SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

280 CHAPTER 6. BIPOLAR JUNCTION TRANSISTORS

1. MinimizingwC


2. MaximizingNd,C


3. Maximizingvs

IncreasingNd,Cand decreasingwCboth lead to higher electric fields in the collector, thus
decreasing the breakdown voltage. Therefore, materials with larger bandgaps and higher electron
velocity characteristics (such as InP) are preferred for collector regions.
In figure 6.1c, we showed the current-gain cutoff frequencyfTversus drain currentJCfor a
state-of-the-art InP-based bipolar transistor. Indeed, we see that initially,fTincreases withJC.
However, asJCbecomes larger,fTsaturates and eventually begins to drop onceJC>JKirk.

6.6.2 HighInjection:ThermalEffects ......................

At high injection levels there is thermal heating of the bipolar device since a power level of
ICVBCis dissipated. As the temperature of the device changes the current usually increases
further. This is due to the exponential dependence of the injection current and the increase in
the recombination time (which increases faster than the increase in the base transit time), which
increases the base transport factor. As the current increases, a further increase in heat dissipation
occurs until the device can be burnt out if proper design considerations are not met.

6.6.3 Base Width Modulation: The Early Effect ................

As seen clearly in our discussion of the Kirk Effect, the quantityWbnthat appeared in our
derivation for the current-voltage characteristics is not the metallurgical base widthWb,butthe
distance which electrons must diffuse before they are swept into the collector by large electric
fields. ForWbnLbwe can see from equation 6.3.17 that the collector current

IC∝

1

Wbn

We s aw t h a tWbncan be affected by the collector current densityICfor high injection conditions.
Additionally,Wbn(and thereforeIC) also vary with the applied base-collector biasVBC.This
non-ideal behavior is known as the Early Effect. The physical reason for it is illustrated in
figure 6.21. An increase inVBCat a fixed emitter-base voltage results in an increase in the base-
collector depletion width and a subsequent decrease inWbn. This results in an increase in the
slope of the minority carrier profile in the base, resulting in an increased collector currentIC.As
can be seen in figure 6.21b, the Early Effect results in a finite output resistance of the transistor,
which we will now show is

Ro=

VA

IC

(6.6.14)

whereVAis called the Early voltage.