Transcript EE 5340 Semiconductor Device Theory Lecture 22 – Spring 2011 Professor Ronald L.

EE 5340
Semiconductor Device Theory
Lecture 22 – Spring 2011
Professor Ronald L. Carter
[email protected]
http://www.uta.edu/ronc
Project Discussion – Ideal
Diode equations
• Ideal diode, Jsexpd(Va/(hVt))
– ideality factor, h
• Recombination, Js,recexp(Va/(2hVt))
– appears in parallel with ideal term
• High-level injection,
(Js*JKF)1/2exp(Va/(2hVt))
– SPICE model by modulating ideal Js term
• Va = Vext - J*A*Rs = Vext - Idiode*Rs
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Project Discussion – Ideal Diode
Forward Current Equations
Id = area·(Ifwd - Irev)
Ifwd = forward current = Inrm·Kinj + Irec·Kgen
Inrm = normal current = IS·(eVd/(N·Vt)-1)
if: IKF > 0
1/2
then: Kinj = (IKF/(IKF+Inrm))
else: Kinj = 1
Irec = recombination current =
ISR·(eVd/(NR·Vt)-1)
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SPICE Diode
Model
• Dinj
– N~1, rd~N*Vt/iD
– rd*Cd = TT =
– Cdepl given by CJO,
VJ and M
t
• Drec
– N~2, rd~N*Vt/iD
– rd*Cd = ?
– Cdepl =?
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Derivation Tips
q 1  dvA 
T j  T EMP T jA 

  273.15
k N  d lniD  min
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Gummel-Poon Static
npn Circuit Model
C
RC
B
RBB
B’
ILC
IBR
ILE
IBF
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB
RE
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Gummel-Poon Static
npn Circuit Model
C
RC
B
RBB
B’
ILC
IBR
ILE
IBF
Intrinsic
Transistor
ICC - IEC = {IS/QB}*
{exp(vBE/NFVt)exp(vBC/NRVt)}
RE
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Gummel Poon npn
Model Equations
IBF = ISexpf(vBE/NFVt)/BF
ILE = ISEexpf(vBE/NEVt)
IBR = ISexpf(vBC/NRVt)/BR
ILC = ISCexpf(vBC/NCVt)
QB = (1 + vBC/VAF + vBE/VAR ) 
{½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
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Charge components
in the BJT
**From Getreau, Modeling the
Bipolar Transistor, Tektronix, Inc.
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Gummel Poon
Base Resistance
If IRB = 0, RBB = RBM+(RB-RBM)/QB
If IRB > 0
RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))
[1+144iB/(p2IRB)]1/2-1
z=
(24/p2)(iB/IRB)1/2
From An Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors,
by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997.
RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB
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BJT Characterization
Forward Gummel
vBCx= 0 = vBC + iBRB - iCRC
iC
vBEx = vBE +iBRB +(iB+iC)RE
iB = IBF + ILE =
ISexpf(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)
iC = bFIBF/QB =
ISexpf(vBE/NFVt)/QB
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iB
+
vBEx
-
RB
RC
vBC +
+
vBE
RE
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BJT I (A) vs. Vbe (V) for the G-P model Forward Gummel
configuration (Vbcx=0)
1.E-02
1.E-03
1.E-04
Ideal F-G
Data
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
1.E-11
1.E-12
Ic
1.E-13
Ib
1.E-14
1.E-15
iC and iB (A)
vs. vBE (V)
N = 1  1/slope
= 59.5 mV/dec
N = 2  1/slope
= 119 mV/dec
1.E-16
0.0
0.2
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0.4
0.6
0.8
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BJT Characterization
Reverse Gummel
vBEx= 0 = vBE + iBRB - iERE
vBCx = vBC +iBRB +(iB+iE)RC
iB = IBR + ILC =
ISexpf(vBC/NRVt)/BR
+ ISCexpf(vBC/NCVt)
iE = bRIBR/QB =
ISexpf(vBC/NRVt)/QB
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vBCx
+
RC
iB
RB
iE
vBC +
+
vBE
RE
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BJT I (A) vs. Vbe (V) for the G-P model Forward Gummel
configuration (Vbcx=0)
1.E-02
1.E-03
1.E-04
1.E-05
Ideal R-G
Data
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
1.E-11
1.E-12
Ic
Ie
1.E-13
Ib
1.E-14
1.E-15
1.E-16
0.0
0.2
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0.4
0.6
0.8
iE and iB (A)
vs. vBE (V)
N = 1  1/slope
= 59.5
mV/dec
N = 2  1/slope
= 119 mV/dec
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Ideal 2-terminal
MOS capacitor/diode
conducting
gate,
area = LW
Vgate
-xox
SiO2
0
L
silicon substrate
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Vsub
y
0
tsub
x 15
Band models
(approx. scale)
metal
qfm=
4.1 eV
for Al
Eo
silicon dioxide
Eo
qc
Ec
Eg,ox
EFm
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p-type s/c
Eo
ox
qcSi=
~ 0.95 eV 4.05eV
~ 8 eV
Ev
qfs,p
EFp
Ec
EFi
Ev
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Flat band condition
(approx. scale)
If
Ec  Efp  0.85eV
Then
Efm  Efp  0.8eV
 VFB  f fm  f fp
Al
q(fm-cox)=
3.15 eV
EFm
 0.8V  Vg  Vs
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Ev
p-Si
q(cox-cSi)=3.1eV
Ec,Ox
Eg,ox
~8eV
 fMS
for flat - band cond
SiO2
qffp=
3.95eV
Ec
EFi
Ev EFp
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Equivalent circuit
for Flat-Band
• Surface effect analogous to the extr
Debye length = LD,extr = [eVt/(qNa)]1/2
• Debye cap, C’D,extr = eSi/LD,extr
• Oxide cap, C’Ox = eOx/xOx
C’Ox
• Net C is the series comb
1
1
1


C'tot C'D,extr C'Ox
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C’D,extr
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References
* Semiconductor Physics & Devices, by
Donald A. Neamen, Irwin, Chicago,
1997.
**Device Electronics for Integrated
Circuits, 2nd ed., by Richard S. Muller
and Theodore I. Kamins, John Wiley
and Sons, New York, 1986
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