SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

236 CHAPTER 5. SEMICONDUCTOR JUNCTIONS

Ec

eΦBe

-Wn 0 Wp

eVd2

Ev

EFp

ΔEc

ΔEv

eVF

eΦBh

EFn

Ec

eΦBe

-Wn 0 Wp

eVd2

Ev

eVF EFp

eΦBh

EFn

(a) (b)

notch graded region

Figure 5.11: Band diagrams of (a) a forward biasedabruptp-njunction and (b) a forward biased
gradedp-njunction

Referring to figure 5.11a, for an abruptp-nheterojunction, the barriers to hole injection (φBp)
and to electron injection (φBn)aregivenby

eφBh=Eg 1 −(EF−Ev)p−(Ec−EF)n−eVF (5.6.14)

eφBe=e(Vd 1 −VF) (5.6.15)

=Eg 2 −(EF−Ev)p−(Ec−EF)n−eVF−eVd 2 +ΔEc (5.6.16)

Since we are assumingNa>> Nd,thetermeVd 2 in the expression forφBeis small and can be
omitted. The difference in the two barriers is given by

eφBh−eφBe=Eg 1 −Eg 2 −ΔEc=ΔEv (5.6.17)

The ratio of electron current to hole current in ap-nhomojunction is given by

(

In

Ip

)

hom

=

DnNdLp

DpNaLn

(5.6.18)

In thep-nhomojunction, the barrier seen by electrons is the same as that seen by holes, and
the only means of controlling this ratio is through doping. In an abruptp-nheterojunction with
negligible barrier discontinuity at the conduction band edge, the barrier seen by electrons is