solution

For a GaAs crystal, the polar optical phonon scattering mobility µp0 given by (8.69) can be simplified to

where  = h –ωl/kB, a0 = h –2/mq2, and Z0 = /T ; ωl is the angular frequency of the longitudinal optical modes, and χ(Z0) is a quantity defined by Howarth and Sondheimer.5 For pure GaAs, the longitudinal optical phonon temperature is equal to 416 K (i.e., the LO phonon energy h –ωl ≈ 36 meV), and µp₀ ≈ 10,000 cm²/(V·s) at 300 K.

The ionized impurity scattering mobility µi is given by

The piezoelectric scattering mobility is given by

Assuming that Matthiessen’s rule prevails, the total electron mobility for this GaAs crystal can be approximated by

Using the above expression, plot the electron mobility versus temperature for this GaAs crystal for 100 K _I = 10¹⁶, 10¹⁷, and 10¹⁸ cm^−3.