SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.4. BIPOLAR JUNCTION TRANSISTORS: A CHARGE-CONTROL ANALYSIS 319

relationship between the currents and the stored charge, the charge control model, and then
determining the delays associated with modulation of stored charge. We shall discuss the small
signal model of the bipolar transistor after the charge control model, since that allows the reader
to better appreciate setting up the continuity equations for the minority carriers.
The charge-control model, presented in this section, establishes relationships between the
currents and stored charge in the device. These relationships are quite useful for calculating
delays. In section 7.5 the response of bipolar transistors to small signals is derived using the
charge-control framework.
The two junctions of the BJT can be biased in several ways to produce four operating modes
for the transistor, as was shown in figure 6.8. When the device is used for small-signal amplifica-
tion, it remains biased in forward active mode. Hence, the analysis of the device in this mode is
sufficient for deriving the response of the device to small signals (section 7.5). For large-signal
applications, in addition to forward active mode, the device will also at times switch to saturation
and cutoff modes. We will now briefly discuss behavior in all four modes and concentrate on the
forward active mode in section 7.5.
Forward Active Mode
In this mode the emitter-base junction (EBJ) is forward biased, while the base-collector junction
(BCJ) is reverse biased. We will use the subscriptFto denote various terms in the forward active
mode. The currents are given by the Ebers-Moll model discussed in section 6.3.3 (eVCBkBT
in this mode):

IE = IESexp

(

eVBE

kBT

)

+αRICS

IC = αFIESexp

(

eVBE

kBT

)

+ICS (7.4.1)

Here we assume that the emitter and collector current have the same direction. If we express
IESexp (eVBE/kBT)in the second equation using the first equation, we can write

IC = αF(IE−αRICS)+ICS

= αFIE+ICS(1−αFαR) (7.4.2)

UsingIE=IB+IC,wehave

IC=αFIB+αFIC+ICS(1−αFαR) (7.4.3)

or

IC =

αF

1 −αF

IB+

ICS(1−αFαR)

1 −αF

= βFIB+(βF+1)ICS(1−αFαR) (7.4.4)

where
βF=

αF

1 −αF

(7.4.5)

βFrepresents the forward active current gainIC/IBfor the transistor.