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Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2002
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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Diode Switching
• Consider the charging and discharging of a Pn diode – (Na > Nd)
– Wd << Lp
– For t < 0, apply the Thevenin pair VF and RF, so that in steady state • IF = (VF - Va)/RF, VF >> Va , so current source
– For t > 0, apply VR and RR
• IR = (VR + Va)/RR, VR >> Va, so current source
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Diode switching(cont.)
+
+ VF
VR
DRR
RF
Sw
R: t > 0
F: t < 0
ItI s
F
FF R
VI0tI
VF,VR >>
Va
F
F
F
aFQ R
VR
VVI
0,t for
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Diode chargefor t < 0
xn xncx
pn
pno
Dp2W
,IWV,xqp'Q
2N
TR
TRFnFnndiff,p
D
2i
noV/V
noFn Nn
p ,epV,xp tF
dxdp
qDJ since ,qAD
Idxdp
ppp
F
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Diode charge fort >>> 0 (long times)
xn xncx
pn
pno
tF V/Vnon ep0t,xp
t,xp
sppp
S Jdxdp
qDJ since ,qAD
Idxdp
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Equationsummary
Q discharge to flows
R/VI current, a 0, but small, t For
RV
I ,qAD
Idxdp
AJI ,AqD
I
JqD1
dxdp
RRR
F
FF
p
F
0t,F
ssp
s
,ppt,R
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Snapshot for tbarely > 0
xn xncx
pn
pno
p
F
qADI
dxdp
p
RqAD
Idxdp
tF V/Vnon ep0t,xp
0t,xp Total charge removed, Qdis=IRt
st,xp
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I(t) for diodeswitching
ID
t
IF
-IR
ts ts+trr
- 0.1 IR
sRdischarge
p
Rs
tIQ
constant, a is qAD
Idxdp
,tt 0 For
pnp
p2is L/WtanhL
DqnI
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Band model review (approx. to scale)
qm
~ 4+V
Eo
EF
mEFp
EFn
Eo
Ec
Ev
EFi
qs,n
qs ~
4+V
Eo
Ec
Ev
EFi
qs,p
metal n-type s/c p-type s/c
qs ~
4+V
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Ideal metal to n-typebarrier diode (m>s,Va=0)
EFn
Eo
Ec
Ev
EFi
qs,n
qs
n-type s/c
qm
EF
m
metal
qBn
qVbi
q’n
No disc in Eo
Ex=0 in metal ==> Eoflat
Bn=m- s =
elec mtl to s/c barr
Vbi=Bn-n=
m-s elect s/c
to mtl barr Depl reg
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Ideal m to n s/c barr diode depletion width
xd
x
qN
d
Q’d =
qNdxd
x
Ex
-Em d
d
mx qN
xE
dxdE
xd
(Sheet of neg chg on mtl)= -Q’d
dctsmnBnbi
d
'jsemi,nma
d
abid
N/NlnVV
xC , VVV ,
qN
VV2x
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Real Schottkyband structure*
• Barrier transistion region,
• Interface statesabove o acc, p neutrl
below o dnr, n neutrl
Dit -> oo, qBn= Eg- o
Fermi level “pinned”
Dit -> 0, qBn= m - Goes to “ideal” case
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Fig 8.4* (a) Image charge and electric field lines at a metal-diel intf (b) Distortion of the potential barrier due to image forces with E=0 and (c) const E field
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Ideal metal to n-typeSchottky (Va>0)
qVa = Efn - Efm
Barrier for electrons from sc to m reduced to q(Vbi-Va)
qBn the same
DR decr
EFn
Eo
Ec
Ev
EFi
qs,n
qs
n-type s/c
qm
EF
m
metal
qBn
q(Vbi-Va)
q’nDepl reg
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Ideal m to n s/c Schottky diode curr
t0B
2sT
tasmssm
tabiDsa
s,ntbiDs
mmmss,nssma
mmmss,nssm
V/expT*AJ
1V/VexpJJJJ so
,V/VVexpNn ,0V
constv ,V/VexpNn and
,qvnJqvnJ ,0V
qvnJ ,qvnJ
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D DiodeGeneral FormD<name> <(+) node> <(-) node> <model name> [area value]ExamplesDCLAMP 14 0 DMODD13 15 17 SWITCH 1.5Model Form.MODEL <model name> D [model parameters] .model D1N4148-X D(Is=2.682n N=1.836 Rs=.5664 Ikf=44.17m Xti=3 Eg=1.11 Cjo=4p M=.3333 Vj=.5 Fc=.5 Isr=1.565n Nr=2 Bv=100 Ibv=10 0uTt=11.54n)*$
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Diode Model ParametersModel Parameters (see .MODEL statement)
Description UnitDefault
IS Saturation current amp 1E-14N Emission coefficient 1ISR Recombination current parameter amp 0NR Emission coefficient for ISR 1IKF High-injection “knee” current amp infiniteBV Reverse breakdown “knee” voltage volt infiniteIBV Reverse breakdown “knee” current amp 1E-10NBV Reverse breakdown ideality factor 1RS Parasitic resistance ohm 0TT Transit time sec 0CJO Zero-bias p-n capacitance farad 0VJ p-n potential volt 1M p-n grading coefficient 0.5FC Forward-bias depletion cap. coef, 0.5EG Bandgap voltage (barrier height) eV
1.11
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Diode Model ParametersModel Parameters (see .MODEL statement)
Description UnitDefault
XTI IS temperature exponent 3TIKF IKF temperature coefficient (linear) °C-1 0TBV1 BV temperature coefficient (linear) °C-1 0TBV2 BV temperature coefficient (quadratic) °C-2 0TRS1 RS temperature coefficient (linear) °C-1 0TRS2 RS temperature coefficient (quadratic) °C-2 0
T_MEASURED Measured temperature °CT_ABS Absolute temperature °CT_REL_GLOBAL Rel. to curr. Temp. °CT_REL_LOCAL Relative to AKO model temperature
°C
For information on T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL, see the .MODEL statement.
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The diode is modeled as an ohmic resistance (RS/area) in series with an intrinsic diode. <(+) node> is the anode and <(-) node> is the cathode. Positive current is current flowing from the anode through the diode to the cathode. [area value] scales IS, ISR, IKF,RS, CJO, and IBV, and defaults to 1. IBV and BV are both specified as positive values.In the following equations:Vd = voltage across the intrinsic diode onlyVt = k·T/q (thermal voltage)
k = Boltzmann’s constantq = electron chargeT = analysis temperature (°K)Tnom = nom. temp. (set with TNOM option
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• Dinj– N~1, rd~N*Vt/iD– rd*Cd = TT =– Cdepl given by
CJO, VJ and M
• Drec– N~2, rd~N*Vt/iD– rd*Cd = ?– Cdepl =?
SPICE DiodeModel
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DC CurrentId = area(Ifwd - Irev) Ifwd = forward current = InrmKinj + IrecKgen Inrm = normal current = IS(exp ( Vd/(NVt))-1)
Kinj = high-injection factorFor: IKF > 0, Kinj = (IKF/(IKF+Inrm))1/2otherwise, Kinj = 1
Irec = rec. cur. = ISR(exp (Vd/(NR·Vt))- 1)
Kgen = generation factor = ((1-Vd/VJ)2+0.005)M/2
Irev = reverse current = Irevhigh + Irevlow
Irevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)]Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)}
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vD=Vext
ln iD
Data
ln(IKF)
ln(IS)
ln[(IS*IKF) 1/2]
Effect
of Rs
t
a
VNFV
exp~
t
a
VNRV
exp~
VKF
ln(ISR)
Effect of high level injection
low level injection
recomb. current
Vext-
Va=iD*Rs
t
a
VNV
2exp~
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References
Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.
MicroSim OnLine Manual, MicroSim Corporation, 1996.
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