SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

5.6. SEMICONDUCTOR HETEROJUNCTIONS 239

Ec

Ev

+

Fe = -e

Fh = +e

(a)

Ec

Ev

+

Fe = 0

Fh = +e

(b)

Ec

Ev

+

Fh = +e

(c)

Fe = -e

E

E

Eh

Eh

Ee

Figure 5.13: (a) Band diagram when an electric field is applied to a homogeneous semiconductor.
(b) Quasi-field causes a force on holes but not on electrons. (c) Quasi-field in which electrons
and holes feel a force in the same direction.

An interesting phenomenon arises in semiconductors with graded bandgaps, such as the bipo-
lar transistor emitter-base structure shown in figure 5.11b. In the graded region, the bandgap
is not constant, so the slopes in the conduction and valence bands are no longer equal. Hence
the forces acting on electrons and holes in this region are no longer equal in magnitude. It is in
general possible for a force to act on only one type of carrier, as shown in figure 5.13b, or for
forces to act in the same direction for both electrons and holes, as in figure 5.13c. Such behavior