For a GaAs crystal, the polar optical phonon scattering mobility Âµp0 given by (8.69) can be simplified to
whereÂ = h –Ï‰l/kB, a0 = h –2/mq2, and Z0 = /T ; Ï‰l is the angular frequency of the longitudinal optical modes, and Ï‡(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 –Ï‰l â‰ˆ 36 meV), and Âµp0 â‰ˆ 10,000 cm2/(VÂ·s) at 300 K.
The ionized impurity scattering mobility Âµi is given by
The piezoelectric scattering mobility is given by
Assuming that Matthiessenâ€™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 cmâˆ’3.