Electron and hole mobilities of GaN with bulk, quantum well, and HEMT structures

Electron and hole mobilities of GaN are calculated for three-dimensional (3D, bulk) and two-dimensional [2D, quantum well (QW), and HEMT] structures, including scattering processes of acoustic deformation potential, polar optical phonon, piezoelectric, ionized impurity, and so on. The calculated mobilities for 2D structures are strongly dependent on quantum well structures and impurity densities, although the temperature dependence of the mobilities behaves in a similar way to bulk values. In the present analysis, energy band structures of GaN are calculated by the empirical pseudopotential method including spin–orbit interaction, and then the electron effective mass of the conduction band and the hole effective masses of the valence bands are evaluated, which are used for the calculations of electron and hole mobilities. The calculated valence band structure of the heavy, light, and crystal field splitted valence bands reveal complicated dispersion due to the spin–orbit interaction. The obtained electron effective mass m c = 0.145 m is isotropic, and the heavy hole effective mass in the c ∥ plane is m hh ∥ = 1.20 m, while in the c ⊥ plane, the band edge effective mass is m hh 0 ⊥ = 0.55 m and the over all fitted heavy hole effective mass is m hh ⊥ = 1.20 m. The light hole effective masses are m lh ∥ = 1.35 m and m lh ⊥ = 0.165 m. Both of the electron and hole mobilities are limited by ionized impurity scattering at low temperatures and by polar optical phonon scattering at high temperatures. Calculated electron mobilities are 7100 cm 2 / V s for bulk, 4600 cm 2 / V s for high electron mobility transistor (HEMT), and 3600 cm 2 / V s for QW at room temperature and calculated hole mobilities are 450 cm 2 / V s for bulk, 450 cm 2 / V s for HEMT, and 500 cm 2 / V s for QW at room temperature. All the expressions for scattering rates and respective mobilities are derived for 3D and 2D (QW and HEMT) structures and enable readers to calculate electron and hole mobilities in different structures with parameters given in the table or modified ones.