ee 5340 semiconductor device theory lecture 15 – spring 2011
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EE 5340 Semiconductor Device Theory Lecture 15 – Spring 2011. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc. q(V bi -V a ). Imref, E Fn. E c. E FN. qV a. E FP. E Fi. Imref, E Fp. E v. x. -x pc. -x p. x n. x nc. 0. Forward Bias Energy Bands. - PowerPoint PPT PresentationTRANSCRIPT
EE 5340Semiconductor Device TheoryLecture 15 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc
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Forward Bias Energy Bands
1eppkT/EEexpnp ta VV0nnFpFiiequilnon
1/exp 0 ta VV
ppFiFniequilnon ennkTEEnn
Ev
Ec
EFi
xn xnc-xpc -xp 0
q(Vbi-Va)
EFPEFNqVa
x
Imref, EFn
Imref, EFp
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Law of the junction: “Rememberto follow the minority carriers”
tbia
np
pna
tbi
nopo
pono
ponot
nopo
t2i
datbi
VV-Vexpn
npp ,0V when and
,VV-expn
npp get to Invert
.nnlnVp
plnV
nNNlnVV
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Law of the junction (cont.)
dnonapop
ppnnppopppop
nnonnnona
Nnn and Npp injection level- low Assume
.pn and pn Assume .ppp ,nnn and
,nnn ,ppp So . 0V for nnot' eq.-non to Switched
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Law of the junction (cont.)
ta
pta
n
ta
ta
tbi
tbia
VV
2ixpp
VV
2ixnn
VV
no
2iV
V
ponopo
n
VV
nopoVV-V
pn
ennp also ,ennp
Junction the of Law the
ennepn
np have We
enn nda epp for So
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ptapop
ntanon
VV-
pononoVV-V
pon
tbiaponno
xx at ,1VVexpnn sim.
xx at ,1VVexppp so
,epp ,pepp
giving VV-Vexpppp
tbi
tbia
InjectionConditions
6
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Ideal JunctionTheory
Assumptions• Ex = 0 in the chg neutral reg.
(CNR)• MB statistics are applicable• Neglect gen/rec in depl reg (DR)• Low level injection applies so that
np < ppo for -xpc < x < -xp, and pn < nno for xn < x < xnc
• Steady State conditions
7
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Ideal Junction Theory (cont.)
ppcn
ncnp
xxx- ,Jq1
dtdn
tn0
and , xxx ,Jq1
dtdp
tp0
CNR the to Equation Continuity the applying
and , 0tn
tp case, (static) state steady the In
8
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Ideal JunctionTheory (cont.)
ppc
nnp
2p2
ncnpp
n2n2
ppx
nnxx
xxx- for ,0Dn
dxnd
and ,xxx for ,0Dp
dxpd
giving dxdpqDJ and
dxdnqDJ CNR, the in 0E Since
9
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Ideal JunctionTheory (cont.)
)contacts( ,0xnxp and
,1enxn
pxp B.C. with
.xxx- ,DeCexn
xxx ,BeAexp
So .D L and D L Define
pcpncn
VVpo
ppno
nn
ppcLxLxp
ncnLxLx
n
pp2pnn2n
ta
nn
pp
10
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0.1
1.0
10.0
100.0
1000.0
1.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 1.E+20Doping Concentration (cm̂ - 3)
Diff
usio
n Le
ngth
, L
(mic
rons
)electrons holes
Diffusion Length model
2imim
min N36E5.4N18E7.71sec45
L = (D)1/2 Diffusion Coeff. is Pierret* model
11
Minority hole lifetimesMark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991
The parameters used in the fit are
τo = 10 μs, Nref = 1×1017/cm2, and CA = 1.8×10-31cm6/s.
2DAorefD
op NCNN1 τ
ττ
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Minority electron lifetimesMark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991
The parameters used in the fit are
τo = 30 μs, Nref = 1×1017/cm2, and CA = 8.3×10-32 cm6/s.
2DAorefD
on NCNN1 τ
ττ
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Excess minoritycarrier distr fctn
1eLWsinhLxxsinhnxn
,xxW ,xxx- for and
1eLWsinhLxxsinhpxp
,xxW ,xxx For
ta
ta
VV
npnpc
pop
ppcpppc
VV
pnpnc
non
nncnncn
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Forward Bias Energy Bands
1eppkT/EEexpnp ta VV0nnFpFiiequilnon
1/exp 0 ta VV
ppFiFniequilnon ennkTEEnn
Ev
Ec
EFi
xn xnc-xpc -xp 0
q(Vbi-Va)
EFPEFNqVa
x
Imref, EFn
Imref, EFp
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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
aVV
popp
1epxp t
aVV
nonn
16
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Minority carriercurrents
1eLWsinhLxxcosh
LNDqn
xxx- for ,qDxJ
1eLWsinhLxxcosh
LNDqn
xxx for ,qDxJ
ta
p
ta
n
VV
npnpc
nan
2i
ppcdxnd
nn
VV
pnpnc
pd
p2i
ncndxpd
pp
17
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Evaluating thediode current
p/nn/pp/nd/a
p/n2isp/sn
spsns
VV
spnnp
LWcothLND
qnJ
sdefinition with JJJ where
1eJxJxJJ
then DR, in gen/rec no gminAssu
ta
18
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Special cases forthe diode current
nd
p2isp
pan2
isn
nppn
pd
p2isp
nan2
isn
nppn
WNDqnJ and ,WN
DqnJ
LW or ,LW :diode ShortLN
DqnJ and ,LNDqnJ
LW or ,LW :diode Long
19
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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]
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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 = qni
2Dn coth(Wp/Ln)/(NaLn) = qni
2Dn/(NaWp), Wp << Ln, “short” = qni
2Dn/(NaLn), Wp
>> Ln, “long”Js,n << Js,p when Na >> Nd
21
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Diffnt’l, one-sided diode conductance
Va
IDStatic (steady-state) diode I-V characteristic
VQ
IQ QVa
Dd dV
dIg
tasD V
VdexpII
22
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Diffnt’l, one-sided diode cond. (cont.)
DQt
dQd
QDDQtDQ
Qd
tat
tQsVa
DQd
tastasD
IV
g1Vr ,resistance diode The
. VII where ,VI
Vg then
, VV If . VVVexpI
dVdIVg
VVdexpIVVdexpAJJAI
Q
23
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Charge distr in a (1-sided) short diode
• Assume Nd << Na• The sinh (see L10)
excess minority carrier distribution becomes linear for Wn << Lp
pn(xn)=pn0expd(Va/Vt)
• Total chg = Q’p = Q’p = qpn(xn)Wn/2
xn
x
xnc
pn(xn
)
Wn = xnc- xn
Q’p
pn
24
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Charge distr in a 1-sided short diode
• Assume Quasi-static charge distributions
• Q’p = +qpn(xn,Va)Wn/2
• Q’p =q(W/2) x
{pn(xn,Va+V) -
pn(xn,Va)}• Wn = xnc - xn (Va)
xn
xxnc
pn(xn,Va)
Q’p
pn pn(xn,Va+V)
Q’p
25
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Cap. of a (1-sided) short diode (cont.)
p
x
x p
ntransitQQ
transitt
DQ
pt
DQQ
taaa
a
Ddx
JpqVV
VI
DVI
V
VVddVdV
dVA
nc
n2WCr So,
. 2WC ,V V When
exp2WqApd
2)W(xpqAd
dQC Define area. diode A ,Q'Q
2n
dd
2n
dta
nn0nnn
pdpp
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Evaluating the diode current density
pnpd
p2isp
npna
n2isn
spsns
VV
spnnpaD
LWcothLN
DqnJ
,LWcothLN
DqnJ
sdefinition the with JJJ where
1eAJAxJxJVi
then DR, in gen/rec no gminAssu
ta
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General time-constant
npannnn
ap
ppp
pnVa
pn
VaD
Qd
CCC ecapacitanc diode total
the and ,dVdQCg and ,dV
dQCg
that so time sticcharacteri a always is There
ggdVJJdAdV
dIVg
econductanc the short, or long diodes, all For
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General time-constant (cont.)
times.-life carr. min. respective the, and side, diode long
the For times. transit charge physical
the ,D2W and ,D2
W
side, diode short the For
n0np0p
n
2p
transn,np
2n
transp,p
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General time-constant (cont.)
Fdd
transitminFgC
and 111 by given average
the is time transition effective Thesided-one usually are diodes Practical
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References1 and M&KDevice Electronics for Integrated
Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the model.
2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.
3 and **Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997.
Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.