BJT Ebers Moll Model
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Transcript of BJT Ebers Moll Model
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ECSE-2210, Microelectronics Technology, Prof. E. F. Schubert
Chapter 21page 1
BJTEbers-Moll-model
Ebers-Moll Model
(Developed by Ebers and Moll in 1954)
Also called the Coupled Diode Model
Two diodes: The EB and CB diode
o Charge distribution in the Base:
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ECSE-2210, Microelectronics Technology, Prof. E. F. Schubert
Chapter 21page 2
o Under Normaloperation (Subscript N), it is pC= 0
Using pC= 0 and the results of the last chapter, we have:
EEN paI ECN pbI (1)
o UnderInvertedoperation (Subscript I), it is 0E p
Using pE= 0 and the results of the last chapter, we have:
CEI pbI CCI paI (2)
o In Eqs. (1) and (2), it is
p
B
p
pcoth
L
W
L
DAea (3)
p
B
p
pcosech
L
W
L
DAeb (4)
o Superposition of the two currents:
EIENE III (5)
CE pbpa (6)
)1e()1e( /n0/n0 CBEB kTeVkTeV pbpa (7)
CICNC III (8)
CE papb (9)
)1e()1e( /
n0/
n0 EB
kTeVkTeV CBpapb (10)
The superposition of normaloperation currents and invertedoperation currents
yields two equations (Eqs. 7 and 10) valid for anyoperating condition.
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ECSE-2210, Microelectronics Technology, Prof. E. F. Schubert
Chapter 21page 3
o The four currents IEN, IEI, ICN, and ICIcan also be written in the following way:
Normaloperation (VBE= forward VCB= reverse)
)1e(
/
ESEN EB
kTeV
II (11)
)1e( /
ESNENNCN EB
kTeV
III (12)
N current amplification in normal operation
Invertedoperation (VEB= reverse VCB= forward)
)1e( /
CSCI CB
kTeV
II (13)
)1e( /
CSICIIEI CB
kTeV
III (14)
I current amplification in inverted operation
Superpositionof Normaland Invertedoperation:
(Why are we allowed to superimpose?Linear processes)
1e1e /CSI/ESEIENE CBEB kTeVkTeV IIIII (15)
1e1e /CS/ESNCICNC CBEB kTeVkTeV IIIII (16)
these are the Ebers-Moll Equations
o Ebers-Moll Equations have general validity
(Normal and Inverted operation)
o
Eq. (15): Emitter currentFirst term: Diode equation (EB)
Second term: A current controlled by CB diode
o Eq. (16): Collector current
First term: A current controlled by EB diode
Second term: Diode equation (CB)
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ECSE-2210, Microelectronics Technology, Prof. E. F. Schubert
Chapter 21page 4
We can construct an equivalent circuit from the Ebers-Moll Equations
o Ebers-Moll equivalent circuit for alloperating conditions:
o Ebers-Moll equivalent circuit for normaloperating conditions:
CB diode is reverse biased 0'C I
Ebers-Moll equivalent circuit is the bridge between internal device physics and
electronic circuits.
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ECSE-2210, Microelectronics Technology, Prof. E. F. Schubert
Chapter 21page 5
Ebers-Moll output characteristic:
