24.2 Bipolar Transistors
695
From (24.6), the hole current densities at x = 0 and x = w are given as
2
j Ep = j p (0) = e
D B
L B
δ p E coth
w
L B
− δ p C csch
w
L B
(24.8a)
j Cp = j p (w) = e
D B
L B
δ p E csch
w
L B
− δ p C coth
w
L B
.
(24.8b)
From (24.4a,b), the electron current densities at x = −x E and x = x C are given (with δn E = δn(−x E )
and δn C = δn(x C )) by
j En = j n (−x E ) = e
D E
L E
δn E
(24.9a)
j Cn = j n (x C ) = −e
D C
L C
δn C .
(24.9b)
The emitter current density is (similar to (21.131))
j E = j p (0) + j n (−x E )
= e
D B
L B
δ p E coth
w
L B
− δ p C csch
w
L B
+ e
D E
L E
δn E .
(24.10)
The collector current density is given as
j C = j p (w) + j n (x C )
= e
D B
L B
δ p E csch
w
L B
− δ p C coth
w
L B
− e
D C
L C
δn C .
(24.11)
In these equations, only the diffusion currents are considered. Additionally, the recombination currents
in the depletion layers must be considered, in particular at small junction voltages.
24.2.2 Current Amplification
The emitter current consists of two parts, the hole current I pE injected from the base and the electron
current I nE that flows from the emitter to the base (Fig. 24.5a). Similarly, the collector current is made
up from the hole and electron currents I pC and I pC , respectively.
The total emitter current splits into the base and collector currents
I E = I B + I C .
(24.12)
The amplification (gain) in common base circuits
α 0 = h FB =
∂ I C
∂ I E
=
∂ I Ep
∂ I E
∂ I Cp
∂ I Ep
∂ I C
∂ I Cp
= γ α T M ,
(24.13)
2 coth x ≡ cosh x/ sinh x, cschx ≡ 1/ sinh x.
695
From (24.6), the hole current densities at x = 0 and x = w are given as
2
j Ep = j p (0) = e
D B
L B
δ p E coth
w
L B
− δ p C csch
w
L B
(24.8a)
j Cp = j p (w) = e
D B
L B
δ p E csch
w
L B
− δ p C coth
w
L B
.
(24.8b)
From (24.4a,b), the electron current densities at x = −x E and x = x C are given (with δn E = δn(−x E )
and δn C = δn(x C )) by
j En = j n (−x E ) = e
D E
L E
δn E
(24.9a)
j Cn = j n (x C ) = −e
D C
L C
δn C .
(24.9b)
The emitter current density is (similar to (21.131))
j E = j p (0) + j n (−x E )
= e
D B
L B
δ p E coth
w
L B
− δ p C csch
w
L B
+ e
D E
L E
δn E .
(24.10)
The collector current density is given as
j C = j p (w) + j n (x C )
= e
D B
L B
δ p E csch
w
L B
− δ p C coth
w
L B
− e
D C
L C
δn C .
(24.11)
In these equations, only the diffusion currents are considered. Additionally, the recombination currents
in the depletion layers must be considered, in particular at small junction voltages.
24.2.2 Current Amplification
The emitter current consists of two parts, the hole current I pE injected from the base and the electron
current I nE that flows from the emitter to the base (Fig. 24.5a). Similarly, the collector current is made
up from the hole and electron currents I pC and I pC , respectively.
The total emitter current splits into the base and collector currents
I E = I B + I C .
(24.12)
The amplification (gain) in common base circuits
α 0 = h FB =
∂ I C
∂ I E
=
∂ I Ep
∂ I E
∂ I Cp
∂ I Ep
∂ I C
∂ I Cp
= γ α T M ,
(24.13)
2 coth x ≡ cosh x/ sinh x, cschx ≡ 1/ sinh x.