SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

6.5. BJT DESIGN LIMITATIONS: NEED FOR BAND TAILORING 265

6.5 BJT DESIGN LIMITATIONS: NEED FOR BAND

TAILORING AND HBTs

So far in this chapter we have assumed that the emitter, base, and collector are made from the
same material, Of course this need not be the case since as we have noted in previous chapters
heterostructures can be fabricated with ease. In this section we will see the tremendous advan-
tages of using heterostructure concepts in bipolar transistors. In the BJT, once a material system
is chosen the only flexibility one has in the device design is the doping levels and the device
dimensions. This is not optimum for high-performance devices. Let us examine the material
parameters controlling the device performance parameters. We have seen that for the narrow
base width case

α=

[

1 −

peoDeWbn

nboDbLe

][

1 −

Wbn^2

2 L^2 b

]

(6.5.1)

and the current gainβis

β=

α

1 −α

(6.5.2)

We have already noted that forβto be high, it is essential that: (i) the emitter doping be much
higher than the base doping, i.e., for annpndevice (neopbo); and (ii) the base width be as
small as possible. In fact, the productpboWb, called the Gummel number, should be as small as
possible. However, a small base with relatively low doping (usually in BJTsneo∼ 102 - 103 pbo)
introduces a large base resistance, which adversely affects the device performance. From this
point of view, the Gummel number should be as high as possible.
One may argue that the emitter should be doped as much as possible maintainingneopbo
and yet having a high enough base doping to ensure low base resistance. However, a serious
problem arises from the bandgap shrinking of the emitter region that is very heavily doped.
If we assume that hole injection across the EBJ is a dominant factor, the current gain of the
device becomes

β=

α

1 −α

nboDbLe

peoDeWbn

(6.5.3)

If the emitter bandgap shrinks by|ΔEg|due to doping, the hole density for the same doping
changes by an amount that can be evaluated using the change in the intrinsic carrier concentra-
tion,

nie(Eg−|ΔEg|)=nie(Eg)exp

(

|ΔEg|

2 kBT

)

(6.5.4)

whereΔEgis positive in our case. Thus the value ofpeochanges as

peo(Eg−|ΔEg|) ∝ n^2 ie(Eg−|ΔEg|) (6.5.5)

= peo(Eg)exp

(

|ΔEg|

kBT

)

(6.5.6)

The bandgap decrease with doping is given for Si by (Ndis in units of cm−^3 )

|ΔEg|=22. 5

(

Nd

1018

·

300

T(K)

) 1 / 2

meV (6.5.7)