SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

52 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

Experimental

bandgap

EG(eV)

Type of Temperature dependence

Compound bandgap 0 K 300 K of bandgapEG(T)(eV)

AlP Indirect 2.52 2.45 2.52 – 3.18× 10 −^4 T^2 /(T+ 588)

AlAs Indirect 2.239 2.163 2.239 – 6.0× 10 −^4 T^2 /(T+ 408)

AlSb Indirect 1.687 1.58 1.687 – 4.97× 10 −^4 T^2 /(T+ 213)

GaP Indirect 2.338 2.261 2.338 – 5.771× 10 −^4 T^2 /(T+ 372)

GaAs Direct 1.519 1.424 1.519 – 5.405× 10 −^4 T^2 /(T+ 204)

GaSb Direct 0.810 0.726 0.810 – 3.78× 10 −^4 T^2 /(T+ 94)

InP Direct 1.421 1.351 1.421 – 3.63× 10 −^4 T^2 /(T+ 162)

InAs Direct 0.420 0.360 0.420 – 2.50× 10 −^4 T^2 /(T+ 75)

InSb Direct 0.236 0.172 0.236 – 2.99× 10 −^4 T^2 /(T+ 140)

Table 2.1: Bandgaps of binary III–V compounds (From Casey and Panish, 1978).

This integral is particularly simple to evaluate as 0 K, since, at this temperature

1

exp

(

E−EF

kBT

)

+1

=1ifE≤EF

=0otherwise

this gives

n=

∫EF

EC

N(E)dE

We t h e n h ave

n =

√

2 m^30 /^2

π^2 ^3

∫EF

EC

(E−EC)^1 /^2 dE

=

2

√

2 m^30 /^2

3 π^2 ^3

(EF−EC)^3 /^2

or

EF−EC=

^2

2 m 0

(

3 π^2 n

) 2 / 3

(2.7.3)

The expression is applicable to metals such as copper, gold, etc. In Table 2.2 we show the
conduction band electron densities for several metals. The quantityEF,which is the highest oc-
cupied energy state at 0 K, is called the Fermi energy. We can define a corresponding wavevector