Page 192 - Electrical Properties of Materials
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174 Principles of semiconductor devices
Fig. 9.12 Emitter current
The emitter current as a function of Emitter voltage
time when the emitter voltage is
suddenly increased. It looks like the
current response of a parallel
RC circuit. t t
Let us look again at the p–n junction of the p–n–p transistor. When a step
voltage is applied in the forward direction, the number of holes able to cross
into the n-region suddenly increases. Thus, in the first moment, when the in-
jected holes appear just inside the n-region, there is an infinite gradient of hole
density, leading to an infinitely large diffusion current. As the holes diffuse
into the n-region, the gradient decreases, and finally the current settles down
to its new stationary value as shown in Fig. 9.12. But this is exactly the beha-
viour one would expect from a capacitance in parallel with a resistance. Thus,
when we wish to represent the variation of emitter current as a function of
emitter voltage, we are entitled to put a capacitance there. This is not a real
honest-to-god, capacitance; it just looks as if it were a capacitance, but that
is all that matters. When drawing the equivalent circuit, we are interested in
appearance only!
Including now both capacitances, we get the equivalent circuit of Fig. 9.13.
We are nearly there. There is one more important effect to consider: the fre-
quency dependence of α. It is clear that the collector current is in phase with
the emitter current when the transit time of the carriers across the base region
is negligible, but α becomes complex (and its absolute value decreases) when
this transit time is comparable with the period of the a.c. signal. We cannot go
∗ Not to depart from the usual notations, into the derivation here, but α may be given by the simple formula ∗
we are using j here as honest engineers
do, but had we done the analysis with α 0
our chosen exp(–iωt) time dependence, α = 1+j(ω/ω α ) , (9.22)
we would have come up with –i instead
of j.
where ω α is called the alpha cut-off frequency. The corresponding equivalent
circuit is obtained by replacing α in Fig. 9.13 by that given in eqn (9.22). And
that is the end as far as we are concerned. Our final equivalent circuit represents
fairly well the frequency dependence of a commercially available transistor.
We have seen that the operation of the transistor can be easily under-
stood by considering the current flow through it. The frequency dependence
is more complicated, but still we have been able to point out how the various
reactances arise.
It has been convenient to describe the common base transistor configuration,
but of course the most commonly used arrangement is the common emitter,
†
The full expression for i e should con- shown in Fig. 9.14(a). Again, most of the current i e from the forward-biased
tain a term dependent on the emitter-to- †
collector voltage. This is usually small. emitter–base junction gets to the collector, so we can write
Look it up in a circuitry book if you are
interested in the finer details. i c = αi e , (9.23)