Page 106 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

MONOLITHIC PROCESSING 87

In the normal mode of operation 7 of an n-p-n transistor in the CE configuration, the
emitter-base junction is forward-biased (i.e. V BE > 0) and the collector-base junction is
reverse-biased (i.e. V BC < 0). Therefore, the collector current I c consists of two terms,
the main term being a fraction a F of the emitter current and the other being the reverse
saturation current I Co of the collector-base junction diode; hence

I c = a FIE + Ico (4.15)

where the constant a F depends on the doping and dimensions of the diode according to

2
1 W\
<*P*1-- ( — } (4.16)
^ V '-'n /
where L n is the diffusion length of the injector carriers in the base of width W and is
about 10 um for silicon. As mentioned earlier, the reverse saturation current I Co for a
silicon diode is about 1 nA.
From Kirchoff's current law, the collector current can be related to the base current by

because I E + I B + I C = 0 (4.17)
1 — a F 1 — a F
A second characteristic parameter is also defined and is called B F. It is related to a F by

(4.18)
1 -a F 1 + B F
These two parameters are used to describe the currents flowing through the CE-configured
transistor in the forward-active region, and they can also be defined from Equations (4.15),
(4.17), and (4.18) as
aIc dl c
ap=-±orftp=-± (4.19)

Ideally, ap takes a value close to unity and ftp takes a value that is large.
The typical measured input characteristic IB — V BE and output characteristic Ic — VCE
of an n-p-n transistor are shown in Figure 4.22. The input characteristic is that of a diode
with a threshold voltage that is about 0.7 V corresponding to a silicon transistor. The
output characteristic shows all the possible regions of operation for the transistor.
As mentioned in the preceding text, the transistor is normally operated in the forward-
active region (V BE > 0; VBC < 0) where the forward current parameters of a F and ftp
apply. In this region, the output characteristic may be described by a simple model
(excluding the breakdown region) in which the collector current is given by

r a T 7 co V CE\ ,1 „„,
/c = ftplB ~ -: - exp — — - ) - 1 (4.20)
q
1 - ap I \ kT/q ) J
7
All voltages and currents have the opposite sign in p-n-p transistors.