$# + ):!$",:&>,&(8 3+)A!E&>! &>3 !9 & l"! = #') .3+) = &-& = &(3 & l#$"! = #') &>!$#$4 !`A!<&d1*8 &(#B4 & f H 4 ^ 4 ^ + ' )A. & H >&>,&(8 3+)A!4'4 & = 4&>& b +g' pn8 M H8 G6*3+)'8d&544 4)A60&>!*&5# ^ .

^ . F H 4 ^ 4 ^ + % 4 | ^ 4 ^ + [ g' R H X ):6&(! !ª * 4^8 "!*!$&>, $&>,&(8 3+)A!$4.)A3 + &B& = &>3^8>A! bFRV B $4& & ] + &M:3)*!$#*4 &3DB ] &C&d1*8 &(#c4 &C)A. + & H > &(,&58 3+)A! 4'4 & =A4#'&>6 8 &(# ! b ?g' p2/ d ; &(4& 8 A!*!*&>,4 "3+& 0A&(! .3) = &>,&(8 3):!$4 )A.# 0&(3&(! &>!$&>300 /9 V G+A Q=Q@D VKCW<T A VJV 'TA V F #;*& ) &&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &(3+:8 )A! ! & l#$A! = #') A,,) !ª S$8 $ + ):!$4 )A!$,t/& j &(&>! "!$# H &(,&58 3+)A!4 ! +* 4-6"3? = & &>3%3+& = & ; &(3&>.)A3+&0 &A#*# + ):!$", 8 "!*!$&>, !$8>3&5A4&(4<):!*,r + &6*3+)A/"/ , "! &>,&(8 3):! &>! &(3+4 &kl#$"! = #') .3) = &^& = 7 &(34 #'&0'A!$#c,&(A#$4%/ $ 4 )G"! !$8>3&5A4& ! &<8*3+3&(! * + < 8 $A,,r 4f!*) )A/*, )A3 + f+ &l"! = #') 4 ! &:3)*!$#*4 &%)A.+ & >t&>,&(8 3+)A!c4'4 & = /0&d.):3& + & H &>,&(8 3+)A!c&>! &>3?4 &Cl#$"! = #') < 4 & ,,'4&>& ! + & !*&d1 H]&(8 )A!2",47)C&d1*8 &5#B4 &(4_)". + & > &(,&58 3+)A!<4'4 & =/0&(8>) = &-:8>8d&544 /*,& ! * 4 4 !9:,&> &(,&58 3):! *!*!$&>, !9^3+& = & ; &(3&>.)A3+&0(4 A3 + !ª.3+) = & &>1*8 &(#W4 & f 4"! ^ 4 ^ + ' ! A&>!$&>3?", "! A#$# + ):!$",-8 "!*!$&>, )+ &E& = 7 &(3 4 )A60&>!$&(# *,&(:# !9 ) "!D&>1'8 &(#D4 &E)". & f H 4 ^ 4 ^ + ' 47&(& b ?g' pn8 .

-;,,+/'%RQ± ±'( ?0+ g± -+ %] ## /

^ . F H 4 ^ 4 ^ + % 4"! ^ 4 ^ + g' RAR ^ H 4 ^ 4 ^ + ^ [ g' R ; $ 4c:#*# )A!$A, 4 !9A,&b>t&>,&(8 3+)A! 8 "!*!$&>, #'&548>3 /&5# /# g' R H )A3@/ g* R:R 4):!*,rT6)44 /$,& ."! ) + &cl"! = #') 8>A!ª8 &@/0& j &>&(! H A!$#

&(,&58 3+)A!4 & g' R 4@.`$,:$,,&(# &(3 47&%", )09 + & &>!$&>30 # &>3>&(!$8d& H 4 ^ p % 4"! ^ p = . ",,^/& j &(&>! ^ . A!$# ^ +* 4 8 "!$!*&>, &<&d1*8 &5#D4 &`8>"!$!*) /0& $4&(# S< !T&d1* = 6$,& 4 t &>! +b g* pn/ J d< ^ "!$# ^ + &E3+&(46&58 r &k3+&(4)A!$A!$8d&k8d):!$# )A!$4^ . F H 4 | ^ 4 ^ + % 4 | ^ 4 ^ + 4^ . F H 4 ^ 4 ^ + % 4"! ^ 4 ^ + A3&-)A/ !*&(# X A4&(#<)A! + & A4+4 = 6 + ):! g' : + & # &>3+&>!$8>& ∆

^ F ^ % ^ ! &° & )A, :& ^ /0& j &>&(! "!# ! b ?g' pn 4 + &>!7 t &>! /# d ∆

^ F H 4 ^ p % 4&! ^ p % H 4 | ^ p % 4 | ^ p6 [ g' R ]; &%6*3+)'8d&(4+4&(4 ,&(:# !ª )a&d1*8 &5#<4 &(4_)". + & > &(,&58 3+)A!<4'4 & = "3+&-#'&548>3 /0&(# ! &k.):,,) !ªJH'&(8 + ):!

$- + - " TV@RHX RX#U0\NP@V VYVYX#RTHV KX STZ XOX#\ 'X#XV L9V * &2eRHXU0\NPSV % 4 YT`\TPSVYL9R L9VYVYX#R%PSV \ X 'P@RHRX#U0\PSN " T X YX\P U0TH\X " \L;\X'% P (\ YX eRHXU\NPSV " $%\XZ !8d& ! 4 !9:,&> &(,&58 3+)A! *!$!*&>, !ª 3& = & 4 4+8 & = 8>",,r 4 ) ! !b g* ! * 8 B+ & !# = /0&>3f)".0&>,&(8 3):!$4h8>"!'ª$8 $ & /0& j &>&>! A!$# H X !*) "!<:#*# )A!$A, 3+A!$4760)A3 8 A!*!*&(, 4 ):6&(!*&(# ` 4 /0)A3?#'&>3+, !*& #') 7 &5#, !*& 6$"3?",,&(, ) &G/0)A3?#'&>3+, !*& ) + & 2 )*,) = /T/*,)'8+nA#'&<3+& = & H&(,&58 3):!$4 & C 4C)A60&>!*&5# !T3+&(4)A!"!$8>& ) & b &>3 = ,& &>, )A. + &G+DEE G V,DB *< : ! )B&>1'6*, ! + & ):3 !A,& $4%8>)A!$4 #*&>3 % A6*60&>!$4- k/ :4 ^ + + A3 !9 &': & ):, A& ^ A,):!9 &`6$ +T !$# 8( &5#D/ &`#*:4 &5# , !*& !b g* ; &C3+&(460&(8 +t &C&(!*&>30c4+8 & = &(4%.)A3 # 0&(3&(! & ):, A&54 nc= A3:&(# ! b ?g' pnB/# A!$# J $A3&e r &(! ! b ?g' / &>3+& & :&+ &G)A6*60):4 &`# 3+&(8 + ):! ! ^ n 4 "3 !9 .3+) = + & 2 )*,) = / /*,)'8+nA#*&B3+& = &)A. H &>,&(8 3):!$4 I # XNL;\THP@V # PSTV]\ 4 < ^ & l#$A! = #') 9 4 ! & 2 )*,) = /G/*,)]8+n:#'&3+& = &a)A. H &>,&(8 3):!$4 & 4&>& b +g* / 7

^ R ^ 4 ^ + ^ . ^ ^ H ^ 4 ^ + [- ))!+)S ) F v ) .;#±E#)!)!+)ª ) F r ) 0³

I ³ #&;,-;+,,+L/' %

∆DS V( )V

(D)BS

-e

-e

E(N+1,0)

E(N,m’)

E(N,0)Groundstate

Transition

GroundstateTransition

-e

-e

E(N+1,0)

E(N+1,k’)

E(N,m’)

E(N,0)

(c)Quantum Dot Discharging:

N,0 N+1,0

N+1,0 N,0

N,m’

N,m’

(b)

Transition

closed disabled

Transition

opened

Coulomb Blockade

(a)

Excited StateTransition to

opened

µ(n,V ,V )

µ

µV

(S)BS DS V( ) (α)

(β)

(γ)

(δ)

(ε)

(α)(β)

(γ)

(δ)(ε)

Additional Energy Leveldue to Excited State

Regime of Single-Electron TunnelingRegime of Coulomb Blockade

Additional Channel on Collector Side by Reaching Excited Statewith Discharging

VBS

VDS

VBS

BS DS

Celch

eVDSEelch

N

N+2 N+2

N

N+1

N+2

N+1

N+2

N+1

N+1

N N

N+1

N+1

N+1

N

N+1N

N+1

N

NN+1

0

-;,,+/'%RQ± ±'( ?0+ g± -+ %] ## I

¦ #r " ¬ ¦ ¬ -0 ! ° !)tb° !"³ ³ .Y#?0+70° 3 ±#± !#)Q, ")!&+)!+,,#&;,@ #+) ¦ ;, !M !@ !±0 +g± /Q *±,+±) ! ¬ ;+# ! ! !M, !#")!&H+)!+,'##+)! !#"+" ! .)!))9M ;±0)! #)! E)!TO&± +" ! °%% $ %+)!+,# !#1+± % $+)!+,#+³ ¦ ¬ (#"/ , °+ ) F $)+o !±0 +g± ! ¦ ¬ ! ¦ ¬ ¦ % ¬ ³0 'g,% ¦ ¬ .# ±#±0 )@ #+)9 !L;+g±Ev),)!g/$ "% 0# ±0/3+#± !#"° ! #?0+ g± 1b $ 9 $'&H+)!+,'1/01+ ³ = !Y !Y± ¦ , ¦ ¬,¬ + /%1b, " r "##±0&1 $ %@ ¦ $ ¬ &H+)!+, 1/01+ /°1, !#"*r '#?0+ g±31b $ %Q ¦ $ ¬ &H+)!+, 1/01+ ³ = '), N; g +± /7 ++g± !#"@++,7.vQ !1#L. /' ##+)! !#" +,±#± !"e $ +)!+,r ° !, ¦ ,+ !"³ ³ ¬ ³

I # XNL;\THP@V # P@THV]\ 4 + #'&58d3+&(:4 !9 + &: & )A, 0A& ^ "4 !9A,&b>t&>,&(8 3+)A! 3?"!4760)A3 /0&(8>) = &(4 60):4+4 /*,&< ^ 4 !$8>& &(3&^ H ^ 4 ^ + F ^ 4&>& b g* / 7M H A3 + !ªD.3) = &.A3+)0*!#*4 &G)A. + & H >t&>,&(8 3+)A!4]4 & = ! &@l#$"! = #') = "1 = = &>!*&(3 4^)A/ !*&5#T.)A3k"! &>,&(8 3+)A!,&( ] !ª & l#$"! = . + & l#$A! = #') &>!#*4 ! + & A3+)0*!$#$4 &)". & >t&>,&(8 3+)A!c4'4 & = #< ^ + &C&(!*&>30 ^ H ^ 4 ^ + )A. &a&>,&(8 3+)A! 4P$4 &>!*)9 E )k3&5A8 A!3*!*)'8(8b*6 &(#G4 & _+ & b &(3 = ,& &(,:)A. + &8d)A,,&(8 )A3 b ):3 ^ ^ ^ 4 !9A,&b>t&>,&(8 3+)A! 3?"!$46):3 3+& = !$4 60):4+4 /*,&k4 !$8d&

^ . ^ H ^ 4 ^ + ^ [ g' R g:I # XNL;\THP@V # PSTV]\ 4 < ^ $ ! & & )A, 0A& ! &(3 ",9#*&b:$!*&5# /# g* R gA ""!cA#*# + ):!$",$8 "!*!*&(, 4 )A60&>!*&5# !@3+&(4)A!$A!$8d& ) &C8>)A,,&58 )A35s ; &>3+& 4`A!*) + &>3@8 "!$!*&>,-.)A3G&>,&(8 3+)A!$4KE+A FRQ &Dl#$"! = #*) H "3 !9 .3+) = &°A3+)0*!$#$4 & f H 4 | ^ 4 ^ + ' )". & H >t&>,&(8 3+)A!D4'4 & = ! &l#$"! = #') ""!G&>,&(8 3+)A!`8("!`&(4+8>"60& .3) = &l#$A! = #') f ) &8>)A,,&58 ):34) + &<l"! = #') 4 ,&>. /& * !# !T"! &d1*8 &5#4 & f 4"! ^ 4 ^ + ')". & > &(,&58 3+)A! 4'4 & = 4&>& b +g* 8 d ; * 4 /&58d) = &54 6)44 /$,&E ^ .

H 4 | ^ 4 ^ + % 4"! ^ 4 ^ + F ^ 4 g' R l & + &&(,&58 3+)A!j !$4<&(!*)0ª &>!$&>30 ) :!$# "!j$!*)'8>8b$6 &5# 4 & B &b &(3 = ,& &>, )". &<8d)A,,&(8 )A3 X `):6&(! !9 +* 4 8 A!*!*&(,]<4 !9:,&a&>,&(8 3+)[email protected]+) = &kl#$"! = #') 8>"!,&5 & ) & 8>)A,,&58 ):3/ FRV bB 3+A!$47.&>3 !9 &Wl#$"! = #') D ! ) A! &d1*8 &5#4 & DB ! ) & A3+)0$!$#*4 &<)". + & > &(,&58 3):! 4'4 & = ]< 4 ! &@8>:47&B)"."!c:#*# )A!$A,$8 "!$!*&>,'.3+) = &C& = &(3-4 #'& &(4&C8 "!$!*&>,4 9+ &C8>)A,,&58 ):34 #'&<A3& A&(! .3) = &>,&(8 3+)A!$4 )". # &>3+&>! &(!*&>30*/9 0: ! V GA QQ]D VCW<T A V;V ,TA ,V F ; &-A#*# )A!",A8 A!*!*&(, !8d3+&(A4&(4 ):!*,r & 6*3):/$"/ , "!D&>,&(8 3+)A! 4 ,&( ] !9 &<l#$A! = #*) ) + &<8d):,,&(8 )A34 #*&

I ¯ ³ #&;,-;+,,+L/' % i *& ) + &G6)44 / , D)A.9)A/ ! !ª"! &d1*8 &5# 4 & f H 4 ^ 4 ^ + ')A. + & H > &(,&58 3+)A!T4'4 & = /# $!*!*&>, !9 .3+) = & = 7 &(3 ! ) + &Bl#$A! =#') + &E3&(, )A! g* R l: A4 )@/&°:&>!*&(3+A, r~ &5# )^ F H 4 ^ 4 ^ + % 4"! ^ 4 ^ + g' R p

^ H 4 ^ 4 ^ + ^ . [ g' R ; * 4 3+A!$4 )A! /0& j &>&>! + & "!# + & H >t&>,&(8 3):! 4'4 & = 4 !$# 8> &5# ! b ?g' 8 ; &EA#$# + ):!$", 4 !9A,&b>t&>,&(8 3+)A!8 A!*!*&(, #'&(4+8d3 /0&(#/ g* R l: )A3/ g* R p 4):!*,tT60):4+4 /*,& ."! ) &@l#$A! = #*) 8>"! ª$8 $ &@/0& j &>&>! H A!$# &(,&58 3):!$4 & g' R 49.`$,:$,,&(# ª &>3 4&0", )9 c+ &C&(!*&>30@# 0&(3&(!$8d& H 4 ^ p % 4"! ^ p = . ",,/& j &(&>! ^ . A!$# ^ $ 48 A!*!*&(, &E&>1*8 &(# 4 &<8>A!*!*) /0&°$4&(# 4&>& b +g* / J 7d< ^ "!$# ^ + &E3&54760&(8 r &k3+&(4)A!$A!$8d&k8d):!$# )A!$4 H 4 | ^ 4 ^ + % 4 | ^ 4 ^ + F ^ 4 H 4 ^ 4 ^ + % 4"! ^ 4 ^ + FE^ A3&-)A/ !*&(# X A4&(#E):! + & :44 = 6 + ):! g* & # &>3+&>!$8>& ∆

^ F ^ % ^ ! + &°: & ):, :& ^ /0& j &>&>! "!# ! b ?g' 4 + &>!7 r &(!/ d ∆

^ F H 4 ^ p6 % 4"! ^ p % H 4 | ^ p % 4 | ^ p [ g' R L; * 4 3+&(4*, 9 4 &>3B4 = ,A3 ) + & 3+&(4*, g' R ] .)A39):6&(! !9<"!cA#$# + ):!$",8 "!;>!*&(, .)A3&(,&58 3+)A!4 &>! &(3 !9 &<l#$A! = #*) .3+) = & = 7 &>3C4 #'&

$- + -/ % " X # L;NL;\X YL9V]\TH\L;\T@X "3# X#U0\NPUP # P)(\ YX L9V P (\ YX*" 2 eRHXU\N P@V " $%\XZ J P)% %T`O=RHXZ l:! > g* R:R #'&548>3 /&54 + & 4 $ + ):! &>! A! &d1*8 &5# 4 & )". & H >&(,&58 3+)A! 4'4 & = 4B3+&(:8 &(# &>3+&(:4 Z l! 5 g* R p #'&548>3 /0&(4 & 8d)A!# + ):! .)A3A!G&>1*8 &(#c4 &)A. + & >t&>,&(8 3+)A!@4'4 & = /0&(8>) = !ª<A8>8>&(4+4 /*,& m ! + &:&>!*&(3+A,8(A4& &(3& & ! ",94 &@/&>.)A3+& *!*!*&(, !9 4E"! &d1*8 &5# 4 &0 + &(4&@3&547)0>!$A!$8d& 8>)A!$# + ):!$4 !$8d,r$#'& & ) ",%&(!*&>30 )".&d1*8 &5# 4 &(4E)A. C+D V 4'4 & = 4* 8 = 0A&54 &<46&58 3)48>)A6@3+ &(3 8d) = 6*,&d1 X C . + & ! ", 4 &E)". + &<l#$"! = #') /&>.)A3+& & H + &>,&(8 3):!&(! &>3?4 &Bl#$A! = #*) .3+) = + &E& = 7 &(3 4 ", '4 &°:3)*!$#*4 & f 4 | ' )A.+ & >t&>,&(8 3):!4'4 & = 47&(& b +g' L &(! g' RAR 3&5#;$8d&54 )

^ . F H 4 ^ 4 ^ + % 4 | ^ 4 ^ + g' | ^ H 4 ^ 4 ^ + ^ [

-;,,+/'%RQ± ±'( ?0+ g± -+ %] ## I

< 4%<8>)A!$4&(l#*&(!$8d& &C# 4 "!$8>& ∆^ ! &a/$A8+: &>t4)0*3?8d& ):, :&-.3+) = &/0)A3?#'&(3, !$& ) + & 2 )0*,) = /;>t/*,)'8+nA#*&3+& = &)A. &>,&(8 3):!$4 ) )A60&>! !9 &:#*# )A!$A, 8 "!$!*&>, ):! + &E& = 7 &(3C4 #'& 4 r &(!/

d ∆^ F H 4 ^ p % H 4 | ^ p [ g' H

H = ,"3h.):3 + &8 "!$!*&>,4 ) + &8d):,,&(8 )A35s m . & ! ",'4 &-)A. + & l#$A! =#*) /0&d.)A3+& + & + &>,&(8 3):!@,&5 &(4 + &al#$A! = #') 9 ) &C8d):,,&(8 )A3 49A, '4+ &:3)*!$#*4 & f H 4 | ' )". & H >t&>,&(8 3+)A!@4'4 & = 4&>& b g* L &(! g' R p 3+&(#;8d&(4 )^ F H 4 | ^ 4 ^ + % 4&! ^ 4 ^ + g' R

^ H 4 ^ 4 ^ + ^ . [; & # 4 "!$8>& ∆^ ! & /$:8+# &b>47)*3+8>& )A, 0A&D.3+) = & /0)A3?#'&>3+, !*& )+ & 2 )0*,) = //*,)'8+nA#'&^3& = &a)A. H &(,&58 3):!$4 )G)A60&>! !9 &E:#*# )A!$A,8 "!*!*&(, )A! &<8>)A,,&58 )A34 #'& 4 r &(!/ d ∆

^ F 4 ^ p % 4 | ^ p [ g' A !$#'&>3 4$8 8d):!$# )A!$4 !$#*&>&(#*l"! r &E4760&(8 3+):4+8d):6#@)A. & H >A!$# + & >t&>,&(8 3+)A!4'4 & = 8("! /&E#'):!*&E47&(6$"3? &>,r0 P$4 # 4 !90 4 &(#/ &4 * . )". & 3 /0)A3?#'&(3, !$& ! & ^ ^ + 6$,A!*& 4&>& b g' L / s +* ! + & 4 !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9^3& = &-)". "!$# H &(,&58 3+)A!4Tl#$"! r & 46&58 3)48>)A6T)". & H >t&>,&(8 3):! 4'4 & = 4<#*)A!*& + 3+&(460&(8 G ) &/0)A3?#'&>3+, !*& ) & 2 )*,) = / /$,)'8+nA#'& 3+& = &)A. &(,&58 3):!$4 &>3+&(:4 Gl#$"! + r &k46&58 3+):4+8d):6G)A. + & > &(,&58 3):!4'4 & = 4 #'):!*& 3&54760&(8 - ) + &^/):3+#'&(3, !*& ) + & 2 )*,) = //*,)]8+#>A#'& 3+& = &%)A. H &(,&58 3):!$4 K c ; * 4 4h60):4+4 /*,& .0. :4 "!#B8d) = 6*,& &3&(,"1* )A! ) & :3)*!$#*4 &k)". + &B8d):!;:$!*&5# &>,&(8 3):!T4'4 & = ! + &l#$"! = #') )'8>8*3?4a/0&d.):3& &G!$&d1 k *!*!$&>, !9T6$3)'8d&544 3)9 )A!*&)". &E/"3+3 &>3?4-4 A3 4 ) & &>3 !*& +t & # &>3+&>! + A,98d)A!#;$8 "!$8>& ! b g* g !$# 8> &54 ,&(:4 .):3947) = &&d1*8 &5#c4 &54 3+&>,n1* )A!@#')]&(4 !*) )'8>8b$3 +* ! & = &5"! = &

F f * + f /0& j &>&(! 4$8>8>&(4+4 r &G&>,&(8 3+)A!$4k6A4+4 !9 3+)09 + & l#$"! = #') o H # r & ,, 8d) = & /A8+ ) $ 4`&b &(8 B ! H]&(8 )A! g' * ; &l#*&54 + ):! "3 4&(4(s< 3& + &>3+&c) + &>3<.&( *3+&(4 !$# 8> !9 < & ! + A,-4 &(4k.):3 & *!$!*&>, !ª6$3)'8d&544EA3& ! &3&54760&(8 r & A3+)0$!$#*4 &(4 ; * 4 )A6 8 ,,%/0&:#*#'3+&(4+47&5# !+ &k.)A,,) !9JH]&58 )A!4 ))!+)S ) F

r ) .;± )!))S ) F r ) 0³ « ))!+)S ) F v ) .;#±E#)!)!+)ª ) F r ) 0³

II ³ #&;,-;+,,+L/' %

V(S)BS DS V( )

DS V( )V(D)BS

E(N,2)

E(N,1)

E(N,0)

E(N,1)

E(N,0)

E(N+1,2)E(N+1,1)

E(N+1,0)

(a)

Discharging

Relaxation

Relaxation

Charging

Relaxation

E(n,k)

(b)

suppressed

E(N,2)

VBS

VDS

Bαe

N+2N+2N+1

N+1

N-1N

N-1

N+1

N

0

N-1N

E(N+1,k) - E(N+1,0)

E(N,m) - E(N,0)

Bαe

-07#b3&;,,+/ 3$'&#± ¦ $ ¬ &H+)!+,1/01+ g;3±° ' t)=13 E## ±0 ;#v ##) !" +,%1, !') ! +/0' "±01. +&;+ $ &H+)!+,j1/1 ³ ¦ ¬ #?0+ g±1 ;+g g±.@3+) ?#b ! 0++,' e+&;+ $ e"±01 ++0 ;#v #?=##+)! !#" 7$ +=%O +))t+³ ¦ ¬ -O %@ , !#")!&H+)!+,##+)! !#"" ! °+*S$ ± ¦ $ ¬ +)!+,# % ## ± = ±,g±%)! !#+ O% ;±0)! v;+# !#"% ±#± !#)ª #+)ª3 + ° , , ±0± Tv ±°#?0+ g±1 ¦ $ ¬ &H+)!+, 1/01+ ³ = M±# g±&±,+±)! + O ;±)! !#+r L;+ !#" ±± !)Y ##) %)!)!+e, ±#± #r3± T? !+±1M%= %$'&H+)!+, 1/1 ³ = +,° #+)!,+,,g±% !% #)! #)! O± +" ! ° , !#+ # ;ª+)!+,#3 # ±0 !) ?0g±ª³ '%&2"< =9;"$ % 7( ,C< & ?A $%CB@7 3"? $4 %4% " '% ( - " % % 8 % 1 0OB@49;"3 $7( " )5%"$&- . "m 4 6)44 /$,& )B8>)A!$4 3$8 - &a6)4 )A!4 .)A3-)A60&>! !9GA#*# )A!",4 !9A,&b>t&>,&(8 3+)A! 3+A!$4760)A3 8 "!*!$&>,4 ! & ^ ^ + 6$,A!*& . &%]!*) &E&(!*&>30 46&58 3+`.)A3

#1, !%],, #)! #&;, = + )t± !#+ I + & > A!$# & H >t&>,&(8 3+)A! 4'4 & = ! &Gl#$"! = #*) < 48 & = &<.):3#*) !9c47) 4#'&>3 t &(# &>3+&co R rts & $4fA4+4 = & & ) A,]&>!*&(3k460&(8 3+C.)A3 & > A!$# + & H >t&>,&(8 3+)A!4'4 & = A4 4 ) ! ! b ?g' H| b ):3C4 = 6*, 8 #'&A&>!$&>3?A8b ! + &`46&58 3 = 4A/$4&>! & + !$8d3+&(:4 !9 l"! = ! = /&(3 !$#'&>1 & &>!$&>30 )". + & >&(,&58 3):! 4 &54 !$8d3+&(:47&54 ; & # &>3+&>!$8>&(4/& j &(&>! + & &(!*&>30 4760&(8 3 = )".+ & H >t&>,&(8 3+)A! 4'4 & = A!$# )47&D)A. & > &(,&58 3):! 4]4 & = .)A3:$1]&5#60) &>! ", ^ p A3&G#'&>!*) &5# ! &`.):,,) !9:4 V BA QTgFRVFHD Q QbB 0F T ; &T"3+&6$,) 7 &5# ! b ?g' H| / 3+&(46&58 9 ) & &>,&(8 3+)]8 & = 8(",*60) &>! ",4 )A. & = &>3A!$#E8d):,,&(8 ):3 3+&>6*3+&(4&>! &5#^/# + & ):3 r~ ):! ",A, !*&(4 X E8 A!9 !9 M: &9&>,&(8 3+)'#'&60) &>! ", ^ ) /## ^ ) ",, 3?"!$4 + ):!&(!*&>3 &(4 A3&k4 $ . &(# 3&(, r &(,t ) ^ . A!$#

^ / % ) # ^ ) ; & 48 & = &)A. b +g' H| / 4G8d)A!4 3$8 &5# ! &.)A,,) !9 s b 3?4 B & 3+A!$4 + ):! &>!*&(3 &54 H 4 % 4 | .3+) = &:3)*!$#*4 &)A. & >&(,&58 3):! 4]4 & = ) & :3)*!$#><A!$# &>1'8 &(# 4 &(4@)". & H >t&>,&(8 3+)A!4'4 & = | 4 H 4 R 4 ddd "3+&96*,) 7 &(#`",)A!9 & &(3 + 8(",A&(!*&>30kn1 4 ; & &d1*A8 &>3 8>A,*6)4 )A!)". $ 4-,:#*#'&(3 3+&(46&58 - ) ^ . "!$# ^ #'&>60&>!#*4%):! &):6&(3+ )A! 60) ! ! + & ^ ^ + 6*,A!*& ; & 3+&(46&58 +t & ,& &(,4 A3& = A3:&(#/ | 4 Mo< c )A3 t~ )A! A, # 4 A!$8d&54= r &(! / & 3+A!$4 )A! &>!*&(3 &54 H 4 | % 4&! ! | 4 H 4 R 4 ddd + &E,A#*#'&(3 )". 3+A!$4 + ):!&>!$&>3 &(4 H 4 % 4&! + | 4 H 4 R 4 ddd "3+&C6*,) &5# = "3A&(#@/ !4 M &k)A/ !7:3 #>t, A&G6$ 7 &(3! !$)]#*&(4E&5A8 !$# 8( !9 A!W&>!*&(3 ,& &(, + 3&54760&(8 ) ^ . "!$# ^ .):3^ 3?"!$4 + ):! /0& j &>&>! & >"!$# & H >t&>,&(8 3+)A!4'4 & = 7X + & &(3 + 8(",47):, # , !*& 8>3)44 !ª !*)'#'& !4 A,, 3?"!$4 + ):!$4@"3+&8>)A!*!$&(8 &(# ! )A, !9 & 4+ = &c4 & f 4"! ' )". & >t&>,&(8 3+)A! 4'4 & = X &#$A4 &(#@):/*, l#*&C, !*&0 & 3?"!$4 )A!$4 ! ):, ] !9 + &a4+ = &C4 & f H 4 ' )". & H >t&>,&(8 3+)A! 4'4 & = "3+&@8d)A!$!*&(8 &(# ; &c"3+3) 4C)A! + &c8d):!*!*&(8 !9 , !*&(4 !$# 8> &T60):4+4 /*,& # 3&58 + ):!$4@.)A33&(,"1* )A! ! & 4'4 & = .)A3 :$1]&5# &>,&(8 3+)A!! = /&(3 Y< !W6$ + .)A,,) !9 + &A33+) 4 ,, &>!$# <+ & 3+A!$4 + ):! /0& j &>&(!+ &°A3+)0$!$#*4 &(4'#'&>!*) &5#/ | 4 | M) ) ! &>3+6*3+& @* 4c4+8 & = & ) #'&(3 r & &D60):4+4 /*,& 3?"!$4 + ):!$4`.)A3 & t &>!@#'3? !;>t4)0$3+8>& )A, :& ^ + "!#: &b>47)*3?8d& )A, 0A& ^ ; )<48>8d&(&(# :8d)A!9>4 #'&>3 + &k.)A,,) !9@4 & = &>! 4(sH < # 3&58 3?"!4 )A!.3) = f 4"! ' ) f H 4 ' 4):!*,r",,) &(# .

^ . H 4 ^ p % 4&! ^ p [; &G!*)'#'& !4 :4 ), &`/&(,) ^ . !] 3+&>3+&(l# 4 &E.):3^4$8 3?"!$4 )A! 4 + E+ &c4 & f 4&! ' 4 + & ! + A,94 &0 & f 4"! ' A4k/0&>&(! 6$3&(6$"3+&(#/ T6$3&58d&>&5# !9 6*3+)'8d&(4+4 ; * 4 = ` A6*6&(! #;*& ) # 3+&(8 < 3?"!$4 )A!.3) = H > &(,&58 3+)A! 4 &a)A3%/@3+&>,n1* + ):!`.3+) = > &(,&58 3):! 4 &C)".* &(3-&(!*&>30 < 3?"!$4 + ):!c.3+) = f H 4 ' ) f 4"! ' 4%):!*,t@&(!*&>3A& 8>",,r",,) &(# . H 4 ^ p % 4"! ^ p ^ [

I ³ #&;,-;+,,+L/' %

(a)

eVDS

(b)

(c)

E(N+1,2)

E(N+1,1)

E(N+1,0)

E(N,2)

E(N,1)

E(N,0)

EnergiesTransition

(0,2)

(0,1)

(0,0)

E(N+1,k) - E(N,1)

E(N+1,k) - E(N,0)

(2,0)

(2,1)

(1,0)

(1,1)(2,2)

(1,2) E(N+1,k) - E(N,2)

N+1

(0,1)EC

(1,1)EC(0,0)EC

(1,0)E

Groundstate

E(n,k)Total Energy

E(N+1,0) - E(N,l)

Collector

Extended Energy Scheme

Used TransitionsNomenclature:(m,k): Transition between

(V ,V ) Values

Emitter

and

Transition Energies at Distinct BS DS

Level Spectrum:

µ Celch

µelchE

µ Celch

µelchE

N,m N+1,k

1 2l=0

#1, !%],, #)! #&;, = + )t± !#+ I

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I ³ #&;,-;+,,+L/' % &@8("! 4 =@= "3 r~ &As m . & 3?"!$4 )A! !4 4k60):4+4 /*,&0 ",, 3?"!$4 + ):!$4^"3+&&(!*&>3A& 8>",,rc6)44 /$,& * 8 "3+&

I 3&5A8 &5#A,):!9 + &<4)A, # &(3 + 8(", , !*& 3+A!$4 )A! &>!$&>30c/0&>,) ^ . $)A3I 3&5A8 &5#A,):!9 + &<#*:4 &5#):/*, l#*&E, !$& + 3+A!$4 + ):!&(!*&>30 A/) & ^

& $4E"6*6$,t +* 4k3&54*, ^ ) &c4 $ + ):! #*&>6 8 &(# ! b g' H| / sH A3 + !ª.3+) = | 4 | _A,):!9 &4)A, # , !*&0 3?"!$4 )A!$4<.3) = + &K:3)*!$#*4 & f 4 | ' )&>1'8 &(# 4 & f H 4 ' )". & H > &(,&58 3):! 4]4 & = "3+& .)0*!# = A3:&(#/ | 4 d@ !*,r & 3+A!$4 + ):! | 4 H 4 60):4+4 /*,&k4 !$8d& 4 3?"!4 )A! &>!*&(3c, &(4/0&>,) ^ . ; &>3+&d.):3& + &G4 & f H 4 H ' 4a3+&(:8 &(# S< ! 4 "3 !9 .3+) = | 4 | $A,):!9 &B#*A4 &5#, !*& + & 3?"!4 )A! H 4 | 4C3&5A8 &5# $ 8 8("!*!*) /&$4&(#T4 !$8d& , &54 /0&>,) ^ ; &>3+&d.)A3+& & 3?"!4 )A! f H 4 | ' f 4 H ' 4!*) &(!*&>3A& 8>A,,rc",,) &(# b 3) = | 4 H )A!*,r | 4 | C 47):, #, !*&0'/0&>,) ^ . A!$# H 4 H #*A4 &(#, !*&*"/0) & ^ ,&(:# )`60):4+4 /*,& 3+A!$4 + ):!$4 b 3+) = H 4 H ]",4) H 4 | 4C3+&(:8 &(#TA,):!9 + &G4)A, #T, !*& H !$8>& , &(4^/&(,) ^ . + & 3?"!$4 + ):!f 4 H ' f H 4 | ' 4 &(!*&>3A& 8>A,,r ",,) &(# m !T4 =@= "30.)A3 + &<4 )A! !b g* H| / &k.):,,) !ª 3+A!$4 )A!4"3+&a&(!*&>3A& 8>",,rA8(8d&(4+4 /*,&As | 4 | Z 2 s f 4 | ' f H 4 | ' 4 | 4 H Z 2 s f 4 | ' f H 4 H ' 4 H 4 H Z 2 s f 4 H ' f H 4 H ' 4 H 4 | Z s f 4 H ' f H 4 | ' [; & 3?"!4 )A! f 4 H ' f H 4 | ' /9 !*) f & 3?"!4 )A! f H 4 | ' f 4 H ' 460):4+4 /*,&0 &(3&5A4 ",, ) + &>3 3+A!$4 )A!4 A3&^/ # 3&58 )A!", 9< ,, &547& 3?"!4 )A!$4A3& = A3:&(# ! ) ",&(!*&>30 46&58 3? 4 ) ! b g' H| m 4 + &7A& 3?"!$4 + ):!f 4 | ' f H 4 H ' !*) ",,) &(# #;*& ) ) &(3B4&>,&(8 + ):! 3*,&(4E/0&(4 #'&(4E&(!*&>308>)A!$4&>3 )A!* &(! ",, 3+A!$4 )A!4 #'&(4+8d3 /&5#T"/0) &<"3+&E!*) $4+"/*,&<4 !$8>& &547&A3&, !9A&5# ) | 4 H ZC m . $ 4 A& 3?"!$4 )A! )'8(8b*3?4 + &>! ",, 3?"!$4 + ):!$4@#'&b>4+8d3 /0&(# "/0) &k"3+&k&>!*&(3:& + 8(",,t A,,) &5# m ! 8d)A!8d,r$4 )A!* &T#;]!$ = 8>4@)A.^4 !ªA,&b>t&>,&(8 3):! 3?"!4760)A3 G 4@3? &>3c8d) = >6*,&d1 h4 !$8d&/# )A60&>! !9 3?"!$4 + ):! ) !*& &d1*8 &(# 4 & )". + & ):3 & H >t&>,&(8 3+)A!@4'4 & = 0A&>!$&>3?",,tB )A,& 47&(3 &(4f)A.0) &(3 3?"!$4 )A!$4f/0& j &>&(!/0) + &(,&58 3+)A!@4]4 & = 4f/&58d) = & &>!$&>3A& + 8(",,t<A,,) &(# ; & 4+8 & = & 6*3+&(4&>! &5# !b g* H| / ",,) 4 )&d1'6*,)A3+&`4'4 & = + 8(",,t &547&`&>!*&(3:& + 8(",,t 6)44 /*,& 3?"!;>4 + ):!$4A4#*&(4+8d3 /0&(# "/0) & ) #')]&(4 ,))'4_, A& ! & ^ ^ + 6*,"!*& m ! b +g* H:H & /):3+#*&>3+, !*&(4#'&(3 r &5#c.3+) = &%:8 )0$4 &(!*&>304760&(8 3 = A!$##*&(4+8d3 /0&(#/ &E3&(, )A!$4

H 4 ^ 4 ^ + % 4"! ^ 4 ^ + F ^ . 4 g' "] H 4 ^ 4 ^ + % 4"! ^ 4 ^ + F ^ g' :g:A3&6*,) 7 &(# ! + & ^ ^ + 6*,A!*& X !4 Z & /0)A3?#'&>3+, !*&D#'&(8>3 /0&(# / g' " 4 = A3:&(# / !4 #2 #'&(4+8d3 /0&(# / g* gAM ; &W/0)A3?#'&>3+, !*& .)A3

#1, !%],, #)! #&;, = + )t± !#+ I 4 !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9 ) A3+#$4 + & 2 )*,) = / /*,)]8+n:#'&c3& = &(4E"3+&@&(l# r >A,&(! C ) | 4 | Z A!$# | 4 | T2a>X ):3+#*&>3+, !*&(4 ! )A, !9 &>1*8 &(# 4 &`8>A! )A!$,tD/0&47&5# +* ! + &^4 !9A,&b>t&>,&(8 3+)A! $!*!*&>, !9@3& = &A!$# + &>3+&a):!*,r . + & ! ",4 & A4a/&(&>! 3+&(:8 &(#D/T"!*) &(3C6*3+)'8d&544 ; &`, !*&54 !4 Z A!$# !4 T2 "3+&#*3+ ! A4 * 8+, !*&^.)A3 ^ + 4 ^ &>3+& &547& 3+A!$4 + ):!$4 /&58d) = &E60):4+4 /*,&.):3 * &>3 f ^ + f ; &>3+& 60&(0 ! + &# &>3+&>! ", 8d):!$#;$8 A!$8d& 4`&d1'60&(8 &(# b )A3a&d1* = 6*,&0 &G/0)A3?#'&>3+, !*& H 4 H Z 4k#'3? ! A4^ +* 8+ , !*&G". &(3^8>3)44 !ª, !*& H 4 | T2 /&58>47& + & ! ",04 & f 4 H ' .):3 H 4 H Z /0&(8> = &C ,A/*,& 9 &8>3)44 !9 H 4 | T2a; &T6 7 &>3+! )". 3?"!$46):3 460&(8 3)48>)A6 )". b +g* H:H 4c)A/ !*&5# / 8d)A!9>4 #'&>3 !ª# 3&58 ^ 3?"!$4 )A!$4^/0& j &>&>! & "!$# & H > &(,&58 3):! 4]4 & = !$#'&(3 * 4:44 = 6 + ):! 47&(& = 4 ) /0& 60):4+4 /*,& ) 8>)A!$8>,t$#*&T)A! & ! ",4 &E.):3 &(:8 D 3?"!$4 )A! ] 4 /$,& ! + & 3?"!4760)A3 4760&(8 3 = !'.)A3 $!$ &>,r0 .8>&>3 ! 3+A!$4 )A!4C"3+&B!$) A,,) &(# &G4 )A3 4C!$) 47) &5A4 :4 + &<.):,,) !9&>1* = 6*,&a4 ) 4>s & 4-:44 = & + & 3?"!$4 + ):! !4 Z & f 4"! ' f H 4 ' 4k!*) 6)44 /$,&c", )09 &(!*&>3A& 8>A,,r ",,) &(# >X f H 4 ' = : /0&c)A/9> !*&(# .3) = 3&(,"1* )A! .3) = 4 & f H 4 ' )". * &(3^&(!*&>30 $ 8 :43+&(:8 &(# /# + & 3?"!$4 )A! ! 4 ZC ; &>3+&d.):3& 3?"!$4 + ):!$4 ! )A, !9 &c4 &f H 4 ' "3+&E!*) &(!$"/*,&(#D/ !4 Z /ª / ! 4 Z s X )A3?#'&>3+, !*&54 )". ! 4 T2&(!$#@)A! ! 4 Z !$4 &5A#@)A. !4 ZC ; &(3&>.)A3+&0".3+) = & 3?"!$460)A3 4760&(8 3 = !:&>!*&(3+A, &E8>"!$!*) 8d):!$8d,r$#'&%*! = / *)0$4,r)A! & ! ",_4 &< #*# )A!$A,C8 "!$!*&>,4 * 8 A3& )A60&>!*&5# .3) = A3+)0*!#*4 &(4@A4 & ! ",4 &<A3&E&(!$# !9 + &</0)A3?#'&>3+, !*&54 | 4 | Z "!$# | 4 | T2a2 A!T/&`8d)A!8d,r$#'&(# !+ &D)A6*60):4 &D# 3+&(8 )A! ",, + ):4&D/):3+#*&>3+, !*&(4G&(!$# !9 G &D/0)A3?#'&>3+, !*&54)A. 4 !9A,&b>t&>,&(8 3+)A! *!*!$&>, !9 "3+&@#9*& ) 3?"!$4 + ):!$4 ! )A, ] !9T:3)*!$#*4 & !'.)A3 $!$ &>,r !*) s & $4@,)) G & .)A,,) !9 &d1* = 6*,& &TA4+4 = & + & 3?"!$4 + ):! &>!$&>30 .)A3 H 4 H 4 + & 4+ = &DA4B.)A3 | 4 | d ; &>! H 4 H Z . ",,4 ! b +g' HAH D QV,D &@/0)A3?#'&>3+, !*& | 4 | Z "!$# 4E:8 r &(# + | 4 H T2 .):3 !;>8>3&5A4 !ª f ^ + f ; &(3&>.)A3+& R H T2 * 8 4k, !9A&5# ) H 4 H Z &(!$#*4E",4))A! &/0)A3?#'&(3, !$& | 4 | ZC / ] )$4-.3) = b g* H:H 3?"!4 )A!$4 4"! + H 4 % 4&! ^ H 4 g' 0l & "!&>!*&(3@,& &>, "/0) & &%:3)*!$#*4 & 3+A!$4 + ):!"3+&a8("!$# #* &(4-.):3):6&(! !9A#$# + ):!$",h8 "!$!*&>,4 ):! &`& = &(3^4 #*&0 &>3+&(A4 3+A!$4 )A!4 4&! H 4 % 4&! ^ H 4 g' p & + A! &(!*&>30D,& &(, /&(,) & 3?"!4 )A! &>!*&(3T/& j &(&>! A3+)0*!$#$4 &54= )A60&>!DA#*# )A!", 8 "!$!*&>,4 )A! &E8d):,,&(8 ):3 4 #'& m ! &e:$3?4 8(A4&0'B!$& 8 "!*!*&(, 4C8d3+&( &5# .)A3aA!T&>,&(8 3+)A!D&>! &(3 !9 + &`l#$A! = #') &(3&5A4 ! &4&(8>)A!$#D8(A4&k !*& 8 "!$!*&>, 4C8>3&5 &(#.)A3 &(,&58 3):!$4 ,&5 ] !9 + &Bl#$A! = #*) m !W"!",)00 )*H'&(8 + ):! H R & :$3?4 ):!*&c8>"! /& #*&>!*) &(# A4kA! m &>,&(8 3+)A!;>t, A& m8 "!*!*&(, &>3+&(:4 &<4&(8>)A!$#)A!*&E:4 m ):,&> , :& m 8 A!*!*&(,

³ #&;,-;+,,+L/' %

Transition Energies

(c)

(a)

(b)

(0,2)

(0,1)

(0,0)

(2,2)

(2,1)

(2,0)

(1,0)

(1,1)

(1,2)

(0,1) E

(1,1) E(2,2) E

(0,0) E

(1,2) E

(0,2) E

(2,0) C

(2,1) C

(1,0) C

(0,0) C

(0,2) C (1,2) C (0,1) C (2,2) C

(1,0)

(2,1)(2,0)

(1,1) C

Total Energy

VBS

VDS

E

EE

0

N+2

N+1

N CollectorEmitter

Extended EnergyScheme

Threshold Lines for AdditionalChannels

E(N,2)

E(N,1)

E(N,0)

E(N+1,2)

E(N+1,1)

E(N+1,0)

³ &;,-;+,# ) & O ,= %& O ##

¦ #r#" ¬ ,)tb ! ; ! ++ )o+#"/)!7$ +)!°±4;±0)! !#+ ¦ ) F ) ¬ )t# ¦ ¬ # # +#"/&;+, !%" $ + ! ! )!g± +#"/ )±±±# ##g±1/' ,, ! !+" !+ ¦ $ ¬ 7 ¦ $ ¬ ±#)!,g±K ! ¦ ¬ ³ª !+)!± *¦ $ ¬ ¦ $ ¬ 7 ¦ $ ¬ .@ ³ ³.@ %,, ! !; ! ++ ="##±1+³ j #" !#" =" b)$ ) " ) .b =+"/M)±±* ! 'rg±J. ³ ³.0 ,)!7$ +)!o+ ° ! +,##>v +, ! ) $)!#+ = Og±° ¦ ¬ ³= +,,#, ! ° !" =L;+ ±#±0 ! !)ª #+);' + ° ,oo +)!), t±0±0# " ;±) ! 't " ±0 ! ! ) ³ S +,;±) !+ )) , !")!&H+)!+,3##) !"+" ! °L. /e ° " ; #)!³ / , ! b M t)1 ;+ g g± RQ±1b+b g g±b *;±0)! !#+%, ")!&H+)!+,#+)! ". T? !+± 1b+%,)!) / r°,, !#" # @;±0)! ! ! )!g±0e /# g±3 !# )@1b³

m ! 8d):!$8d,r$4 ):! .3+) = &>1'6&(3 = &>! A, 3?"!$460)A3 460&(8 3 = 4 !*) 4 3? .):3 "3?# ) &>1 3+:8 *! = / *)0$4,r & &>!*&(3 46&58 3+W.):3 & >`A!$# & H > &(,&58 3+)A! 4'4 & = b *3 &(3 !'.):3 = )A! A/) @ & 4'4 & = :4 )W/0&8>)A,,&58 &(# A!$# !$8d):360)A3? &(# ! ) & ! &>3+6*3+& )A! )A.C48 "! &>1'6&(3 = &>! A, 3+A!$46):3 4760&(8 3 = ?A $%CB@7 $" 0OB@49;"3 &- - DE!"3 .17/"3 "3- _ 17)+%,"$- . "H !9:,&> &(,&58 3):! 3+A!$46):3 B 4G8>47&5#W/# &3+&>69*,4 t & &>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3>:8 + ):! )A! + & 4,A!$# #'&548>3 /&5# ! = & ", 4'4 & = 4a/ &G&>,&(8 3+):4 8<4 !9:,&>&(,&58 3):! 8 "3 !9 &>!*&(3 o< 4c#'&548>3 /0&(# ! 2 "6 &>3 #'&(4+8d3+&(:4 !9+ &B4 t~ &E)". "! 47,"!# & !*& 8E&>!$&>30 )A. + &E&>,&(8 3+)A!$4A& 4 l#$"! +t~ &(# ; &4 !9A,&b>t6$"3 8d,&^,& &>, 46$:8 !9 ∆

J

K+K !$8>3&5A4&(4 "!#& &(!&>1'8>&>&5#*4 ; &%&>!*&(3a4+8 & = & )a#'&(4+8d3 /0&%4 !ªA,&b>t&>,&(8 3):! 3+A!$46):3 + 3)9 ^+ &%l#$"!9> = #') < !$8d,r$#'&54BA,,960):4+4 /*,& 3?"!4 )A!$4</& j &(&>! & >a"!# & H >&(,&58 3):!B4'4 & = ni &>60&>!$# !9k):! & 3+&>, +t &-4 t~ &%)". & 4 !9:,&> &(,&58 3):!<8 "3 !9&(!*&>30 "!# &^l#$A! +t~ + ):!&>!$&>30 ∆

J])A!*&k8>A!# 4 + !ª0 4 &^.):,,) > !9c8>:47&54>s

I b ):3- = & A, 47,"!# + &a4 !9A,&b>t&>,&(8 3+)A!c8 "3 !9<&(!*&>30 4 &^#') = !$A! &>!9>&>30c4+8>A,&:s 5∆

J ; &E4 !9A,&b>t6$A3 + 8>,& &>1*8 + ):!46&58 3 = 4 8d):! !#9>)047,r#'&(!$4&0 & & 3?"!$4 + ):!D&>!*&(3 &54/& j &(&>! & >-A!$# & H >&>,&(8 3+)A!4'4 & = A3&^",47)@#'&(!$47& ;< 44A& 8 &(# ! b +g* H R 9 &(3c3+&*,A3 A!$#*! .)A3 = 3+& ):!$4f)". 2 )0$,) = /@/*,)]8+n:#'& 4 )0*,#G/& ):/$4&>3 &(#GA4 ^.`$!$8 + ):!c)". : & ):, A& ^ A!$#`#*3+ !;>4)0*3?8d& )A, 0A& ^ + "i *& ) & #*&>!$4& &d1*8 )A!46&58 3?k)". = & A, 47,"!$#:8d):! !#$)0$4,t@A#$# + ):!$",04 !9:,&> &(,&58 3+)A! 3?"!4760)A3 8 A!*!*&>,4 "3+&a):6&(!*&(# D !8d3+&(A4 !9 f ^ + f 4&>&)* + ^ + 8 "3?A8 &>3 4 + 8(4 !b H L b H H| "!$# b H H:H M

Q °# !+ !#"+;+ t)8. ! /$ ∆% £¤ © « ³

¯ ³ #&;,-;+,,+L/' % >(a) (b) (c)

Metal Island Quantum Dot Atom-Like Dot

(d) Empty Dot (N=0)

Ec >> ∆ εqu qu qu

N-1

N

N+1

N-2

VDS

Ec << ∆ εEc ∆ ε

N+2

N-1

SourceDrain

N-1

VBS

N+1

N

N-1

N+1

N

N-2

N-1

N

N+1

N-2

N-1

N

N+1DSeV

N+1

N

0 0 0

0

1

2

0

V V VDS DS DS

12

3

VBSVBS

VBS

j ±0+g, !#" /# !g) , +%3 ±/.Q 4 %& °+ !g) +"/&H)!7$ +)&#+ !#"∆% !g, ±. ° !" 7$ #?0+++±. %, !#")!&+)!+, b" !#"'+#"/

±M3 M+)!+,&H+)!+,7 ! ! !K @&# ±0g³ j !#g, !#"% !

∆% ¥

.0 #)! @1)!TO±0+" !Q ! ¦ ) F ) ¬ #)#0$b,/ °#± ° ! , ! ),.# ;/.± %)!+,# @;=*±#±0 ! !)ª #+)! ++0 ' , !#")!&H+)!+,#+)! "e+" °³

I b ):3_ ]6 8>A,l#$A! = #') ):/ !*&5#E/E4 3$8 *3 !9 /9*,r = &>3 A, & l#$"!;>r~ )A!D&>!*&(3 ∆

J 4C8d) = 6$A3+A/*,& ) &<4 !9A,&b>t&>,&(8 3+)A!D8 "3 !9@&>!*&(3 s 2

∆

J ; &T&>1'8 + ):! 460&(8 3 = 4 # 48>3& & 8>,)47& ) + & 3+&(46&58 +t &

³ #&;,-;+,,+L/E/1,)!/0 !#" "# !+)± %A3+)0$!$#*4 & ; & 4 A6&54 )". & 2 )*,) = /@/*,)'8+nA#'&3+& ):!$4 A3 !c4 t~ & + &a&(,&58 3+)A!! = /0&>3 A!$#:#*# )A!$A, 8 "!*!*&(,4 ! + &E4 !9A,&b>t&>,&(8 3+)A! *!*!*&(,> !9@3& = &E4 )0$,#/&E3+&(4)A, &5# 47&(& b +g' H R / MI m ! 8>A4& )".a3+&(A,,r 4 = A,, 4,A!$#*4 &Tl#$"! +t~ )A! #;*& ) + &T8d):!;:$!*& = &(! #') = !$ &(4 n , :& !T ) = 4>s ∆

J5 9< , = ):4 !*)cA#*# )A!", 8 A!*!*&>,4 "3+&&d1'60&(8 &(# ) /&D):6&(!*&(# +* ! &D4 !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9 3& = &D4 !$8>& &`4 !9:,&> &(,&58 3):! &>1*8 + ):!T&>!*&(3 &54$4$A,,r&>1*8d&>&5#*4 &G8d,A4+4 8>A, 4 !9:,&>&>,&(8 3+)A! 8 "3 !9 &>!*&(3 4&>& b g' H R 8 d & = ! 4+8d&(!$8d&54@)". &D&(,&58 3+)A!9>&>,&(8 3+)A! ! &(3+:8 )A! ! &

>t&>,&(8 3+)A!4'4 & =O= 4 ,, #'&(, r &(3 ,) >t&>!*&(3&d1*8 )A!4 m ! &<8>A4& &<l#$A! = #') /0&(8d) = &(48d) = 6*,& &(,t& = 6 )A.f8>)A!$#;8 )A!9>/"!$#B&>,&(8 3):!$4 + & 2 )0$,) = /B/$,)'8+nA#'& 3+& )A! F | 4f!*) 8d,):4&(#B:4 !$# 8( &5# ! b +g' H R # H$8 D 3+A!$46):3 46&58 3+ &>3+&E)A/$4&>3 &5#/ ) &(! ) &(! < $4 > !9S ; A3$8 aA!$#@8d) )A3A&>3?4%o g r H$8 2 )0$,) = /;>t/*,)]8+n:#'&-3+& ):!':& 4 !@6*3 !9>8 6$,&@8d,):4&(# /# !9)0 & :$3?4 &>,&(8 3+)A!T.3+) = + & ",&>!$8>&`/$A!$# Fy| s; &B# 4 "!$8>& ! &GA#*# + ):!T&>!*&(3 &54 ^ F H % ^ F | /&58d) = &54C"/0)0 + &E3+&>, r &(,tc,"3A&k4& = 8>)A!$#9$8 )A3 m 4 /$A!$#;:A6&(!*&>30 ?A $%CB@7 $"/0OB@:9;"< <9>7BO1 O1 BB 1% FDE %!"$9J4 & &CA,3+&(:#;`6$3&547&(! &(# ! b +g* R 8d)A!#;$8 "!$8>& = &(:4$3& = &(! 4 &>3?44 ^ ^ + 2 | .)A3 A3 !9"! A6*6*, &5# = :!*& + 8%:&>,# &B.)0*!# C+ &`# 4> "!$8>& ! & 2 )*,) = /T/*,)'8+nA#'&`):4+8 ,, + ):!$4 "3 &54 = 0A!*& 8°:$&(,# s Z A8 2OX 6&5 4 * . 44, : ,t # 0&(3&(! ,r0 & 4 ) 4 8 "3?A8 &>3 4 8 m = 0A!*& 8:&>,## 4760&>3?4 ):! m b *3 + &>3 = )A3+&0 &k60&(0 & 4 ! + & 2OX 4 "3+& = )'#;*, &(# ; &&0&58 4@A3& !#'&>60&>!$#*&>! )".C60):4 +t &):3`!$&: r & = A!$& 8 :&>,# ):3 &>! >+ ):! b 3+) = &547&E):/$47&(3 )A!$4 &E8>)A!$8>,t$#*&As < 6*6*,r !9c = A!$& 8 :$&>,# ) &l#$A! = #') 4'4 & = 8 "!ªA&(4 + & &(!*&>30 4760&(8 3 = )A. & &>,&(8 3):! 4'4 & =8>)A!;:!*&(# ! &al#$"! = #*) ; * 49,&(:#*4 )`8 A!9A&54 ! & 3?"!$4 + ):!c&>!*&(3 &54/0& j &>&(! + & >BA!$# & H > &(,&58 3):! 4'4 & = ! & l#$A! = #') .):3:$1]&5#c&>,&(8 3+):4 86) &(! + A,4 ^ p )A! &k4$33+)0*!# !ª<&>,&(8 3+)]#*&(4 ; &k8 "!ªA& ! + & 3?"!$4 )A!&(!*&>3 &(4 H 4 ^ p 4 % 4"! ^ p 4 !$#;$8>&(#/#+ & = 0A!*& 8:$&>,# Kh8("! /0&8d) = 6&(!$4 &5# / 8 "!9:& ! "! "6$6*, &(# : & )A, 0A&0$.)A3 !$4 "!$8>&0 ^ ; &(3&>.)A3+&0 & ",r*&(4^)". &c"6$6*, &(#: & )A, 0A&^ * 8 .`*,t:$,, &E3&547):!$"!$8>&^8>)A!$# + ):!$4

H 4 ^ 4 ^ + 4 % 4"! ^ 4 ^ + 4 F ^ . 4 g' 0 H 4 ^ 4 ^ + 4 % 4"! ^ 4 ^ + 4 F ^ 4 g' ML.):3B):6&(! !ª 3?"!$460)A3 8 "!$!*&>,4h"3+&4 * . &(# ",)A!9 + & ^ "1 4 :[ 8 Z *&(! VAE

o H l r #'& = ):!$4 3? &5# * 4 !$#c)A. 3+A!$46):3 460&(8 3)48>)A6 ! = :!*& + 8:$&>,#

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DSeV

(a) (b)

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Magnetic Field B [Tesla]

-4

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Magnetic Field B [Tesla]

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'"9+ )ª+#±+± ¥ ± ) ! "/,+)!M " 0 ±1/01+ !"³ ³ ! "# ! )t± #))!+)]% 0#) %* ¯ ( -J.# °g&,g± % r## ) F v ° "# #+)± #" 7 17# ¦ ¬ r±0 !0&,+ $) " ) . ¦ ¬ r ) 7 ¦ ! +" #+,&+&;#±o ± ¥ ± ) -J.#) O3# ± ¥ ± ) ¯ - ¬ ³ , , ! !±0 +! Y±0+"+/ ! "±01=+ &ª] ¦ ¬ &H+)!+,%1/01+ ++0+³ ¦ ±L0g±Et ³ + !)³' I ¬ ! H L2L H ; & = :!*& + 8:$&>,# A4)A3 &(! &(# 6&(360&>!# 8*,"3 ) + & 6*,"!$&)A. + & 3 R i l"! = #') 3+&(A, r~ &5# ! "! < , 3k < 4/63k < 4> & &>3+):4 3$8 *3+&/46*, > &54 i *& ) + & &( 8>)A!;:!*& = &>! < ! &c6*,"!$&3?B ? Q FHG W;EtAB ) &= :!*& + 8:$&>,#)A3 &(! + ):!#*&b:$!*&5# / &k46*, > &C&>,&(8 3+)'#'&(4 &k4760&(8 3 = 4-#*) = ! &5# /@)A3+/ ",0&b &(8 4 ; & = & )'# A4-/&(&>!K47&5# /c47& &>3?",SA3+)0*64 ) &d1'6*,)A3+& + &&(,&58 3):! 84 38 $3&)".Cl#$"! = #') 4 ! $ = A!$& 8 :&>,# .)A393+& ] & 47&(& .)A3 !$4 "!8d&<o H l g r d m ! b g* H A4) = &)". )0$39) !c#* A3&c4 ) ! .3) = + &l#$"! = #') 6*3+&(4&>! &5# ! b +g* H &>3+& & = 0A!*& 8:$&(,# 4 A6*6*, &5#?9ABAEEE ) + &B6$,A!*&E)". & j )0>t# = &>!4 )A!$A, &>,&(8 3+)A!T4'4 & = i *& ) &c4 3+)A!9 8d)A!9:$!*& = &(! .)A3 + & R i&Z H ! + & A3+) # 3+&(8 + ):! )A. & & &(3)4 3$8 *3+&0>)A3+/ ","&0&58 4_A3&9# = ! 4 &(#B"!$# + &9):/$47&(3 &(# = :!*& + 8=:&>,## 46&(3+4 ):!$4k"3+&`,&(4+4k8d) = 6$,&>1] A,,) !9 )D# 4+8b$4+4 &c6$3 !$8 6*,&(4^)". 3?"!$460)A3 46&58 3)48>)A6 + A6*6*,r !9c = :!*& + 8 :$&(,# m ! b +g' H + &<# 0&(3&(! ", 8>)A!$#;8 A!$8d&<#8* + # ^ + = &(:4*3+&(# ^ + F| = ; 4 6*,) &(# !A3+&'48(",&CA4 E.`$!$8 + ):!)". &^/$A8+ & )A, 0A& ^ "!$#c)A.

³ #&;,-;+,,+L/E/1,)!/0 !#" "# !+)± + & = A!$& 8M:$&>,# /0& j &>&(! % H g ; "!$# H g ; ! | [ g ; 4 &>64 K m ! b +g* H /4 = ,"3 = &(A4*3+& = &>! 4 A3& 4 ) ! .):3 ^ + F % | [ p = ; m ! b ?g' H / &/A8+: &b> ):, :&^3+& ):!$4 &(3&G4 !9A,&b>t&>,&(8 3+)A!;> $!*!*&>, !9 )'8>8*3+4 "3+&B/*3+)::#>&(!*&(# 4 !$8d& &D# 0&(3&(!$8d&/& j &(&>! + &&(,&58 3+)'8 & = 8>A,%60) &(! ",4<)". & = &>3A!$#W8d):,,&(8 )A3 A4</0&>&(! !8d3+&(A4&(# < #*# )A!", 3+A!$46):3 8 A!*!*&(,4<#9*& ) &>1>8 &(# 4 &(4@)". &Tl#$A! = #*) /&58d) = &T:8>8d&544 /*,&D"!# + & = 0A!*& 8:$&>,## 46&(3+4 )A!$4`)". ^ .)A3@):6&(! !ª + &(4&T8 "!*!$&>,4`/ + &D3&547):!$"!$8>&8>)A!$# )A!4 g' 0 A!$# g' ML "3+& ] 4 /*,& ; & = 0A!*& 8 :$&>,# /& ] )*3 4<4 =@= & 3 8 !8 "!9 !9 &<4 A! )". & = :!*& + 8e:&>,# ; &*6*60&>3 "!$#B,) &>3h/0)0*!$#$"3 &54 ^ + A!$# ^ )".*&5A8 4 !9A,&b>&>,&(8 3+)A! *!*!*&(, !9 3& = &4 ) + &D4 = & = A!$& 8 :&>,# # 4760&>3?4 ):!A4@6*3+&(# 8 &(# / 8d):!$# )A!$4 ^ ^ + 4 ^ + 4 F ^ + %3&54760&(8 r &>,r^ ^ 4 ^ + 4 F ^ &(3& + &a# &>3+&>!$8>& ^ % ^ + F f ^ + f 4 FRQ,? Q Q=VB)". & = A!$& 8 :&>,# "!# #'&b:!*&(# /# + & &d1 &(3!$A,,r"6*6$, &(#D#'3? !;>47)*3+8>& )A, :& ^ + o H 2L r ; $ 4 4 + &c4 = & = :!*& + 83:$&(,# # 4760&>3?4 )A! * 8 4k)A/$4&>3 &5# % "! 4 $ !9:,t4 = ",, / A4 ):, :& f ^ + f ! b +g* H ; &° !9'4 )A/$4&>3 "/*,& ! b g' H `8("!/0& #'&(! + :&(# 8d3+):4+4 !9:4 )".$# 0&(3&(! = :!*& + 8 :$&>,#<# 4760&>3?4 ):!$4 ! b +g* H / = "3A&(#/A33+) 4 d ; &>3+&d.):3&; !9'4 ! & = 0A!*& 8e:$&>,#D# 460&>3?4 )A!D)". &/0)0$!$#*"3 &(4 ^ + "!$# ^

)A.T4 !9A,&b>t&>,&(8 3+)A! *!$!*&>, !ª 3& = & !# 8( &8 "!9:& ! & 8 A3+:8 &>3@)". & :3)*!$#*4 & )". & ><)A3 H >t&>,&(8 3+)A!4'4 & = 8 A!9A& ! &`l"! = ! = /0&>3?4 s ; & A3+)0*!#*4 &^)A. &Bl#$A! =#*) C 4a#*&A&(!*&>3? &E& &(3 .):3 & > )A3 + & H > &(,&58 3+)A! 4'4 & = &(4&= 0A!*& 8M:&>,# A,t*&54 & 4 | F 4"! Mi &>3+&>! = :!*& + 8e:&>,# # 46&(3+4 )A!$4A3& ] 4 /*,& ! b +g' H / m !D6*3 !$8 6*,&0):!*&D4 )*,# /0& A/*,& ) #'&(3 r &.`*3 &(3 !'.):3 = + ):! A/) `+ & = A!$& 8K:$&>,##*&>60&>!$#'&(!$8d&k)A. & 3+A!$4 + ):!&>!$&>3 &(4 H 4 ^ p 4 % 4"! ^ p 4 /0& j &>&(! 4 &(4G)". + & "!# & H >t&>,&(8 3):! 4]4 & = )". + & l#$A! =#*) .3+) = 4$8 = &(:4*3+& = &(! 4 ) & &(3 ! ! &>3+6*3& !9 &a4 * . )A. ^ ",r*&54 K .`*,:,,4 + &<8d):!$# )A! g' 0 )A3 g* 2L: ):!*& :4 )@/&<8("3+&d.`*, sI ! &):!*& A!$# & = 0A!*& 8:$&>,#c8 "!ªA&(4 + & 4 &(4 )A. + &Cl#$A! = #*) I ! + &@) + &>3 "!# + & = 0A!*& 8 :&>,# ",4) 0&58 4 + &c4 &54^)". + & R iZ H&>,&(8 3+)'#'&(4*A8 !9cA4,&(:#*4*A!$# )". & = & ", &>,&(8 3)'#'&54$4&(#DA4 &54>s ; &&>,&(8 3+)A! 8^4 &54 )". + &k&>,&(8 3+)]#*&(4"3+&C&(!*&>3A& 8>A,,r 4 $ . &(#D"!$# &<#*&>!$4 )".f4 &(4 4 8 "!ªA&(#/ & = 0A!*& 8 :$&>,# ; &-, &>3f&0&58 8>47&54_^8 "!ªA& ! & &>,&(8 3+):4 + 8%&>! ] 3+)A! = &(! )". & l#$"!9> = #*) s < 49# 4+8b$4+47&5# ! 2 A6 &(3 + & # 0&(3&(!$8d&54 )". & E+G VBD T V1A VFHG 60) &>!;>+ A,49)". &&(,&58 3+)'#'&(4%"3+&Q]D V= r &(!`/ & &>1 &>3+!$A,*&>,&(8 3 8(",*8 3?8b "):!*,r &# &>3+&>!$8>&(4 )A. + & E+G V BDG FHG+AE 60) &>! ",4 )". + & &>,&(8 3+)'#'&(49A3& t &>!@/ & 2VB Q@AE*A??@E!F )A, :&(4 ^ ^ + '& 8 d m ! 3 !$4 8^8>)A! :8 ):, A&54%/0& j &>&(! G UL. ) ± '"9 )+#±+± ¥ ± ) ! /)0 +±&+ ¥ ) v ) S ³

³ #&;,-;+,,+L/' % + &&>,&(8 3+)]#*&(4f,&(A# )kE4 * . )". &C&>,&(8 3)4 + 8 60) &(! ",')". &Cl#$"! = #') / p d ∆ ^ p M ; 4 + &# &>3+&>! ", 4 * . ^ d # )A. + &A6*6*, &5# & )A, :& ^ 3&5l 3+&(# )T3+& = !W E &c3&547):!$"!$8>&`60):4 )A! .)A3<):6&(! !ª 3?"!$460)A3 8 "!*!*&(,'8("! /&E):/ !*&5# .3+) = g' 0 g* 2L: "!$# &<4 * . )". &&(,&58 3+):4 8C60) &>! ", )". + &E&>,&(8 3+)'#'&(4 = :!*& + 8 :$&(,#Wo R H A H g" r s d ^

F H 4 ^ 4 ^ + 4 % 4"! ^ 4 ^ + 4 % d " p

p d ^ p [ g' | ; &k&544&>! ", 3+&(4*, )". g' | 4(s; & = &5A4*3+&(# = :!*& + 8':$&(,# # 4760&>3?4 ):! )". &c"6$6*, &(# : & )A, 0A&^ .`$,:$,, !9 + &c3+&(4)A!$A!$8d&c8d):!$# )A! .)A3<):6&(! !9TD!*& 3?"!$4>6):3 8 "!$!*&>, 4D#;*& ) + & 8 "!9:& ! H 4 ^ 4 ^ + 4 % 4&! ^ 4 ^ + 4 :*1'&(# &(,&58 3+):4 8 6) &>! + A,4 ^ p 9A!$# #;*& ) &k8 "!9:&(4 ! + &E&>,&(8 3+):4 + 8^60) &>! ", )A. &<4*3+3+)0*!$# !9G&>,&(8b> 3+)]#*&(4-/# "3 )A!$4 ! &^8d)A! A8 ):, A&54 !$#;$8>&(#c/ & = A!$& 8:$&>,# ; &(3&>.)A3+&0 . ^ p 4 *!9]!*) ! & ! &>3+6*3+& )A! )". & = &5A4*3&5#= :!*& + 8o:$&>,#<# 4760&>3?4 ):! ^ 4 # 8b*, K x) & &>3>4 !$8>& &%,A4 &(3 = ! g' | 8("!</0&%3+&>6$,:8d&(#^/%$4 !9 d ^ p F ;^ p . t &(4_ 8d):! 3 /9 + ):! )a",, = A!$& 8:$&>,#B# 46&(3+4 ):!$4 2 ):!$47&5l#*&>! ,r053+&>, A/*,& !'.)A3 = )A!`"/0)0 h &= :!*& + 8 :&>,# # 46&(3+4 )A!W)". H 4 ^ 4 ^ + 4 % 4&! ^ 4 ^ + 4 :*1'&5# &>,&(8 3+):4 8C60) &>! ",4 ^ p 8>A!/0&a):/ !*&5#/ G# 3&58 8d) = 6$A3 4)A!)A. j ) = 0A!*& 8M:&>,# # 46&(3+4 )A!$4

.1%-9!57(*0 % , 8 49;"3 $% ?_ %&CB@7 3" ? $, )+%,"$- ./"$m . &>1'8 &(# 4 &54<)". + &&(,&58 3):! 4'4 & = ! &Dl#$"! = #*) /0&(8>) = &:8>8>&(4>4 /$,& $4$",,t & 8*33+&>! c+ 3)9 & l"! = #') 4 !$8d3+&(:47&5# 7X c$ 4 4^!*) k 3*& !W",,98>:47&54a:4 4 /*,& ! &G&>1'6&(3 = &>! A,f#$ )". b ?g'qg &>3+&!*&: r &# &>3+&>! ",8d):!$#;$8 A!$8d& )'8>8b$3+4(s ; &&(,&58 3 8>", 3?"!4760)A3 4&>& = 4 )/0&4*6*6*3+&(4+47&5# /# A8(8d&(4+4 !9 8>&>3 !W&d1*8 &(# 4 &(4 4 +* 4<60):4+4 /*,& m !+ &k3& = &a)".f4 !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9S &k! = /0&>3)A. &>,&(8 3+)A!$4 ! + &El#$"!;> = #') ª$8 $ &(4k/ )A!*&c#;*3 !9D&>,&(8 3):! 3+A!$46):3 < :$! &#'3? !;>47)*3?8d& )A, :&0&>,&(8 3):!$4^)".-# &>3+&>! &>!*&(3 ! &@& = 7 &>3E"3+&`8>) = 6& !9 ! &>! &(3> !9 &cl#$A! = #') A!$# &>,&(8 3):!$4^)". # &>3+&>! &>!$&>30 ! + &cl#$"! = #') = !o !o+,/#++ : ' 7 M ) ' ' +1 ¦ ,++) ! ¦ 0³ ¯ ¬,¬ .0 ³ ³.0 " Y °+)!+,1 ! ;+ ) ) ' !" $ +Q/. ° #"°o % + ° !g); ) ' @ +)!+,±0 ³

³ j/0 ° = - ")!&(), #&;, = " ## A3&8d) = 60& + !9 .)A3G,&( ] !ª &Dl#$"! = #') G ) 8d)A,,&(8 )A3 ; & &>,&(8 3+)A!$4`"3+&G+D ? V FRQ o H # r :4 !$8d& $ ! + &3+& = &)". 4 !9:,&> &(,&58 3+)A! $!*!*&>, !9<)A!$,t7D Q &(,&58 3):!W8("! $!*!*&>, + = &:s i *& ) & 3+&>6ª*,4 r &c&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3>:8 + ):! *!*!*&(, !9 )".%&(,&58 3):!$4M4 !9D# &>3+&>! 8 "!$!*&>,4 4^!*) k !$#'&>60&>!#'&>! )".&5A8 ) &>3 D Q KE!F _VF T%FRQ G B V1AFRQ GbFRV T V1A V T 'F <VE+A V1DCbErDG FRQ D TgFRQ E S E+G V BD Q*VW3QQbEFRQ AV BD W V D V bB°G 9A Q=Q E T ; &^#9! = 8(4%)A. 4 !9:,&>&(,&58 3):! 3?"!4760)A3 a+ 3+)09 l#$"! = #') 4 ,, /0&c# 4+8b44&(# ! &`.):,,) !9/A4&(#)A!D = :4 &>3&(l#$ )A!D"6*6$3)A8 $-.- L&%\X#N L9\THP@V KV %L;\ (1PSN X'%UNT`O=THV \ YX VYL9Z TU% P (" THV @RHX eRHXU\NPSV NL9V % # PªN \< :$3?4 "6*6$3)A8 D ) &G#;]!$ = 8(4a)A.%4 !9:,&> &(,&58 3+)A! *!*!$&>, !9 ! l#$A! =#*) 4'4 & = 4@ = A4 &(3`&5l )A!4`A!$4 ~ o R HAH g L H " rts < . &>3@6*3+&>6$A3 !9+ &@l"! = #') k ! &@4 & f 4&! ^ p' &cl#$"! = #') 4'4 & = #'& &>,)A64 !D8 "!9 !ª 44 &E/0&(8($4&I 4 !9:,&k&(,&58 3+)A!4 A3&k&(! &>3 !ªªI 4 !9:,&k&(,&58 3+)A!4 A3&k,&( ] !9ªI &<&>,&(8 3+)A!D4'4 & = ! + &Bl#$A! = #') 3+&>,n1'&(4 )c4 &E)". ,) &(3&>!*&(3)". &<4+ = &k&>,&(8 3+)A! ! = /0&>3')A3I &E&>,&(8 3):! 4'4 & = 4&>1*8 &(# ) G4 &E)A. * &>3&>!$&>30 )A.f4+ = &k&>,&(8 3+)A!! = /0&>3 ; &(4& 3?"!$4 )A!$4 8("! /0& #'&548>3 /&5# / 3? &(4 t] !9 & = & 4+8>A,&D.):3 &3+&(460&(8 +t &^8 "!9:&(4 H$8 3+ &(48("! /&<#*&>3 t &(#.3) = b &(3 = m 4:)A,#'&>! 3*,&co L r < 3?"!4 )A!c.3+) = + &k4 & f 4"! ^ p ' ) f H 4 ^ p ' 4 & &>3 !#;$8d&5#/E"!B&>,&(8 3):!<&>! &>3 !9C.3) = & 47)*3?8d&%):3 .3+) = + & #*3+ !B4 #'& X ) +E *!$!*&>, !ª6$3)'8d&544&(4 )]8(8b*3e*!$#*&>3^&>!*&(3 8>)A!$4&>3 )A!D/0& j &>&(! ! + A,fA!$#7:$!",f4 &B)".+ &4'4 & = & H 4 ^ p % 4"! ^ p % J F | &(3& J #'&>!*) &54+ &k&>!*&(3c)". &k&>,&(8 3+)A!&>! &(3 !9 ; & VW3QQbE!FRQ BA V

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³ j/0 ° = - ")!&(), #&;, = " ## + & ! ", 4 & .):3 + &C.):,,) !9 *!*!*&(, !9G6*3)'8>&(4+4 4-A, '4 & :3)*!$#*4 &)A. + &k3&54760&(8 r &^&>,&(8 3):!4'4 & = & 4A4+4 = & X &>1*8 &(#D4 &(4 )A. & > &(,&58 3+)A!4'4 & = "!$#\)A. & H > &(,&58 3+)A!4'4 & = "3+&^:8>8d&544 /*,& ; &= :4 &>3 &(l#$ )A!$4 /0&(8>) = &°*!$#'&(3 4 + ):!$"3 8d):!$# )A!$4.):3 &°:3)*!$#*4 &^)". & >t&>,&(8 3+)A!D4'4 & = s|BF # 4 | # F

Lc +

KMLc d H 4 | % .

Lc +

K?Lc d 4 | "

c

Lc

L d 4&! 4.):3 & X &>1'8 &(# 4 &(4)A. & > &(,&58 3):!4]4 & = H ! X s

|BF # 4"! # F L +

KMLc d H 4 | %

Lc

L d 4&! 4.):3 &°:3)*!$#*4 &^)". & H >t&>,&(8 3):!4'4 & = s|BF # H 4 | # F .

Lc +

KMLc d 4 | %

Lc +

KMLc d H 4 | "

c +

KMLc +

K?L d H 4 4.):3 & &>1'8 &(# 4 &(4)A. & H >t&>,&(8 3+)A! 4'4 & = H s

|BF # H 4 # F . Lc +

K?L d 4 | % +

K?Lc +

K?L d H 4 4 + &<8d):!$4 3+ !

" # c

H 4 " # c

4&! F H [H')A, !9`.)A3 4"! ].3+) = g'qg" + &<4 + ):!$"3 8b$33+&>! 4#*&(#;$8>&(# )* . 4 X F

+K

4 &>3+& +

K F " # c

L +

KMLc Y

K4

F " # c

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KML Y

K[ g'qg p ; & &>3 = 4

"!# +

K 8("! : ! /0& ! &(36*3+& &(# A4 + &D, .& = &(4c)A. &3+&(460&(8 +t & 8 "3A&c4 & ! &l#$A! = #') &5A8 A#$# + ):!$",-8 "!*!$&>, + &<8b$33+&>! 4 !$8>3&5A4&(# /

I ³ #&;,-;+,,+L/' %

* . H 4 X % * . 4 X F d . +Kd" # co r d "

# co r "

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# co r . + K d " # c o r "

# co r 4

* . 4 X H % * . 4 X F d +Kd" # c

o r d " # c

o r " # c

o r " # c

o r + K d " # c o r " # c

o r 4

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o r" # c

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KMLc 4

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KML +K 4

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L +K +

KMLc [; & !$8d3+&(:47&k/0&(8>) = &(44 = 6*,&k.)A3 &>3 A4 =G= & 3 8 $!*!*&>, /$"3+3 &>3?4(s K Nb )A3 .

Lc +

KML

L +

KMLc 4 "!$# 2 X 4 + &>!* . H 4 X % * . 4 X F d

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KML 5

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KMLc 4 "!$# 2 X 4 + &>!* . 4 X H % * . 4 X F d

L +K +

K?Lc [

) ) ! &>3+6*3+& &k3+&(4*, g'qg p X c)A60&>! !9cA! :#*# )A!$A, 8 "!*!$&>, )A! && = 7 &>3C4 #'&0 &<3? &k.)A3CA!D&>,&(8 3):!D&>! &(3 !9 &Bl#$"! = #') C 4 !$8>3&5A4&(# ; &(3&>.)A3+& + &, .& = &

! * 8 B+ &l"! = #') 3+& = !$4 !G >t&>,&(8 3+)A!4 &0 4a3+&(#;$8>&(# 0i $& ) & !$4 A! "!$&>)04 3+&>,n1* + ):!*!*) * !9 :4C8 A!9A&5#.):3 &>,&(8 3):!$4h,&5 ] !9 & l"! = #') 4 !8d& .)A3 +* 4 & ! ",$4 & 4 4 ,, &:3)*!$#*4 & )". & H > &(,&58 3):!`4]4 & = s &, .& = & +K ! & H >&(,&58 3+)A! 8 "3A&C4 &C3+& = !$4Q*!$0&58 &(# + &k4 = F

+K 43+&(#;8d&(#*"!$# &(3&>.)A3+& &<8*33+&>! * . F !$8>3&5A4&(# 47&(& b g' H / MH = ,"3 ):6&(! !ª<"!cA#*# + ):!$",*8 A!*!*&(,')A! & 8>)A,,&58 )A394 #'&:s ; &3? &.):3<"!W&>,&(8 3+)A! ,&5 !9 &l"! = #') E 4 !$8d3+&(:47&5# 3+&(#;8 !9 & , .& = &

+K )A. + &Cl#$A! = #*) /0& !9 ! H > &(,&58 3+)A!G8 "3A& 4 & Ai *& ) & !$4 "! "!*)$4%3+&>,n1* )A!c.3+) = + &k&d1*8 &5#4 &^)". & >t&>,&(8 3+)A!4'4 & = & ! ", 4 &a.):3A#*# !9@"! &>,&(8 3+)A! .3+) = & = &>3 4 ", '4 &%:3)*!$#*4 &C)A. UL. !,#) ±+, ;+*), =)! g !#+, ± ± ) ¥ ; ! +17 !. #)! @.1 g,% !1 !+± $ +± !"³/³g3± !"³/³Lv1,#"°1/0 ° °, !##+)H#, !*e °)9, ")!&H+)!+,,, 1g³

³ j/0 ° = - ")!&(), #&;, = " ## + & >t&>,&(8 3):! 4'4 & = & &c, .& = & ! & &(,&58 3+)A! 8 "3A&@4 &3+& = !$4*!$ &(8 &5# !X C + +K &G4 =

F +

K 4 3+&(#9$8d&5# 0A!$#+ &>3+&d.):3& &<8b*3+3&(! * . F !8d3+&(A4&(# 4&>& b g* H 8 d &`8("! 8d):!$8d,r$#'&:s !$4 A! "!$)0$43+&>,n1* )A! + &`8*3+3&(! 4 !$8>3&5A4&(# &(:8 A#$# + ):!$",'8 A!*!*&(,'/&58d) = !9k ,"/$,&-/&58>47& & 3? &%.):3h&(! &>3 !9 ,&5 ] !9 &al"! = #') % 4 !8d3+&(A4&(# ) A3+#*4 + & ):!*& 3+&(4&>3 ) 3 &>3+&(:4 &3? &E)".9,&( ] !9 &(! &>3 !ª ) &B) + &>3a3&547&(3 ) 33& = !$4*!$0&58 &(# s ; &B, .&+ = &a)". )A!$&a8 A3:& 4 & 4 4 )A3 &(! &>3+&(:4 + &C, .& = &C)A. &^) + &>3-3& = !4$!$8 "!ªA&(# ; &B4 $ + ):! ",,) 4 ) #')460&(8 3)48>)A6 )A. & > "!# H >&(,&58 3):!4]4 & = !$#'&(6&(!$#'&>! ,t A4 r &(! ! b g' L*H !$8>& ! &G#* c)". b +g* g !*&: r &<# 0&(3&(! ",f8d)A!#;$8 "!$8>&E)'8>8b$3+4 & & )<8>)A!$8>,t$#*& 9$ 4 4 !$) 8>) = 6*,& &(,t 3*&.):3 &al"! = #') 4'4 & = &>3+&

TH\ YP \ XRHL L;\THP@V - + )0 . A4 "!$#D8d) = 6*,& &k3+&>,n1* + ):! &

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L .

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f 4 | ' f H 4 ' f 4 | ' .)A3 | 4f H 4 | ' f 4"! ' f H 4 | ' .)A3 ! | 4A3&k",,) &5# & .

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|BF # H 4 | # F . Lc +

K?Lc d 4 | % "

# c

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Lc +

K?L d 4 | %

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K?Lc d H 4 | % "

# c .

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KML d 4 | 4.):3 & X &d1*8 &(# 4 &54)". & > &(,&58 3+)A! 4'4 & = H ! X s

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KMLc d H 4 | % .

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[H]):, ] !9 & = A4 &(3 &(l#$ )A!$4 /#^&d1'6*3+&(4+4 !9 H 4 | + &-4 )A!$A3a8b*3+3&(! 4 3 7 &>!TA4* . 4 X F d

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³ j/0 ° = - ")!&(), #&;, = " ##

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Lc +

KML +K r Y K )".04 & f H 4 H ^ p ' &>1'8>&>&5#*4 & = &("! = &

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L +K +

KMLc * . 4 X [

& $4A&(!*&>3?", r~ &As & A4+4 = & "! A#*# + ):!$", 8 A!*!*&(, !4 Z )A60&>!4):! + && = &>3 4 #'& 47&(& b +g' H gAd + )0 3+&>,n1* + ):!f"! &(,&58 3):! :4 ),&( &T4 "3 !9 + & ! ",^4 & f H 4 ' m . & 3+ &D.):3#') !9 4) 4,) + &>! &Gl"! = #') 3+& = !$4 ! + & H >t&>,&(8 3+)A!T4 & f H 4 'A!$# &c, .& + = & +K /0&(8>) = &(4k,)A!9TA!$# = & &(! &d1*8>&>&(# ", # + )0 +* 4 :#*# )A!$A,08 "!*!*&(, m ! 4$8 B8(A4&0 &E4 !9:,&> &(,&58 3):! 3?"!$46):3 - 3+)0ª + &al#$A! = #') % 4-/*,)'8+A&(#@,&(:# !9 )<!*& +t &C# 0&(3&(! + A,08>)A!$#9$8 "!$8>& +):6&(! !9 !4 Z X h )^)A/ ! +* 4h&0&58 f 4h!*) !*&58d&544+"3 _+ & l#$A! =#*) 3& = !$4 ! &k4 & f H 4 ' 47&(, .js X 3+&>,n1* )A! + & H >t&>,&(8 3+)A!4'4 & = = : &>!$# ! A! &>!*&(3:& + 8(",,t,) &>3C4 & f H 4 ' 4&>& b g' H g /

N+1,k

N,l’

(a) (b) (c)

N N+1 N N+1 N+1 N

E(n,k)

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(l,k) E (l,k) E (l,k) E

J >;+# !#"3 e,#, ! ¦ ¬ ().ª %, !#")!&H+)!+,,#&;,M ° " ;#)!TOg± ;+g#, ¦ ¬ 1# ±e+ r .)!#". ! ° $ . ¦ ¬ - ± )t ?0g±Nr $ .1 $ )!"K)! 'v ! °L. ¦ ¬ 0# ±0 !,# v,g± % #?0+ g±'1 $ % $ +)!+,1/1 ± 1 O !#" ³L,Q)!) +,= +)0++,,+ ! !)))!g±e+" b $ ± '"9+ )+#±## >;±) ! ¦ ¬ (o³

³ #&;,-;+,,+L/' % .3+) = &(3& "!`&>,&(8 3):!B&548("60& )E8>)A,,&58 ):3 4f#'&>6$3&544&(# m 4fA,4)C60):4+4 /*,& + A!E&d1*8 &5#<4 & f 4"! ' )A. & > &(,&58 3):!<4'4 & = 4 3+&(:8 &(# 4&>& b ?g' H g 8 A!$#.3+) = &>3+& + & 3?"!$4 + ):! )@"! H >t&>,&(8 3+)A! 4'4 & = 4-/$,)'8+A&5# H !$8d& &4 & f 4"! ' A4h/0&>&(!G3+&(:8 &(#B/ &4 & f H 4 ' & /$,)'8+ !ª^)'8(8b*3?4 +):6&(! !ª + & 3?"!4 )A! !4 Z H = ,"3C8>)A!$8>,t4 )A!$4 8("!D/&<#*3+ !.)A3 ):6&(! !ª:#*# )A!$A, 8 "!*!$&>,4-):! &<8>)A,,&58 ):34 #'& ? %&%4% DE#"3 8 4-F4%,"$ 4 " ?A $%< "3%#"34 * ! + & 2 ):!$4 "! m ! &>3?A8 )A! [ )'#'&(,24 !9:,&> &(,&58 3+)A! *!*!*&(, !9 4h#'&548>3 /&5#/ 3+A!$4 )A!4E)".4 !9:,&c&(,&58 3+)A!4^.3) = D4 !9:,&> 6$A3 + 8>,&c4 & ! &c& = 7 &>3 ) "! *!*)'8>8*6 &(# 4 !9A,&b>t6$A3 + 8>,&4 & ! &Dl#$"! = #') "!# &>! ) A!*!$)]8(8b*6 &5#<4 !9:,&> 6$A3 + 8>,&94 & ! + &-8>)A,,&58 )A3 m . &T ?ªA V FHAE*) &>3+,A6a/0& j &>&(!4 !ªA,&b>t6$"3 8d,&-4 &(4 ! + & l"! = #') "!# ):4& ! + & ,&5A#*4 4f# &>3+&>! .)A3+ &c# &>3+&>! 4 &(4^)". & l#$A! = #*) + &>! & *!*!$&>, !9 = 3 1 &>,& = &(! "3 &(4 m = ,&5A# )k!*& r & # 0&(3&(! ",'8d):!$#;$8 "!8d& . &46$ + A,') &(3,"6)A. "!W&>1'8 &(#W4 !9:,&> 6"3 8d,&G4 & 4k,) H<< ; ) !$4)A!W"!$# 8d) )A3A&(3+4Go H g | r ! H LML R Mi &A&(!*&>3?A8 ! + &G&>!*&(3 46&58 3 = )A. & >t&>,&(8 3+)A! 4]4 & = 4 n /#T46 !#'&A&(!*&>3?A8)A3a)A3+/ ",h#'&:&>!*&(3+:8b #;*& )3) + ):!$",_4 =@= & 3 n ",,) 4.)A3= )A3+& 60):4+4 /*,& 3+A!$4 )A!4 4+ = & &(!*&>30 H]& &>3?",^8 "!$!*&>,4A3& )A60&>!*&5# !6$A3+A,,&>, ],&5A# !9 )cA! &(! A!$8d&5#4 &(6;> , A&E8 "!ªA&k)". &<8*33+&>! i` & ! = "!*! VMAE

o H gn rf6) ! &5#T)0 C+ &`46 !T)A3 &(! + ):! 4 $4",,t8>)A!$4&>3 &5#C.):3h *!$!*&>, !ªa6*3+)'8d&544 ; &(3&>.)A3+&9!*) ",, 3?"!$4 + ):!$4_/& j &(&>!B4 &(4)A. + & "!# & H >t&>,&(8 3+)A!@4'4 & = "3+&60):4+4 /*,& 2X GA#*# !9BA!@&>,&(8 3):! ) & l#$A! = #') ):3 0 !9 )0 "! &>,&(8 3+)A! .3+) = + & l#$A! = #') &&(,&58 3+)A!! = /0&>3 8 A!9A&54 /#c):!*&0 + & ) A, 476 ! )". + &k&>,&(8 3+)A!D4'4 & = ! &l#$A! = #') / K "!$# + &<476 ! 6*3+) Pj&(8 )A! / K s$ 4"! KF $ H 4 4 "!$# $ 4"! KF $ H 4 [ g'qg L; 3+A!$4 + ):!$4 /0& j &>&>! >0A!$# H > &(,&58 3+)A!E4 &(4 !*) .`*,t:$,, !9 + &(4& T ?@FRQ T SE+G VFHD QKB W;E T"3+&%.):3/ #*#'&(! ; & 3+&(46&58 +t & *!*!*&(, !9 = 3 1B&>,& = &(! /0&(8>) = &(4~ &>3+)GA!$# + &>3+&d.):3& + &E3&54760&(8 r & $!*!*&>, !9c3+ &

) + ):!$", 4 =G= & 3 ! + & 8d):!;:$! !9D6) &(! + A, )". & l#$A! = #') &>!;>4*3+&(4 `+ & A!90$,A3 = ) = &(! = 4G A)])'# l#$A! = ! = /0&>3 ) #'&548>3 /0&+ & >t&>,&(8 3):! 4 &(4 m ! &>3 8>",l"! = #') 4:&(,&58 3+)A!49"3+& $!*!*&>, !9`A,):!94$8 ^4 =@= & 3En1 4>s :& & 46 ! & 6*3+) Pj&58 )A!B)". + &"!9*,A3 = ) = &(! =):! ) +* 4 n1 4 4 )*,#/0&<Gl#$A! = ! = /&(3/& !ª@8>)A!$4&>3 &5# ],&5A# !9@",47) )4&>,&(8 )A! 3*,&(4 .):3 3?"!$4 )A!$4 /0& j &>&>! >%A!$# H >t&>,&(8 3+)A! 4 &54 2)A3+3+&>, &5# &>,&(8 3+)A! 4'4 & = 4G"3+&!*) #*&(4+8d3 /0&(# / 4 !9:,& H], &(3@#*& &(3>= !$"! )". 4 !9:,&> 6$A3 + 8>,&E4 &(4 n A!D:44 = 6 + ):!)A. + & 2 )A!$4 A! m ! &>3?A8 + ):![ )'#'&(, ; &()A3+& + 8(", )A3'4 )A. $ [ !$"3+& V=AE

o H g:g r ] A,:8 ):4 V AE

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³L -# ° ,/°± +)!#, ! %A3& #'&>3 r &(# .3) = &>!*&(3W8>)A!$4 #'&>3? + ):!$4 m #*& = )A!$4 3? &(4 &T8>) = 6*,&d1 ! ! &(36*3+& + !ª &d1'60&>3 = &(! ", #* ) .`*3 + &>3c:44 = 6 )A!4`A/) `+ &D#;#>! = 8(4 H'&>6$A3+ &E4760&(8 3+):4+8d):6#c)A. & >%A!$# & H >t&>,&(8 3+)A!D4'4 & = 460):4+4 /*,& . &k3+&(46&58 r & A3+)0*!#*4 &(4 "3+& + & ! ", 4 &(4-.):3 + & *!$!*&>, !ª6$3)'8d&544&(4 ; 3+&(l# 3&54<"! !$4 A! "!$&>)04B"!# 8d) = 6*,& &3+&>,n1* + ):! 6*3+)]8>&(4+4/0&d.):3&k&5A8 *!*!$&>, !9c& &(! < 6*6*,r !9@ = :!*& + 8:$&>,#0&58 4 + &a&(,&58 3):! 8a4760&(8 3 = )". + &al#$A! =#*) ; 3+A!$46):3 4760&(8 3+):4+8d):6#E :! &#'3+ !9>t4)0*3?8d& ):, A& ",,) 4 )^.):,,) &# 46&(3+4 )A!$4C)". 3?"!4 )A! &(!*&>3 &(4C/& j &(&>! + & A3+)0*!$#$4 &54/9 ",4) &d1*8 &5#4 &54a)A. + & > "!$# H > &(,&58 3+)A! 4'4 & = ; &c8 A3+:8 &>3C)A. + &@3&54760&(8b>+t &°A3+)0*!#*4 & n #'&(4+8d3 /0&(#D/ 4C4& )A. l#$A! = !# = /0&>3?4 n= 8 "!ªA& = 0A!*& 8°:$&(,# ) & &(3 &>! 60&>3.)A3 = !9 3?"!$460)A3 4760&(8 3+):4+8d):6# ! = 0A!*& 8 :$&(,# )A!*& = E & ) 0A& ! )TA8>8>)0*! 8 "!ªA&(4 ! &c8d):! A8 )A, 0A&(4-)". &k,&(:#*4"!$#: &^&>,&(8 3+)]#*&(4(s < 4 ",3+&(A#9G60) ! &5#) ! 2 A6 &(3 &c&(,&58 3+)'8 & = 8>A,h60) &>! ",9# &>3+&>!$8>&(4EA!$# !$) k &@&(,&58 3+):4 8B60) &>!;>+ A, # 0&(3&(!$8d&54 "3+&%:*1'&(# / + &<&(,&58 3 8>",_8 3+8 s ; &E&(,&58 3+)A!T4'4 & = ! &l#$A! = #') 9 4 47&(!$4 +t & ) &&>,&(8 3 8:$&(,#@"!# + &>3+&d.):3& ) &&(,&58 3+):4 860) &>! ", A3 + ):!$4 * ! = A4 &(3%&5l )A!cA6*6*3+):A8 G% A49/&(&>!# 4+8b$4+47&5# % + )A60&>!9> !9GB8 A!*!*&>,0)". A! &d1*8 &(#4 & + &^8*3+3&(! 4-!*) !*&58d&544+"3 ,r !$8>3&5A4&(#c/9 = ",47) #'&58d3+&(:47& ; $ 4 4c",4) ):/$4&>3 &(# A4@!*&: r &T# 0&(3&(! + A, 8d):!$#;$8b> "!$8>& ! & &>1'6&(3 = &>! A,-#* 9 !$# 8( !9 + H # 0&(3&(! B *!*!$&>, = 3 1&(,& = &>! 4E&>1 4 < & $ !9 + & *!*!*&(, !9 3? &(4^.)A3 &# &>3+&>! 8 A!*!*&(,4 R !$4 A! "!*&()0$4 3&(,"1* )A! 4f"/47&(! "!$# &>1'8 &(#G4 &(4_)".$,)A!9a, .& = & &>1 4 &>1*8d&>&5# !9 + & = &(A! + = &c)". 4 !9:,&@&>,&(8 3+)A! 3?"!$460)A3 a+ 3)9 &@l#$A! =#*) &>!D!*) 3&5A8 * !9 * 4 &d1*8 &(#D4 & < 4 = 6*,& * + ^ + 8 "3?A8 &>3 4 + 8 )". El#$A! = #') 4'4 & = #')]&54 !*) ",,) )<3+&>, &M*!$ = / 0*)$47,r@4 &>6;>t, A&a8 "!9:&(4 ! * + )G8d&>3 ! 3+A!$4 + ):!$4 ! &l#$A! = #*) ; &k8>) = 6*,&d1 4 6"3 ",,tc3+&(4)A, &5# / = &(:4*3 !9 + &E8b*3+3+&>! ):3E# &>3+&>! + A,%8d):!$#;$8 "!8d& ! + &@.`*,, ^ ^ + 6*,"!*& m ",,) 4 )T&d1 3?A8 & &>3aA! &d1*8 &(# 4 &<)A. & >-):3 & H >t&>,&(8 3+)A!T4]4 & = /&58d) = &54:8>8>&(4+4 /*,& b *3 &(3 + & 3+A!$4 + ):!<&>!*&(3^# &>3+&>!$8>&(4h"3+&%&>1 3+:8 &(#<8>)A3+3&58 ,r^/## 4 !90 4 * !9 /0& j &>&>!`8 "!*!$&>,4 /0& !9C):6&(!*&(# !<3+&(4)A!"!$8>& )a4)0$3+8>&9)A3h#'3+ ! ; & j ) )A, 0A&54 ^ "!# ^ + A,,) ) *!*& )kA!<6)4 )A!G)". ^ 3+&>, +t &>,r ) ^ ):3 ^ + 9"!# )W#*&b:$!*& + &T# 0&(3&(!$8d& ^ ) ^ + !$#'&>60&>!#'&>! ,r ; &>3+&d.)A3+&0(.)A3f8d&(3 !`8>) = / !$ )A!$4_)". ^ ^ + & 4 $ )A! 4h&d1*8d&(6 )A!", s; & # &>3+&>!$8>& ^ H % ^ 4h)A/ !*&5#E.3+) = & = n1 = = ^ + A,t*&-.)0$!$#.):3 & 2 )*,) = //*,)]8+n:#'&k3& )A! +

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I ³ #&;,-;+,,+L/' % )A.>t4 &<)A. &`,&5A#*4a4*60&>3+60):4&(# ) & 3?"!4760)A3 46&58 3? P$4 #'&(4+8d3 /0&(# .)A3 !$4 "!8d&0 o H gML r Mi &(4+8d3 / !9 + &C#;]!$ = 8>49/#G = A4 &>3%&(l#$ + ):!c"6*6*3+)::8 m 3 )'#')21 ; &b>):3 m o R r A,,) 4 ) !8d,r$#'& + &>3 = ",-&b &(8 4 ; & 8b*3+3&(! 4 &>6$4`4 = &5"3B) /+ &>3 = ",9A8 r )A!4 X k & "6*6*3+)::8 3&5 4k&5A8 4 !9A,&b>t&>,&(8 3+)A! *!*!$&>, !96*3+)'8d&544`8d3+):4+4 !9 *!*!*&(,/$"3+3 &(3BA4G 4 !ªA,&"!# !#'&>60&>!$#*&>! & &(! G ! &4&>!$4& + @+ &>3+& 4G!*)Wl"! = = &58 "! 8>A,-6 A4& 8>)A3+3&(, )A! /0& j &>&(! j )):3 = ):3& *!$!*&>, !ªT& &(! 4 m E 4E#'&>!$) &5#WA4_T W QV FHAEVW3QQ E!FRQ m 4&>& = 4 )/0&@6*,0$4 /*,& . .)A3 !4 "!$8>&0 &@l#$A! = #*) < !$#'&>&5# 3+&>,n1'&54 ) 4 A3+)0*!$#;>4 &D/& j &(&>! $!*!*&>, !9 & &>! 4c4 !$8d&D/ 3+A!$4j.&(3 !9W&>!$&>30 )WW/ &l#$A! = = &58 "! 8>A,6 :47& 8>)A3+3&(, )A! 4 #'&54 3):&(# 7X c+ & &>1]60&>3 = &(! ",#* !$# 8> & + 3&(,"1* )A! 4 !*) 6*3+&(4&>! n ,&(:4 n ! 4) = &B8(A4&(4 $i $",6$ "3+3+A!9A& = &(! 4CA,,) I ) &(4 ^+ &@6 :47&@8d) &>3+&>!$8>&B)A.-&>,&(8 3 8(", 3?"!$460)A3 + 3)9 l#$A! = #') 4'4 & = 4 H;$8 !#T)".9&>1]60&>3 = &(! 4 &>3+&<6 )A!$&>&>3+&(#D/)A/ "!# 8>) ):3:&>3?4Co H l | r

& 6 , ! # #&%;' %

Z ,&58 3 8>A, 3+A!$46):3 f 3)9 kl"! = >#') 4'4 & = A4f/0&>&>! # 4+8b$4+4&(# ! &6$3& )04&H]&58 )A!4 ! &>3 = 4a)A. 2 )0$,) = / /*,)'8+nA#'&@"!$# 4 !9:,&> &(,&58 3+)A! *!*!*&(,> !9 & 3& = & = /0&>35s ; &(4& &b &(8 4G"3+& 8>47&5#W/# &&>,&(8 3+)A!;>t&>,&(8 3+)A! ! &>3>:8 + ):! )A. & &(,&58 3):!$4<8d):!;:$!*&5#W)A! & H Z ; 47,"!# ):!*,t 6$"3 ",,r 4+8d3+&>&>!$&(#/ + &T4*3+3+)0*!$# !9 &>,&(8 3+)]#*&(4 b )A3c4 = A,, #*3+ !;>4)0*3?8d& )A, 0A& + &D&>,&(8 3+)A! 3+A!$46):3 /& j &(&>! #'3? ! A!$# 47)*3+8>& 4%$4$A,,r /*,)'8+A&(# "!# ):!*,rT.)A3<8>&>3 ! A,t*&54<)A. &&>,&(8 3)4 + 8@60) &>! ",4B)A. & 4*3+3+)0*!$# !9 &>,&(8 3)'#'&54B 4 !9A,&&(,&58 3):! 8>A! &(! &>3 + & 47,"!$# "!# ,&( &`/0&d.):3& &c!*&d1 &>,&(8 3+)A! 8>"! .)A,,) ; &l#$"! = #') ` :4E/0&>&>! #'&>!*) &5# A4</0& !9 &(0],tW8d)*6*,&(# ) #'3+ ! A!$#4)0$3+8>&%47) _+ & *!$!*&>, !ªa& &>! 4 + 3)9 < & *!$!*&>,'/$A33 &>3?4 "3+&%8>)A!$4 #*&>3+&(#:4 /& !ª !$#*&>60&>!$#'&(! s Z !*&>30 8>)A!$4&>3 + ):! A3 = &>! 4 .):33&5"3+3+A!9 !9`4 !9A,&&(,&58 3):!$4-8>) = / !$&(# + = A4 &(3 &5l#$ + ):!"6$6*3)A8 8("6 *3+&(4 /$A4 8 .&5 $3&54)A. &^#;]!$ = 8>49)A. &>,&(8 3):! 3?"!$460)A3 3+)09 @ &al"! = >#') 4'4 & = ; * 4T W Q=VFHAE!V W3Q=Q E!FRQ #'&(4+8d3 6 )A! 4#*&>!*) &(#D:4 DB V 9D0D V +DB o R H| r ) & &>3 * 4 47&5l$&>! ", $!*!*&>, !9G#*&(4+8d3 6 + ):! 4 !$8>) = 6*,& &k4 !$8d& #')]&54!$) 0A& ! ) 8d)A!4 #'&>3? + ):! + &(!*&>30 3+&(l# 3+& = &>! 48("! /&E3? 4&(#.)A3 4 )A3 + = & & &>! 4f:8>8d):3+# !9 )

& 4&>!]/0&>3 *!8d&>3 ! E3+&>, + ):!<.)A3f&(!*&>30E"!# + = &AsX T8d):33+&>, + !ª *!$!*&>, !ª& &>! 4a)A. j ))A3 = )A3+&B&(,&58 3+)A!4C&(! &>3 !ª"!# ,&( > !9 + & 4,A!$# A VAE D T V7V &TA VF + &C! = /&(3%)". &(,&58 3):!$4 )A! & 4,A!$#S$8 $ &(4f)A!$,t`)A!@4 ):3 f+ = & 4+8>",& < 8 "3 !9a):3 # 4+8 A3 !9^)". & l#$A! =#*) /W"!W&>,& = &>! "3 8 A3:&@)]8(8b*3?4E):!*,tWA4B"! ! &>3 = &(# &4 & )". 4 )A3 , .& + = &T):3 n A4G/0& &>3#'&>!*) &5# n FB VWªAEE [C WªA QVWOWªG VWªA V FHD QT H;$8 8>)A3+3&(, &5# *!*!$&>, !9W& &>! 4 ! ):, ] !9 j ) ):3 = ):3&&>,&(8 3):!$4@8>0$47&&>,&(8 3+)A! 3+A!$46):3 /0& j &>&>!c4)0*3?8d&A!$#@#'3+ !@& &>! ! &3+& = &(4 &>3+& 4 !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9 n & -W3+&(8 A3 !9 )". + & 47,"!$# / 4 !9A,&T&>,&(8 3+)A! n 4c&>!$&>3>:& + 8(",,t4*6*6$3&544&(# o H p(r S< 4&d1*8>&>6 &(# + &(4&B8>)A3+3&(, &(# *!$!*&>, !ª 6*3+)]8>&(4+47&54A3&M$4",,tc4 3+)A!9:,tc# = ! 4 &(# + #'&58d3+&(A4 !9 & *!*!*&(, 8>)0*6$, !9B/0& j &>&(!l#$A! = #*) "!#,&(:#*4 ) & &(3 $ 4 4 !*) 3*&%*!$#'&(3C",, 8 3+8 = 4 "!$8>&(4(sI !#'&>3 8d&>3 ! 8d)A!# + ):!$4 + & l#$A! = >#') 4'4 & = /0&(8d) = &(4 8d)A!#;$8 +t & !D) &>3 & )A,& 2 )*,) = /;>t/*,)'8+2:#'&E3+& = & oFRV ErD BgFRQ V AV M?bB SA VW;B I ; &^8d)A!#;$8 "!$8>&a3+&(:8 &(4 &^)A3?#'&(3%)". R Q * 8 4%&5l", ) &k8d):!$#;$8b> A!$8d&k)A.f@46 !9>t#'&A&(!*&>3? &a):!*&b># = &(!$4 ):!$", 8 A!*!*&>,9o gl g p(r

0³ ±0°( "9 °-0 !")!M %&Ho-/01+ &>3+&0 &@#'&(4+8d3 6 )A! )A. 2 )0*,) = / /*,)'8+2:#'&`A!$# 4 !9A,&b>t&>,&(8 3+)A! $!*!*&>, !9/= A4 &(3&5l#$ + ):!$4/$3&5'4#') ! & &>! ! + & 8>A4& )A. &5 $!*!*&>,<8>)0*6$, !9 ; &c&0&58 8>"!W/0&# 48$4+47&5# / $4 !9 = )4 4 = 6$,& = )'#'&(, n &&Q bB6TD QF M?;W;BgFRV D bE o H l H r $ 8 A4CA,4)c/0&>&>!$47&5# )#'&(4+8d3 /0& + &D Q0D +G Vo H l R r ;Z 1'6&(3 = &>! A, !# 8( + ):!$4 ) + & ):!$#')c&b &(8 ! c4 !9A,&<l#$"! = >#') 4'4 & = 4 4 )A6 8k)". * 4 2 A6 &(3

-@ $ 0/ %-F 1 % " ./I $4%,"$ % &9;"3%9>% " ', ,- 0/ 921# ,-F #"

m ! b l$ H + & &>1]60&>3 = &(! ",a47& *6 )A.E 46*, > & l"! = >#') 4'4 & = 44 ) ! ; &a4 3$8 *3+& 4 &(3B4 = ,"3 ) & ):!*& ",3+&(A#9B#'&(4+8d3 /&5#GA!$#$4&(# !+ & 2 "6 &>3?4 "!$# g'*i &>3+&>! 4 &<4 r~ &k)". &<l#$A! = #*) "3+&( A4/0&>&(! 3&5#;$8d&5# ; $ 4 A4E/0&>&(! A8 $ & &(# / + &4 = ",,&(33A&() = & 3 8@4 r~ &)". &46*, > &@&(,&58 3+)'#'&(4 n !$) H | ! = A4 & )A60&>! # = & &>3</0& j &>&(! &. &:$!ªA&>3?4 n A!$# /#A& !9 & j )0>t# = &>!$4 )A!$A,h&(,&58 3):! 4'4 & = 8>,)47&(3 ) & & &(3)4 3$8 *3+&@4*3. A8>& n + &#'&(6 )A. + & < ,83k < 4763k < 4 & &(3)MP*!$8 )A! 4!*) g | ! = Km ! b l$ H / & = &(A4*3+&(#* + ^ + 4 ^ 8 A3+:8 &(3 4 8>4 "3+& 6*,) &5# ; &A3& A&(! & = 60&>3? *3&a)". "/0)0 | = J2 ,&5"3+,t 3+&>& 2 )0*,) = /c/*,)'8+nA#*&3+& ):!$4f"3+& ] 4 /*,& A!$#@A# P7:8d&(! f ) + &(4& & 4 !9A,&b>t&>,&(8 3+)A! *!*!$&>, !9E3+& = &54 &(3&-4 &>6;>t, A&-8 "!9:&(4 ! + &%8b$33+&>! * + +< !8d3+&(A4 !9 f ^ + f "3+&9!*) 8d&(A/*,& !$# 8> !9 3+A!$4760)A3 8 "!*!*&(,4 3)9 &d1*8 &5#4 &(4 ; &(4&^A3&a/& 7 &(3 )@47&(& ! b l$ R &(3& &# &>3+&>! ",]8d):!$#;$8 "!8d& #2* + # ^ + = &(A4*3+&(#`"3+)0*!$#B8 )47&(! 2 )0$,) = /;>t/*,)]8+n:#'& 3+& )A! 4-6*,) 7 &(# ! & ^ 4 ^ + 6*,A!*& H &>6;>t, :&8 A!9A&54 ! * + ^ + "6$6&5"3 ! #2* + # ^ + ^ + A4C6&5'4 60):4 r &00/9 A,4)`!$&: r &E = 6*, $#'& 47&(&IH]&(8 )A! g' :dX $! !ª & ) &(3<476$, >1: &@&>,&(8 3+)]#*&(4 + & *!*!*&(,%8d)*6*, !9 ) 47)*3+8>&A!$#D#'3+ ! 4 !$8d3+&(:47&5# ª< 4 47&(&>! ! b l* R &</):3+#*&>3+, !*&(4 /0& j &>&(! 2 )0*,) = //*,)'8+nA#'&"!#G4 !9A,&b>t&>,&(8 3+)A! 3?"!$46):3 3+& ):!$4f4 = &5"39) s i *& ) &C3&5#;$8d&5#, .& + = &)". 4 !9:,& &(,&58 3+)A!4_):! &l#$"! = #') n)'8>8*6$ )A! 4 60):4+4 /*,& +* !& 47&(!/0&>3*!8d&>3 ! k3+&>, )A!B)".$&(!*&>30k"!$# = & ; & /):3+#'&(3, !*&(4 n #'&(3 r &5#/@4 3 8 &>!*&(3`8d):!$4 #'&(3+ )A!$4 n "3+& !*)<,)A!ªA&>3 &(,,0#'&b:!*&(# ; &^4 3):!9A&(3 & *!*!*&(, 8>)0*6$, !9ª & ,&(4+4 ] 4 /*,& 4 + & 2 )*,) = / /*,)'8+nA#*& 3& )A! ) & &>34 3 !9 ! b l$ R 4 &^)'8>8b$33+&>!$8>& )". <6&5 ! &^# 0&(3&(! + A,08>)A!$#9$8 "!$8>&#2*,+ # ^ + ^ + F| $ 8 c 4Q]D V:T ;F 6VFRQ @ &: & ):, :& ^ :4 4$4$A,,r &@8>:47&G#;*& )):6&(! !98 A!*!*&(,4C.)A3k4 !9:,&> &(,&58 3+)A! *!*!*&(, !9 ; $ 4 O vo - ( ± !,+,,g±' ! % . $ $S&# )ª±0 °#, ! /$ Q*;,g)+±Q/ % °@'+±#e , #1 )!)O +7 "3 @v# !)! /* *# %&±o1/01+ ³ )!/' !O0 !" &#)! ,&"M1,#0 ! ! 0&±+ !#"° ± !1#+° ¯ ( - ! #)± )!)!/)+±33±07#)! !K% ¯ ( -! ° E;,, # !)! / v ° !"7Q## ±; ! ++ "),± "+³

& BY ,Q )!/ ! )! @0& BY)!TO±0 +" ! ° )

-50 -40 -30 -20 -10 0 10 VDS [m

V]

-2-1

0

1

2

VBS [V]

20

0

-20

IDS [nA]

(b)

(a)

500 nm

VG1,S VVG2,S

V VVG4,S

VB,S

VGaAs Buffer

GaAs

AlGaAs : Si

AlGaAs

GaAs Substrate

20 nm

0.5 mm

++

+ ++

++

+++

+

0.3 m

10 nm

20 nm

µ

µ

µ

2DES

Backgate

0.5 m

AlGaAs/GaAsSuperlattice

0.64 m

GaAs +

+++

++


50 nm

G3,S

G5,S G6,S

Backgate

Source

ID,S

D,S

Drain

¦ ¬ -0Mª # %&±]1/01+ #, !"&#)! ,&H" * #, )!) /e±7) ! &± ! °+#, !)+)!+,'1/01+ ¦ #t ¬ -g# !#"&),0& ° !,+L; ! "Q%S °)&#)! ,&" "+³ = $) "+ #)! !g±o 1,#0+]b !#± !g+±ª³ ¦ !" ¬RL,Q1& ,) R 9 , 1, + !#" ¯ ( -Kb ## # ;+)! ! =,0&+ ¦H¯ ( - ! +)!+,%+#+,b ! ¯ P g < 9 G #±e+)!+, °L# !)! /C G M e+ ;be% I ³ ¯ ¬ ³ ¦ ¬ ,+ °g,0g±Mv# !3S ± !&H,+$ ) " ) ±° TO" b&H,0+ $ )!" ) F ³ = $ ) "+#)! !g±' &#)! ,&H" b+)!+,±b O 7 ?0g±ª³ = °g,0+ °+ ! ;&v °g± b%;0% ! );,/³ ¦ ±0L+± r ³-0 ° ± ¯ ¬BD SCFHA T7A Q@D AE W#')]&(4<!$) : G ! ) &6 8 $3& )A.C4 !9:,&> &(,&58 3+)A! 3?"!4760)A3 A!$# #')]&(4 !*) )]8(8b*3 !T",, 2 )0*,) = //$,)'8+nA#'&k3+& ):!$4 < 4C#'&548>3 /&5# ! 2 A6 &(3 + )0 *!$!*&>,h8d)0$6*, !9 ) &<,&(:#*4 &>,&(8b> 3):!$4f8d):!;:$!*&5# ! + & l#$"! = #') ) !` ) A,]&>!*&(3<4760&(8 3 =y 4 ^ p $ 8 8>"! /&@,"/0&>,&(# /# + &@6$"3? = & &>3 &>3+& F | #'&>!*) &54 + &A3+)0*!#>

0³ ±0°( "9 °-0 !")!M %&Ho-/01+

VDS [mV]-2 0 2

dI/dVDS [e2/h]

0 0.2 0.4

VDS [mV]-1 0 1

dI/dVDS [e2/h]

0.25 0.5 0.75 1

VDS [mV]-1 0 1

dI/dVDS [e2/h]

0 0.25 0.5 0.75

(a)

0V [mV]DS

0V [mV]DS

0V [mV]DS

(b) (c)

BS

V

-2 2 -1 1 -1 1

10.50.500.40

dIDS /dVDS [e /h]2

Increasing Tunnel Coupling to Leads

& #)! Q) O±%" ! ! E ?0g±# ;$ %o+)!+,#M+ #+± ! ## ±3'; O = .± '"9+ )+±+ !-#)!,+± !"/0,g)! $ , ) ± ) F ³ ¦ ¬ ¦ ¬ 3##+)=)! "K 3)+± !° g,g± /g±0#+ !#"K E$ ) "+3#)! !g±K -# ° &)! !"1,#0.±7 !g± ! !"³ ³+0³ = O" bC$) " ) F E;+j±11g± O +7 3 ° ) @4) O±°+" !S³ -, O0 !"K !M ++0,+#+3Q ;g%O ! ±0 "9+ t)]+±+##± ) % ¦ ¬ ! ±QQ 'r ! ! ) F ³= ! +& t=# ) /e !Y ±0+ #g± ! ±0#"9+ !-## %&±0 1/01+ °+³¦ ±0L+± r ³-0 ° ± $ L ¬4 &B)A. & >t&>,&(8 3+)A! 4'4 & = ; & ) ",h&>!*&(3D#*&>60&>!$#*4^/0&(4 #*&(4^) + &>3^6$>3? = & &>3?4<):! & &(,&58 3)4 8 60) &>! ",4 ^ p )". &D&>,&(8 3+)'#'&(4 46*, > &54/$:8+: &0]47)*3?8d&E"!$# #'3? ! 4$33+)0*!# !ª + &<l#$"! = #') ; )@#*&(4+8d3 /0&k&>,&(8g> 3):! 3?"!$460)A3 C 3)9 T+ &cl#$"! = #') k ! &G3+& = &`)A. &5 $!*!*&>,98>)0;>6*, !9 ) & ,&(:#*4 & &>!*&(3 &54E3+&(l# 3&5# .):3`:#*# !9 & H + &>,&(8 3):! ! ) + & >t&>,&(8 3+)A! 4'4 & = m &(,&58 3+)A!9> , :& m 6$3)'8d&544 "!# .)A3 !9 ) & + &(,&58 3+)A! .3) = + &Wl"! = #*) m )A,&b>t, A& m 6$3)'8d&544 & ) /0& 8>)A!;>4 #*&>3+&(# ; $ 4 :4T#'&(4+8d3 /0&(# ! 2 A6 &(3 g ,&(:# !9 ) + & &(!*&>30 48 & = &4 ) ! ! b +g* &(3& &eA3+)0$!$#*4 & &>!$&>30@# &>3+&>!8d&(4 ^ H ^ p6 H 4 | ^ p % 4 | ^ p /& j &(&>! & H > "!$# & >t&>,&(8 3+)A!4'4 & = "3+&^6*,) 7 &(#.)A3 # 0&(3&(! /9 :*1'&5# ^ p 3+&>, +t &>,r ) & b &>3 = ,& >&(,4 & &a&(,&58 3+)'8 & = 8>A,$60) &(! ",4 ^ "!$# ^ + )". &^47)*3+8>&aA!$# #'3? !,&(:#*4 < 4fC3& = !$#'&(35/E8 "!9 !ª )A!*&-)". + & "6*6*, &(# )A, :&(4 + &(4&-&(!*&>30^,& &(,4^ ^ p + ddd 4 % H 4 4 H 4 ddd A3& n !:$3?4 "6$6*3)21 = )A! n, !$&("3+,ra4 * . &(#k3+&>, +t &>,r ) & b &>3 = ,& &(,4 * ,& + &%# 4 "!$8>& ^ H ^ p %^ ^ p /0& j &>&(! &-,& &>,4 3+& = !$4_8d):!$4 "! m ! &-8>:47&%)". ^ H ^ p ^ ^

+ ^ ^ p &>!*&(3D/$"3+3 &>3?4 &>1 4 .)A3E"! &>,&(8 3):! &(! &>3 !ª)A3

,+)bg± ! & ()!+, ##+)! !#" ##+)! !#" ,&( ] !9 ; &>3+&d.)A3+& ,) & = 60&>3? *3+& 4 !9A,&b>t&>,&(8 3+)A! 3?"!4760)A3 c 4/*,)'8+:&(#A!$# &"3+& ! + & 3+& = &c)". 2 )*,) = / /*,)'8+nA#'& 2OX &>3+& &! = /0&>3B)".&(,&58 3):!$4E)A! + &l#$A! = #') B 43:*1'&(# ) &>!$& &(3 ^ H ^ p , &54/0& j &>&(! & b &(3 = ,& &>,4 )A.947)*3+8>&B"!#T#'3+ !T,&(:#*4 &B! = /0&>3^)". &(,&58 3+)A!4):! &^l#$A! = #') - 4S$8 $ + !9`/& j &(&>! "!$# H '"!$#4 !9A,&b>t&>,&(8 3+)A! *!*!*&(, !9 + 3)9 &<l#$A! = #') /0& j &>&(! 4)0*3?8d&k"!# #*3+ !D8>A!)'8>8*3 < 4T4 ) ! ! b +g* l 2 )0*,) = / /*,)'8+nA#'& "!# 4 !ªA,&b>t&>,&(8 3):! 3?"!4760)A3 3+& = &54 "3+& .)0*!$# A4 .`$!$8 + ):!O)". #'3? !;>t4)0$3+8>& )A, 0A& ^ + "!$# : &>4)0$3+8>& )A, 0A& ^ ; &c/0)0$!$#*"3 &(4E/0& j &>&(! 2)*,) = / /*,)'8+2:#'& "!# 3+A!$4>60)A3 3+& = &54 "3+& t &>!E/ & 8>)A!$# )A! _+ &%3+&(46&58 +t & ^ ^ p 4h& &(3A, A!$&(# ^ )A3 ^ + ] r] !ª j ) # 0&(3&(! 47,)A60&(4C.)A3 &`/0)A3?#'&>3+, !*&54 !+ & ^ 4 ^ + 6*,A!*& $ ! & 4 !9A,&b>t&>,&(8 3+)A! 3+A!$46):3 3+& = &(4k :$! &#*3+ !;>4)0*3?8d& )A, 0A& ^ + F ^ + % ^ A#*# )A!", 8 "!$!*&>,4 ! & 3+A!$4>60)A3 3)9 &Bl#$"! = #') /&58d) = &` ,"/$,& * 8 T &k/0&>&(! 3&(, &5# )&>1*8 &(# 4 &(4@)A. &D8>)A!;:!*&(#

>B"!$# H >t&>,&(8 3):! 4'4 & = 47&(&*H'&(8 + ):!g* ]M ; &c/):3+#'&(3, !*&(4k.):3<)A60&>! !9 &547& :#*# )A!$A,%4 !9:,&> &(,&58 3+)A! 3?"!4760)A3 8 "!*!*&(,4`"3+&#'&548>3 /&5# / H 4 ^ p % 4&! ^ p6 F ^ 4 ^

+ & &@"3+& ! + & ^ 4 ^ + 6$,A!*&6$"3?",,&>, ) &a/):3+#*&>3+, !*&(49)". &C3&54760&(8b>+t & 2 )0*,) = / /$,)'8+nA#'&cA!$#W4 !9A,&b>t&>,&(8 3+)A! 3?"!$460)A3 3+& = & 4&>& b g* H:H d< ` &547&/):3+#*&>3+, !*&(4 60&(0'4 ! &# 0&(3&(! ", 8d)A!#;$8 "!$8>&#2* + # ^ + 8("!/0&G&d1'6&58 &(# ; &G60&( , !*& ! b l* R 8G ^ + Fy| 4a!$) 6$"3?",,&(, )D)A!*&`)".+ &(4& /):3+#'&(3, !*&(4h"!$#`8>A! &>3+&d.)A3+& !*) /& 3+&>, &(# )^4 !9A,&b>t&>,&(8 3+)A! 3?"!4760)A3 + 3+)09 &<l"! = #') ; &@l#*&(4 )A! "3 4&(4 & + &>3 + &`60&(0T, !*& ! b l* R ^ + F | 8>A! /0&&>1'6*, !$&(# / *!*!*&(, !9G)". j )B&(,&58 3):!$4 !*&(A3,r &E4+ = & + = & H$8 8>)A3+3&>, &(# j )>t&>,&(8 3+)A! $!*!*&>, !9 4h#'&>!*) &5#<A4G+D VW3QQ E!FRQ & & )a# 4 !90 4 &54760&(8 A,,r@/& j &(&>! j )3 !$#*4-)"._8>) *!*!*&(, !9 )A!*,r ] 3 $A,08 "3A&C8 A!9A&:s

I 3DE S,E!F eG+D VW3QQbE!FRQ 0sA"!`&>,&(8 3+)A!G,&5 &(4 & l#$A! = #*) "!$# =G= &5# &(,t &>3+&(n. &>3 A!&(,&58 3+)A! &>! &>3?4 I E+G VBD QS,EF .G+D V W3Q=Q E!FRQ "! &>,&(8 3+)A! &(! &>3?4 &@l#$"! = #') "!$# =@= &b># &>,r &(3&5n. &>3 "! &>,&(8 3+)A! ,&5 &54

m ! /0) 8>:47&54 & & )@# 4 !90 4 & &>3 & )A,& 3+A!$47.&>3 )'8>8b$3+4 EtA T SV FHG+AEE & & ! ", A!$#:$!$", &(!*&>3 &(4 )A. + &<l#$"! = #') 4 &<4+ = & ):3FRQbErA T VFHG+AEE & + & "3+&E# &>3+&>! M b *3 &(3 = )A3+&0 & ! &>3 = &(# &<4 &E)".+ &B&(,&58 3):! 4'4 & = ! &`l#$"! = #*) 8("! /0&`.A3+)0*!$#$4 &B)A3aA!T&d1*8 &5#4 & $Z 1* = 6*,&(4 )A. &(4&<8>A4&(4 A3&E#'&(6 8 &5# ! b l* "!$# b l* $ ' $ $4:"3 ? 8 49;"3 $,% ? %&%4% 8 :9;"< %?A $%&2B@ 3" " "" 7( ,% 8 % 1I P@RHX RT SX7UPª\ VYV XRTHV s & 4a:44 = & + ^ &Gl#$A! = #') ^ 4 ! & 2 )0*,) = / /*,)'8+2:#'&B3+& = &

g 0³ ±0°( "9 °-0 !")!M %&Ho-/01+

E(n,k)

at Threshold:(c)

µEelch

µCelch

I C

E I

µCelch

(d) beyond Threshold:

E I I C

µCelch

E I I C

E(N,0)

E(N-1,0)

StateIntermediate

Initial State

E(N,0)

Final State

E(N,l)

E(n,k)

(a) via Groundstate:

via Excited State:(b)

Hole-Like Inelastic CotunnelingHole-Like Elastic Cotunneling

E(N,0)

E(N-1,0)

StateIntermediate

E(N,0)

Final State

µEelch

µEelch

E(N,0)

Initial State

E(N,0)

Final StateE(n,k)

E(N-1,m)

µCelchµE

elch

IntermediateState

Initial State

1 2

Emitter

2eVDS

2’

1

1’

E∆

E∆

eVDSE∆ E∆

1 2

ε

E∆ E∆

ε

2 1

2 1

2

1

21

N Collector

ε

N

Emitter

Collector

N

CollectorEmitter

CollectorEmitter

N

,+)bg± ! & ()!+, ##+)! !#" ##+)! !#" g J ¦ Tr0" ¬ )!&H)! O %+##+)! !#" ,QK+)!+,)!g/$ + + ±0/. ° °+± +) /Cv))! ! +± /+)!+, " ±g³:, #" " 1% ## ±3;+°) / $ ,)!)!/³ = +, +#+)! "Q0&++,,+3 $ !,)! g± / !± !gb !#" +&;+ $,#, ! 3)+"/&;+,# ¦ ) ' ¬ S >## ±0/.#± ;+)! ! !3 Q#"/', ° ! ,#, !+" !+ ¦ ) ' ¬ 7 ¦ 7 ) ' ¬ v, ")!&H+)!+, " "#)!,g±+) $ )!/K %+)!+, + ° !g) ;+ t)! %= °)!g±+³] o !# )Y± ) 1 $'&H+)!+, 1/01+ ! ±0 /$ ' ° +"/ . +##) !" +, ! ±+g± ² )t1 !² ¦ ,+ ¦ ¬ ± ¦ ¬,¬ .S ! !,'°² !#+)1& ² ¦ ,+ ¦ ¬ ± ¦ ± ¬,¬ ³9 ¦ ¬ +)1 !%##+)! !#"3++0 $ t M"#±01%%Y ¦ $ 7 ¬ &H+)!+, 1/01+ .S ! ¦ ¬ $ t #?0+ g±71 % ¦ $ 7 ¬ &H+)!+, 1/01&+ ³HUL. ¦ ¬ /# + !" +"/.1 ∆

vgb "' e ! °g± b1 ¦ ¬ ³ ¦ ¬ #)t1 ! +##+)! !#"°, vQ M$'&H+)!+,1/01+ 3.#?&+ g±e1 ! /# +* t; ! +e o), + ° !g);+ )!*; )!g±v#)' #))! !#" ¦ $ ) ' ¬ 7 ¦ $, ) ' ¬ M ) ³ BY/±K ! + )±.ª °%± °+##+)! !#"+,,+>;+ °/$ !)#)! !± !gbg± /' ! °#? #)!+ ! ¦ ± ¬ .v ! ∆

∆ .%

:

± % : ³

! & :3)*!$#*4 & f 4 | ^ p6' )A. + & > &(,&58 3+)A! 4]4 & = < ! &>,&(8 3+)A!,&( ] !ª ) "3?#*49"!& = 6 c8d):,,&(8 )A3 4 &C)". &(!*&>30 J ^ 3+A!$47.&>3?4 &l#$"! = #') C ! ) & A3+)0*!#*4 & f % H 4 | ^ p ' 4 ) ! ! b l* @):3 n= )A3+& :&>!*&(3+A, n ! ) + &<4 & f % H 4 e ^ p ' )". b l* / H$8 )A,&b>t, :&^6$3)'8d&544 3+&(l# 3&54 &E&(!*&>30∆ F

J % H 4 e ^ p % 4 | ^ p | 4 Hl$ H "!#T8>"!D):!*,t )A3 . + &B, .& = &

)". + &`4 & f % H 4 e ^ p6' 4C4 ):3 &(4 = &(#/# & 4&>!]/0&>3'*!8d&>3 ! 3+&>, + ):!)A._&(!*&>30A!$# = &

∆ d PQ [ Hl$ R !#'&>3T8d):!$# )A! Hl* R &W4 & f % H 4 e ^ p2 ' 8>"! /& 8>)A!$4 #*&>3+&(# :4 FB VWªAEFRQV bB FHA V T V1A V ", = ):4 E =@= &(# &>,r #'&58> !9D/# "!W&>,&(8 3+)A!&>! &>3 !9 + & l#$"! = #') .3) = "!W& = 7 &>3B4 & &>!*&(3 J . ^ .

&>! &(3 !9S &c&(,&58 3):!;>t4'4 & = ! & l#$A! = #') 8 A!9A&54 4B4 & ) &G6$3& )04 ! ",94 & b l$ A!$# / )A3 nT= )A3+&':&>!*&(3+A, n ) &4 & f 4&! ^ p ' b l* 8 M$X 4$8 3+A!$4 + ):! + &<4'4 & = : !$4 &(!*&>30∆ . F 4&! ^ p6 % % H 4 e ^ p2 % J . | [ Hl$ ; & ) &>3?",,*6*3+)'8d&(4+4 4 )A3 !ª + )0 ] ):, !9E&>!*&(3G8>)A!$4&>3 + ):! . &&>!$&>30 : ! Hl$ P$4 8>) = 60&>!$4+ &(4 .)A3 + &E&>!$&>308>):4 l* H &

∆ ∆

. F | [ Hl$ ]G U v O %07$ !/ +1 ) ' bQ ° !,+±% ° 1bO#±')S+" !+ ! )!)S± " °+³

g ¯ 0³ ±0°( "9 °-0 !")!M %&Ho-/01+ H !$8d&^.)A3 J . A!$# J + &E3+&(4 3 8 )A!$4 J . ^ . A!$# J ^ &d1 4 ,) & = 60&>3? *3+&0]4$8 <8d) *!*!$&>, !9G6*3+)'8d&(4+4 4-&>!*&(3:& 8>A,,r@",,) &(#*!#'&>3 &8d):!$# )A!

4"! ^ p6 % 4 | ^ p6 F J . % J ^ . % ^ F f ^ + f [ Hl$ g: &>, + ):! Hl*qgA &>1'6*3&544&(4 + & &(!*&>30 # &>3+&>!8d& J . % J )". & &>,&(8g> 3+)A!T&(! &>3 !ª"!# &`&>,&(8 3+)A! ,&( ] !9 :4 )3+&b$&58 C+ &B&(!*&>30D# 0&(3&(!$8d&/& j &(&>! ! ", "!$# :!$", 4 &)". & >t&>,&(8 3+)A! 4]4 & = ! + &l#$A! =#') 7[ )A3+&>) &>3 + &T60):4+4 /*,& &(!*&>30 # &>3+&>!$8>&D/& j &(&>! &d1*8 &5# 4 & A!$#A3+)0*!#*4 & 4%, = &(#c/ &CA6*6*, &5#c/ A4 f ^ + f /0& j &>&(! & &(,&58 3)'8 & = > 8(", 60) &>! ",4 )". &E,&(:#*4 ++ &E8d) *!*!$&>, !9G6*3+)'8d&(4+44P$4 #'&548>3 /0&(# '"!&d1*8 &5#4 &^)". + &El#$"!;> = #*) @ 4G)A/ !*&5# *!$#*&>3c8d):!$# )A! l*qgA ", )9 + &Tl#$"! = #') @ 4 ! + & 2 )0*,) = / /$,)'8+nA#'&3& = & ; * 4`&d1*8 &5# 4 & f 4"! ^ p ' 8>A! !*) A8 :4 & ! ", 4 &`.):3B8d) *!$!*&>, !ªT6*3)'8>&(4+47&54a,&(:# !9 )T) &(3E&d1*8 &5#4 &(4 m ! :&>!*&(3+A, .f@4 & f 4"! ^ p ' 4 :8>8>&(4+4 /*,&0'@4 & f 4&! ^ p ' 4&>!*&(3:& + 8(",,tc3+&(:8 &(#/#8d) *!*!*&(, !9 .

4"! ^ p % 4"! ^ p F J . % J ^ . % ^ F f ^ + f [ Hl$ l

H !$8d& J . % J 8>"! /0&T& &(3 60):4 +t &T)A3 !*&: r &0 + & l#$"! = #*) 8>A!/&D&>1'8 &(# )A3c8>A! ,)]):4&&(!*&>30 / 8>)A3+3&(, &(# &>,&(8 3+)A! &>1*8 "!9:&/0& j &>&(!l#$"! = #') A!$#,&5A#*4 . f ^ + f | K ) &0 & 6$3):/$"/ , .)A3 8>) $!*!*&>, !9 6*3+)]8>&(4+4 4 * &(3 + & ,) &(3 &&>!*&(3 8>):4 Hl$ H 4<.):3 + & ! &(3 = &5# & 4 & b )A3' r &>! ^ p &60):4 > )A!D)". &B&>!*&(3c,:#*#'&>3 4 ^ p % % H 4&! ^ p 3+&>, r &(,t ) &&>,&(8 3+)]8 & = 8(",f60) &(! ",9)A. + &c,&5A#*4 4%:*1'&5# s:H "3 !9 .3) = & A3+)0*!$#;>4 & f 4 | ^ p ' aA! &>,&(8 3):!I,&5 ] !9 ) & b &(3 = ,& &>,`)". & 8d)A,,&(8g> ):3 J \F ^ A!$# 3?"!$47.&>3 !ª + & l#$"! = #') T ) + & A3+)0$!$#*4 &f % H 4 | ^ p ' A4 + & ! &(3 = &5# & 4 &-3+&(l# 3&54 & ,&(A4 &>!*&(3 8d) = 6"3+&b l* "!$# / "!$# :4 &(3&>.)A3+& + & * &54 6*3+)A/$A/ , D.)A3< ):,&> , :&8d) *!*!$&>, !9E6$3)'8d&544 . !*) ) + &>3-47&(,&58 )A!@3*,&(4 & G+ &C8d) *!$!*&>, !ª 3?"!;>4 )A!4 I RXU\NP@V+RHT SX7U0PS\ YV VYXRHTV sm !$4 &(:# )". 4 "3 !9 4$8 8d):33+&>, &(# j )0> &(,&58 3+)A! 6*3+)'8d&(4+4k/ A!W&>,&(8 3):!,&5 ] !9 + &-l#$A! = #') )A,&b>t, A&96$3)'8d&544 5"!E&(,&58 3+)A!<8("!<&(! &>3 & l#$"!;> = #') &(,&58 3):!;> , A&%6$3)'8d&544 2,&(:# !ª )kA! ! &(3 = &(# & 4 & H&>,&(8 3+)A!$4f):! + & l#$"! = #') 4&>& b l$ ] s ; & l"! = #') 9 4 3+A!$4j.&(3&5#.3) = f 4 | ^ p ' ) f 4"! ^ p ' ] & ! &(3 = &5# &E4 & f H 4 ^ p2 ' Z ! &(3 !9G)". "! &>,&(8 3+)A!D8d):4 4 + &E&>!$&>30∆ . F H 4 ^ p %

J. 4 | ^ p6 | [ Hl$ p

,+)bg± ! & ()!+, ##+)! !#" ##+)! !#" g; &k, .& + = &

)". * 4 4 & A4 )@/&<4 )A3 ∆ . d PQ [ Hl$ ; &^&>!*&(3G8>):4 - 4 8d) = 60&>!$4+ &(#c/ &a&(!*&>30: ! + "!&>,&(8 3):! ,&( > !9ª

∆ F

J 4"! ^ p % H 4 ^ p | [ Hl$ L

2) = 6$A3 !9 Hl$ p A!$# Hl$ L *4$8 @8>) $!*!*&>, !9c6*3+)]8>&(4+4 8>"! /0&E&d1'6&58 &(# .

∆ . ∆

F | Hl* H| 4 .`*,:,,&(# + J . +^ . A!$# J ^ ,&5A#*4 ) &E3+&(4 3 8 )A! 4"! ^ p % 4 | ^ p F J . % J ^ . % ^ F f ^ + f 4 Hl* HAH * 8 4 + & 4+ = & A4B.)0*!$# + Hl$ g: .):3 + & )A,&b>t, A&8>) *!*!*&(, !9 6*3)0>8d&544 m . & 4 & f 4"! ^ p ' 4A8>8>&(4+4 /*,&0f.`*3 &>34 &(4 f 4&! ^ p ' "3+&&>!$&>3A& + 8(",,t A,,) &(# . Hl* l: 4 .`*,t:$,,&5# ; &>3+&d.)A3+&0d4 A3 + !ª f 4&! ^ p ' A!$#^&>!$# !9 f 4&! ^ p ' & &(,&58 3+)A!9>A!$# )A,&b>t, A&C8>) *!*!*&(, !9G6*3)'8>&(4+4-A3&a&>!*&(3:& 8>A,,rc",,) &(# &k4 = & + = & K ) &0 4 !$8d& ) & &(3# 0&(3&(! ! &>3 = &5# & 4 &54A3&$47&5# ! :&>!*&(3+A, &6$3):/$"/ , /0& j &>&(! )A,&b>t, A&EA!$# &>,&(8 3):!;>t, A&k8d) *!*!$&>, !9c6$3)'8d&544 = /0&# &>3+&>! 2&54760&(8 A,,r . & &(!*&>30<8>):4 4 .)A3 & ! &>3 = &(# & 4 &"3+&-# &>3+&>! ):3 & *!*!*&(, !9 8d)*6*, !ª:4# 0&(3

&<8>A! 8>)A!$8>,t#'&^.)A3,) & = 6&(3+ *3+&AsI b ):3 8d):33+&>, &(# *!*!$&>, !9c)A. j )@&>,&(8 3+)A!$4 ! & 2 )*,) = /D/*,)'8+nA#'&k3+& = &8d):!;:$! !9 &(,&58 3):!$4 ! &cl#$"! = #') &G&(!*&>30 # &>3+&>!$8>&`/0& j &>&(! & ! A, "!$# &e:$!$A, 4 &a)A. & > &(,&58 3+)A!4'4 & = ! &El#$A! = #') :4 )`/0&k,&544 + "! &E&(!*&>30 !$#') ):6&(!*&(#/ &<#*3+ !;>4)0*3?8d& )A, 0A&/0& j &>&>! &E&>,&(8 3)'8 & = 8(", 60) &(! ", )". 4)0*3?8d&k"!$# #'3? ! I H !$8d&B3&(, )A! Hl$ g: "!$# l* HAH A3& !$#'&(6&(!$#'&(! )". &B&>,&(8 3+):4 8a60) &>!;> ",4 ^ p &a/):3+#'&(3, !*&(49.)A39):6&(! !ª`4$8 8d) *!*!$&>, !9B6*3)'8>&(4+47&54 , & ! & ^ 4 ^ + 6*,"!$& ^ + F f 4&! ^ p6 % 4 | ^ p f 6$"3?",,&>, ) & ^ "1 4 #< 4 !$# 8( &5# ! b l$ g + & A3& , !9A&5# )G/0)A3?#'&>3+, !*&54 ! &4 !9:,&> &(,&58 3):! 3?"!$460)A3 3+& = & $4 !9 + &c3&54760&(8 r &c4 & f 4&! ^ p' .):34 !9:,&> &(,&58 3):! 3?"!4760)A3 I b ):3 ^ + F| + & ! ", A!$#:$!$A, 4 &a)". + &k8d) *!*!*&(, !9`6*3)'8>&(4+4 & &4+ = & &>!$&>30 m - 4-#*&>!*) &(#A4 bEtA T VFHG G+D V W3Q=Q E!FRQ H !$8>& + &^l#$A! = #') - 4$4$",,rk.)0*!$# ! &:3)*!$#*4 & + & ! + A,*"!$# :$!$",*4 & )".k8>) $!*!*&>, !96*3+)'8d&(4+4 , &< + &°A3+)0*!#*4 &a&(!*&>30 & *&d1*8 &(#D4 &(4"3+&^!*) 3+&(:8 &(#

g I 0³ ±0°( "9 °-0 !")!M %&Ho-/01+

at Threshold:(c)

(d) beyond Threshold:

E(N,0) E(N,0)

µEelch

E I

µCelch

I C

E(N,0) E(N,0)

Initial State Final State

IntermediateState

E(N+1,0)

E(n,k)

µEelch

E I

µCelch

I C

µEelch

E I

µCelch

I C

µEelch

µCelch

(a) via Groundstate:

via Excited State:(b)

Electron-Like Inelastic Cotunneling

E(n,k)


IntermediateState

E(N+1,0)

E(N,0)

E(N,l)

Electron-Like Elastic Cotunneling

E(n,k)


IntermediateState

E(N+1,k)

1 2

E∆ E∆

ε

1 2

1 2

1

E∆ E∆2

εN+1

Emitter Collector

1

E∆2

ε

Collector

E∆

N+1

Emitter

ε

1

2

Collector

2’1’

1 2

Emitter Collector

N+1

N+1

Emitter

,+)bg± ! & ()!+, ##+)! !#" ##+)! !#" g ¦ #t@#" ¬ ()!+,&H)! O3##+)! !#" ,7+)!+, ## ±/. ! ° °g± )!/ v))! ! +± /°°+)!+,')!g/$ !#" ±g³, " ° "o1bo ) ±0*;g*) / $ ,)!)!/³ Q ,#)! +g±°b= 0++,,++,+&;±0 " )!&H)! O##+)! !#">++,,Y ! ° ! !"³ ³ ³ ¦ ¬ +)1 !+##) !"++0 $ Q o"##±1b%9 ¦ $ ¬ &H+)!+,%1/01+ . ! ¦ ¬ $ #?0+ g±e1; ¦ $ ¬ &H+)!+,°1/01+ ³U. ¦ ¬ /# + !" +#"/%1∆ Jro+ !#" ! °g± 1b ¦ ¬ ³ ¦ ¬ +)1 !+##) !",#1&vª *$'&H+)!+, 1/01+ j#?0+ g±1b ! /# +@ ; ! + +)!+&, + ° !g)J; ) %@ )+± r#)' )!)! !#" ¦ $ ) ' ¬ 7 ¦ $ ) ' ¬ M ) ³BY/± ! )±J.S °°#±K °e+##+)! !#"E++,,*;+ °e $ !))! #± !gbg± /' ! 3T?# #)!+ ! ¦ ± ¬ . v ! ! ∆

∆

. % : ±% :

³

µSelch

µDelch

VDS

N+1

12

1

2

N+2N+1

N-1

N+1

N

0

N-1

N

N-1

N

VGS

N

DrainSource

Electron-Like Cotunneling

E(N,l) - E(N,0)e

ε E(N+1,0) - E(N,0)

E(N+1,0) - E(N,l)

Hole-Like CotunnelingE(N,0) - E(N-1,0)E(N,l) - E(N-1,0)

Elastic CotunnelingInelastic Cotunneling

N+1N+2

-O *,#&;,]+" ##>## %&±ª1/1 !M ¦ ) ) ¬#)³ )! @ )!TO±0" !.+ !#" $ +)!+,# ! ## ±0/.;±) !+3K±0 ! jb ! ! +)1 !K+##) !"7+±0 !#"7 ! #?0+ g± 1b $'&H+)!+,j1/1 ;++ °+-;,, #)!³ = +, ;±0)! !#+ +#± +&; $ ;±) !+% , !#")!&H+)!+,.,&;, #+)!, "° M °M#?0+ g±1³ !" (#"/., + ° ±+ °#1, !"3 +)!+,&± )&)! O %##+)! !#"3g; ++0 = b O g± ¦ ) ) ¬ L;b ! ; !/.0) #" ± '"9) / ! + !" +±/M o#"/%+1vY ! °g±0 o1³ % *g, )!&H)! O +##) !" ° " ± ° #³I b ):3 f ^ + f | + & ! ",-"!$#:$!$A,94 &@)A. & > &(,&58 3+)A! 4'4 & = ! &l#$"! = #') 8>A!# &>3 !&(!*&>30:/9 + &!*&>&5# !*) ; &(3&>.)A3+&0 &El#$"!9> = #*) 8>"! /0& &d1*8 &5# A!$# 8("! ,)]):4& ! 4&>1*8 + ):! m .G4$8 "!&>!$&>30 3+A!$47.&>3C/0& j &>&(! l#$"! = #') "!$#T,&(:#*4 )'8(8b*3?4048 8d):33+&>, &(#j )>t&>,&(8 3):! $!*!*&>, !9c6*3+)]8>&(4+4 4#*&>!*) &(#D:4%FRQ EtA T V FHG G+D V W3Q=Q E!FRQ

g 0³ ±0°( "9 °-0 !")!M %&Ho-/01+ H !$8d& !`C4 = ",,l#$A! = #') ):!*,tk.& &d1*8 &(#<4 &(4h"3+&9.)*!$# !GC8d&(3 !&(!*&>30 !$#') 8>,)47& ) &3A3+)0*!$#$4 &*/$:4 8>A,,r):!*,t &>,A4 8>A, 8d) *!$!*&>, !ª)'8>8*3?4 ; * 4 4# &>3+&>! .)A3 = & A,>t, :&kl#$A! = >#') 4'4 & = &>3+& !$&>,A4 88>) $!*!*&>, !9 4A,4)G.)0*!$#D 4 = ",, #'3? !;>47)*3+8>& )A, :& !$8d3+&(:4 !9 f ^ + f /&A):!$# D/):3+#*&>3+, !*& #'&548>3 /&5#W/ + &.A&(!*&>3?", 3+&b>, + ):! l* l: = ):3&@"!$# = )A3+&@)]8(8b*6 &5# 4 &(4k)A. + &@& = 7 &(3B"!#*!$)]8(8b*6 &5#4 &(4 )A. + &<8d):,,&(8 ):3 8>"! /0&°$47&5#.)A3 4$8 &>,&(8 3):!;>t, A&k"!$# ):,&> , A&E8d) *!;>!*&(, !9 6*3+)]8>&(4+47&54 ! )A, ] !ª & 4+ = & ! ",A!$#j:$!",4 &(4 f 4"! ^ p ' A!$#f 4"! ^ p ' 47&(& b l* # "!# b l$ # M ; &>3+&d.)A3+&0 !$) 6&5 /9 = )A3+&c4 &(6;> , A&B8 A!9A& ! + &G# &>3+&>! ",h8d):!$#;$8 "!8d&B#2*,+ # ^ + 8("! /0&B&>1]60&(8 &5# + & &(3 + 8(", /0)A3?#'&>3+, !*& ! + & ^ 4 ^ + 6*,"!*&E#'&548>3 /&5# /# Hl* l:d< 4 c *3!4@)0 %8d) *!*!$&>, !9 8("! "3?#',r &d1'6*, ! & ~ &>3+)>t/ :4@"!*) = A,t):/$47&(3 &(# ^ + F | ! b l$ R >2 )A3+3+&>, &5# *!*!*&(, !9 6$3)'8d&544&(4 ! ):, ] !9= )A3+&<&(,&58 3+)A!4 & )/& 0A&>! ! ) A8>8>)0*! m !:&>!*&(3+A,0# 0&(3&(! 8>:47&54.)A3+ &<l#$"! = #') & )c/0&<# 4 !9 4 &5#,&(:# !ª ) # 0&(3&(! /0& ] )0*35s

I ; &T&>!$&>30 ,A#$#'&>3 4 ^ p % % H 4"! ^ p2 ddd 4 %H 4 4 H 4 ddd A!$# 4<60):4 + ):!W3&(, r &>,r ) & &>,&(8 3+)]8 & = 8(", 60) &>!;> ",4 )". + &W,&5A#*4 #'& &>3 = !*&54 &W! = /0&>3D)A.B&>!*&(3 ,& &>,4 * 8 "3+& )A. = 60)A3 A!$8d& I ; &(4&k,& &(,48("! /&E& + &>3 #'&A&(!*&>3? &^):3 !*)A!;>#'&A&>!$&>3? & I ; & *!*!*&(,8>)0*6*, !9C4 3+&>!9 "!# & & = 60&>3? *3&-"3+&9)". = 60)A3 A!$8d&(#'&:$!;> !ªk# &>3+&>! /0& ] )0*3 )A. + & l#$"! = #') *!$#'&(3%4 = & 8>)A!$# + ):!$4o r &(!`/ ^ p ; &kl#$A! = = &58 "! 8>A,6 A4&E8d) &>3+&>!$8>& 4#'&(4 3+)A&5# + !$8>3&5A4> !ª & = 60&>3? $3& Z &>! 6"3? = & &>3 A,t*&54 &>3+&a4 !9:,&> &(,&58 3):! 3?"!$46):3 )]8(8b*3?44$8 8>)A3+3&>, &(#D&>,&(8 3+)A! *!*!*&(, !9& &(! 4 = )'# .` + &B3+&(4*, 8d) = 6$"3+&(# ) &`)A3 )'#')21+ &>):3 ; &>3+&0 & &>!*&(3 8>):4 4c.):3 & ! &>3 = &(# & 4 & "3+& & ,) &(4 m ,&(:#*4k.)A3 !$4 A!$8d& ) B TbD Q@A QVVW3QQbEFRQ . ^ ^ p 4B", :!*&(# +W &&(,&58 3+)'8 & = 8>A,-60) &>! ",4 ^ "!$# ^ + s ; &Tl#$"! = = &(8 A! 8>", 6 A4& 4^6*3&547&(3 &(# .):3^&(,&58 3):!$4C6A4+4 !9 + & 4,"!$# b )A3E4 = ",,hl#$A! = #*) k + &(,, 6*3+)A!*)*!$8d&5# # 48>3& &&d1*8 )A! 46&58 3 = + & , !*&b>4 "60&)A. 2 )0*,) = //*,)'8+nA#'&k):4+8 ,, )A!$4 3+&(4& = /$,&54 ,) & = 60&>3? *3+&k )A3+&>! ~( A! o HAH g r m ! & .)A,,) !9S & ,,E3&54 3 8 )0*3?4&>, &(4 ) 4 = A,,El#$A! = #') 4.)A3*!#'&>3?4 "!$# !9 & ~ &>3+)>t/ A4 "!$) = ",rc)A/$4&>3 "/*,& ! b l$ R 0 -FB& DE4 " 0,"3 $% -FB9;"? % C% - B " 1 DE4X &d.):3&k4 "3 !9 n G/*3 &d. * 4 )A3 8^3+& ] & s 4$A,,r &^3+&(4 4 r] @)". = & A,0#'&58d3+&(:47&54 3&5#;$8 !9 & & = 60&>3? *3+&a#;*& ) &C3+&(#;$8>&(#c&(,&58 3):! 48( 7 &>3 !ªB - &(3 = ",06 ):!*)A!4%"!#c/&58d) = &54-8>)A!$4 A! ,) & = 60&>3? *3&`, = &(# / + &@4 8G# 4)A3?#'&(3 ! & )4 8d3'4 ",_, 7 8d&

0³ A, - ! #)! ±) ! -,#"e = ,±0, #0 !/ ±) g

ResistivityIncrease of

Res

istiv

ity

40 800

Cu

Cu with0.2 % Fe

ε0

ε0( )

ε +U

εF

Temperature [Kelvin]

second electron

(a) Kondo Effect (b) Anderson Impurity Model

Fermi level

electron seafirst electron

impurity site (degenerate !!)

¦ ¬ ±K#"9+ ! ±0 )!0g± ! #0 ! !+e ! 3 g, ! +, !1 $ / b) ! + ;b³ ¦ ¬ = 0,Q±0, / °±0+)ª±+, ;+)!+, !Q)!7$ ) % « ;#±eM3 ! / ;+)! ! ° )!7$ +) %%9 ±0# !#± ! ! gA;+# !g± + /j &# !&Hj & 0&± ! j+)!+, ±0#.##+)! !#" ; ! +% ! # / , #±e+± !+##±ª³ ++# !@/M ! +)!+,# ° ° !,,,g± )! ! ;0+±0#° M !.+"/ ³.&(, / &D8>)A!$#9$8 + ):! /$A!$# &(,&58 3):!$4 m ! & H L: | m 4 c A4G)A/$4&>3 &5# o H l" r+ ! 8>)A! 3?"3 ) * 4&>1'6&58 )A! + & 3+&(4 4 r] !8d3+&(A4&(4c0: ! ,) & = 60&>3? $3&B.)A3 = & A,4^, :& 2 * 8 !$8d,r$#'&c4)>8>A,,&(# = :!*& + 8 = 6ª*3 &(4, A& 2 ) ):3 b & ! 8d)A!8d&>! 3+ )A! )A.a,&(4+4 A! H 4&>&D4:& 8 ! b l$ l dm B )])0 ", = ):4 | :&(A3+4 &>! ! H Ll" *! )A!#') #'& = ):!$4 3+ &5# o H l:g r 46 !;>48( 7 &>3 !ª )".B8d):!$#;$8 )A! /$A!$# &(,&58 3+)A!4 &547& = 0A!*& 8 = 6ª*3 &(4&>1'6*, !4 * 46 &>!$) = &>!*):! ; 4 * 43+&(4 4 +t] !$8d3+&(:47& ! = & ",4 = :!*& + 8 = 6ª*3 &(4 4<8(",,&5# D Q0D +G V < !*) + &>3 = )'#'&>, ! 3+)'#;$8>&(#/ ]f I< !$#'&(3+4)A! ! H L0l H o H l H r n + &%4)>8>A,,&(# &Q bB6TD QF M?;W;BgFRV D bE n 8("!A,4)C/0&$4&(# )k#'&(4+8d3 /0& & &544&>! ",6 '4 8>4 ; & < !$#*&>3?47):!

= , ):! A!GA!$#+ & ):!$#') = , ):! A! = "6 *!$#*&>3 8d&>3 !c8>)A!$# )A!4Co H l0l r ; &58 ! l$&(4 &/0&>&(!G#*& &(,):6&5# ! & .):,,) !ª :&("3?4 n #*&>!*) &(#@:4_! = &(3 8>A,'3&(!*)A3 = ", t~ )A!:3)*6 &(8 ! l#*&54f6 ):!*&>&(3&5#</ 3 ,4)A!Do H l p5r n ",,) !9 )E4)A, & &547& A!$#&>1 &>!#'&(# = )'#'&(,4 * 8 6$3&5# 8 _+ &-.)A3 = )A!`)".$!*):!;> 3 t] ", = A!>t/0)]#9k4 &54 A6*6*3+):A8 $ !9`,) & = 60&>3? *3+& ; &`/$A4 8 !ªA3+&(# &>!$8>&(4 .)A3 + & < !$#'&(3+4)A! = 69*3 = )'#'&>,f"3+&<4:& 8 &(# !b l$ l / s < ,)]8(", t~ &(# &>,&(8 3+)A! 8@4 & n 8>0$4&(# .)A3 !$4 "!$8>&@/# /)*!$# &>,&(8b> 3):! 8B4 & )A! = 6ª*3 )A! n 4^& = /0&(#*#'&5# ! b &(3 = 47&5 )A.-8d):!$#;$8 )A!/"!$# &>,&(8 3):!$4 ;Z ,&58 3+)A!4 )". &c8d):!$#;$8 )A! /"!$# 8>"! )A6 / l"! = = &>8 "! 8>A, *!$!*&>, !ªB)A! ) * 4 = 69*3 @4 &CA!$# ] 8>& &(3+4+ H !8d& + &C&(!*&>30 J c.):3<D4 !9A,&@&>,&(8 3+)A! E & = 69*3 4 & 4k/&(,) & b &>3 = ,& &>, J 8 )A. &8>)A!$#9$8 + ):!/$A!$# &>,&(8 3+)A!$4 &E&(!*&>30 ,& &>, J c + & = 69$3 4 & 4A, '4

g 0³ ±0°( "9 °-0 !")!M %&Ho-/01+ )'8>8*6 &(# /#TA! &>,&(8 3+)A! m = 60)A3 "! ^ 4 &@:44 = 6 + ):! k &G&>!*&(3D,& &>,8("!D/&`)'8>8b$6 &5#D/& + &>3k"!T&(,&58 3+)A! T+ &`l#$A! = ! = /0&>3^476 !;>1*6T)A346 !;>t#*) ! n + &<&>!$&>30 ,& &>, 4 QbBA V ; &E)'8>8b$6$ + ):! / j )@&>,&(8 3+)A!$4 &B4+ = & + = & 4C4*6*6*3+&(4+4&(#D4 !$8>& * 4 3+&(l# 3&54 ) ) &>3?8d) = & & 2 )0*,) = /3+&>69$,4 ):! )A! * 4 4 &k#'&548>3 /&5# / &a6$A3+ = & &(3]A!$# + &^&>!*&(3G,& &>,0.)A3+ &<47&58d):!$#&(,&58 3):!, &54 &(3&>.)A3+&E"/0) & & b &>3 = ,& &>, J c

J8 H]):, ] !9 + & < !$#*&>3?47):! = 69$3 = )'#'&>, D $3!$4 ) D 8>"!$!*) /& 3&5 &5# ! 6&(3 *3+/$ + ):! ,) & = 6&(3+ *3+&As !*,r 8>)A!$4 #'&>3 !ª & ,) &54 >):3+#'&(3 *!*!*&(, !9 6$3)'8d&544&(4_4 A3 + !ª &(,:4 + 88d) *!*!$&>, !9 /& j &(&>! = 69;>3 D"!# b &(3 = 47&5#'&548>3 /0&(# ! &`6*3+& ] )0$4H]&(8 )A! 4C!$) &>!*)9 @< ,) & = 6&(3+ *3+&0:",, * &(3>t)A3?#'&>3 8>)A3+3&(, &(# *!$!*&>, !ª<& &>! 4 & )E/0& !$8d,r$#'&5#n = "!#> /0)'#; 4 & 4a.)A3 = &5# #'&>!$) &5# :4 + & D Q 0D T6V,A V ; &(3&>.)A3+&0 & ! &>3+!$A, #*&A3+&>&)".a.3&(&(#') = ! )'8>8b$6# !9 & = 6ª*3 4 &D/# W46 !;> $6 )A346 !;>t#*) ! &(,&58 3):!D:8 4 A4a"!D&b &(8 r &B4+8> 7 &(3 !9 = &(8 "! 4 = .)A3^8d)A!#;$8 + ):!/$A!$#G&>,&(8 3+)A!$4 ; & ):!$#')E4 & 4 &>,,$#'& &(,):6&5#`/0&>,) &C4)>8>A,,&(# )A!$#*) & = 6&(3+ *3+& r &(!/ o H l r

F R d &d1'6 % N w J 8 % J c z d w J c % J 8 z [ l* H R ; & )A!#') & = 60&>3? $3&c#'&(6&(!$#*4k)A! & *!*!*&(,98d)*6*, !9T#'&548>3 /0&(# / FPQ

*):! &^&(!*&>3A& 8a# 4 A!$8d& J 8 % J c *"!#):! &^):!;>4 & ! &>3?A8 )A!&(!*&>30 m ! H L0 j ) 69$/*, 8> )A!$4 m 3^, ~ = A! "!$# [ ZC o H l2L r ; K A!$# ]f #') 4'4 & = 3&547& = >/*,&(4"! &>1 &>!$#*&(# < !#'&>3?47):! = 69$3 = )'#'&(, X +* 4 "!",)009 , !9 .3+) =l#$A! = >t#*) 4'4 & = 4 ) )A!#')T6 '4 8>4 4' r &(! < /) B &>! :&("3?4E, &>3 !H LML0i` 3^):,# "/0&>3>&3^):3+#*)A!<"!#<8d) )A3A&(3+4fo H p H r]8>)0*,#<#'& = ):!$4 3? & & )A!$#*)&0&58 &d1'60&>3 = &(! ",,t ! l#$A! = >t#*) 4'4 & = 4 8>)A!;:$3 = &(# / 23+)A!*&(! & VAE

o H p R r_A!$# $ H'8 = # VAE

o H p r ; &B#* G)". $ H'8 = # VAE

)A/ !*&(# !)*3C,"/0)A3? )A30*"3+& $4&(# &>3+& ;Z "3+, &(3 &d1'60&>3 = &>! 4C/ iB ",6 A!$# 8d) )A3#>&(3+4 o H p r )A! <4 = ",,08 A3:& 3?"6c& = /0&(#*#'&5# ! $ !4 , 8d):!c! 3 #'& = & = /*3?"!$&/0& j &>&(! = & ", &(,&58 3)'#'&54 &k",47)G/0&>&>! ! &>3+6*3+& &(#DA4 + & )A!$#*)`&0&58 ; & = A6*6 !9 )". &Gl#$A! = >t#*) 4'4 & = )A! ) & &>1 &>!#'&(# < !#'&>3?47):! = 69*3 = )'#'&(, 8d)*,# )A3 *!$#'&(3 &k.):,,) !9G8>)A!$# + ):!$4 4&>& b l$ p sH ; &&(!*&>30 ,& &(,4 J c "!# J c )A. & < !#'&>3?47):! = )]#*&>,"3+& #'&>! :$&5# ++ &E,& &(,4 ^ ^ p A!$# ^ H ^ p6 $3&54760&(8 r &>,r R < , )9 ! = )4 l#$"! = #') 4 4^!*) &(l#$A, ) H + &3S$8 $ + ):! ! &&>,&(8 3):!W!# = /0&>3`A3& A, = )4 3+&(4 3 8 &5# ) A!$# H . &,& &>,476$:8 !9:4 ^ R ^ p % ^ H ^ p A!$# ^ ^ p % ^ % H ^ p "3+&<,A3:&B8d) = 6$"3+&(# ) & + &>3 = ", &(!*&>30 "!# & *!$!*&>, 8d)*6*, !ª F PQ $ & &>,4%#;$& )B&d1*8 &(# 4 &(4-)". & )A3 H &>,&(8 3):!4]4 & = 4 )*,#c/&&>!*&(3:& 8>A,,r &(,,*4&>6"3? &5#k.3+) = &:3)*!$#*4 & )A3h!*) :8>8d&544 /*,& #;*& )

0³ A, - ! #)! ±) ! -,#"e = ,±0, #0 !/ ±) g )])`4 = ",, *!*!*&(,08>)0*6*, !9 ) &a,&5A#*4-"!$#62)A3-47&(,&58 )A!3*,&(4 4&>&&H'&(8 + ):!g' L:d$ ; ) )A/$4&>3 & & , &>3 # 48$44&(# )A!$#*) 3&547):!$"!$8>& ! + & 3+& ):! )". &>,&(8 3+)A!$4E8>)A!;:$!$&(# ) & #') & 0BD W3Q T V,A V KD V S E+G V BD Q T T V D QV D V 9A T V,DjC Q BA V & j ) )A3 )A)A!", >t&>,&(8 3+)A! 4 &544 )0*,#<&>1 4 h+ &A3+)0*!$#$4 &-&>!*&(3 s 4 H ^ p % 4 | ^ p F| 4$",,r0$@46 !D#'&A&>!$&>3?A8b 4 :44 = &(# i *& ) + &@#'&:&>!*&(3+:8b08d) *!*!*&(, !9 3+)09 T &Gl#$A! = #') 8>A! )'8>8b$3 ! & &(3 4 & < 8 $A,,r + &Tl"! = >#') 4'4 & = 6*3+&d.&(3+4@/0) + 4 &54 & + &C4'4 & = 4 !$4 &>!$&>30B/G#') !9B8>)A3+3&(, &(#`&>,&(8 3+)A! $!*!*&>, !9B60&>3 = "!*&(! ,t 6*6 !9 + &B46 ! )A3 &>! )A! ,&5A# !9 )c!*)@6*3+&d.&(33+&(# 46 !9> 60)A,"3 t~ + ):!)A! &l#$A! = #') 4 & ; & ):!$#')B4 & 4 #'&(4+8d3 /&5# A4 <46 !9>t4 !ªA,& 4 & H !$8>&.):3C8d):33+&>, &(# $!*!*&>, !9ª&>,&(8 3):!$4 & )8>) = &E.3+) = )'8>8b$6 &5#T4 &(4 ! &,&(:#*4 "!$# & )G&>!$# !*!*)'8>8*6 &(#4 &54 ! + &k,&5A#*4 &k&>,&(8 3+)A! 8C4 &54 B+ & b &>3 = ,& &>, "3+&)A. = 60)A3 "!8d& Z A,t !9 + &D4 = 6*,& < !#'&>3?47):! = >6ª*3 = )]#*&>, ]8>)A3+3&(, &5# = "!#> &(,&58 3+)A! *!*!*&(, !9G6*3+)]8>&(4+47&54%/0& j &>&(!#') A!$#3+&(4&>3 ) 3 4 ,&(A# ) 4 "3+6 6&5 ! &&0&58 r & #'&>!4 W)".a4 & #'&>!$) &5#:4C46&58 3+A, .`*!8 )A! J C & = 69*3 T4 &B6 !*!*&5# ) & b &(3 = ,& &>, J 8)A. + &<3+&(4&>3 ) 3 4 C 47&(& b l$ M ; $ 4a4 A36D60&(0# 4A6*60&("3?4 . + & & = 6&(3> *3+& )". & 4'4 & = 4 !8d3+&(A4&(# "/0) & & ):!$#') & = 60&>3? *3& 47&(&b l$ / M< , )09 J c J 8 A!$# J c

J8 :#;*& ) * 4%&0&58 +t &a#'&(!$4 G)".4 & 9 & b &(3 = ,& &>,)A! & = 69$3 G4 & 3&54760&(8 r &>,r0l#$"! = #') 4 & + &>3+& 4-<6&5 ! + &k# &>3+&>! + A,8d):!$#;$8 A!$8d& + 3+)09 @* 4 = 69*3 3&54760&(8b>+t &>,r0 l#$"! = #*) "3+)0$!$# ^ + F | ; * 4C6 !*! !9 ) J 8 4 !$#'&>60&>!#'&>! )".+ &G6)4 )A! )A. J c /0&>,) J

8 m 0&58 4C):!*,t + & ):!$#') & = 60&>3? *3& & + & & = 60&>3? *3+&G/0&>,) * 8 & )A!$#') 3+&(4)A!$A!$8d&@4 *3? &(4 < 4<#'&548>3 /0&(#

E(N,1) - E(N-1,0)

E(N+1,0) - E(N,1)

E(N+1,0) - E(N,0)

E(N,0) - E(N-1,0)

ε

Quantum Dot System

( ) ε 0

ε

(Extended) Anderson

ε +U0

F

Impurity Model

Source

N+1

Drain

N

degenerateSource Drain

J !#" ) %&±91/01+ = ¦ #?+±0g± ¬ ,Q#±, ! #0 !/ °±+)³, ±0+"+/ ! "#±01%] $3&), 1/01+ ! /# g±9³ = ±+"+#/. ! !±0 +g± / e±#)!&H)! !#³ QL.; ±"+/K ! @,Q±0, /% °±+)ª !T?)! !)!/' ! !3 ° ! +/³

0³ ±0°( "9 °-0 !")!M %&Ho-/01+ / Hl$ H R 4^,) &54 .)A3 J 8 % J c F Jc % J 8 & ! & = #*#',&`)A. &2

)*,) = /</$,)'8+nA#'& 3+& = &0 &(3& J 8 % J c F R < _+* 4f60):4 )A! l* H R 3+&(A#$4

F R d &d1'6 % N [ l* H b )A3-G8d&(3 ! 3? )</0& j &>&(! A!$# ' & F d + & )A!$#') & = 60&>3? *3+& !$8d3+&(:47&54, !*&5"3+,t b )A3 2 | [ R d A!$# ",r*&54 F H = &%; ) F R= &%;' $ 8 A3& ]6 8>A,%.):3 + &6*3+&(4&>! &(# l#$A! = >t#*) 4'4 & = 4 &)A/ !

F g | = ) H|| = >X &(,)

&@l#$"! = >t#') 4'4 & = #'&548>3 /&5#/ & < !$#'&(3+4)A! = 69*3 = )'#'&>,:/&58d) = &54_8>)A!$#;8 r &%) &>3 + & )A,& 2 )0*,) = //*,)'8+nA#'&^3& = &a3+&(:8 * !ªB& &>! &<8>)A!$#;8 A!$8d& R Q * 8 4 &(l#$A, ) &8>)A!$#;8 A!$8d&G)". D476 !;>#'&:&>!*&(3+ &G)A!*&>t# = &>!4 )A!$A, 8 "!*!$&>, &>3+&@!*) *!$!*&>,/$A33 &>3?4-A3&k6*3+&(4&>! ; $ 4 /0& ] )0*3 44A& 8 &(# ! b l* 8 b 3+) = &E#'&(6&(!$#'&>!8d& Hl$ H R )". & ):!$#') & = 60&>3? *3& ):! + & *!$!*&>,8>)0*6*, !9 - 4-8>,&5"3 - &>! A!$8 !9 + &k8d)0$6*, !9 4 !$8d3+&(:47&5# ; $ 4 48>)A!$4 4 &(! % + + &C&>1]60&>3 = &(! ", #* E6*3+&(4&>! &(# ! b l$ R s < :$1]&5# & = 6&(3> *3+&0$ 6&5T#'& &>,)A6$4C ^ + F| + !8d3+&(A4 !9 & *!$!*&>,f8d)*6*, !9 ; &if T < TK

εF

Kondo Resonance T > TK

εF

(a)ε

A( )ε

(b)ε

A( )ε

(c)

0VDS0VDS

VGS

IDS

Conductive due to Kondo Effect

VGS

IDS

Coulomb-BlockadeOscillations

= 3&;+,)r## ¦ % ¬ 7 E## ±0 , M #+M 7 )! ° Y $# ! !#"##+)#+#)! !#" +#"/ , + °#,g±;#r³ ¦ ¬ ;+)! ! ±0+ ;bL. ¦ ¬ %; $ ±0M+ ; ¦ t ³-0 ° ±.L °Y ¦ % 7% « ¬ ¥ ¯ . ¥ . F < ¥ )v ¦ ¬ ± gr ¦ ¬,¬ ³ * !#g, !#" ±0 0&H,$) "L. ! )!Q&;+,)r## #"++³ ! *;+O=bQ#?;+g±.# !#g± -; ° @)!7$ +)!% )+±+³ ' . `³ ¦ ¬ */# !1+r v !3@ ±0 1bv) #)!)+±. ±0o ! !" ) /°±0# $ $ ! )! #)! )!TO±0 +" !S³ ,o !" %+ ;bL. ±1 !±+1,g/+± #±3 #,#) #)! @ ) O±,+ !)!) !+%$g±ª³

0³ I +1@ , S( ?; ! °+) L;, !+ g±0 !g± /Q ,Q±0, #0 / ±+) 60&(0 4Q:$3?4 )G/0&k4&>&(!8d,):4& ) &k4 !9:,&> &(,&58 3+)A!9> *!*!*&(, !9<60&(0]4'"!$# +.`$3 + &>3 !$8d3+&(:4 !9 & *!*!$&>,8>)0*6$, !9 ! + & = #$#',&C)". + & 2 )*,) = /G/*,)]8+n:#'&3+& = & b $3 + &>3@&d1'60&>3 = &(! 4`A3&6*3+&(4&>! &5# ! &.)A,,) !9 4$6*6):3 + !ª &, !9 ) ):!$#')G6 '4 8>4 ?A42"+7( $" 8 B@ =-F4%,"3 7B@ 3"$ : $ &9;"3 O1 " % =2,% -FB& " 1 DE4b 3+4 9 4 &54 &(# & & = 60&>3? $3& #'&(6&(!$#'&(!$8d& )A. + & ~ &(3)0> / :4hA!*) = A, &(4 &(! n/BA6*6*,r !9E = :!*& + 8Q:$&(,# n & #*&A&(!*&>3?A8E)". &&(,&58 3+)A!@4]4 & = 8>)A!;:$!$&(# ! + &l#$A! = #') X ) 3+&(4*, 4`8d)A!9:$3 = ` 4B&>1'6&58 &5#W.3+) = ):!$#')3+&(4)A!"!$8>& .- + - QXZ # XNL;\*NX X # XV YXV UXm ! b l$ L 9d ~ &>3+)>t/ :4 "!*) = ",r 4 6*3&547&(! &(# = &(A4*3+&(#^)A!E4 = ,A3 l#$"! = >#*) 4'4 & = /9 *!#'&>3 /& 7 &>3 &d1'60&>3 = &>! ", 8d)A!# + ):!$4 A! &a):!*&C6*3+&(4&>! &(# ! b l$ R ; &`6&5 ! &`# 0&(3&(! ",f8d)A!#;$8 "!$8>&`#2* + # ^ + ^ + F | 4 4 3):!9A,r`&>1'6*3&544&(#c F R g = !8d3+&(A4 !9 & & = 6&(3+ *3+& ) |0|= 4&>& b l* L / $ 4E60&(0 # 4A6*60&("3?4 &>3+&(A4 + &@) + &>3k.&5 $3&54 ! &# &>3+&>! ",h8d):!$#;$8 "!8d& ! & ^ 4 ^ + 3+& = &<3+& = ! A, = ):4 *! &(8 &(# m ! b l$ L 8 + & & = 60&>3? *3&#'&(6&(!$#'&(!$8d&)A. & # &>3+&>! ",*8>)A!$#9$8 "!$8>& A,):!9+ & 3+:8d& = "3A&5# ! b l$ L 46*,) 7 &(# s < ,) & = 60&>3? $3& + & 60&(0 ^ + F | &d1*8d&(&(#*4 Q F |0| = &@60&(0 4E8>) = 6*,& &>,r # 4+"6$6&5"3+&(# &>3+&(A4 + &</$:8+A3+)0*!$# 4!*) 8 "!9 !ª & = 60&>3? *3& ; &<):/$4&>3 )A!)A.a 6&5 ! + &T# 0&(3&(! + A, 8d):!$#;$8 "!8d&D# 4+"6$6&5"3 !9 + !$8>3&5A4 !ª & & = 60&>3? $3& 4 ! l#$A, r &WA3+&>& = &>! & 6*3+&(# 8 + ):!$4 )".@ ):!$#')3+&(4)A!"!$8>&0'"!$#K: 4 ) &E&(4 = &° t &>! + l* H M< &5A8 : &>t4)0*3?8d& ):, :& A,t*& ^ & )A!$#') & = 60&>3? $3& 4%E# &>3>&(! )A!*& ; &6&5 & 4 )0*,#&P$4 #'&>60&>!$#@):! &3? + ) & + & & = >60&>3? *3+&^#'&(6&(!$#'&(!$8d&< + &E3+&(46&58 r &e: & ):, :&C60):4 + ):! 8("! /&E3+&(4+8>A,&5# H;]4 & = 8 = &(:4$3& = &(! 4 &E/&(&>!*!#'&>3 0A&>! o H p:p# H p L R r1#'& = )A!$4 3? > !9 !$#'&>&5#D"! *! r &>3?4+", /& ] )*3&d1 4 4*8>)A!;:3 = !9 & ! &>3+6*3+& )A! .- + - T(\THV \ YX X @XV X#NL9U T`\ L @V X#\TUTXR ; ) ! &(4 : & & + &>3<T#'&A&(!*&>3?A8T&d1 4 4E.)A3 & A3+)0*!$#$4 &@)A. + &c&>,&(8b> 3):! 4'4 & = 8>)A!;:!*&(# ! &Gl#$A! = #') 0 = 0A!*& 8%:$&(,# 4^"6*6*, &(# ! &6$,A!*&c)". & j )0>t# = &>!$4 )A!$A, &>,&(8 3):! 4'4 & = 4&>& b l* H| M ; &# &>3+&>!9>+ A, 8d):!$#;$8 A!$8d&E#2* + # ^ + 4 = &5A4*3+&(# ! + & ^ 4 ^ + 6*,"!*&k.):3 "3 )$4= 0A!*& 8:$&(,# ",r*&54 m ! b l* H| / &E#* @"3+&k4 ) .)A3 F | ; F R; 9A!$# F ; < 476$, 7+ !9 )A. + & )A!$#') 3+&(4)A!$A!$8d& 4@):/$47&(3 &(# 4*6*6$3&544 ):!)A. + &<# 0&(3&(! + A, 8d):!$#;$8 "!8d&E ^ + F |

¯ 0³ ±0°( "9 °-0 !")!M %&Ho-/01+

VDS [mV]-1 0 1

d

I DS/d

VD

S [e

2 /h]

0.5

0.75

1

1.25

50

100

200

400

800

T

[mK

]

VDS [mV]-1.0 0.0 1.0

VG

[V

]

-0.56

-0.55

-0.54

dI/dVDS [e2/h]0.0 0.5 1.0 1.5

VDS [mV]-1.0 0.0 1.0

VG

[V

]

-0.56

-0.55

-0.54

dI/dVDS [e2/h]0.0 0.5 1.0 1.5

DSdI /dVDS [e /h]2

(a) (b)

dI

/dV

DS

DS

[e /h

]2

(c)

GS

V

0 1-1[mV]DSV

1.5

T= 25 mK

-0.55

-0.54

-0.56

0 1.00.5

[V]

0 1-1[mV]DSV

T= 800 mK

DS[mV]V

-1.0 0 1.0

1.0

0.0

0.5

50

100

200

400

800

T [mK]

;0±7;+#±++ *& # )!/ ¦ ¬ '"9+ )]+&±+ ± ¥ ± ) "/0,g)! % ¦ ) ) ¬ #)L. °g,g±e < ¯ ³, ! +)!)J##++± +& # # ) /° !oL, $ g± !3 #)! E) O±+" ! °³¦ ¬ ,=< .# & # # ) / ! $ !, #)!³ ¦ ¬ '"9+ ) +±0#&+Y,+Y± ¥ ± ) $0+³ ) !e = ° ±±)!=# )! @ #)! O±=+" °)!#" °)! !# !±0 +g±7 ! ¦ ¬ r°±0 '"9++ ;0$)!#+" $ !" , ±³= ? ! )TrQ $)! ±EvQ ,+O+ !" +1+ ;b³ = ,+Qb"9,g³ ¦ ±0L+± r °g,0+ °+o ³-0 ° ± ¯ S '0Q)%;,/ ¬

0³ I +1@ , S( ?; ! °+) L;, !+ g±0 !g± /Q ,Q±0, #0 / ±+) L

(a)

VDS [mV]-0.5 0 0.5

VG

[V

]

-0.65

-0.64

-0.63

-0.62

VDS [mV]-0.5 0 0.5

VDS [mV]-0.5 0 0.5

2

1

2

3

4

6

8-0.2 0.20

0.05

0.1

VDS [mV]

B [

T]

G

[e0 /

h]

-4 -2 0 2 4 6 8

-0.2

0

0.4

B [T]

V

DS [

mV

]

(b)

(c)

B

V [mV]DS

V

[m

V]

DS

∆e V DS∆

gµ BB

VDS [mV]0 0.5-0.5

-0.62

-0.64

-0.65

-0.63

[V]

VB

S

VDS [mV]0 0.5-0.5

VDS [mV]0 0.5-0.5

0 Tesla 2 Tesla 4 Tesla

00.2-0.2

[e /

h]2

dI/d

V

-0.2

0.4

0.2

0

-2 0-4 4

= 2

+-|g|=0.46 0.02

2 6 8

Magnetic Field B [T]

0 T

1 T

2 T

3 T

4 T

6 T

8 T

0

DS

0.1

¦ ¬ , "# #+)± !#)! !g± ! #) ## ±1/01&+ ³ ¦ ¬ '"9+ ) +±0##+e± ¥ ± ) ! ¦ ) ) ¬ )# !"/0,g)!v + ± '"9 " !1 +)± $)++³ = .±#b bO + ##±° ° +#± & K ,e% !"³ ³ ¯ ³ ¦ ¬ ++± ¥ ± ) $+³ ) %O +. !K ° ±±)! %Y #)! @ #)! O± " ! ° rM± '"9 ³ >$ !,)!/ .; & # # ) /.&#)! ! ! "# ! )t±9³ = &#)! , !#" ∆ ) ¦ ¬ #oM ! !+ ;++ &) , !#"0³

I 0³ ±0°( "9 °-0 !")!M %&Ho-/01+ ; * 4 4 &d1'60&(8 &(# s + "6*6*,r !ª + & = :!*& + 8:$&(,# + & 476 !;>#'&A&>!$&>3?A8b 49, . &(#/# & 0&(& = "!c&(!*&>30 F ^ &(3& #'&(!*) &(4 + & "!$# & . A8 )A3A!$# ^ & X ) 3 = A!$& ):! H !$8d&< ^ + F| ):!*,t&>,A4 8a6$3)'8d&544&(4 A3&^6)4>4 /$,&:46 !9> 6 6*3+)'8d&544&(4 /@8d):33+&>, &(# *!$!*&>, !ª`"3+&C4*6*6*3+&(4+4&(# ; & ! &>3+!$",#'&A3+&>&`)".9.3+&>&5#') = 8("! !*) ,)A!9:&>3^/&$4&(# ; & )A!#')4 &@8>"!$!*) #'& &>,)A6 ; * 4E/0&(8>) = &(4E# &>3+&>! :$! & / A4 )A, :& ^ + : 7+ !ª ) + & 0&>& = "!W&>!;>&(30 f ^ + f F H]6 !;> 6 ª$8 $ )A!$4^/0&(8d) = &G60):4+4 /*,&c ! / !$&>,A4 88>)A3+3&(, &(# *!$!*&>, !ªª%4 = ,A3 ) :4c#'&(4+8d3 /0&(# ! H'&(8 + ):! l* R .):3 &,) &54 > ):3+#*&>3-8>)A3+3&(, &5# $!*!*&>, !9c6*3+)]8>&(4+4 n + &<8d) *!$!*&>, !ª m !$#'&(&(# 8>",8b$,>+ ):! o H p g H p L H p l r 8d)A!9:$3 = 60&(0'4 ! &^# 0&(3&(! + A,08>)A!$#9$8 "!$8>&C4 )0*,#/0&E)A/$4&>3 "/*,&k &E3+&(460&(8 +t &k/ :4*A, + )0ª + 3+&(#9$8d&5# = 6*, #'& ; &E46*, 7+ !ªª & + & )A, 0A&^# &>3+&>!8d& ∆^ + /0& j &>&(! + & ^ + ",r*&(4 * 8 &@60&( "6*60&(A3+4^)A! & &>3B4 #*&(4^)". ^ + F | 4 )*,# 3+&b$&58 kj 8d& &0&(& = "!B&>!*&(3 ; &-3+&(460&(8 +t & ",r*&54 ∆

^ + "3+&%6*,) &5# &>3?4$4 & A6*6*, &5#= :!*& + 8e:&>,# ! b l$ H| 8 i &5#;$8 !9 &G47,)A60&B# ∆^ + # .3+) = &G#* A!$#K4 !9

F H^

# # F HR ^ #

∆^ + # 4 l* H ] &`&>1 3?A8 &(# f f F | [ l | [ | R * 8 4E8d,):4& ) & > . :8 )A3k)". /9*,r3k < 4 !$# 8> !9 476 !;>#'&A&>!$&>3? & :3)*!$#*4 & 4<6$3&547&(! F | .):3 $ 4

2)*,) = //*,)'8+nA#*&^3+& = &

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:_ .JFo=5?,1mF,.#/#1cANF(/oAJ/@/&[email protected];.JF@/,8PFl2 @G(1<6S2S4E6S8PG,=S2 ?,AJF@/ M

+F47AJ251.JIAJFO17G;1<4E=513/ s=S?,1d6S1<2',MK=.JI;Ac47.JZ[G#=LAY=58:.JF(ANM#.JG;176LAY=S8P.BFj8C24E.BF@258:/#1<6513/jAB2%9(1<8PF Vd65.BF (8KI=5?,1OF8@Zj9;176m.NI1<MP134h=56S.JF(2f?@AB29;171<Fn1"8@AJM`.B6u1J17Fn9(1<MP.YV=S?,1O4L?,.g21<F47658P=58C47AJM sAJM)@1 ? ?

∆ ? -@b ?,1\G,6S.J9@AJ9,8PM:8P=0w.NI2 (4L?AJFk1<656S.J6W8C2

& '& (& )*+ ∆ ), # ? ? - ? $ - .

Vd?,1<651/ ? 8:2mAJ/,/,1</x8:Fq=5?,1[AN6!+@Zl1<Fg=f.NI # W=5.k8PF(/#8:4<AY=S1c=5?@AN=0 ? 8:F: - -

k)igf5hUi skf 0fWu v0ugfUki5h7u Uu +Fq=S?,1j4<AJ251X.NIA:_ (.JFx=5?@1jF,.#/#1

=S?,1X6S1<2',MK=m.NIAw47.JZ[G#=LAY=58:.JF(ANM`.BG(1<6SAN=58:.JF

8C2\4E.BF@28C/#1<6513/nAJ2m9;178:F Vd6S.JF ;8KI=5?,1[F,Zj9;176c.JI17M:1<4E=56S.JF@2m?@AB2m9(1<17F1"8@ANM%.B61J1<Fl17,4E1713/#1</&Aj4E1765=SAJ8PFYANM ,1 $

$ ∆ $ -gb ?,1fG,6S.J9(AN9,8:MP8P=0XI].B6=S?,8:2176S65.B68C2*J8 J1<Fk9&=S?,1X2',Z .JI`=5?@1cG,65.B9@AN9@8PM:8K=S8P132W.NI%?@A98PF $

& 7 & _ & *+ ∆ , # $ $ $ " $ - _

b ?@1AB252',Z[G#=58:.JF I].J6=S?,1G,6518P.&@2x4E.JF(28C/#176LAY=S8P.BF@2kViAB2w=S?@AY=x=5?@1y2"=LAY=51 d8C247.J6S65134h=SM) .J9#=LAN8:F,1</R8PI&=5?@1F,Zj9;176.NIw1<MP134h=S65.BF@2Q8C2nAJ9(.(B1D=5?,1z4E6S8K=S8:4<ANM YANM ,1 ? ?

∆ ? AJF@/D=S?,1q2"=LAY=51 :_ 8C2l47.J6S65134h=SM).J9,=SAN8:F,13/y8PI=5?@1F,ZO9(1<6[.NI

1<MP134h=S65.BF@2i8:2W9;17M:.YV =S?,1X4E6S8K=S8:4<ANM YANM ,1 $ $ ∆

$ - 2W=5?@1m6S17G@651321<[email protected]=5?,1 BANF(/[=5?,1 P_ g2=SAN=5147.+,MC/[F,.N=i?@A9J1fAJF&.(J1<65MCANGAX4E1<6=LAN8:F&17M:1<4h=S65.BF&F,Z!

9;176 9;1E="Vi171<F $ AJF@/ ? ?@AJ2=5.l9;17M:.JF ,F@AJZj9,8 +,.&@25M)l=5.l.JF@19,8:F@AN6!w2=SAY=S1.B6\[email protected],1&.JIW9;.N=S?D8KI 8C2X9;1E="Vi1717F ? ANF@/ $

-eb ?,1<6517I].J6S1 =S?,1o4L?,.B8:471<2\I].B6A25Z[AJMPM4L?(ANFB1∆ ? $ 8:FH=5?,1[17M:1<4E=56S.JFHF8@Zj9;176c9;1E="Vi1717FH=5?@1l9@8PF@AJ6'

2=SAN=5132dAN6S1

∆ $ ∆

? ∆

8PI∆ 8:2W1J17F

ANF@/ $ - _J_

∆ $ ∆

? ∆ _ 8PI

∆ 8C2W.#/,/ - $ - _3T

2c=5?@1wF,Zj9;176L2\.NId17M:1<4E=56S.JF@2 $ ? AN6S1lMCAN6!J1 =5?@1w2 ,Z 8:F $ - . \4<ANF9;117=517F(/#1</x=S. - %258:F $ - fAJF@/ $ -

"gF - : - . dAJF@/ "BF - $ - _ W6S1<2',MP=8:F

& 7

*+ ∆ ,17G T T 1 - " # *+ 17#G T% T 1 - +" #

$ - _<^ Vd?@176S1O=S?,1 28 JF8C2\I].J6X4<ANMC4,MCAY=S8PF & 7 & & \Vd8K=S? ?

ANF@/H=S?,1 258 JFc8C2*I].J6~47AJM:45,M:AN=58:F & 7 & _ & Vd8K=S? $ -3b ?,11<656S.J6*G,6S.J9(AN9,8:MP8P=0m9(134E.JZ[1321"8@ANMI].B6 ,ANF@/ P_ ,8PI $ ? -+F 1 8 - - =5?,1m176S6S.J6G,6S.J9(AN9,8:MP8P=0&47AJM:45,M:AN=513/&9 @28:F $ - _<^ 8C2iG,MP.J==S1<//B176

2'@2O=5?@1x4L?(ANFB1k.JI=5?@11<MP134h=S65.g2"=LAY=58C4w1<F,176!+∆ - .BFy=5?@1F@./,1x4<ANG@AB4E8P=5.B6 1 -9;1E="Vi171<F :_ ,AJF@/ ,2"=LAY=S1

∆ - 1 - )

∆ - T ∆ T 1 -

$ - _7a$

Vd?@8:4L? 8C2wF,.B65Z&ANM:871</z8:F 1 8) - - H9y=S?,1q=5?@176SZ[AJM1<F,176!+ " # -b ?,1n/#8;1<651<Fg=45,6!J1<29(1<MP.BFX=S.O/#8176S17Fg=W4L?(ANFB1∆ 8:Fw=S?,1F,ZO9(1<6i.JI17M:1<[email protected]=S?,1F@./,1

9;1E="Vi171<F=5?,1j2=SAN=5132 (AJF@/ P_ -;b ?,1cG@AN6LANZ[17=5176fAJMP.BF&1<AB4L?q4,6!J1\.NI B8)B17F∆8C2c=S?,1F,.#/#1k4<ANG@AB4E8P=SANF(4E1 1 - -~b

?@1oM:8PZ[8P=58:F4<AJ251<2c.JIfM:AJ6'B1oANF(/D2Z&ANM:M∆ AN6S1

! #"$&%'

∆N

∆N=2

∆N=4

∆N=6

∆N=8

∆N=10

N=5∆

fQ*0= 0

CY

∆Nlarge

∆N=4

∆N=6

∆N=8

∆N=10

∆N=3

N=5∆

∆N=7

∆N=9

-1010

-1510

-2010

-510

Prob

abili

ty o

f B

it E

rror

Per

r

1

∆EY / k TB

0 50 100 150 200

fQ*0= 1

2

CY

-1010

-1510

-2010

-510

Prob

abili

ty o

f B

it E

rror

Per

r

1

∆EY / k TB

∆N=1∆N=2

∆N=3

∆N=7∆N=9

large

∆N=1

(a)

’0’:

’1’: 12

fQ*0= +

0 50 100 150 200

Maximum ’Offset Charge’:(b)

Bit Errors Due to Thermal Fluctuations of the Electron Number

No ’Offset Charge’:

"$ GbH JLIMcLKMOLR % " 6U "$ R U " b` " ` ] ∆ 6 3 6 ∆

o6 h h h h ! #"$&% ` ' &

∆ 3 6

∆o6 ( & ) h h h h ` F`

" ∆ "$*%,+ 6 R VU- 3 ?[

∆ ./ . "$ /`

∆ 8` ` R QU ! !"$. "[0 3

"$1 23 R54 4 U 3

" 6 R54 4 U ∆ 3

∆ 3

∆ 6 " $ % 7 &8 9 /,8:2S4@2S251</k8PF=5?@1\I].JM:MP.YVd8:F

# (∆ :<;

b [email protected]:8:/l4@6'B18:F 1 8 ->=#-?= I].J6MCAN6!J1 ∆ 2?,.YVf2`=5?@1iM:8:Zl8P=A@ " #CBED &NT 1 -

Vd?,176S1=S?,1n6S1"8,8:6S1</ 1<F,176!+

∆ - ?@AB2o9;1<47.JZ[1HAJMPZ[.g2"=8PF@/,17G;17F@/#1<Fg=.JIc=5?,117M:1<4E=56S.JFF,ZO9(1<6uAJF@/=5?,1O. *217=m4L?@AJ6'B1<2

8 - 1 -) .NI - 1 .J6=5?,8C2uMP8:Z[8K= =S?,1O2',Z 8PF =- _<^ 4<ANF&9;1uAJG,G,6S.s8:Z&AY=S1</l9[AJF&8PFg=S15J6LANM;ANF@/wVd8K=S?/@258PFX=5?,1m176S65.B6%I ,F@4E=58:.JF

=5?@1

1<656S.J6iG,6S.J9@AJ9,8:MP8P=0 & 7 & 7 & & & 7 & _ & i8C2W1E#G,6S1<2S213/o8:Fo=S?,8C2dMP8:Z[8K=u98

& 7

F∆ HG

1E#G D T 1 -@ "$#I ) /

F 17#G D T 1 -@ " #I ) /

_ 1765I KJ ∆

-aA@ " # " =- _/L

b ?@8:2&6S17G@651321<FB=L2[=5?@1Q65132 @MK=oVd?@8:4L? VWAJ2wAJMP6S1<AB/ B8)B17F 8PFR_ .&=8= 9[- % - "g=S178:FM TYaTN`Vd?,.[=S6513AY=513/.JF,M &=5?@8:2u2G;1<478:AJM47AJ251 -(b ?,1c176S65.B6WG,65.B9@AN9@8PM:8K=0 & 7 8:F =- _/L

/,17G;17F@/,2j.JF=5?@1w6SAN=58:.q.NId2"=S.J6S1</17M:1<4E=56S.B2=SAN=58C4[17F,1<6'&∆ - =5.x=S?,176SZ&ANM17F,1<6'&@ " # - +F[=S?,1fM:8PZ[8P= & 7HO _ =5?,1 (6S2==51<65Z .NI;=5?,1uAJ2'gZ[G#=S.N=S8:4W6S17G,6S1<2517Fg=LAY=58:.JF I].B6 =#- _PL MP13AJ/,2W=S.

& 7 _Q R

∆ - &@ " #

) 1E#G ∆ -a-@ " #I =- _

AJF@/kV1\.J9,=SAN8:FqAJ2dAJFk132"=S8PZ&AY=S1c.NI~=5?,1X4L?(ANFB1u.JI~1<MP134h=56S.B2=SAN=58C4m17F,1<6'&[=5?,1cZ[8:F,8Z ,Z YANM ,1

∆ - ∆

B- ∆ B- S aA@ " # ) M:F & 7 " =- _ =

" R5T UVU /W XZY[K\t[] R

H^ U ^ \`_a " R5T U 3 2 R bVUdc b e [

" R W [ U 3 X Yt[] R

[ UfY.g Q X [ih aj>k R U j Y R

Umlnl

j [ j>o 2p

! #"$&%'

b ?,1<6517I].J6S1 8K=\6S1"8,8:65132∆ - ∆

B-8PFH.J6L/#176u=5.kI ,M @MPM%=S?,1[/#17Z&ANF(/Q=S?@AY=m=5?,1

/#1328:6S1</k176S65.B6G,6S.J9(AN9,8:MP8P=0 & 7 8:[email protected]=2',65G(AJ2S213/ -`y,

∆ : 1 .J6j25Z&ANM:M ∆

=5?,1<651o8:2OAQ2"=S65.BFQ/#1<G(1<F@/#17F(4E1wI].B6

∆ B-

.BF ANF@/.BF ∆9;178:Fl./@/w.J6i15B17F -b ?,8C2i9(134E.JZ[132.B988:.+@29[=5?,1uI].JM:M:.YVd8PFl4E.BF@28C/#1<6SAN=58:.JF

1 .J6∆ D &NT 1 - B @ " #

=5?,1 @6L2"=~=51<65ZR8:FO=5?,1d2',ZR.NI =- _<^ `/#.BZ[8PF@AN=5132`=S?,1i176S65.B6G,6S.J9(AN9,8:MP8P=0!

& 7 S 17#G ∆ T ∆

D T 1 -@ " #

" =- _ !

b ?,1<6517I].J6S1~=5?,1Zl8:F,8:Z ,Z∆ B-

8:Fc17F,1<6'&∆ -

∆ D &NT 1 -

I ,M @M:MP8:F =- _ ! 8C2*J8 J1<Fk9

∆ B- S a @ "$# ) MPF & 7 =- _ .

Vd?,1<651/,1\=S.O=S?,1X4E6S8P=58C47ANM YAJM),1

∆

∆ _ _ T

∆

8PI∆ 8:2f15J1<F =- T

AJF@//,1\=S.l=5?,1X47658P=58C47AJM sAJM)@1

∆

∆ _

_ _ _∆ I ) _ _

∆ ) _ T I 8PI

∆ 8C2W./@/ " =- T#_

b ?,1x6S1"8,8:6513/y1<F,176!J8:1<2∆ B-

=5.DAJ4L?,8:15B1k471765=SAN8:F & 7 & & [ANF@/ & 7 & _ & lAN6S1M:8:2=513/o8:F b AJ9,M:1 =- _I].B6f2.BZl1;YANM ,132d.NI∆ AJF@/

Y b ?,1IAB4h=5.B6 J8 J1<F\98"gF - =#- T ANF(/"gF - =- T#_

47.JFJ1<6'B1%Vd8K=S?X8PF(4E6S1<AJ258:F∆ =5.,F,8P=0 -@b ?@2

=- _ = 8C2d.J9#=LAN8:F,1</AgAN8:F -Y b ?,1WMP.YVi1<2=17F,1<6'&

∆ B-

I].J69;178:Fc9;17M:.YV Ac4E1<6=LAN8:FO1<656S.J6%G,6S.J9(AN9,8:MP8P=0c.#4745,6S225171[ANMC25. 1 8) - =#-?= I].B6 ∆

_[AJF@/ kVd?,8C4L?48:17MC/,2u=5. _V&Yao8:F =#- _ . AJF@/?,17F@471\=5.

∆ B- S @ " # ) MPF & 7 " =- TJT

b ?@2=5?,8C2uMP.YVi1<2=17F@176!+o8C2u651"&@8P6S1</8:Fq=5?,1l47AB21X.JI651<G,651321<Fg=58:F&=5?@1O/#8;1<6

17F@4719;1E="Vi171<F gAJF@/:_ 2=SAY=S19l=5?,1\AN9(21<[email protected]@651321<[email protected]@1uAJ/@/#8K=S8P.BF@ANM17M:1<4E=56S.JF.JF=5?@1oF,.#/#1w4<ANG@AB4E8P=5.J6 -$

.YV1J176\=S?,8C2X6S1"8,8:65132;J176!H25Z&ANM:M4<ANG@AB4E8=SAJF@4E1;YANM ,1<2 1 -

/,1\=S.O=S?,1c6S17MCAY=58:.JF∆ B- D &NT 1 - -

" R 0 U K n " 3 3 "*

3 "* ` " 0

"$ 3 3 3 "

∆ 3 h h 3 h h

∆ 3 h h b h h b

∆ 3 h h `b h h `b

∆ 3 b h h b h h b

∆ 3 h h h h

∆ 3 h h h h

∆ 3 h h b h h b

McL3PQL " 1` " R VU R 0 U " 8∆ 6 3

Yb1" $ % 9 23 R R 0 U

# h h h h1 / 2 " > ∆ ] &

b` "$ R " 3 U n \ "

∆ 3

∆ 3 > 9 7 "

Y .B651<.(J176=5?,1c9,8P=f6S17G,6S1<2517Fg=SAN=58:.JFk98k.JF,1\1<MP134h=56S.JF8C2%J1<6'o2517F(28P=58 J1m=5.&9(AJ4#

J6S.+@F@/H4L?(AN6!J1<2\Vd?@8:4L?yAJ651 (4h='(AY=58:FnAJ65.&,F@/ - 217==S8PF =5?@1

6S1"8,8:651<Zl1<Fg=.JF∆ B-

/#8 J1<6'B1<2f8:FH4<AJ251∆ _j9,=\AJM:25.wI].B6

∆ T 21<1

b AN9,M:1 =#- _ - 1 8:F,8K=S1 YANM ,1<2cAJ651l.J9#=LAN8:F,1</nI].J6∆ ^kI].J6cANF - 1 .J6cMCAN6!J1

∆ =S?,1c6S1"8,8:651<Zl1<Fg=iI].B6

∆ B-

9;1<47.JZ[1<2f8PF@/,17G;17F@/#1<Fg=f.NI -Y21 .B6\M:AJ6'B176 1 - Z[.B651l17M:1<4E=56S.JF@2

∆ ?@A9J1j=5.x9(1&2=5.B6513/Q.JFH=5?@1lF@./,1[4<ANG@AB4E8

=5.B6Z&AN8:Fg=SAJ8PF,8:F[=S?,1O2SANZ[1XM:.YV176S65.B6fG,6S.J9@AJ9,8PM:8P=0 - /YANFg=SA+J1c8C2f=S?@AY=\A&MCAN6!J14L?@AJ6'B1fZ[.+,Fg=W8:2iM:1<2S22517F@258P=58 J1u=5.[Aj258PFBMP1m17M:1<4E=56S.JFo4L?(AN6!J1 @4h=!@AY=S8PFl8:Fw=5?@18:478PF@8K=0w.JIe=S?,1cF,.#/#1\.J6d.BFg=5.l=5?,1cF@./,1 -+F47.JF@47M)(28:.JF

=5.n2',G,G,6S1<2S2c=S?,176SZ&ANM8:F@/(4E1</y9,8K=l176S65.B6S2

AqZ[8:F,8PZ ,Z 17M:1<4

=S65.g2"=LAY=S8:4x1<F,176!+∆ B-

?@AJ2w=5. 9(12"=S.J6S1</z.JF =S?,1nF,.#/#147AJG@AJ478K=S.J6&=S./#8C2"=S8PF &,8C2?&6S17M:8:AJ9,M:1f9(17="V1<17F&=S?,19@8PF@AJ6' ANF@/[=S?,19@8PF@AJ6' :_ 2"=LAY=51 - 1 8 - =#- ! AX25?,.YVf2∆ B-

&@ " # J176L2'@2 1 -I].J6WA.B8)B17F & 7 _ .B9#=SAJ8PF,13/[I]6S.JZ 1 8 -=-n=-gb ?,8:2/,8:A+J6LANZ6S15B1<ANMC2W=S?@AY=uI].J6 & _ AJFQ2Vd8P=S4L?,8:Fw1<F,176!+

∆ -

_ L6@ " #?(AJ2i=5.[9;1X2"=S.J6S1</ -,b ?@8:2WZ[1<AJF@2 ∆ -

a " ^O1 I].J6 # ^ [- "!$# \ / &%('()+*,%-.)0/('()+*213)413)+*+56 %798;:9<=1>:9%(1>?@/(A9B/('()+*7C/(A.-D1>? 6 )FE9)+*+?@/GHB i

! #"$&%'

-1610

fQ*0

= 12

fQ*0

= 12

= 10-19err

P

Node Capacitance CY [F]E

lect

ron

Num

ber

N∆

CapacitorExample

CapacitorExample

CY

(d) Example:SiOMetal- 2 -Metal Capacitor

CY = 3 10 F. -17

50 nm

3 nm 50 nm

ε. = 4(

0

100

200

300

400

Cha

nge

of E

lect

rost

atic

Ene

rgy

∆E

Y

-20 -18 -1410 10 10

(a)

min

Effective Length [m]-8

10-6

10-4

10-2

10k

T B

-20 -18 -16 -1410 10 10 10

100

1000

10

1

Effective Length [m]-8

10-6

10-4

10-2

10

(b)

Node Capacitance CY [F]

T= 300 K

T= 300 K

2.0

1.5

1.0

0.5

Vol

tage

Sw

ing

∆VY

[V]

(c)

0.0 -20 -18 -16 -1410 10 10 10

Node Capacitance [F]

GIHKJLMOL L R U F` ∆ 6 ` 6 ` # 2 3 h h 3

! "$ nh h A 3 _ " g] 1`

& K1` ! 9 3 6 6 n& 8 "

n` "3 3 X R

U R R UAUN[ 9

" & 8 " R QU &∆ ( ` 6 8& R 6U T ` &

∆o 6 ` 6 R QU!F[ " ? Z * " 8 6 Y

"$ +F 1 8 -=- ! 4W=S?,16S1"8,8:6513/[Z[8PF,8:Z @Z J.JMP=SA+J1f25Vd8PF

∆ - Q T∆ B- 1 -

[email protected]==513/ B176L2 (2=S?,1WF,.#/#1d47ANG(AJ4E8P=SAJF@4E1 1 - -

+MPM @2=56LAY=S8PFm8C2~=5?,1iI].JM:M:.YVd8PFm1E,AJZlG@MP1

b [email protected] ,1X.NIA[Z[1E=LANM "#8 3 Z[1E=LANMeG,M:AN=51j4<ANG@AB4E8P=5.B6 25171 1 8 - =#- ! / i.NI6L [F,Z 98L QF,Z AN6S1<A

^HF,Z G,MCAY=S1q/#8:2=SAJF@4E1xANF(/ E a?(AJ2O=5?,1q4<ANG@AB4E8P=SANF(4E1 1 S^ ) _ 1 ^ %A 1 - "@4L?wAX25Z[AJMPM47AJG@AJ478K=LANF@471d651"8,8P6S1<2ANM:6513AJ/lA J.BMK=LAJ1f25Vd8:F

∆ - M:AJ6'B176m=5?(ANF - T I].J6 & 7 _ lAN= # ^ [- 9(.&#=j^ ! 1<MP134h=56S.JF(2?(A9J1O=5.q9;1o2"=S.J6S1</4,F@/#1<6c=5?@1<251w4E.JF(/#8K=S8P.BF@2 21<1 1 8 -=- ! 9 - 3IW47.+,6L251=5?@1w9,8P=

6S17G@651321<FB=LAY=S8P.BF&Vd8K=S?o15B17FkMP1325217M:1<4E=56S.JF@28:2WAJM:25.jG;.B2S28:9,M:[email protected]:Fj25Z&ANM:MP1<6F@./,14<ANG@AB4E8P=SAJF@4E132 1 -

ANF(/y?,8 J?,1<6J.JMP=SA+J1o25Vd8:FB2∆ -

9#=l=5?,1x6S17M:8:AJ9,8PM:8P=0.JIf=5?@19@8K=m651<G,651321<Fg=SAY=S8P.BFx8:2=5?,1<Fn2517F@258K=S8)B1X=S.o28:FBMP1O9@AJ4#J6S.+@F@/k4L?(AN6!J1<2V@4h=!@AY=S8PFAJ65.&,F@/ -U=m8:2uV.B6=S?x=5.k17Z[G,?@AB2871lABAJ8PF=S?@AY=m8K=c/#.1<2F,.N=m651"&@8P6S1c=5?@1j9,8P=m6S17G@651321<F =LAY=S8P.BFk9&I]1<V017M:1<4E=56S.JF@2i=S.[6513AJ4L?oZ[8:F,8:Z ,Z 8PFk=5?,1c1<MP134h=S65.g2"=LAY=58C4u17F,1<6'&o4L?@ANFJ1∆ - /#1<Z&ANF@/#13/98HAkM:.YV =S?,176SZ&ANM8:F@/(4E1</H176S6S.J6\G,6S.J9@AJ9,8PM:8P=0q651"&@8P6S17Z[17Fg= - MCAN6!J1F8@Zj9;176i.NI`1<MP134h=56S.JF(2.BFoAXMCAN6!J14<ANG@AB4E8P=5.B6M:1<AJ/@2=S.OAJMPZ[.B2==S?,1\25AJZl1uZ[8PF 8:Z @Z 8PFH17F,1<6'&

AJ4747.JZ[G@AJF,8P13/q9QAk25Z&ANM:M B.JMP=SA+J1O25Vd8:F

∆ - 21<1 1 8 - =#- ! 4 -.YV1J1<6\I].J6<; > oF@./,1o47AJG@AJ478K=LANF@471 sAJM)@1<2c.J=5?,1<6O4E.BFg=56LAN8:FB=L2\9(134E.BZl1o8PZ[G;[email protected]=iAJMPM:.YVd8:F\=5.OZl8:F,8:Z[8(<1=S?,1-B.JMP=SAB1f2Vd8:F

∆ - =S.X=S?,1M:.YV1<6M:8PZ[8P= B8)B17F9oAlM:.YV =S?,176SZ&ANM8:F@/@471</k176S65.B6WG,65.B9@AN9@8PM:8K=0&6S1"8,8:6S17Z[17Fg= - y]!e~q< k*esyl( l] ;g kg<<(Y#<(

b [email protected]@4E1<G#=\.NI/#8 J8P=SAJM~478P6L4,8P=S2 21<1/"134h=58:.JF =- T /#17Z&ANF(/,29@8K=c28 JF(ANM~65132"=S.J6LA =S8P.BF -@b ?,1X/,15J6LAJ/@AY=58:.JF.NI%9,8P=u258)BF@ANM*M:15B17MC2WMP13AJ/,2W=S.&8PF,I].J6SZ[AN=58:.JFxM:.B2S2dANF@/x4E.BZ!G#=SAN=58:.JF@AJM;1<656S.J6L2 - 2d2?,.YVdF8:F 1 8 - =#- . ANF(/o17G@M:AJ8PF,13/o8:Fk=5?,1 1 8)&,6S1 iAJG#=58:.JF

/,8176S17Fg=58CANMJ.JMP=SA+J1BAJ8PF / > / B _&.NIW=5?@1wMP.&J8C4BAN=51&15B176!Vd?,176S1[G,65. /@4E132k/#1J6LAJ/,AN=58:.JF - 8176S17Fg=58CANM;J.BMK=LAB1 BAJ8PF B6513AY=S176w=S?@ANF,F,8P=0 ?@AJ2o=5.z9;12',G,G@651325251</ AY=[=5?,1q9@8K=o258)BF@ANMdM:15B17MC2l=5.DA9J.B8:/ ANZ[G,M:8 ;47AY=S8P.BF .JIuF,.B8:251=5?,6S.+J?=S?,1xF,1E="Vi.J6DVd?,8C4L? Vi.+@M:/ 47A(21x4E.BZlG#=SAN=58:[email protected] =S176[G@AJ2S258PF2515J1<6SAJMM:.+B8:47BAN=5132 - rf.B8:251x2 ,G@G,651325258:.JF8C2[8:ZlG;.J65=SAJFg=&258:F@4E1 F,.J8C21 2.&,6S471<2[AN6S18PF,?@1761<Fg=5M 8:F0/#8 J8P=SAJMu4E8:6L4,8P=S2

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B.JMP=SA+J1xVd?,176S1x=5?@1H/#8;1<651<Fg=58CANM B.JMP=SAB1 BAJ8PF 9;1<4E.BZ[1Q1"8@AJMd=5.y.BF,1 J8 J132[=5?@1. 920 Q; >I. B .JI=5?,1j=56LANF@2I]176m4L?@AN6LAJ4E=51<658C2"=S8:4<2 - Fn8:F,G,=J.BMK=LAB1j47AJF sAJ6'Vd8P=5?@8PFo=5?,8C2i6SAJFJ1uVd8K=S?,.+#=W9,8P=f28 JF@AJM(M:15B17M/#15B6SAB/,AY=S8P.BF&.J6iF,.J8C251uAJ4<4,Z ,MCAY=58:.JF -1 .J6i=5?@1X28 JZ[.J8C/&=S6SAJF@2I]176iI ,F@4E=58:.JF

=S?,1c/#8;1<651<FB=S8:AJM J.BMK=LAJ1 BAJ8PF/ > / B AN=∆ 6 " $ % 1` & & n n n "$ R R 0 U " - U

! #"$&%'

0

1

0

1

V∆ Yout

V∆ Yin

V∆ Yout V∆ Y

in=

Vin

Vin

noise

amplified noise

dV

dVout

in> 1

Vout

dV

dVout

in< 1

Vin

noise

suppressed noiseVout

V∆ Yin

V∆ Yout V∆ Y

in

dV

dVout

in< 1

V∆ Yout

Vin

<

logic threshold

Vout

(b) Degradation:

VY∆ - 2Vnm

Sigmoid-liketransfer functionallows fornoise margins:

Vout

No Degradation:(a)

(c) Noise Amplification: (d) Noise Suppression:

V

dV

dVout

in

V∆ Y

V∆ Y

Vout

in

V Vnmnm

= 1

noise margin

LevelsBit

GIHKJL MOL L a n "[% && (h \fZ& nh R VU & n 1` /` " 6` Qo 7 o 3 /` R cUI_ / o 7 Qo

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=S?,1XMCAN6!J1<6fAN6S1u=S?,1XF,.B8:251XZ&AN6!J8:F@2 -

/(28:F 1 8) - =- . /

=5?,1X25MP.BG(1cAN=fMP.&J8C4f=S?,[email protected]/o8C2d1<2=58:Z&AY=S1</o=5.

gAN8:F/ >/ B ∆ -

∆ - T B _

_ T B ∆ - =- TN^ 1O4<ANM:M`=S?,8C2=S?,1 OV9 => 4L >I. ; 3P4; 3; 4Q 4. 76Q; 0N6O9 H28:F@4E1 J8 8PFo=5?,1O6SAN=58:.9;1E="Vi171<F [email protected]&AN6!J8:F B AJF@/ J.JMP=SA+J1x2Vd8:F

∆ - M:1<AB/,[email protected](2"=S6SAJ8PFg= =- TN^ I].J6~=S?,16S1"8,8:6S1</j/,8176S17Fg=58CANMgAN8:F / > / B AN=~M:.+B8:4=5?,6S1<25?,.BM:/ -Yb A 8:FI].B61E,ANZ[G,M:1fA\F,.B8:251dZ&AN6!J8:FO.JI B

^

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a&L

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> /Q c/,1W=S.=S?,1d17M:1<4E=56S.B2=SAY=S8:4<2`9XVd?@8:4L?O=5?,1W1<F,176!+c9@AJ656S8:176~.NI@=S?,1d/#158C4E1W8C247.JFg=56S.JM:M:1</ -sb .mG,6S.(J1=5?,8C22"=LAY=S17Z[17Fg=ANF@/j8PFl.J6L/#1<6`=S.m.B9#=SAJ8PF!"8@ANFg=58P=SAN=58 J1W/#1<258 JF6!,M:1<2

Vi1&4E.BF@28C/#1<6=S?,1[6513ANM:8(3AY=58:.JFn.NIA r;3 b BAN=51 .J6\8:F8B1765=51<6#f8PF 1 8) - =- _ 1 8:6S2=Vi14E.BF@28C/#1<6ANF&1<MP134h=56S.JF[8:F&=5?@14L?@ANF@F,17M,9;1E="Vi171<F[=5?,1u17M:1<4E=56S./,1<2 8 - 1 - =5?@18:F,G,=uF,.#/#1 =5?@1 BAN=51 .JI~=S?,1O25Vd8P=S4L?,132

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B.JMP=SA+J1 * .JF=S?,1/BAN=51&1<MP134h=56S.#/#1<2 8PF@G#=OF@./,1 \.JIi=S?,1&8:F8B1765=51<[email protected]:F1 8 ->=#- _

AJM:25.[=5?,1j.+#=SG#=-B.JMP=SAB1 + 8 - 1 - =5?@1X.+#=SG#=F,.#/#1jG(.J=517Fg=S8:AJM`.NI~=5?@1M:.+B8:4 gAY=51d8C24L?(ANFB1</ -Jb ?@176S1EI].J6S1i=5?,117F,1<6'&j9@AJ656S8P1<6?,178 J?g=AN=G(.g28P=58:.JF,&8:F[=5?@14L?(ANF,F,1<M@9;1E="Vi171<Fw=5?@117M:1<4E=56S.#/#1<2.NI*=S?,1uFU25Vd8K=L4L?w8C225?,8PI =51</wI].J6WANFw1<MP134h=S65.BFwVd8K=S?6S1<25G;1<4h=W=S.O=S?,1X2',G,G,M w=S176SZl8:F@AJM b 9

D /&% D !.- ) / * D ! - ' ) / /+ =- TYa$Vd8P=5?l=S?,14E.BF@/#8P=58:.JF,! - ! - ' !10 ' 32>_ -Bb ?,1f25AJZ[1i6S17MCAY=S8P.BF[8:2.B9#=SAJ8PF@1</I].B6fANF17M:1<4E=56S.JF8PF=5?@1X4L?@ANF,F@17M*.NIe=5?,1cGU25Vd8K=L4L? 25171 1 8) - =- _ BA - 117G;1<4E=`=S?@AY=e/ + / * -sb ?,1Z[.J6S1AB474@6SAN=51/#1<G(1<F@/#17F(4E18C2`.B9#=SAJ8PF@1</AB2I].BMPM:.YVf2

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) U =- T]L

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8 - 1 -) +

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4 * 4 4 +5 -

b ! #"$&%'

VDD

Y

0 1

1 0

A

r

µS

µD

DS

0V

Input A Output Y

’NOT’(a)

n

p

Gap

µSelch

D

elchµ

DS

without bias:

with bias:

elch

elch

Gap

Y,T

lowering ofenergy barrier

InputNode

OutputNodeY

T

T

S

S

D

GA

D

A G

(b) n-Switch in ’off’-State:

p-Switch

n-Switch

eV

εChannel

Terminal (-)=Supply

Drain= Node Y

Source

eV 0

Supply Terminal (+)

Supply Terminal (-)

Channel

= eV

Channel

A & & h \& nh8 & " 8 68 9 " 8 8 &8 d n & "$ 8 & 8 " ! 8& ] io 6

! ?@AJFJ8:F[2M:8 J?g=5M &=5?@1c8PF,G#= J.BMK=LAJ1\AN6S.+@F@/&=S?,[email protected]/

=5?,1c1<F,176!+&9(AN6S658:176iI].J6

1<MP134h=56S.JF(28C2dM:.YV1<6513/wVd?,8C4L?x/#1<476513AJ251<2=5?,1c6S1<258C2"=LANF@471I].B6d=5?,1cFU25Vd8K=L4L?k9 #"/4 * 4 + 5 ) 1E#G D /&% @ " # _ S 4 +5 ) D /% @ " #

%$ > 9 9 n ! '& ' &

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b A 8:Fk=5?,1w/#[email protected] =#- T8L u9n/ * =5?,1&.&#=5G,=.J.JMP=SA+J1[4L?@ANFJ1

/ + AY=W=5?@1cMP.&J8C4=S?,6S1<25?,.JMC/o9;1<47.JZ[1<2d/,1\=5. =#- TNa 8:ZlG@MP8C4E8P=5M / + /

4 *T4 +5 &

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gAN8:F / +/ *

! -

T9@ " # D U ! - =- T

b . B1E=&/#8;1<651<FB=S8:AJM*J.JMP=SA+J17BAN8:F_AN=O=S?,[email protected]/

/,1k=5.651<M:AN=58:.JF =- T c8P=

6S1"8,8:6S1<2Y Am9(17==S1761<MP134h=S65.g2"=LAY=58C4W4E.&,G,M:8PFm=S.\=5?,1f8:F,G,=F,.#/#1 gAY=S1d17M:1<4h=S65.#/#1 0.NI;=5?@125Vd8K=L4L? =5?@AJFk=S.[=5?,1c.&#=5G#=fF,.#/#10 /#6LAN8:Fx17M:1<4E=56S./,1 .NI`=S?,1X25Vd8K=L4L?

!.-!- =- T =

Y ANF(/kAlZ[8PF@8PZ ,Z *U 8:Fk=S?,1X2',G,G,M B.JMP=SAB1 U

U *U @ " #D )

T! - BAJ8PF ! -

=- T !

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Vi.J6gI ,F@4E=58:.JFn1<FJ8:F,1<176S8PF98 "&(ANFg=',Z Zl134L?@ANF@8:4<ANM4E.BF @F,1<Zl1<Fg=X1 1<4h=c.B6c98

=S?,1 .&,M:.JZj99,M:.#4#YAJ/#1c1 ;134h= - U=uF@171</@2A[I ,F(/,ANZ[17Fg=LANM~Zl8:F,8:Z ,Z 2',G,G@M) J.BMK=A+J1uI].J6fAJMPM25Vd8K=L4L?,1<2W9(AJ251</k.JF17M:1<4h=S65.g2"=LAY=S8:4<ANM:M)w47.JFg=56S.JM:MP8:FO=5?,1c47.JF@/(4h=SAJF@4E1\.B645,6S651<FB= - +Fj=5?,1W47AB21.NI!.- 6 BAJ8PF ) ! -

=S?,16S1"8,8:6S1</c2',G,G,M J.BMK=LAJ1 *U J6S.YVf2/,6SAJZ[AN=58C47AJMPM wAJ2d4<ANF9(1j25171<FoI]6S.JZ =#- T ! - 1 .J6 ! - ! -

F@. BAN8:F8:2dAB4L?,8P1YAN9,M:1AN=fANM:M Z " (] 8 n # 0 b

! #"$&%'

2 3 101gain =

1/3

αA (= α )G

eV

/ k

T

50

40

30

20

10

00.0 0.60.2 0.8 1.0

min

DD

B

1/2 3/5 5/6

20

6

24

0.4

o s s 8& bo s s # / ] " \& / o sOs " & &8 43 p & ' 0 ( &&

! 3 6 ! h 6 h 3

s 3 s q h s h p 3 !o s s " 3 Y 6

17MCAY=S8P.BF@2 =- T = fANF(/ =#- T ! f/,1 @F,1[2515J1<651O4E.JF(2"=S6SAJ8PFg=S2u.JFQ=5?,1l17M:1<4E=56S. 2"=LAY=58C472W.JIe=S?,1X25Vd8K=L4L? - U=f8:2fG@AN65=d.NIeVd?(AY=/#1 @F,1<2A (217I ,M*=56LANF(28C2"=S.J6 -b A 8PF =#- T .

=S?,1uZ[8:F,8:Z ,Z *U 8PFo=5?,1\2',G,G,M J.BMK=LAJ1 U 6S1"8,8:6513/[I].J6

471765=SAN8:F2gAN8:F.JI=5?@1qF,1E="Vi.J6DAJ4h=S8PFAB2[A r 3 b gAY=S1k8C2[G,M:.N==S1</z8:F 1 8 - =#- _B_B176L2 @2 !.- - 1<2=jG;1765I].J6SZ[AJF@4E1 8 - 1 -) MP.YVi1<2= U 8C2c.J9,=SAN8:F,13/I].J6 !.- 6 _ M

Z[.B2=j=S?,1Vd?,.JM:1o8:Z&AJ14L?@AN6!J1wI].J6[ANFy1<MP134h=56S.JF8PFD=S?,1x4L?@ANF,F@17Mi8:2l8:F@/@471</y.BF=S?,1 gAY=51c1<MP134h=S65.#/#1 8PF@G#=\F,.#/#1 -b ?,1j6S1"8,8:6513/x2 ,G@G,M),B.JMP=SAB1X/#8 J176!J132WI].J6!.- 6 !

- 8 - 1 -) Vd?,17Fl=5?@1f8PZ&A+J1d4L?@AN6!J1iI]6LAJ4E=58:.JFl8PF@/@4E13/[.JFl=5?,1F,.#/#1d17M:1<4E=56S./,1

/#6SAJ8PF[1<MP134h=56S.#/#1~9;1<47.JZ[1<21"8@ANM@=5?,1fI]6SAB4h=58:.JFl8:F@/@471</&.BFO=S?,1f8:F,G#=F,.#/#1 gAY=S11<MP134h=56S.#/#1 - ]~~q<3e kg*~]YyO; *3,`|* g

b ?,1[8:Fg=517Fg=S8P.BF17#8:2=S2 .NIW4E.+@6S251=5.qZ[8:F,8:Zl871[=S?,1w2=SANF(/#9QG(.YVi176\.JI=5?@1&MP.&J8C4

gAY=51O8PF.J6L/#1<6=S.kM:.YV1<6=S?,1[G(.YVi176\4E.BF@2',Z[G#=58:.JFAJ2uIAN6\AJ2mG;.B2S28:9,M:1 - ?,8C4L?H6S1 2=56S8:4E=58:.JF /#.D178C2= 8K=S? 4L?@ANFB8PFyAN9,6!,G#=SM)=5?,1Q8:F,G,=7J.BMK=LAB1k=S.=5?,1nMP.&J8C4gAY=51

=S?,1j.&#=5G,=mF,.#/#1l47AJG@AJ478K=S.J6?(AJ2d=S.o9;1jM:.BAB/#1</q9

∆ - 8PFHAo4E1<6=LAN8:[email protected]= IQ -#b ?,8:26S1"8,8:65132Aj45,6S651<FB= 8 * =5?@65.&J?&=S?,1u25Vd8P=S4L?o8:F&=S?,1 .JF +2"=LAY=S1

"$ /,17M:8)B176S8PFj=5?,1c4L?@AJ6'B1 1 - ∆ - 9&Vd?,8C4L?o=S?,1\F,.#/#1\Vd8K=S?4<ANG@AB4E8P=SAJF@4E1 1 -

?@AJ2i=S.6S1<4L?(AN6!J1</wVd8K=S?,8PF=S?,1X/#17MCA9&=S8PZ[1

8 * 1 - ∆ -

=- ^ +Fn=5?,1[9;1<2=\4<AJ251O.JI.+@6B17F,1<658C4j25Vd8K=L4L?

=5?@8:2 .JF*4@656S17Fg= 8 * 8:2m6S17MCAY=S1</Q17#G(. F@17Fg=58CANM:M)w=5.l=5?,1 . ;4,6S651<Fg= 8(!

"! S 8 * ) 17G D !.- ∆ -@ " # I =- ^,_ Vd?@176S1!.-R8:2[AgAN8:F=5?,1q4L?@AJ6'B1&I]6LAJ4h=S8P.BF8:F@/@471</.JFy=S?,18PF,G#=&F,.#/#1 BAY=S11<MP134h=S65.#/#1 -

.YVi15J1<6cI].J6[A r 3 b BAN=51AJ2l2?,.YVdFD8:F 1 8 ->=#- aB9 =5?,1x4L?@ANFJ1

∆ - 8:F =5?@1H8:F,G#=,J.BMK=LAB1QVd8K=S? 25Vd8K=L4L?,8:F47A+@251<2A4E.BZ[G,MP1<Z[17Fg=SAJ6' 4L?@ANFJ1∆ - 8:F=5?,1k.+#=SG#= B.JMP=SA+J1

8P=5?,1<6X=5?@1oF m.J6jGU25Vd8K=L4L?D8:2j8PFy=5?,1 . %2=SAY=S1

AJF@/=5?@176S1EI].J6S1/,F(/#176[/#6LAN8:F U25.+@6S471 J.JMP=SA+J1&9,8CAJ2O8:FD=5?,1k.J6L/#176O.NI∆ - 2 U -

b ?@176S1EI].J6S1 AJM:25.o=S?,1&Z[.#/#8 ;47AY=S8P.BFH.JI=S?,1&17F,1<6'&q9@AN6S6S8P1<6m9q=S?,1&4L?@ANFJ1l8PF=5?@11<MP134h=S65.g2"=LAY=58C4XG;.N=S17Fg=58CANM.JI=S?,1[.+#=SG#=cF,.#/#1 /#6LAN8:Fn1<MP134h=56S.#/#1l.NI=S?,1&2Vd8P=S4L? ?(AJ2=5.[9;1\=SA B17Fk8PFg=5.&AB474E.&,Fg= - 2dAl47.JF@251"8,1<F@4E1u=5?@1c651<M:AN=58:.JF =- ^,_ ?@AB2i=5.[9;1Z[.#/#8 @1</x/@1u=S. =#- TNa =5.

(! S * ) 1E#G D ! - ! - ) ∆ -@ " # =- ^BT

b ?@1 .JF;=5. . *4,6S651<Fg=u6LAY=58:.o8C2mAJ4747.J6L/#8:F&=5. =#- ^gT A 1<4h=S1</n98=S?,1[17M:1<4h=S65. 2=SAN=58C472W.JI`=5?@1X2Vd8P=S4L? -b ?,1w2=SAJF@/#9QG;.YV1<6 #$ & +' G;176XM:.+B8:4 gAY=51 /,1[=5.x=S?,1w4@656S17Fg=cMP13A YAB1 8"!=S?,6S.+B?[=5?,1\2Vd8P=S4L?o8PF&=S?,1 . +2"=LAY=51 8C2i1<2=58:Z[AN=513/w/,1=5. =- ^BT ANF(/ =#- ^ %=S.

# $ & +' "! ) U S 1 - ∆ - U ) 1E#G D ! - ! - ∆ -@ " # =- ^J^

o/,1 @F,8:F[=S?,1 4./ &478P1<F@4 1 AJ4h=S.J6 1 - ∆ - U# $ & (' ) S 8 * "! =- ^Na$

=S?,1jG;1765I].J6SZ&[email protected]:FJM:1jM:.+B8:4.BAY=S1X8C2u4L?@AJ6SAB4h=S176S8(<1</ b ?@1j1w478P1<F@4IAJ4E=5.B6

9;1<47.JZ[1<2WVi.J6L251u8PIe=S?,1X/#8C25258:G@AY=S1</k17F,1<6'& 1 - ∆ - U /@1u=S.w2Vd8P=S4L?@8PFl=S?,1c9,8P=2=SAN='@2i8C2W?,8 J?

AJF@/w8PI~8P=d651"8,8P6S1<2WAOMP.BF[/#17MCA9[=58:Z[1kI].J6d/#.B8PFO=S?,8C2d2Vd8P=S4L?,8:F -U=[9;1<4E.BZ[1<2l9(17==S176[8KIu=5?,1x/#8C25258:G@AY=S8P.BF2,F@/,176&2"=LAY=S8P.BF@AN6!47.JF@/,8K=S8P.BF /,1k=5.H=5?@1

M:1<A YAJ1\4@656S17Fg= 8(! 9(17="V1<17F=5?@1X2 ,G@G,M)w=5176SZ[8PF(ANMC2W8:2d?@8)B?,M)k2 ,G@G,651325251</ - \ Fr87:9 " 8 K ! o sOs / r 7 " ] ! K 8" 8 / &

! #"$&%'

b ?,1f1w478P1<F@4OIAJ4E=5.J6J8 J1<2A\Zl13AJ2',6S1WI].J6=S?,1f6LAY=S8P.c9;1E="Vi171<F[=5?,1fG;.YVi176/#8:2S258PG@AN=58:.JFc/,1=5.f25Vd8K=L4L?,8PFWI].J6`/#.B8PFW47.JZ[G#=LAY=S8P.BF 1 - ∆ - U ANF@/k2"=LANF@/$U9[G(.YVi176W/#8C25258PG(AY=58:.JF/,1u=5.lMP13A YAB1 (! ) U - ?,8 J?1w4E8:17F@45zIAJ4h=S.J68:2k6S1"8,8:6513/ ANM:MP.YVd8:FDI].B6k?@8)B?,M) 8:Fg=515B6SAN=513/ 4E8:6S45,8K=L2Vd8K=S? Z[8:MPM:8P.BF@2[.NIuMP.&J8C4 gAY=5132jVd8P=5? A2"=S8PM:Md6513AJ25.JF@AJ9,M:1wMP.YV G(.YVi176&4E.BF 2 ,Z[G#=S8P.BF -

b .#/,A9 2 30" 1 b 2d8:FQ/#8)B8K=LANM8:Fg=51J6LAY=513/x4E8:6S45,8K=L2d. 176 8 * 8(! _ .(8 - 1 - AJF1 &478P1<F@4wIAJ4h=S.J6d.JIeMCAN6!J176i=S?@ANF_ .Y- . 8P=5?&=S?,1f1w478P1<F@4OIAJ4E=5.J6 =#- ^Ja

=5?,147.JF@2=56LAN8:Fg=.JF[=S?,1 J.BMK=LAB1f2Vd8:F∆ -=S.X2 ,G@G,65132522=SAJF@/#9XG;.YV1<6/#8C25258PG(AY=58:.JF[9,=/#17M:8)B176S8PFu=S?,1f6S1"8,8:6513/O25?,.B6=/#1<M:A9

I].BMPM:.YVf2I]65.BZ =#- ^B^

∆ - ∆ *- @ " #D ) M:F w4E8:17F@45 1 AJ4E=5.B6 )

_!1- ! - =- ^8L

3u6c8PIW=5?,1oAJ656LANFJ17Z[1<FB=\.NId1<MP134h=56S.#/#1<2cAJMPM:.YVf2m=5.x=LA B1 !- !.0 ! - _wAJF@/!.0 ! -

6S17MCAY=58:.JF =#- ^&L 6513AJ/,2

∆ *- @ "$#D ) MPF &478P1<F@4 1 AJ4h=S.J6 )

T^ !1- _ =- ^

+F 1 8 ->=#- _sT =5?,1lMP8:Z[8K=mI].J6 ∆ - J8 J1<FQ9 =- ^ d8C2u25?,.YVdFxI].J6\/#8;1<651<Fg=m1 !478P1<F@4lIAJ4E=5.B6S2WAJ2iAjI ,F@4h=S8P.BFk.JI.! - - UI`=S?,1m17M:1<4h=S65.g2"=LAY=S8:4<2.JI=5?,1c25Vd8K=L4L?k/#18:AN=51<2I]6S.JZ ! - _ ?@8)B?,176.B.JMP=SA+J1w25Vd8PFg2

∆ - AN6S1&651"8,8P6S1</ - 25G;1<4E8CANM:M QI].J6OM:AJ6'B1F,.#/#1x47AJG@AJ478K=LANF@471<2 1 - 8 - 1 - M:AJ6'B1wIANF.&#=[AJF@/ MP.BFnVd8:651M:8PF,132

=S?,8C2O6S17MCAY=S8P.BF

6S1@134h=L2[=5?,1H/#.JZ[8:F@ANFg=k47.JF@2=56LAN8:Fg=[.BF∆ - [email protected]=o2Vd8P=S4L?,8:Fy/#1<M:A9zANF@/ M:.YV

2=SAJF@/#9[G(.YVi176WAN6S16S1"8,132"=S1</ -b ?,1m651"&@8P6S1</&Z[8:F,8:F8@Z∆ *-

8:F7B.JMP=SA+J125Vd8PF∆ - /,8)B176!J1<2I].B6 !1- 6 !

- -+Fy4E.BF@4EM @258P.BFM:8:Zl8P=58:Fq=S?,1 B.JMP=SA+J1&2Vd8:F

∆ - ANF(/=5?,1w1 w4E8:17F@45nIAB4h=5.B6=S?,1j6S17MCAY=S8P.BF =- ^8L %B8)B1<2AJF,.N=S?,176m4E.BF@2"=S6SAJ8PFg=.BFx=5?,1l17M:1<4E=56S.B2=SAN=58C472f.JIAo25Vd8K=L4L?

.BG(1<6SAN=51</o9k4E.BFg=56S.JM:MP8:F[ANF17M:1<4h=S65.g2"=LAY=S8:4m17F@176!+&9@AJ656S8P1<6 - 3u6%8C4E1;J1<6S2SA

Y AJ/x17M:1<4E=56S.B2=SAN=58C4cAN6S6SAJFJ1<Zl1<Fg=WM:1<AB/,2d=S.&=5?@1j6S1"8,8:651<Zl1<Fg=.NIA&MCAN6!J1 B.JMP=SAB12Vd8:F

∆ - - 3uG#=58:Z @Z8 - 1 -) MP.YVi1<2= J.BMK=LAB12Vd8:F [email protected]=SANF(/#9mG;.YVi176

8:2dAB4L?,8:15YAN9,M:1mI].J6 ! - 6 _ -Y21 .B6 !1- ! - =5?,1k2Vd8P=S4L?y4<ANF,F,.J=j9;1w='@65F,13/. 28:F@471&=5?,1oMP.YVi176S8PFq.NIW=5?,1

17F,1<6'&k9(AN6S658:176f9=5?@1l4L?@AJFJ1 ∆ - .JI=5?,1[/#6LAN8:F +2.&,6S471 J.BMK=LAJ1 (2"=c4E.BZ

G(1<F@2SAY=5132lI].J6[=S?,1q658C251k9y=S?,1,BAN=51 +25.+,6L4E1 J.BMK=LAJ1∆ - -b ?,176S1EI].B651 8PFz=5?@8:2

45 & > " ?& & - 8 7 6 > "$ n &] " & % ' &"r87:9 3 " " =Z /Z " " 5 " / "$ " # & n 8

& % H

αA (= α )G

102

104

108

1012

αA (= α )G

ln108

/ k T B

0 0.2 0.4 0.6 0.8 1.0

(b)2.0

1.5

1.0

0.5

0.0

Efficiency Factor =

T = 300 K50

0

10

20

30

40

∆VY

0 0.2 0.4 0.6 0.8 1.0

Efficiency Factor =(a)

ln

10

10

102

4

8

1012

1210

ln104

22

∆V[V

]Ym

in

min

1/31/3

∆o 6 &

∆o 6 " "

/ " [ ! 8

∆ 6 " $ % ]! &

∆ 6

" % 3 A 0 &8

! 3 6 ! h 6 h 3

Fs 3 h Fs h 3 &∆

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i `f`',$*~," $5$ $` ;#',B#e,5 +, f` d) X' fW HuB'@%5#y% ',L'@O" +#~,"u

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/#6LAN8:Fk9&=S?,1 BAN=51\17M:1<4E=56S./,1m8C2d6S1"8,8:6513/ -

! #"$&%'

b ?,1321\G,6S.JG;1765=58:1<2d4L?(AN6LAJ4h=S176S8(<1uA @251EI ,M`17M:1<4h=S65.g2"=LAY=S8:4<ANM:M)w47.JFg=56S.JM:MP13/&=S6SAJF@28C2=5.J6 -b ?,132117M:1<4E=56S.B2=SAY=S8:4o651"8,8P6S17Z[1<FB=L2jAJM:25.H/#1<Z[.JF@2=56LAY=S1oVd?I].J6[A 30" 1 b `2G(AY=58CANM*/#8:Z[17F@258:.JF@2?@A9J1=5.l9(1\25?,658:FB1</&9[=5?@1m2SANZ[1fIAB4h=S.J6

/#132547658:9;1</w9

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25.+@6S471&9,8:AB2 1xAN6S1&6S1<2=56S8:4E=51</=S.Q=S?,1k258PFJM:1 U17M:1<4h=S65.BF=',F,F@17M:8PFH651J8:Z[1 -eb ?@145,6S651<FB=%8C2~4<AN6S658:1</j9X28:FJM:1W17M:1<4E=56S.JF@2~G@AB25258PFf=5?@1d8:25M:AJF@/X.BF,1W9c.JF,1 - +Fl47.JFJ1<F

=S8P.BF@ANM 30" 1 b 2 =5?,1 [email protected],M:.#4#YAJ/#1O1 1<4h=\[email protected]=\G,651321<Fg=mANF(/x=5?,1<6517I].J6S14L?(AN6!J1d47AJ656S8P1<6S2AJ651G@AJ2S28:F\=S?,1u4L?@AJF,F,1<M@ANM:Z[.B2=8PF(/#17G;17F@/,17Fg=5M [Vd?,8:4L?kANM:MP.YVf2%=S.8:F@476513AJ251=S?,1X4E.BF@/@4E=SANF(4E1\9o4L?@AN6!J1\AJ4<4,Z ,MCAY=58:.JF -

.YVnIAJ6`47AJFmVi16S8:251Vd8K=S?XAW28:FJM:1 U17M:1<4E=56S.JFu=56LANF@258C2"=S.J6=5?@1 .BFh=S. . 34,6S6S17Fg=

6LAY=S8P. * (! b .n.J9#=LAN8:FH=S?,1 .JF~4,6S6S17Fg= * 1 - ∆ - 6S1"8,8:6513/nI].B6c=5?@125Vd8P=S4L?,8:Fl=58:Z[1

A[28:FJM:1c17M:1<4E=56S.JFk?@AJ2i=S.&G@AJ2S2i=5?,1c8C25M:AJF@/o8:F=5?,1\=S8PZ[1

D8 *

D 1 - ∆ -

=- ^ =

b ?@8:2O651"8,8P6S17Z[1<FB=[/#1 (F,1<2O=5?@12=56S17FJ=5? .NIf=S?,1o=!,F,F,1<Md4E.+@G,MP8:F.NId=S?,1x8:25M:AJF@/=S.q=5?@1kM:1<AB/,2

8 - 1 - 8K=&/#1E=S176SZ[8PF,132X=S?,1oVd8C/=S? ANF(/?,178 J?g=O.JId=5?,1k='@F,F,17Mi9@AJ656S8P1<69;1E="Vi171<Fo8C2MCANF(/oANF(/wM:1<AJ/@2 - 8P=5?q2Vd8P=S4L?@8PFl. x=S?,1m=56LANF@258:2=5.B6

=5?@1u1<MP134h=56S.B2=SAN=58C4

1<F,176!+j9@AN6S658:176∆ AJ658C251<2~I].J64L?@AN6!J8:Fu=5?,1f8C25M:AJF@/

F,.J=A 1<4E=58:F\=5?@1d=',F@F,17M;4E.+

G@MP8:F\=5.X=5?,1fM:1<AB/,2 - 20 .R5 > ;$. / I.$ .47.JZ[1<28:Fg=5.XG@M:A9 MK=S?,.+B?

=S?,1f1<MP134h=56S.JF[I]6S.JZ 25.+,6L4E1WI]1<17MC2=5?@117F@176!+j9(AN6S658:176∆ ∆

=5?,1u8:25MCANF@/&4<ANF9;1i.4<4,G@8P13/X9XANFO17M:1<4h=S65.BFX8PI@=5?@1M:8KI]1i=S8PZ[1iI].J6e=5?,1W1<MP134h=56S.JFj.JFX=S?,1W8:25MCANF@/Vd?,8C4L?

4<ANF9(1&132"=S8PZ&AN=51</H9 8:2X25?,.B6=\17F,.&J?

∆

-b .x1sAJM)(AY=51[=S?,1[6SAN=58:. * 8(!

Vi1l47.JF@258:/,176 @6S2==S?,1O=56LANF@25Z[8:2S2.BFQG,6S.J9@AJ9,8:MP8P=0 ∆ fI].J6cAJFQ17M:1<4E=56S.JF

G(AJ2S28:FX=S?,1\8:25MCANF@/o8KIe=5?,1\.#4745,G@AY=S8P.BFoVi.+,MC/o47.B2==S?,1m17F,1<6'&∆ +Fo=S?,1c2"=S65.BF

=!,F,F,1<M4E.&,G,M:8PF6S15J8:Z[1j=S?,1w4E.B656S1<25G;.JF@/#8:Fo=56LANF@25Z[8:2S28:.JFnG,65.B9@AN9@8PM:8K=0Q/,17G;17F@/,2

b ! #"$&%'.BF

∆ B8)B17Fx9kA :`.J6S17Fg= <8:AJFoI ,F(4h=58:.JF - b ?,1<6517I].J6S1u=S?,1j45,656S17Fg=WI]6S.JZ 2.&,6S471

=S.[/,6SAJ8PF M _B_/L/N9;1<47.JZ[1<2

__ ∆ T

=- ^ !

b ?,1 .JF(4,6S651<Fg=i8C2d.J9,=SAN8:F,13/wI].B6∆

ANF@/2?@.+,MC/kI ,M (MPM

8 * 1 - ∆ - =- ^ .

b ?,8C2 ,#1<2i=S?,1cG,6S.JG;.J65=58:.JF@AJMP8P=0lIAJ4E=5.J6d8:F =- ^ ! =5. * -(b ?,1 . (4,6S651<Fg= "!8C2W651<M:AN=513/w=S.[=5?,1 .JF(4,6S651<Fg= * /,1\=S. =#- ^ ! Vd8K=S?x658C28:Fl=5?@1X17F,1<6'&&9@AN6S6S8P1<6

∆ 9

(!8 *

__ ∆ T

dVd?,176S1∆ D ) ! - ! - )

∆ - =- a

1<M:AN=58:.JF =#- a 1E#G,6S1<2S2132=5?,1\I].BMPM:.YVd8PF

25?,.J65=eM:8PI]1=S8PZ[1 .JI@17M:1<[email protected]=5?,1i8:25MCANF@/OANM:MP.YVf2eAM:1<A \45,6S651<FB= 8(!9(17="V1<17FX25.+,6L4E1AJF@/c/#6LAN8:FX/,1=S.d='@F,F,17M:8:FfVd?,8C4L?X/#17G;17F(/,2`Vd8P=5?∆ 9

A :`.J6S17Fg= <8:AJFk.BF * -,b ?,1 . (4@656S17Fg= 8"! 8:2fF,.[MP.BFJ1<6i17#G(.BF,17Fg=58CANM:M 2 ,G@G,651325251</k9

∆ AJ2W8P=f.#4745,6S2I].B6fA[G,6S1\47M:AB25258C47ANM9@AJ656S8:176 - 8P=5? =#- a iANF(/ =- ^ .

=5?,1X2=SAJF@/#9wG;.YV1<6 # $ & +' 47AJFk9;1c1<2=58:Z&AY=S1</k=5.

# $ & +' "! )∆ - 1 - ∆ - ) _ D T ) ! - ! -

1 - I S D I ) ∆ -! - ! - I ) 1 -T I ! =- a@_

3u98P.&@25M)ANFq8:F@4E6S1<AB21c.JI

∆ - /#.1<[email protected]=?,1<MPGn?,176S1c=5.2 @G,G,6S1<2S2dMP13A YAB1cVd?,8C4L?8C28:Fo4E.BFB=S6SAJ6'jG(.g25258P9@MP1d8:F&[email protected]*AJF&1E#G;.JF,1<FB=S8:AJM(/#1<G(1<F@/#1<[email protected]=5?,1 .BFN=S. . 4,6S651<Fg=6SAN=58:.X.JF

∆ - M:1<AB/#8:FX=S. =#- ^B^ - 132"=S658C4h=S8PF # $ & +' ANF@/&G@65132547658:9,8:F&I].B6*J8 J17F 1 -

ANM:MP.YVf2.JF,M wAj471765=SAN8:FFQ4T IQ ;$Q∆ N-

8PF7J.BMK=LAJ1u2Vd8:F∆ -

∆ - ∆ N-

D ) T ! - ! - )

1 - I ) #%$ & (' =- agT " " ! " 8 [% 8" 3 & & " n & Q ∆ Y

∆ 3 / " ^ ∆ 3 h ∆ HYb " "$ & c e 8 & & & ' n # %

0 -[ ] "$ Vd?@8:4L? B.g132/#.YVdFx=S.y71<65.wI].J6u25?,.B6=u25Vd8P=S4L?,8:F&=S8PZ[1

6S1<25G(134h=58 J1<M)x/#1<M:A9k=58:Z[1

AJF@/lM:AJ6'B1WF,.#/#147AJG@AJ478K=LANF@471<2 1 - -Jb?,1M:AJ6'B1<2=YAJM),1WI].B6

∆ -AN6S1dG(.g25258P9@MP1WI].B6!.- 6 _ - 1 .B6 !1- 2 ! -

=5?,1cM:.+B8:4 r 3 b gAY=51c/#.132WF,.N=fVi.J6wAY=fANM:M - 1<M:AN=58:.JF =#- a J8 J132&/#8:65134h=5M y=S?,1 4./ / +0 I.E> L ..10 20 I. I6 0 /.E>, ;$.". 1 /; C I.J>( >IQ w4E8:17F@45 1 AJ4E=5.B6 S *8(! _ D T ) !.- ! - 1 - I =- aB^

b ?@2=S?,1w1w478P1<F@4nIAJ4h=S.J6c.JIdA " b 8:2cM:8:Zl8P=513/9Q=5?@1w6SAN=58:.x.NIW=5?,1&6S1"8,8:6S1</

/,17MCA9O=S8PZ[1 o8:Fk25Vd8P=S4L?,8:FO=5?,1m9,8P=d2=SAN='@2WAJF@/&=S?,1uF@./,1\4<ANG@AB4E8P=SAJF@4E1 1 - -:eAN6!J1

F@./,1Q47ANG(AJ4E8P=SAJF@4E132[ANM:MP.YV .JF,M AMCAN6!J1x/#17MCA9y=S8PZ[1 - 3=5?,1<65Vd8C21=S?,1QM:1<A YA+J145,6S651<FB= 8"! AJF@/[=5?@176S1EI].J6S1d=S?,1m2=SAJF@/ U98lG;.YV1<6 #%$ & +' 8:28:F@4E6S1<AB213/ - +F 1 8 -=- _7a=S?,1n1 w4E8:17F@45IAB4h=5.B6 =- aB^ &8:2kG,M:.N==S1</ B176L2 (2[=5?,1F,.#/#1n4<ANG@AB4E8P=SAJF@4E1 1 -

I].B6/,8176S17Fg=f/#17MCA9[=58:Z[1<2 -(b .[6S1<AJ4L?A[2?,.B6=d/#1<M:A9&=S8PZ[1 kI].J6fA[4E1<6=LAN8:Fk1 &478P1<F@4

510

I on

/ Iof

fE

ffic

ienc

y Fa

ctor

1010

10-18

10-20

10-14

108

CY

10-8

α Α − α Y = 1/4

α = 1 Α

010

1015

10-16

10-12

Node Capacitance [F]

10-2

10-4

10-6

Effective Length CY ε0 [m]

VLSI Requirement

-10 10 s

10 s-12

τ = 10 s-8

Example

& 8 ? 8 & > " 7 7:9 6 " & 3 ! " / " "

6 i

6 3 b & 6

" & " 6 [ )/ &

∆ 6

! #"$&%'IAB4h=5.B6

=S?,1cF,.#/#1X47AJG@AJ478K=LANF@471 1 -

?@AJ2i=S.&9(1c6S1<2=56S8C4h=513/w=S. 1 - D )

T ) ! - ! - w4E8:17F(4 1 AB4h=5.B6 =- aJa$

1 .J6 _cF@2 ! !1- _XAJF@/qANFq1 &478P1<F@4kIAJ4E=5.B6.NId_ . 6S1"8,8:6513/oI].B6 :"$

=S?,1uF@./,1m4<ANG@AB4E8P=SANF(4E1f?@AB2=5.l9(1mMP8:Z[8K=S1</o=5. 1 - a ! ) _ . 1 - 1 .J6W2 (4L?k25Z[AJMPM4<ANG@AB4E8P=SANF(4E1<2

=5?,1w258PFJM:1 U17M:1<4h=S65.BFn4L?@AJ6'B8PFk17F,1<6'& D T 1 -

ANM:6513AJ/q17 47171</@2f=S?,1l=5?,1<65Z&ANM~17F@176!+ @ " # AY=\65..BZ =S17Z[G;176LAY='@651 b ?@1O9,8P=c8:2m6S17G,6S1<2517Fg=S1</.BF,M)D9DI]1<V 1<MP134h=56S.JF(2[Z[A 8PFH=5?@16S17G@651321<FB=LAY=S8P.BFyI]6LAJ8:M:1 - 17MCAY#8:FH=5?,1q1 !478P1<F@4xIAB4h=5.B6=S.H_ ?# ]Vd?,8C4L?/#.1<2mF,.N=cANM:M:.YVR?,8)B?n8:Fg=515B6SAN=58:.JF

=5?,1[Z&AY#8:Z ,Z

F,.#/#1w4<ANG@AB4E8P=SAJF@4E1[8C2cMP8:Z[8K=S1</=S. 1 - a ! ) _ 1

Vd?,8C4L?D4E.B656S1<25G(.BF@/,2m=S.QAF,.#/#1qM:8:Zl8P=513/ 9y=5?@1 / IO 4.J> I6 1 - L *Z -b ?@8:2&1 ;134h=S8)B1qMP1<FN=S? &:! 1<2=58:Z&AY=S1<2l=5?@1qG(.g25258P9@MP1 Q4T IQ ;$Q .E> 76 +Q / V: 8CA8K=L2w21<MKI 4<ANG@AB4E8P=SANF(4E1 1 T R MPF& 4

25171 - _B_ Vd?,1<651

4 /#1<F,.N=S1<2f=5?,1XVd8:6S1

6LAJ/#8 @22 &:! iI].J6dA =5.

4 6LAY=S8P.l.NI%AN9;.+#=L - rf.J=51 =S?,1\1 1<4E=58 J1mMP1<FN=S?

&:! 9;1<47.JZ[1<2[Vi.J6L218PI ! - ! - _ - 1 .J6 ! - ! - _ a 8 - 1 - ! _ a ! _ a ! _ TOVd?,8C4L?QZ[1<AJF@2%BAJ8PF 20T[8PFQAJFq8PFB1765=5176uAN6S6SAJFJ1<Zl1<Fg==5?@8:2

1 ;134h=58 J1jMP1<FN=S?Q8:2.JF,M 1 - _ ^ *Z

8PFHAw/#8:17M:1<4h=S658C4cM:8B1 "8 3

Vd8P=5? aVi1X?@A9B1 1 -

^ *Z - 1 6S.JZ =5?@8:2u1<2=58:Z&AY=51 8P=uVi.+@M:/qZ[13ANFx=5?(AY=I].B6mAJF

1 &478P1<F@4[IAB4h=S.J6W.NIi_ ?#u15B17FAjVd8:651m.NI - ^*Z M:17FN=5?xANF(/o6LAJ/#8 @2i.NI`I]17V AN=5.BZ[24<ANF,F,.J=d9(1X/#6S8 J17FVd8P=5?,.&#=f1E,4E1<1</#8:Fl=5?@1cG,65132547658:9;1</o/,17MCA9&=58:Z[1

_mF@2 - !

Hu *$)ug u$ *f! j! ~#`2 0`$ u 0 %%#%!~ $$ 2&V1 F,.YV

?,8)B?,M 8:Fg=515B6SAN=513/ /#8 J8P=SAJM4E8:6L4,8P=S2k2 176w=5?,[email protected],MP1<Z .JI\.(B176

AJMPM;G(.YVi176W/#8C25258:G@AY=S8P.BF - .BFg=56S.JM:MP8:Fj1<MP134h=S65.g2"=LAY=58C47AJMPM [ANFo1<F,176!+l9@AJ656S8P1<69;1E="Vi171<F25.+,6L4E1fAJF@/w/#6LAN8:Fw8C2=S?,1u9;1<2= F,.YVdF&.BG(1<6SAN=58:.JF&Z[.#/#1.JI`Aj25.JM:8:/o2"=LAY=51u/#158C4E1uAJMM:.YVd8PFXZ[8PF,8:Z @Z 8PF&=S?,1 J.JMP=SA+J125Vd8:Fj9;1E="Vi171<F .BFANF@/ . #2=SAY=S1 - .J6S17.(B176

8P=XANM:MP.YVf2uI].J6c47.JZ[G,M:17Z[17Fg=SAJ6'qVi.J68PFk25Vd8K=L4L?,1<2 -*b ?,1&4E.JF(2"=S6SAJ8PFg=S2u=S.Z[8:F,8:Zl871=S?,1 B.JMP=SA+J125Vd8:F∆ - I].B6%651<G,651321<Fg=58:Ff=S?,1i="V.u9,8K=2=SAN=51<2%AJ651i/#8:2S4(25251</XI].J6~=5?,1

478P6L4,8P=d.NIA[MP.&J8C4 r;3 b BAY=S1c8PF=S?,1cG,6S158P.&@2"134h=58:.JF(2 -,b ?,1kAJ651c2',Z[Z[AJ658713/8:F 1 8) ->=- _/LkI].B6X=5?@651<1w/#8176S17Fg=j1<MP134h=S65.g2"=LAY=58C472 ! - _ ! - ! -

T8L

AJF@/! - ! -

_ 8 n P

"! ! &]2 ! & "" 9 8 & & "$ & 7 7:9 $)c e ,# \ Z / / " > "$ d % n ] 3 Y % 3 Y% "$

"[ > ! ! 9 G\ /Y =o25Z[AJMPMF,.#/#1Q47AJG@AJ478K=LANF@471 YAJM),132 1 -

=5?@1Q9,8P=o651<G,6S1<2517Fg=SAN=58:.JF8C2wA ;134h=513/9=5?,1<65Z&ANM)@4E='@AN=58:.JF@2 -b .2 ,G@G,6513252176S65.B6S2 Ak4E1765=SAJ8PFnZl8:F,8:Z ,Z

∆ *-

1 - ∆ - ∆ D T 1 -

.NIW17M:1<4E=56S.B2=SAY=S8:4[1<F,176!+n?@AJ2\=S.q9(1k2"=S.J6S1</.JF=5?@1F,.#/#1W47AJG@AJ478K=S.J6 -3b ?,1W6S1"8,8:6513/cZ[8PF@8PZ ,ZJ.BMK=LAB125Vd8PF

∆ - 8C2~G,MP.J==S1</ J176L2'@2=5?@1&F,.#/#1&47ANG(AJ4E8P=SAJF@4E1 1 -

I].J6\=5?@1&176S65.B6uG,6S.J9(AN9,8:MP8P=0 & 7 _ lAN=c65..JZ=51<Z[G(1<6SAN=',6S1 -,b ?,1c6S1"8,8:6S1<//B.JMP=SA+J1\2Vd8:F[8PF(4E6S1<AJ251<2iVd8P=5?q/#134E6S1<AJ258:F 1 - -Y b .QANM:MP.YV 9,8K=l28 JF@AJM6S1<2=5.J6LAY=S8P.BF AqZ[8PF@8PZ ,Z 8:Fy2',G,G,M B.JMP=SAB1[8:2c6S1"8,8:6S1</

2"=S65.BFJM qA 1<4h=S1</H9x=5?,1[17M:1<4E=56S.B2=SAN=58C472m.NI=S?,1&2Vd8P=S4L? - ",G,G,M B.JMP=SAB1<2.NI2515J1<6SAJM.@ " # D S T Z ?@A9J1j=5.k9(1[ANG,G@MP8:1</

8:F@/#1<G(1<F@/#17Fg=SM)Q.JI=5?@1O.&#=5G,=

F,.#/#1c47AJG@AJ478K=LANF@471 1 - -Y .B65121J176S1=5?@16S1"8,8:6S17Z[17Fg=l/,1=5.MP13A D9=5?,1<65Z&AJMWAB4h=S8)YAY=S8P.BF.JI17M:1<4

=56S.JF(2c.(J1<6jAqG,6S1o47M:AB25258:4<ANM9@AJ656S8:176XM:8PZ[8P=S2j=5?,1o6513/@4h=S8P.BFD.NI∆ - 1<25G(134E8CANM:M)I].J6iMCAN6!J1F@./,1\4<ANG@AB4E8P=SAJF@4E1sAJM)@1<2 1 - b

.[2 @G,G,6S1<2S2=S?,8:2d2=SAJF@/#9&G;.YV1<6i/#8C2 258PG@AN=58:.JFkVd?,8PM:1\ANM:MP.YVd8:FOAl?,8 J?2G;1713/oG;1765I].J6SZ&ANF@4716S1"8,8:65132=S?,1\.JG#=S8PZ ,Z8:F=5?@1w17M:1<4E=56S.B2=SAY=S8:4<2\.NIW=5?@1k25Vd8K=L4L? - %258:Fq=5?@1w1<2=58:Z&AY=51 =- ^J^

=S?,1oZ[8:F,8:Z ,Z8:F4B.JMP=SAB1O25Vd8PF

∆ *-8C2\G,MP.J==S1</H8PF 1 8) - =- _/L&I].J6c6LAY=S?,176\Z[.#/#176LAY=S1 YANM ,132

.NI # $ & +' _&F

_&F@2 - " b ?,1w.BG#=58:Z @Z .JIi1<MP134h=56S.B2=SAN=58C472\I].B6c=5?@1

25Vd8K=L4L?,1<2W8C2!1- _ 65132G;1<4E=58 J17M (! _ -Y "8:FJM:1 U17M:1<4E=56S.JF=56LANF@258:2=5.B6S2.B6w8PF B17F,1<6SAJMW=56LANF@258:2=5.B6S2lVd8P=5?z=5?@8PF AJF@/zMP.YV

9@AJ656S8P1<6S2AN6S1\MP8:Z[8K=S1</8:Fk=S?,178:6f1 &478P1<F@4oIAJ4E=5.J6 S 8 * "! 9(1347A(21

/,1c=S.

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! #"$&%'

P err= 10

-19

T = 300 K


10-18

10-6


10-18


10-18

by thermal activationForbidden due to leak

over classical barrier

Forbidden due to thermal fluctuationsin electron number

α − αA Y = 0.25

α − αA Y = 0.1

αA = 1

2

1

0

VY

[V]

∆V

olta

ge S

win

g

10-16

10-14

10-12

10-4

10-2

Effective Length CY /ε0 [m]

(a)

(c)

(b)

2

1

0

VY

[V]

∆V

olta

ge S

win

g

10-16

10-14

10-12

2

1

0

VY

[V]

∆V

olta

ge S

win

g

10-16

10-14

10-12

Pleak= 0.1 nW= 0.1 nsτ

leak by tunnelingForbidden due to

3

2

1

3

2

1

3

2

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Z @ -, K4K 3 3 / 3Y? / 3 / 3S F-Q/ 3 +4*+ / 53 3 E .Q 8 N?5S 304EOPOO #&I-96vF M !D-9D JOCIF M ID-kV6nGwF669 / . K /K ,-, 3 K 3 E 3 / 53 ; -< < / 53 / > 3 8 W Q/ 3 < 4/P; 3? *G/* 3 yF* / ?@3 < 3 E Q 3 Q V N? %(* # *Q QL* Q@6()" <. ) W5 4 W 6+ 3 ACEDGF77IH-)-9VDEK M &b47 M 66a M !D-a'OCIF M ID-kV6nG!F769 ^ = M " 4EOk ^8/ K ,, . 3 K R 3 3 [. / SN3 E /G 3? / > 3 G/ ?@3 / 53' . / > 3_p &<0F/ 3 4/ %3&? /&Z 35 6V / ?@3 [ / 3 *+ 3P - WQ 3 Q 8 V N? % , 3 ! . $@8"! K Q 3P4EOPOO OcIF M ED-JkV6nG!F7Y MwM 679 /K /9K ,,4 3 K . 3?@3 @ * F/ 3 8/ 53W *F / 3a =FWG/ 3 3 ;'8/ ?@3 6@ /* 3C / SN3 G/ :3 *Q8/ E 3 3C: / 53 @6= / ?03 * 6VF/ %3+? * 3 E Q )", 6 ; N?S @ *++ K 3 ` ,4/ )6 *+ * S 7<. 3 4EOOPO OcIF M ED-kV6nG!F7Y MwM 669 / K- K R / QQQ 3 K 3? ! #*- Q* @7 " 3 ACEDGF77IH-)-9DLK M &4EOOPO / , R / QQ K 3 K 3 3 < /, 3 ; `4/ 3 ; W #* / > 3-> *+ !Q/ > 3 N 4/ 3 ; -< 6WQ/?@3P 4*7/8*+ > 3 /8 3 3 S Q 6 @])* ? L+ @@# # 6 +S F *Q 3 OCIF M ID-!F(9Y MwM 679 / R K K R /K ,-, 3 K 3N53 ^y< *+ 3 3Wr *) * @@ @ "4 $])* * + @@# 8# 6 3 1 `v`WX'Ai-9(X_Y MwM X / K- R , K /K ,-, 3 K 3 3 -< / E 35S *!6V!Q/S 3 ; 4/ 53 ; W #* / > 3> *+ !Q/ > 3 N 4/ *Q > 3Y? + @@# 0@ 3 47 M Xhs5XaOCIF M ID-!F(9 / Q /@K ,-,, 3 K , 3N> 3 #* / 3 ^/ > 3Y? F +Q/ 3 < Q/* 3 p+3 / pQ3 ?03Y 3 Z F *+ + @@# # 6 %W )"962 *@ ! , 0+ L",6F 31 ``WX'A0i 9(Xh MwM X / R-. /K ,-, 3 -Q 3 3 ; < %*+ /* 3 /* p+3 3 K Q-Q > E 6.+ @@# # 6 3s`&'Xs5X 1 `v`WX'Ai 9X / R K . /9K ,, 3 K 3?@3 E ")8/ E 3& /W* 3h? +- Q/S 53&> *+= 3 4 > + @@# # 6 Q@6 % Q 3 K " 3cs5X 1 `vàX_Ai 9(X / K- QK K /9K ,,4 3 3p+3? 6-< > 3 #* 3e? + @@# C +8@ !@;& ;& , @! @@# 8# 6 N . F *+ 3 1 `v`WXWAi-9(X'Y MwM X / K ,-R /9K ,-, 3 -R 3p+3 Z 3 * 6<- 3 F)#"! - 6 ` * % 6< 3s5X 1 `vàX_Ai 9(X / .vR-,, /K ,, 3 . 3 Z 3 3 G/ E 3 ; 30> =< 0/8 > 3 > 3 y<0 ! 3 ? @@# # 6 - 3 1 `v`WX'A0"i-9(X_Y MwM X / K , . /K ,-, 3 3N> 3 4* 3'> 3NS * *Q Q @ # *@+$ ? ' @ -6 F* 3 Ok sD-%6a / R` /GK ,-, 3 3 E 3 [ 3 3+? 5 *+-) U ) **@7] *@ 3+4 f O#&I &9(XPD JOCIF M ID-!F PD-Uà% M 669 /GK Q . K /9K , K 3 4 3 E 3 [ 3 3P: ", 6 6@ - * 3 35> 6G/ @ 8/^ !F(ED6`5D-06OcIF M ID &!F(9 3W: ` : @F/K , -. 3 3 Z 3 [ 3W> ")@ 3: )",@ * @@# @ 3ACEDGF6=IH-"-9xDEK M V4EOPOPO / .Q /K , 3 -, 3 Z 3 [ 3> ") 3vS * ) - ) W + + 35A3IDGF7=IH-"-9DEK M &N4EOPOO / , /9K , K 3-RQ 3 Z 3 [ 3> ")@ 3 [ W-<.L% *N( 3CWF(86aF6 / -R-Q K R Q/9K , 3

4 Q Z' @-R K 3 Z 3 [ 3W> ") 3: )", @ 0 @ 3 f 6nG86 9 DLK ^ DGH"67@Ai-9=!F(9 / K 4-, /K , , 3-R 3 Z 3 [ 3P> ")@ 3 S * 0V @7 " 3tACEDGF6=IH-"-9DEK M &4EOPOO / , / QQ K 3-R-R 3 Z 3 * 3 6% 7)"> 0# ])* 0 *+ @@ ## Ai-9=!F(9x#aDGHv-i / 3 K4K , /K , , 3-R . 3 Z 3 * 3 E 5 6 @7 " # * 5. 3lAi 97wF7 1 /K /K ,-,Q 3-R 3 Z 3 * 3 ])* 0 *+ @7 @* * A0"wX#&I &9(X f X0WDGF~X D WH"X 1 /R R R 4 /9K ,, 3-R 3N 3 53 < % 3_ ) S > # 6 NV N? ! W L",6F 3 ^ wF(ID~(IF M ID-!F(9sD-%6a / -, 4-, /9K ,, 3-R4 3 E 3 535 7<0 0 p+3 ?@3 &<- 3 E $Q" 3c4EOPOOts5XDEKbWD !H-| M M eIF(% M 9 / RQ R K4K4/K ,, 3-R 3N 3 #" 7<.4/_Z 3 !@/ p+3 E &@ 8/ : 3 E *Q 3 *+) )# @F* !N - ` @ 3 / -aD MwM 669 /9K- . -R / -QQ K 3-R-, 3 E 3 *8 70 / :93P ")/ 3 ; < /8 3 <<. 3 - 06 F* %6! 8 **# 6 3+WF(!6WF7 / ,-. K R K / -Q-Q K 3 .Q 3p+3 3 ? 7 G/ 3 Q/: 93 *8 3? @ F% @ F") P @ @# 6 3 / M %I / . K R K R / QQ K 3 . K 3 3 / > 3 8 W 6-<0/ 3 ; `4/ ?@3h 4*7/ > 3? 6 / 3 -< 3? + @@# ])* ) * ? V0 @ 3 ^ !F(ID~(IF M ID &!FO3-W767" /-, .vR / -Q-Q K 3 .` 3N> 3 53~? 3 ; Q*@$# " " 0 334EOPOO s5X DLKNaD !H|! M M (|7EF(% M 9 /9K 4 /K , 3 .R 3 3 ?03 )".C 3 3 ZS"5y< 3 #Wvz69 DEK47 M !-E 9 '67869 -aHJA3IDGH-%F M 9 3E @ : @F/&;* =<! /GK , 3 .-. 3 Z 3 3a? V p+3 %3 , 3 )6 F)#"! N? # % 6 F* 334EOOPO s5X DEKbWD wH|8 M M (|=IF(% M 9 / K .` /K ,4 3 . 3N> 3 ; 3 Z -< *+W p+3 %3 3V? @* N? + - 304EOPOPO s5XDEKaD !H|! M M eIF(% M 9 / ? K ,R /K , 3 . 353 / p+3 *N*4/ SN3 * *+WG/ > 3 > 3 * *+@ 4/ 3 * 4/ p+3e ! /E 3a / 3' G/ 53a #WG/] 3> /&Z 35> WG/ E 3> 8/ SN3a> F/ ?@3 @ / %3 * 8/ pQ3 Z / :3? y. WG/ 3? 7G/W[ 3 G/ %3 )8/Z 3 *+/, e* 3 [ 6 3 @) @SW 7 N?5S , 5 7<@ 3 ^ !F(ED~(=F M ED-&wF(9 f ( !vz( M i / .Q / QQQ 3 . 3 Z 3 53 8 / E 3 *Q W-6@/ > 3 SN3 4/, %3 35p 3 ? @ $ ? J , F +* _ @ # 6 ") Q 3 K F-J*++- 6 ++-+ 3 1 `v`WX'A0"i-9(X_Y MwM X / , RR K /9K ,, K 3 . 3 Z 3 53 8 / E 3 *+ W 6 /S > 3 SN3 3? 6 ? N?S S *y< ? +*y< 34EOOPO #&E-&96vF M wD-D- OCIF M ID-kV6nGwF669 / R, K -Q-. /9K ,-,` 3 ., 3p+3 :3 3P? *Q@ W ? G N?5S 3P4EOPOPOdOC=F M ED-kV6nGwF6Y MwM 679 / L .. /K , 3 Q 3N %3 pS &<0/ ?03 3 *Q,@/` 3 53vS 3 )N 5* R-Q ++* ` N?5S I 6 ? G ACEDGF77IH-)-9VDEK M N47 M 67W M wD-WOC=F M ED-kV6nG!F769 ^ = M " 4EO0k ^8/GK ,, 3 K 3N %3 p+3_S &< 3 ?03 [ 3 E 6", G !

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S *y< ? $ * < Z6+* B - R / /1 K @ @$ *@ * 3 ACEDGF6=IH-"-9 DLKM &47 M 67W M !D WOC=F M ED- kV6nGwF669 ^ = M 4EOk ^ #'IF7!F=&kN"69 M /, - /K ,-, 3 ` 3N> 3 / 3 ^/ 3'? / 3 4/ SN3 *+/ 3a / 3&> 8" / 3c> *+4/V > 3c? <0 3 ? @@# F #" -` 6 - 3ACEDGF77IH-)-9VDEK M &b4EOPOPO / -RR /K ,-,, 3 R 3 3+ * ++/ 3+ * /6 3 N*/: 3 p+3 * / > 3 3> /N 3 3 F 3 - @ . * F% 6 % *+7 6< 3 WF(w|6WF7 / ,-. K R K R / -Q-Q K 3 -. 3 3? a])*8/ 3a? @708/) 3& / ?@35 @ * F/, 53& *` 3 * % 7< *! "# y ? N?S 3PA0"i-9(X f 6n-X / K- .v, /-Q-QQ 3 3 [ 3: @/ 3 ?@3 )8/ 53 3 * 6 / E 3 53 0/ 3 E / 53 3"? 8/ p+3 3 = 3cr *) * V@ *!$ * W *2%0 * @] *) * 3C47 M XYs5X_OCIF M ID-!F(9 / .v, /K ,-,, 3 3 3 3? *< *< > 53 3 ? )# @V 6e] *+ ] *) * 3P`5i-9(XY9 M M X96DX / . / -QQ K 3 3 3 -<0 / 53c? h G/ E 3C? 6 W 3p @ * ] *+ % )# 6 * + 3 / M %= / R-, 0 R-Q /9K ,,-, 3 3 3 -<0G/ 53? h G/ E 3P? 6 W 3Br *) * 6 -% @ * 0( 3 f 6n-X ^ DGH"X'A0"i-9(X / -R R4 / -Q-Q K 3 , 3N53Gr G/ SN3~? (@/(Z 3 53 *8 6<0/ p+3 :3G> * F/([ 3 [ F 8/: 3 * 7 3 , VG. +* L 3] *) * 3A0i 9(X f 6n-X / -R QR-R -Q / QQ K 34-Q 3 3p /S 3& * / 53&? 0#y< W 3 # 0 ])* 0 *+ % > #@ 6! *!#" 3tAi 9X f 6n-XCY MwM X / 0 Q4 Q K /-Q-Q` 34 K 3SN3? ( /Z 3 3 *8 6<0/ p+3 :3> *F/[ 3 [ 78/ B 3 * 7 3E W * > @! e])* ) *+ ! & 3Ai 9X f 6n-XY MwM X / R Q-. /K ,-,, 3

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