6.3. STATIC CHARACTERISTICS: CURRENT - VOLTAGE RELATION 259
The first part represents the hole current injected from the base into the emitter and the second
part represents the hole current recombining with electrons injected from the emitter.
Having derived the current components, in the next section we will examine how material
properties and doping levels can be manipulated to improve device performance. It is useful to
recast the prefactor of the first term in the emitter current (equation 6.3.16) in a different form.
The prefactor, which we will denote byIS(we assume thatWbnLbso thatcothα=1/α),
is
IS=eADbnbo
Wbn=
e^2 A^2 Dbn^2 i
eANabWbn=
e^2 ADbn^2 i
eQGwhereQGis called the Gummel number for the transistor. It has a value
QG=NabWbn (6.3.19)and denotes the charge in the base region of the device (assuming full ionization). As we will
see later, the Gummel number has an important effect on device performance.
To understand the operation of a BJT as an amplifier or a switching device it is useful to ex-
amine the device under conditions of saturation, forward active (or reverse active), and cutoff. In
figure 6.8 we show the band profile and the minority carrier distribution for each of these modes.
Note that in saturation where both EBJ and BCJ are forward biased, a large minority carrier den-
sity (electrons for thenpndevice) is injected into the base region. This plays an important role
in device switching, as will be discussed later. In the cutoff mode there is essentially no minority
charge in the base, since the EBJ and BCJ are both reverse biased. In the forward active mode,
the mode used for amplifiers, the EBJ is forward biased while the BCJ is reverse biased. Under
this modeICIB, providing current gain.
6.3.2 BJTBiasingincircuits...........................
The three terminal bipolar transistor can be biased in one of three different configurations
shown in figure 6.9a. The configuration chosen depends upon the applications. As shown, one
of the terminals can be chosen as a common terminal between the input and output terminals.
The full I-V characteristics of a BJT in the common-base and the common-emitter configuration
are shown in figure 6.9b. In the common-base configuration the cutoff mode occurs when the
emitter current is zero. Note that the emitter current is finite, the collector current does not go
to zero atVCB= 0. The BCJ has to be forward biased at the turn on voltage (∼0.7 V for Si
devices) to balance the injected emitter current.
In the common-emitter mode, the cutoff mode occurs when the base current is zero and indi-
cates the region where the EBJ is no longer forward biased. The saturation region is represented
by the region whereVCE=VBEand both EBJ and BCJ are forward biased.
6.3.3 Current-Voltage: The Ebers-Moll Model .................
It is useful in circuit applications to represent theI−Vcharacteristics derived by us in terms
of a simple physical model. Several models have been developed to do so. Here we will discuss