SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.5. HIGH-FREQUENCY BEHAVIOR OF A BJT 331

(b)

E(x)

wC

x

(a)

|eΔn(x)|

wC

x

d(ΔQC) d(ΔQ'C)

dx

dE+(x)

dE-(x)

Figure 7.13: Induced (a) image charge and (b) electric field due to an injected sheet charge
−eΔn(x)dxat a pointx.

Finally, we can solve forτC.

τC=

ΔQC

ΔIC

=

∫wC

0

(

1 −

x

wC

)

1

ve(x)

dx (7.5.25)

For the case of a constant electron velocityvs,τCis given by

τC=

wC

2 vs

(7.5.26)

The delay analysis for bipolar transistors presented here accurately describes the frequency
limitations of the device and provides us with the tools required to design devices for high fre-
quency operation. However, it does not give us any information about how the device will
perform at frequencies less thanfτ. Since these transistors will ultimately be used in circuits,
we need to be able to determine the frequency response of a circuit containing these devices. It
is therefore necessary to derive a small-signal model of the device that can then be applied in
circuit simulations. We will see in the next section that the discrete components of the bipolar
equivalent circuit can be written in terms of the delays that we have derived.