l08 feb 081 lecture 08 semiconductor device modeling and characterization ee5342 - spring 2001...
TRANSCRIPT
L08 Feb 08 1
Lecture 08 Semiconductor Device Modeling and CharacterizationEE5342 - Spring 2001
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
L08 Feb 08 2
Ideal diodeequation (cont.)• Js = Js,p + Js,n = hole curr + ele curr
Js,p = qni2Dp coth(Wn/Lp)/(NdLp) =
qni2Dp/(NdWn), Wn << Lp, “short” =
qni2Dp/(NdLp), Wn >> Lp, “long”
Js,n = qni2Dn coth(Wp/Ln)/(NaLn) =
qni2Dn/(NaWp), Wp << Ln, “short” =
qni2Dn/(NaLn), Wp >> Ln, “long”
Js,n << Js,p when Na >> Nd
L08 Feb 08 3
Diffnt’l, one-sided diode conductance
Va
IDStatic (steady-state) diode I-V characteristic
VQ
IQ QVa
DD dV
dIg
t
asD V
VdexpII
L08 Feb 08 4
Diffnt’l, one-sided diode cond. (cont.)
DQ
t
dQd
QDDQt
DQQd
tat
tQs
Va
DQd
tastasD
IV
g1
Vr ,resistance diode The
. VII where ,V
IVg then
, VV If . V
VVexpI
dV
dIVg
VVdexpIVVdexpAJJAI
Q
L08 Feb 08 5
Charge distr in a (1-sided) short diode
• Assume Nd << Na
• The sinh (see L12) excess minority carrier distribution becomes linear for Wn << Lp
pn(xn)=pn0expd(Va/Vt)
• Total chg = Q’p = Q’p = qpn(xn)Wn/2x
n
x
xnc
pn(xn
)
Wn = xnc-
xn
Q’p
pn
L08 Feb 08 6
Charge distr in a 1-sided short diode
• Assume Quasi-static charge distributions
• Q’p = Q’p = qpn(xn)Wn/2
• dpn(xn) = (W/2)*
{pn(xn,Va+V) - pn(xn,Va)}
x
n
xxnc
pn(xn,Va)
Q’p
pn pn(xn,Va+V)
Q’p
L08 Feb 08 7
Cap. of a (1-sided) short diode (cont.)
p
x
x p
ntransitQQ
transitt
DQ
pt
DQQ
taaa
a
Ddx
Jp
qVV
V
I
DV
IV
VVddVdV
dVA
nc
n2W
Cr So,
. 2W
C ,V V When
exp2
WqApd2
)W(xpqAd
dQC Define area. diode A ,Q'Q
2n
dd
2n
dta
nn0nnn
pdpp
L08 Feb 08 8
General time-constant
np
a
nnnn
a
pppp
pnVa
pn
Va
DQd
CCC ecapacitanc diode total
the and ,dVdQ
Cg and ,dV
dQCg
that so time sticcharacteri a always is There
ggdV
JJdA
dVdI
Vg
econductanc the short, or long diodes, all For
L08 Feb 08 9
General time-constant (cont.)
times.-life carr. min. respective the
, and side, diode long
the For times. transit charge physical
the ,D2
W and ,
D2W
side, diode short the For
n0np0p
n
2p
transn,np
2n
transp,p
L08 Feb 08 10
General time-constant (cont.)
Fdd
transitminF
gC
and 111
by given average
the is time transition effective The
sided-one usually are diodes Practical
L08 Feb 08 11
Effect of non-zero E in the CNR• This is usually not a factor in a short
diode, but when E is finite -> resistor• In a long diode, there is an additional
ohmic resistance (usually called the parasitic diode series resistance, Rs)
• Rs = L/(nqnA) for a p+n long diode.
• L=Wn-Lp (so the current is diode-like for Lp and the resistive otherwise).
L08 Feb 08 12
)pn( ,ppp and ,nnn where
kTEfiE
coshn2np
npnU
dtpd
dtnd
GRU
oo
oT
i
2i
Effect of carrierrecombination in DR• The S-R-H rate (no = po = o) is
L08 Feb 08 13
Effect of carrierrec. in DR (cont.)• For low Va ~ 10 Vt
• In DR, n and p are still > ni
• The net recombination rate, U, is still finite so there is net carrier recomb.– reduces the carriers available for the
ideal diode current– adds an additional current component
L08 Feb 08 14
eff,o
taieffavgrec
o
taimaxfpfna
fnfii
fifni
x
xeffavgrec
2V2/Vexpn
qWxqUJ
2V2/Vexpn
U ,EEqV w/
,kT/EEexpnp
and ,kT/EEexpnn cesin
xqUqUdxJ curr, ecRn
p
Effect of carrierrec. in DR (cont.)
L08 Feb 08 15
High level injection effects• Law of the junction remains in the same
form, [pnnn]xn=ni
2exp(Va/Vt), etc.
• However, now pn = nn become >> nno = Nd, etc.
• Consequently, the l.o.t.j. reaches the limiting form pnnn = ni
2exp(Va/Vt)
• Giving, pn(xn) = niexp(Va/(2Vt)), or np(-xp) = niexp(Va/(2Vt)),
L08 Feb 08 16
High level injeffects (cont.)
KFKFKFsinj lh,s
i
at
i
dtKFa
appdnn
a
tainj lh,sinj lh
VJJ ,JJJ :Note
nN
lnV2 or ,n
NlnV2VV Thus
Nx-n or ,Nxp giving
V of range the for important is This
V2/VexpJJ
:is density current injection level-High
L08 Feb 08 17
Summary of Va > 0 current density eqns.• Ideal diode, Jsexpd(Va/(Vt))
– ideality factor,
• Recombination, Js,recexp(Va/(2Vt))– appears in parallel with ideal term
• High-level injection, (Js*JKF)
1/2exp(Va/(2Vt))
– SPICE model by modulating ideal Js term
• Va = Vext - J*A*Rs = Vext - Idiode*Rs
L08 Feb 08 18
Plot of typical Va > 0 current density eqns.
Vext
ln J
data
ln(JKF)
ln(Js)
ln[(Js*JKF) 1/2]
Effect
of Rs
t
aV
Vexp~
t
aV2
Vexp~
VKF
ln(Jsrec)
Effect of high level injection
low level injection
recomb. current
Vext-Vd=JARs
L08 Feb 08 19
Reverse bias (Va<0)=> carrier gen in DR• Va < 0 gives the net rec rate,
U = -ni/, = mean min carr g/r l.t.
NNN/NNN and
qN
VV2W where ,
2Wqn
J
(const.) U- G where ,qGdxJ
dadaeff
eff
abi
0
igen
x
xgen
n
p
L08 Feb 08 20
Reverse bias (Va< 0),carr gen in DR (cont.)
gens
gen
gengensrev
JJJ
JSPICE
JJJJJ
or of largest the set then ,0
V when 0 since :note model
VV where ,
current generation the plus bias negative
for current diode ideal the of value The
current the to components two are there
bias, reverse ,)0V(V for lyConsequent
a
abi
ra
L08 Feb 08 21
Reverse biasjunction breakdown• Avalanche breakdown
– Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons
– field dependence shown on next slide
• Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274– Zener breakdown
L08 Feb 08 22
Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
L08 Feb 08 23
Reverse biasjunction breakdown• Assume -Va = VR >> Vbi, so Vbi-Va-->VR
• Since Emax~ 2VR/W = (2qN-VR/())1/2, and VR = BV when Emax = Ecrit (N
- is doping of lightly doped side ~ Neff)
BV = (Ecrit )2/(2qN-)
• Remember, this is a 1-dim calculation
L08 Feb 08 24
Junction curvatureeffect on breakdown• The field due to a sphere, R, with
charge, Q is Er = Q/(4r2) for (r > R)
• V(R) = Q/(4R), (V at the surface)• So, for constant potential, V, the field,
Er(R) = V/R (E field at surface increases for smaller spheres)
Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj
L08 Feb 08 25
BV for reverse breakdown (M&K**)
Taken from Figure 4.13, p. 198, M&K**
Breakdown voltage of a one-sided, plan, silicon step junction showing the effect of junction curvature.4,5
L08 Feb 08 26
Example calculations• Assume throughout that p+n jctn with Na
= 3e19cm-3 and Nd = 1e17cm-3
• From graph of Pierret mobility model, p
= 331 cm2/V-sec and Dp = Vtp = ? • Why p and Dp?
• Neff = ?
• Vbi = ?
L08 Feb 08 27
0
500
1000
1500
1.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 1.E+20
Doping Concentration (cm̂ - 3)
Mob
ility
(cm̂
2/V
-se
c)P As B n(Pierret) p(Pierret)
L08 Feb 08 28
Parameters forexamples• Get min from the model used in Project
2 min = (45 sec) 1+(7.7E-18cm3Ni+(4.5E-36cm6Ni
2
• For Nd = 1E17cm3, p = 25 sec
– Why Nd and p ?
• Lp = ?
L08 Feb 08 29
Hole lifetimes, taken from Shur***, p. 101.
L08 Feb 08 30
Example
• Js,long, = ?
• If xnc, = 2 micron, Js,short, = ?
L08 Feb 08 31
Example(cont.)• Estimate VKF
• Estimate IKF
L08 Feb 08 32
Example(cont.)• Estimate Js,rec
• Estimate Rs if xnc is 100 micron
L08 Feb 08 33
Example(cont.)• Estimate Jgen for 10 V reverse bias
• Estimate BV
L08 Feb 08 34
Diode equivalentcircuit (small sig)
ID
VDVQ
IQ
t
Q
dd
VD
D
V
I
r1
gdVdI
Q
is the practical
“ideality factor”
Q
tdiff
t
Qdiffusion
mintrdd
IV
r , V
IC
long) for short, for ( , Cr
L08 Feb 08 35
Small-signal eqcircuit
CdiffCdep
l
rdiff
Cdiff and
Cdepl are both charged by
Va = VQQa
2/1
bi
ajojdepl VV ,
VV
1CCC
Va
L08 Feb 08 36
References
* Semiconductor Physics and Devices, 2nd ed., by Neamen, Irwin, Boston, 1997.
**Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.
***Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.