390
Compact Models for Integrated Circuit Design
forward transit time of the carriers to reach from the emitter to collector, then the total minority carrier charge due to forward current
I CC is given by
Q
Q Q
Q Q
I
I
DE
E
B E
B
BC
E
E B
B
CB CC
Fdc CC
=
+
+
+
=
+
+ +
=
(
)
τ τ
τ τ
τ
(11.39)
where:
τ Fdc is the total forward delay time consisting of emitter delay τ E
EB space charge layer transit time τ EB
base transit time τ B
CB-space charge layer transit time τ CB
From Equation 11.39, we can write the expression for the diffusion
capacitance C DE (V BE ) due to the applied bias V BE
C V
Q
V
I
V
DE
DE
B E
Fdc CC
B E
BE
( )=
=
′ ′
′ ′
τ
(11.40)
The base transit time τ B is the major contributor of total transistor
delay time τ Fdc given in Equation 11.39. Thus, τ B is the most critical
parameter to determine the speed of BJTs. In the absence of built-in
electric fields in the base (i.e., constant N a ) with low-level injection,
the injected electron concentration n p varies linearly across the base
from n p to n p0  ≈ 0 as shown in Figure 11.17. Therefore, for low-level
injection and uniformly doped base region, the total electron charge
in the base is simply given by
Q
qW n A
B
Bp E
=
1
2
(11.41)
C (n)
B (p)
E (n+)
W B
Q BE
Q BC
Q E
Q B
n p
n p0
p n 0
p n 0
FIGURE 11.17
The components Q E , Q BE , Q B , and Q BC of the total diffusion charge Q DE due to the forward injection of carriers at the EB-junction of an npn-BJT, resulting in the diffusion capacitance, C DE ; n p
is the injected electron concentration at the edge of the EB-depletion region inside the base; p n0
and n p0 are the equilibrium minority carrier concentrations in the n and p regions, respectively;
and W B is the width of the neutral base region.