SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

266 CHAPTER 6. BIPOLAR JUNCTION TRANSISTORS

The expression is reasonable up to a doping of 1019 cm−^3. At higher doping levels, the
bandgap shrinkage is not so large. For example, at a doping of 1020 cm−^3 the shrinkage is∼
160 meV and not 225 meV as given by the equation above. As a result of the bandgap decrease,
the gain of the device decreases according to the equation

β=

DbNdeLe

DeNabWbn

exp

(

−

|ΔEg|

kBT

)

(6.5.8)

were we have assumed full ionization, i.e.

peo

nbo

=

Nab

Nde

(6.5.9)

As a result of this for a fixed base doping, as the emitter doping is increased, initially the current
gain increases, but then as bandgap shrinkage increases, the current gain starts to decrease. From
the discussion above, it is clear that the conflicting requirements of heavy emitter doping, low
base doping, small base width, etc., as shown in figure 6.11, cannot be properly met by a BJT in
which the same bandgap semiconductor is used for the emitter and the base. This led Shockley
and Kroemer in the 1950s to conceive of the heterojunction bipolar transistor (HBJT or HBT),
where theemitterismadefromawide-gapmaterial. In a typical HBT the emitter is made from
a material that has a bandgap that is, say,> 0. 2 eV larger than the bandgap of the material used
in the base. Near the base side, the emitter material composition is graded so that there is a
smooth transition in the bandgap from the emitter side to the base side. A typical example of
an HBT structural layout is shown in figure 6.12a. In the case shown, the emitter material is
AlGaAs, which has a larger bandgap than GaAs, used for the base and the collector. We have
discussed the heterojunction in detail in section 5.6. There we realized that the maximum benefit
is obtained by grading the E-B junction such that the full bandgap differential can be used.
In figure 6.12b we show the band profile for the emitter and the base region. We can see that
ifΔEgis the bandgap difference between the emitter material bandgap and the base material
bandgap, this difference appears across the valence band potential barrier, seen by holes. Thus,
holes in the base see an increased barrier for injection into the emitter. As a result, the emitter
efficiency dramatically increases. The suppression of hole injection current is given by

IEp(HBT)

IEp(BJT)

=exp

(

−ΔEg

kBT

)

The gainβin the device increases by the exponential factor. We have forβin an HBT

β=

DbNdeLe

DeNabWbn

exp

(

ΔEg

kBT

)[

1 −

w^2 bn

L^2 b

]

(6.5.10)

Typically the values ofΔEg/kBTare∼10, so thatβimproves by∼ 104. Due to the heavy
doping now allowed in wide emitter HBTs, the base can be made narrow without too large a
base resistance or the danger of punch through. This also avoids secondary effects such as Kirk
effect and Early effect discussed later.