Hall and drift mobilities in molecular beam epitaxial grown GaAs

A series of nominally undoped and Si-doped GaAs samples have been grown by molecular beam epitaxy (MBE) with Hall concentrations ranging from 10¹⁵ to 10¹⁹ cm⁻³ and mobilities measured at 77 and 300K by Hall-van der Pauw methods. Drift mobilities were calculated using the variational principle method and Hall scattering factors obtained from a relaxation-time approximation to permit cross-correlation of experimental data with drift or Hall mobilities and actual or Hall electron concentrations. At 77K, both high purity and heavily doped samples are well represented by either drift or Hall values since piezoelectric acoustic phonon scattering and strongly screened ionized impurity scattering hold the Hall factor close to unity in the respective regimes. Between n≊10¹⁵ and 10¹⁷ cm⁻³, where lightly screened ionized impority scattering predominates, Hall mobility overestimates drift mobility by up to 50 percent and Hall concentration similarly underestimates n. At 300K, polar optical phonons limit mobility and a Hall factor up to 1.4 is found in the lowest doped material, falling close to unity above about 10¹⁶ cm⁻³. Our calculation also agrees remarkably well with the Hall mobility of the highest purity MBE grown sample reported to date.