Physics and Engineering of Radiation Detection

5.1. Semiconductor Detectors 281

Eg= 1.42 eV

EX= 1.90 eV

EL= 1.71 eV

Wavevector

Holes

Energy

<100> <111>

Figure 5.1.20: Band structure diagram of gallium arsenide showing

energy versus wavenumber (reproduced from (47)). The subscripts of

Erepresent different energy levels. The number in brackets (100 and

111) are the Miller indices. A Miller index represents the orientation

of an atomic plane in a crystal lattice.

T (K)

250 260 270 280 290 300 310

(eV)g

E

1.42

1.425

1.43

1.435

1.44

1.445

Figure 5.1.21: Variation of gal-

lium arsenide band gap energy

with absolute temperature.

valence bands inGaAscan be written as (47)

Nc=8. 63 × 1013 T^3 /^2

[

1 − 1. 93 × 10 −^4 T− 4. 19 × 10 −^8 T^2

+21exp

(

−

EL

2 kBT

)

+44exp

(

−

EX

2 kBT

)]

(5.1.46)

and
Nv=1. 83 × 1015 T^3 /^2 , (5.1.47)