ece606: solid state devices lecture 17 schottkydiodeee606/downloads/ece6… · ·...

Klimeck – ECE606 Fall 2012 – notes adopted from Alam

ECE606: Solid State Devices

Lecture 17

Schottky Diode

Gerhard [email protected]

1


Reference: Semiconductor Device Fundamentals, Chapter 14, p. 477

Presentation Outline

1) Importance of metal-semiconductor junctions

2) Equilibrium band-diagrams

3) DC Thermionic current (simple derivation)

4) Intermediate Summary

5) DC Thermionic current (detailed derivation)

6) AC small signal and large-signal response

7) Additional information

8) Conclusions

2


Metal-semiconductor Diode

M N

Symbols

DN

Metal Wire

N

3


Applications of M-S Diode ….

Originally, Gelena (PbS), Si as semiconductor and

Phospor Bronze for metal (cat’s whisker)

Detectors

www.fz-juelich.de/ibn/index.php?index=674

STM(scanning tunneling microscope)

on semiconductor

Original Bipolar CNT(carbon nanotube)

Transistors

4










8) Conclusions

5


Topic Map

Equilibrium DC Small signal

Large Signal

Circuits

Diode

Schottky

BJT/HBT

MOS

6


Drawing Band Diagram in Equilibrium…

1P P P

pr g

t q

∂ = − ∇ • − +∂

J

( )D AD q p n N N+ −∇ • = − + −

P P Pqp qD pµ= − ∇J E

1N N N

nr g

t q

∂ = ∇ • − +∂

J

N N Nqn qD nµ= + ∇J E

Equilibrium

DC dn/dt=0Small signal dn/dt ~ jωtn

Transient --- full sol.

7


Band-Diagram

DN

Vacuum level

EC

EV

EF

A p D nN x N x=

ΦM

Since NA is large,xp is negligible ..

χ

1. EF flat in equilibrium2. EC/EV in Metal3. Vacuum level in Metal4. Ec/Ev in semiconductor5. Vacuum level in semiconductor

6. Connect vacuum levels

7. duplicate the connections down to Ec/Ev

Charge(metal) = charge(semiconductor)

8


Built-in Potential: bc @Infinity

b MiqVχ∆ + = Φ+ ( )M BbiqV χ= ≡− − ∆Φ Φ − ∆

BC

BDN

k T lnN

= −Φ

qVbi

∆χ

ΦM

ΦB

non-degenerate

neglect

9


Depletion Approximation

ρ

qND

Xn

QM =-QDQD = NDXn

x

Actual Xn

E

x

max

D

0 0

Q D n

s s

qN x

K Kε ε= = −E

xXn

BqφCE

VE

Area negligible

integrate

integrate

Analytical Solution (Simple Approach)

Notice how we neglect xp here, is there a proof?

x

Xn

max

max 2nxφ = − E

φΦmax=qVbi

10


Charge

E-field

Potential

xp

xn

+-

Position

Position

Position ( ) ( )22

0 0

0 0

2 2

2 2

bi

MD

n

pn

s s

pqV

qNqN

k k

xx

xx

ε ε

− +

= +

= +

E E

( )

( )0

0

0

0 ?

nD

s

M

s

D

p

n pM

qN

k

qN

k

N

x

xN

x

x

ε

ε

+

−

=

=

⇒ =

E

E

Complete Analytical Solution

11


Depletion Regions

22

0 02 2pMD

bs

ni

s

qNqNqV

k

x

k

x

ε ε= +

pD MnxN N x=( )

0 02 2 1s sMbi bi

D M D Dn

k kNV V

q N N N q Nx

ε ε= →+

( )02

0s Dbi

M M Dp

k NV

q N Nx

N

ε= →+

xnxp

DN

NM ∞

This is why we can neglect xp

12










8) Conclusions

13


Topic Map


Large Signal

Circuits

Diode

Schottky

BJT/HBT

MOS

14


Band Diagram with Applied Bias…

1P P P

pr g

t q

∂ = − ∇ • − +∂

J

( )D AD q p n N N+ −∇ • = − + −

P P Pqp qD pµ= − ∇J E

1N N N

nr g

t q

∂ = ∇ • − +∂

J

N N Nqn qD nµ= + ∇J E

This works for doping-modulated

Semiconductors.

Does not work for heterostructures

(when the conduction band is not

continuous)

Metal-Semiconductor is a HS

Need theory of thermionic

emission

Band diagram …

15


Depletion Regions with Bias

( ) ( )0 02 2 1s M sn bi bi A

D M D D

k N kx V V V

q N N N q N= → −

+ε ε

( )02

0s Dp bi

M M D

k Nx V

q N N N= →

+ε

xnxp

DN

Forward bias: xn decreaseReverse bias: xn increase

16


Band-diagram with Bias

VA

EC-EF

EC-EF

qVbi

qVbi-V

VA

EC-EF

Forward Bias

Reverse Bias

17


I-V Characteristics

Forward Bias

Reverse Bias

Metal N-typeSemi.

VA

IEc

EV

EFEFS

EFM

Ec

EV

EFEFS

EFM

I

1,2,3

6,7

4

51 – diffusion control2 – ambipolar3 – resistance drop6 – defects – trap assist7 – Esaki

4 – generation current5 – impact ionization

18


EC-EF

qVbi

Current Flow Concept

In Equilibrium:and

are equal

ΦB

VA

EC-EF

Reverse Bias

ΦB

BarrierThe same!M=>S current unchanged!

VA

EC-EFqVbi-VA

Forward Bias

ΦB

Partition problem in2 currentsM=>S S<=M

BarrierThe same!M=>S current unchanged!

q(Vbi+VA)

Barrier smallerM<=S increased

Barrier biggerM<=S decreased

M=>S current Independent

of bias!19


Left Boundary Condition

VA

ECq(Vbi-VA)

( )

(

(( ) )

( )0)m s A s m A

s m As

T

m

A J V

J

J VJ

J

V

V→

→

→

→

= −= −

(0)(

(

(0)

(

0

0 )) 0

0) s m

s m

m

m s

T sA J

JJ

J V J →

→

→

→

= = = −⇒ =

( ) (0) ( )T A s m s m AJ V J J V→ →= −

(detailed balance)

M=>S current independent of bias

We use thermionic emission because:1. EC is not continuous here2. There’s no minority carriers!

20


Semiconductor to Metal Flux

(0)AV

s m

q

kTeJ →=

( )2

bi AV Vq

s khs

TA tm

nq eJ V

−−

→ = − υ

VAEC-EF

q(Vbi-VA)

2

bi AqV qVs th kT kT

nq e e

−= − ×υ

( (0)2

0)biV

s m m s

qs kT

th JqJn

e υ−

→→ = − =

(0)AV

m s

q

kTeJ →=

Only half of them goes to the right

Only the ones above the barrier goes to the right

(0)

( )2

Bqm kT

th

m s

m s A

nJ qV e

J

υ

→

→

Φ−

=

= − M

2

B Aq qVm th kT kT

nq e e

Φ−

= − υ M

12

(0) ( )m Aq qV

m th kT kTm s AT s m

qnJ J e eJ V

υ→ →

− Φ = = −

− M

BΦ

21


Diffusion vs. Thermionic Emission

Fp

Fn

∆n

Fp

Fn

Check that both gives the

same result for a diode…

Thermionic Emission theory is a more general approach, can be used for device so small that no scattering occur (can’t use diffusion!).

22


Schottky barrier diode is a majority carrier device of great historical importance.

There are similarities and differences with p-n junction diode: for electrostatics, it behaves like a one-sided diode, but current, the drift-diffusion approach requires modification.

The trap-assisted current, avalanche breakdown, Zenertunneling all could be calculated in a manner very similar to junction diode.

Intermediate Summary

23










8) Conclusions

24


Energy Resolved Thermionic Flux

( )min

34F

s x xmE E

y zJ q dk edk dkυ

β υπ

∞ ∞− −

→−∞

−

−∞−∞

Ω= − ∫ ∫ ∫

VA

EC-EF

q(Vbi-VA)

~ DOS

minυ

x

Occupation(non-denegerate)

Only movement in thex direction will contribute

to the current flux

2min

*

2

1 υm<Energy

will be bounced back

25


Thermionic Flux from Semi to Metal ..

( )min

34F

s m x y z xE EJ q dk dk edk β

υ

υπ

−∞ ∞

→−

∞ −∞ −∞

−

−

Ω= − ∫ ∫ ∫

( ) ( ) ( ) ( ) ( )min2 2 2* *

2

*

34

x y

c F

z

x y zm m m

xE E

d m d m d mqe e

υυ υββ

υυ υ υυ

π

−∞ ∞−−

−∞ −∞ −∞

+−

+Ω= ∫ ∫ ∫

ℏ ℏ ℏ

( ) ( )

2 22min

3 * ***2 22

3 34

y xz

c F

m mm

E Es m y z x x

q mJ e e d e d d e

υ υυβ βυββ υ υ υ υ

π

− ∞ ∞− −− − −

→−∞ −∞ −∞

Ω =

∫ ∫ ∫ℏ

( ) * 2 * 2 * 21 1 1

2 2( ) ( )

2C x y zC F C FF E E E EE E m m mE E υ υ υ− + ++− =− −= +

EECEF

26


Thermionic Current …

( )* 2

203

4bF C i A AE E qV qV Vq

s m

qm kJ T e e A e

hβ β βπ

→− −= =

π

( ) ( )

2 22min

3 * ***2 22

3 34

y xz

c F

m mm

s m y z xE E

x

q mJ e e d e d d e

υ υυ υβ βββ υ υ υ υ

π

− ∞ ∞− −− − →

−∞ ∞ −∞

−

−

Ω =

∫ ∫ ∫ℏ

π ( )1

2bi AV Vqe β−−

( )min *

2bi A

qV V

m= −υ

( )0 1AqT s m m s

VJ J J A e β→ →= − = −

27

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 28

Some insight of the Thermionic Current …

Compare to the current of p-n diodes…

( )22

1An i

p

qVT

p i

DA n

D n

W N

D n

W NJ q e β

= − + −

( )0 1AqT s m m s

VJ J J A e β→ →= − = − Schottky diode

p-n diode

Both of them depends exponentially on VA, however current of p-n diodes depends more on temperature (since ni depends strongly on Eg), where the Schottky diode doesn’t have that dependence.

However, Eg hides in…

( )* 2

203

4bF C i A AE E qV qV Vq

s m

qm kJ T e e A e

hβ β βπ

→− −= =

The information of material hides in m* The information of doping concentration hides in EF-EC


Recombination/Generation/Impact-ionization

SAME technique as in p-n junction except integrate to xp only

Ec

EV

EFEFS

EFM

EFM

29










8) Conclusions

30


Topic Map


Large Signal

Circuits

Diode

Schottky

BJT/HBT

MOS

31


Series Resistanc

e

Conductance

Diffusion Capacitance

Junction Capacitance

AC response

We will not have Diffusion Capacitance here…

32


( )( )/ 1A Sq V R I moI I e −= −β

0

1

( )SFB

mR

g q I I= +

+β

0

ln ( ) /oA S

I Iq V R I m

I

+ = − β

( )A

So

m dVR

q I I dI= −

+β

gFB

Forward Bias Conductance

m depends on which operation regime you are

RS

33


Junction Capacitance (Majority Carriers)

Junction Capacitance

0sJ

AC

W

κ ε=

0

02( )

sJ

sbi A

D

AC

V VqN

κ εκ ε

=−

Response time – dielectricVery fast propagation

34


No Diffusion Capacitance in Schottky Diode

No minority carrier transport and therefore no diffusion capacitance ..

p-n Diode Schottky diode

VA

n

x

When electrons reach the metal side, they quickly scatter and join the majority carriers there. Nothing is diffusing…

35


Reducing diffusion capacitance in p-n diode

Short minority carrier lifetime in p-n junction diode equivalent to rapid energy relaxation in SB diode.

p-n Diode Schottky diode

VA

n

x

Provide lots of traps

36










8) Conclusions

37


Ohmic Contact vs. Schottky contacts ..

n-Si

n+

OxideMetal

Low Doping Moderate Doping

High Doping

What if we just want the p-n junction? How to reduce the barrier of Metal-Semiconductor?

For majority carriers: there’s not barrier For minority carriers: high doping allows them to tunnel throughMetal will just act like Ohmic Contact

38


Lowering of Schottky Barrier

Ref. Sze/Ng., p. 143

E

qφ1qφB

Semi

x

Metal

---

---

-

-Surface Charge

x

ElectronImage Charge

Metal Semi

qφ1qφB

The fields on the metal must be perpendicular(otherwise there will be tangential current flow which is impossible)as if there’s an image charge(positive) in the metal, results in lowering the barrier height

39


Fermi-level Pinning

Full

Full

Density of States

EcEfEv

Metal MetalSemiconductor

Regardless the workfunction, no modulation in potential. (e.g. Modern high-k dielectrics)

A B

Full

Metal

Full

Metal

EcEf

Ev

Shift in the Band edge

Why sometimes we don’t get conductance at all?

surface states bends EC/EV so that the Fermi level is at the center of the bandgap, they exchange carriers with metals, blocking the bulk semiconductor insideno modulation in potentialbarrier even you connected to different metals.

40


Conclusion

1) Schottky diodes have wide range of applications in

practical devices.

2) The key distinguishing feature of Schottky diode is that

it is a majority carrier device.

3) We use a different technique to calculate the current in

a majority carrier device.

=> thermionic emission.

4) Elimination of diffusion capacitance make the response

of the diodes very fast.

41

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