SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

5.6. SEMICONDUCTOR HETEROJUNCTIONS 235

W(Vbi)=

[

2  1  2 Vbi

e

(

[Na+Nd]^2

NaNd[Na 2 +Nd 1 ]

)] 1 / 2

(5.6.9)

E 1 ,m=

eNdWn

 1

(5.6.10)

E 2 ,m=

eNaWp

 2

(5.6.11)

We can also solve for the band bending on either side of the junctionVd 1 andVd 2 :

Vd 1 =

1

2

WnE 1 ,m=

eNdWn^2

2  1

(5.6.12)

Vd 2 =

1

2

WpE 2 ,m=

eNaWp^2

2  2

(5.6.13)

Current flow in abruptp-nheterostructure

In ap-nhomojunction, the ratio of current carried by electrons to current carried by holes
In/Ipcan be made large by makingNdlarger thanNa. However, in bipolar transistor technol-
ogy, it is desirable to haveNabe large while simultaneously maintaining a large value ofIn/Ip.
This can only be achieved by employing ap-nheterostructure. We will now calculate the current
characteristics of ap-nheterojunction and show how the ratioIn/Ipcan be controlled.
In figure 5.11a, we show the band diagram of thep-nheterostructure from figure 5.9b under
forward bias. In determining the current characteristics of this structure, we make the following
assumptions:

1. The electron and hole components of the current can each be described by thermionic
   emission, similar to the treatment given in section 5.3.3 for the electron current in an
   n-type Schottky barrier. The barrier to hole injection from thepside to thenside is
   labeledeφBhin figure 5.11a, and the barrier to electron injection from thenside to thep
   side is labeledeφBe. The electron currentIn∝exp[−eφBe/kBT], and the hole current
   Ip∝exp[−eφBh/kBT].


2. The downwards notch in the conduction band immediately to the right of the junction does
   not capture electrons or in any way affect the electron current.

The general idea behind the use of heterostructures is that we would like to increase the barrier
that holes must overcomeφBhrelative to the barrier that electrons must overcomeφBe.Inp-n
homojunctions,φBe=φBh=Vbi−VF.Inp-nheterojunctions, these barriers are no longer
equal.