l08 feb 081 lecture 08 semiconductor device modeling and characterization ee5342 - spring 2001...
TRANSCRIPT
![Page 1: L08 Feb 081 Lecture 08 Semiconductor Device Modeling and Characterization EE5342 - Spring 2001 Professor Ronald L. Carter ronc@uta.edu](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f325503460f94c4d6bb/html5/thumbnails/1.jpg)
L08 Feb 08 1
Lecture 08 Semiconductor Device Modeling and CharacterizationEE5342 - Spring 2001
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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).
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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
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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
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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.)
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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)),
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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
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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
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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
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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
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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
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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
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L08 Feb 08 22
Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
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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
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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
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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
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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 = ?
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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)
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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 = ?
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L08 Feb 08 29
Hole lifetimes, taken from Shur***, p. 101.
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L08 Feb 08 30
Example
• Js,long, = ?
• If xnc, = 2 micron, Js,short, = ?
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L08 Feb 08 31
Example(cont.)• Estimate VKF
• Estimate IKF
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L08 Feb 08 32
Example(cont.)• Estimate Js,rec
• Estimate Rs if xnc is 100 micron
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L08 Feb 08 33
Example(cont.)• Estimate Jgen for 10 V reverse bias
• Estimate BV
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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
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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
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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.