SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

2.6. BANDSTRUCTURE OF SOME IMPORTANT SEMICONDUCTORS 49

6 5 4 3 2 1 0

–1

–2

–3

–4

k

ENERGY

(eV)

Eg

GALLIUM ARSENIDE

Direct bandgap

Eg(T=0) = 1.53 eV

Eg(300 K) = 1.43 eV

[111] [100]

Figure 2.13: Bandstructure of GaAs. The bandgap at 0 K is 1.51 eV and at 300 K it is 1.43 eV.
The bottom of the conduction band is atk=(0, 0 ,0), i.e., theΓ-point. The upper conduction
band valleys are at theL-point.

TheL-valley has a much larger effective mass than theΓ-valley. For GaAs,m∗L∼ 0. 25 m 0 .This
difference in masses is extremely important for high electric field transport as will be discussed
in the next chapter.
The valence band of GaAs has the standard HH, LH, and SO bands. Due to the large spin–orbit
splitting, for most purposes the SO band does not play any role in electronic properties.
The bandstructures of Ge and AlAs, two other important semiconductors, are shown in fig-
ure 2.14, along with brief comments about their important properties.

InN, GaN, and AlN
The III–V nitride family of GaN, InN, and AlN have become quite important due to progress
in the ability to grow the semiconductor. These materials are typically grown with a wurtzite
structure, and have bandgaps ranging from∼1.0 eV to over 6.0 eV. This large bangap is very
useful for short wavelength light emitters and high power electronics. In figure 2.15 we show
the bandstructure for nitrides.
It is important to note is that the bandgap of semiconductors generally decreases as temper-
ature increases. The bandgap of GaAs, for example, is 1.51 eV atT =0K and 1.43 eV at
room temperature. In table 2.1 we show the temperature dependence of bandgaps of several
semiconductors.