ABSTRACT
The dc behavior of the BJT can be described by the Ebers-Moll Model. The equations for the model are
(12.1)
(12.2)
and
(12.3)
(12.4)
and
(12.5)
I I V VF ES
= Ê ËÁ
ˆ ˜¯ -
È
Î Í Í
ù
û ú ú
exp 1
I I V VR CS
= Ê ËÁ
ˆ ˜¯ -
È
Î Í Í
ù
û ú ú
exp 1
I I IC F F R= -a
I I IE F R R= - + a
I I IB F F R R= -( ) + -( )1 1a a
where IES and ICS are the base-emitter and base-collector saturation currents,
respectively, aR is the large signal reverse current gain of a common-base configuration,
and aF is the large signal forward current gain of the common-base configuration,
and
(12.6)
where k is the Boltzmann’s constant (k = 1.381 ¥ 10-23 V.C/K) T is the absolute temperature in Kelvin q is the charge of an electron (q = 1.602 ¥ 10-19 C)
The forward and reverse current gains are related by the expression
(12.7)
where IS is the BJT transport saturation current. The parameters aR and aF are influenced by impurity concentrations and
junction depths. The saturation current, IS, can be expressed as
(12.8)
V kT qT
=
a aR CS F ES SI I I= =
I J AS S=
where A is the area of the emitter and JS is the transport saturation current density, and it can be further expressed as
(12.9)
where Dn is the average effective electron diffusion constant ni is the intrinsic carrier concentration in silicon (ni= 1.45 ¥ 1010 atoms/cm3
at 300 K) QB is the number of doping atoms in the base per unit area
The dc equivalent circuit of the BJT is based upon the Ebers-Moll model. The model is shown in Figure 12.2. The current sources aRIR indicate the interaction between the base-emitter and base-collector junctions due to the narrow base region.
