EE 5340 Semiconductor Device Theory Lecture 15 – Spring 2011 Professor Ronald L. Carter...
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Transcript of EE 5340 Semiconductor Device Theory Lecture 15 – Spring 2011 Professor Ronald L. Carter...
EE 5340Semiconductor Device TheoryLecture 15 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc
©rlc L15-10Mar2011
2
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
©rlc L15-10Mar2011
3
Law of the junction: “Rememberto follow the minority carriers”
t
bia
n
p
p
na
t
bi
no
po
po
no
po
not
no
pot2
i
datbi
V
V-Vexp
n
n
pp
,0V when and
,V
V-exp
n
n
pp
get to Invert
.nn
lnVp
plnV
n
NNlnVV
©rlc L15-10Mar2011
4
Law of the junction (cont.)
dnonapop
ppnn
ppopppop
nnonnnon
a
Nnn and Npp
injection level- low Assume
.pn and pn Assume
.ppp ,nnn and
,nnn ,ppp So
. 0V for nnot' eq.-non to Switched
©rlc L15-10Mar2011
5
Law of the junction (cont.)
t
a
pt
a
n
t
a
t
a
t
bi
t
bia
VV
2ixpp
VV
2ixnn
VV
no
2iV
V
pono
pon
VV
nopoVV-V
pn
ennp also ,ennp
Junction the of Law the
enn
epn
np have We
enn nda epp for So
©rlc L15-10Mar2011
pt
apop
nt
anon
V
V-
pononoV
V-V
pon
t
biaponno
xx at ,1VV
expnn sim.
xx at ,1VV
exppp so
,epp ,pepp
giving V
V-Vexpppp
t
bi
t
bia
InjectionConditions
6
©rlc L15-10Mar2011
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
dnp < ppo for -xpc < x < -
xp, and dpn < nno for xn < x <
xnc
• Steady State conditions
7
©rlc L15-10Mar2011
Ideal Junction Theory (cont.)
ppcn
ncnp
xxx- ,Jq1
dtdn
tn
0
and , xxx ,Jq1
dtdp
tp
0
CNR the to Equation Continuity the applying
and , 0tn
tp
case, (static) state steady the In
8
©rlc L15-10Mar2011
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
9
©rlc L15-10Mar2011
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
10
©rlc L15-10Mar2011
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+20
Doping Concentration (cm̂ - 3)
Diff
usio
n Le
ngth
, L
(mic
rons
)electrons holes
Diffusion Length model
2imim
minN36E5.4N18E7.71
sec45
L = (Dt)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
©rlc L15-10Mar2011
12
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
©rlc L15-10Mar2011
13
©rlc L15-10Mar2011
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
14
©rlc L15-10Mar2011
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
15
©rlc L15-10Mar2011
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
16
©rlc L15-10Mar2011
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
17
©rlc L15-10Mar2011
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
18
©rlc L15-10Mar2011
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
19
©rlc L15-10Mar2011
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]
20
©rlc L15-10Mar2011
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
21
©rlc L15-10Mar2011
Diffnt’l, one-sided diode conductance
Va
IDStatic (steady-state) diode I-V characteristic
VQ
IQ QVa
Dd dV
dIg
t
asD V
VdexpII
22
©rlc L15-10Mar2011
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
23
©rlc L15-10Mar2011
Charge distr in a (1-sided) short diode
• Assume Nd << Na
• The sinh (see L10) excess minority carrier distribution becomes linear for Wn << Lp
dpn(xn)=pn0expd(Va/
Vt)
• Total chg = Q’p =
Q’p = qdpn(xn)Wn/2
x
n
x
xnc
dpn(xn
)
Wn = xnc-
xn
Q’p
dpn
24
©rlc L15-10Mar2011
Charge distr in a 1-sided short diode
• Assume Quasi-static charge distributions
• Q’p = +qdpn(xn,Va)Wn/2
• dQ’p =q(W/2) x
{dpn(xn,Va+dV) -
dpn(xn,Va)}
• Wn = xnc - xn (Va)
xn
xxnc
dpn(xn,Va)
Q’p
dpn
dpn(xn,Va+dV)
dQ’p
25
©rlc L15-10Mar2011
26
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
©rlc L15-10Mar2011
27
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
©rlc L15-10Mar2011
28
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
©rlc L15-10Mar2011
29
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
©rlc L15-10Mar2011
30
General time-constant (cont.)
Fdd
transitminF
gC
and 111
by given average
the is time transition effective The
sided-one usually are diodes Practical
©rlc L15-10Mar2011
31
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 m 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.