Semiconductor Device Modeling and Characterization – EE5342 Lecture 12 – Spring 2011
Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002
description
Transcript of Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002
![Page 1: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/1.jpg)
L07 04Feb02 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 7-Spring 2002
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
![Page 2: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/2.jpg)
L07 04Feb02 2
Ideal JunctionTheory
Assumptions
• Ex = 0 in the chg neutral reg. (CNR)
• MB statistics are applicable• Neglect gen/rec in depl reg (DR)• Low level injections apply so that
np < ppo for -xpc < x < -xp, and pn
< nno for xn < x < xnc
• Steady State conditions
![Page 3: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/3.jpg)
L07 04Feb02 3
Ideal JunctionTheory (cont.)
Apply the Continuity Eqn in CNR
ncnn
ppcp
xxx ,Jq1
dtdn
tn
0
and
xxx- ,Jq1
dtdp
tp
0
![Page 4: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/4.jpg)
L07 04Feb02 4
Ideal JunctionTheory (cont.)
ppc
nn
p2p
2
ncnpp
n2n
2
ppx
nnxx
xxx- for ,0D
n
dx
nd
and ,xxx for ,0D
p
dx
pd
giving dxdp
qDJ and
dxdn
qDJ CNR, the in 0E Since
![Page 5: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/5.jpg)
L07 04Feb02 5
Ideal JunctionTheory (cont.)
)contacts( ,0xnxp and
,1en
xn
pxp
B.C. with
.xxx- ,DeCexn
xxx ,BeAexp
So .D L and D L Define
pcpncn
VV
po
pp
no
nn
ppcL
xL
x
p
ncnL
xL
x
n
pp2pnn
2n
ta
nn
pp
![Page 6: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/6.jpg)
L07 04Feb02 6
Excess minoritycarrier distr fctn
1eLWsinh
Lxxsinhnxn
,xxW ,xxx- for and
1eLWsinh
Lxxsinhpxp
,xxW ,xxx For
ta
ta
VV
np
npcpop
ppcpppc
VV
pn
pncnon
nncnncn
![Page 7: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/7.jpg)
L07 04Feb02 7
Forward Bias Energy Bands
xn xnc-xpc -xp 0
Ev
Ec
q(Vbi-Va)
EF
EF
EFi
qVa
x
Imref, EFn
Imref, EFp
1ennkT/EEexpnn ta VV0ppFiFniequilnon
1eppkT/EEexpnp ta VV0nnFpFiiequilnon
![Page 8: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/8.jpg)
L07 04Feb02 8
CarrierInjection
xn-xpc 0
ln(carrier conc)
ln Naln Nd
ln ni
ln ni2/Nd
ln ni2/Na
xnc-xp
x
~Va/Vt~Va/Vt
1enxn t
aV
V
popp
1epxp t
aV
V
nonn
![Page 9: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/9.jpg)
L07 04Feb02 9
Minority carriercurrents
1eLWsinh
Lxxcosh
LNDqn
xxx- for ,qDxJ
1eLWsinh
Lxxcosh
LN
Dqn
xxx for ,qDxJ
ta
p
ta
n
VV
np
npc
na
n2i
ppcdx
ndnn
VV
pn
pnc
pd
p2i
ncndxpd
pp
![Page 10: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/10.jpg)
L07 04Feb02 10
Evaluating thediode current
p/nn/pp/nd/a
p/n2isp/sn
spsns
VV
spnnp
LWcothLN
DqnJ
sdefinition with JJJ where
1eJxJxJJ
then DR, in gen/rec no gminAssu
ta
![Page 11: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/11.jpg)
L07 04Feb02 11
Special cases forthe diode current
nd
p2isp
pa
n2isn
nppn
pd
p2isp
na
n2isn
nppn
WN
DqnJ and ,
WND
qnJ
LW or ,LW :diode Short
LN
DqnJ and ,
LND
qnJ
LW or ,LW :diode Long
![Page 12: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/12.jpg)
L07 04Feb02 12
Ideal diodeequation• Assumptions:
– low-level injection– Maxwell Boltzman statistics– Depletion approximation– Neglect gen/rec effects in DR– Steady-state solution only
• Current dens, Jx = Js expd(Va/Vt)
– where expd(x) = [exp(x) -1]
![Page 13: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/13.jpg)
L07 04Feb02 13
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
![Page 14: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/14.jpg)
L07 04Feb02 14
Diffnt’l, one-sided diode conductance
Va
IDStatic (steady-state) diode I-V characteristic
VQ
IQ QVa
DD dV
dIg
t
asD V
VdexpII
![Page 15: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/15.jpg)
L07 04Feb02 15
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
![Page 16: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/16.jpg)
L07 04Feb02 16
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/2
x
n
x
xnc
pn(xn
)
Wn = xnc-
xn
Q’p
pn
![Page 17: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/17.jpg)
L07 04Feb02 17
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
![Page 18: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/18.jpg)
L07 04Feb02 18
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
![Page 19: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/19.jpg)
L07 04Feb02 19
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
![Page 20: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/20.jpg)
L07 04Feb02 20
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
![Page 21: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/21.jpg)
L07 04Feb02 21
General time-constant (cont.)
Fdd
transitminF
gC
and 111
by given average
the is time transition effective The
sided-one usually are diodes Practical
![Page 22: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/22.jpg)
L07 04Feb02 22
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).
![Page 23: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/23.jpg)
L07 04Feb02 23
)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
![Page 24: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/24.jpg)
L07 04Feb02 24
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
![Page 25: Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002](https://reader035.fdocuments.net/reader035/viewer/2022070417/568153c6550346895dc1bf92/html5/thumbnails/25.jpg)
L07 04Feb02 25
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.