SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

6.4. DEVICE DESIGN AND DEVICE PERFORMANCE PARAMETERS 263

the forward active mode of the device so that we have the conditions

eVBEkBT (6.4.1)

eVCBkBT (6.4.2)

In a well-designed bipolar transistor we always haveWbLb.

Emitter Injection Efficiency

Bipolar transistor gain is intimately tied to emitter efficiency. The emitter injection efficiency
is the ratio of the electron current (in thenpnBJT) due to the electron injection from the emitter
to the total emitter current. Thus,

γe=

IEn

IEn+IEp

(6.4.3)

For high emitter efficiency,IEpshould be minimal. Under the voltage approximations made we
have from Eqns. 6.3.16 and 6.3.18,

IEp = −

eADepeo

Le

exp

(

eVBE

kBT

)

(6.4.4)

IEn ∼= −

eADbnbo

Lbtanh

(

Wbn

Lb

)exp

(

eVBE

kBT

)

(6.4.5)

Thus the emitter efficiency becomes

γe=

1

1+(peoDeLb/nboDbLe)tanh(Wbn/Lb)

(6.4.6)

If the base width is small compared to the electron diffusion length, the tanh(Wbn/Lb)can be
replaced by(Wbn/Lb)andwehave

γe∼=

1

1+(peoDeWbn/nboDbLe)

∼ 1 −

peoDeWbn

nboDbLe

(6.4.7)

Thus forγeto be close to unity, we should design the device so thatWbnLeandpeonbo.
Thus a small base width and a heavy emitter doping compared to the base doping are essential.
Of course, the base width cannot be arbitrarily reduced.

Base Transport Factor

The second part of the device gain is related to how electrons injected from the emitter move
over the base. The base transport factor is the ratio of the electron current reaching the base-
collector junction to the current injected at the emitter-base junction. As the electrons travel
through the base, they recombine with the holes so that the base transport factor is less than