SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

74 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

TYPE I

HETEROSTRUCTURE

A

B

TYPE II

HETEROSTRUCTURE

BROKEN GAP TYPE III

HETEROSTRUCTURE

B

B

Bandgap A A

Figure 2.30: Various possible bandedge lineups in semiconductors A and B.

heterostructures, both the conduction and valence band edges of material A are above the con-
duction band edge of material B. In figure 2.31 we show bandlineups for a number of different
material systems.
In figure 2.32 we show a schematic of a type I quantum well made from a smaller bandgap
material B sandwiched between a large bandgap material A. To understand the electronic prop-
erties of the quantum well we use the effective mass approach and the discussion of Section 2.2.
The key difference in semiconductor quantum wells is that we need to use the effective mass
instead of the free electron mass.
The confinement of electrons and holes by quantum wells alters the electronic properties of
the system. This has important consequences for optical properties and optoelectronic devices.
In an infinite quantum well the confined energies are

En=

π^2 ^2 n^2

2 m∗W^2

(2.10.3)

The energy of the electron bands are then

E=En+

^2 k‖^2

2 m∗

(2.10.4)

The two-dimensional quantum well structure thus creates electron energies that can be described
bysubbands(n=1, 2 , 3 ···). The subbands for the conduction band and valence band are
shown schematically in figure 2.33.