The hole mobility enhancement mechanism of wurtzite (0001)-oriented gallium nitride (GaN)/AlN heterojunction quantum well (QW) under stress engineering is investigated to overcome the low hole mobility, which is considered to be the fundamental obstacle toward the realization of GaN-based complementary electronics. The hole mobility model is obtained by the six-band stress-dependent $\textit{k}$ $\times$ $\textit{p}$ Hamiltonian and the Kubo–Greenwood formula, taking the scattering rates of acoustic phonon, polar optical phonon, and surface roughness into account. Using these methods, the microscopic relationship between stress and hole mobility can be predicted according to the variation of 2-D valence subband dispersion. We demonstrate that the biaxial tensile stress is not a desirable way in the hole mobility enhancement because a large compressive strain induced by the pseudomorphic GaN/AlN heterointerface has to be overcome. We also find that due to the efficient achievements in both effective mass reduction and hole scattering suppression, the uniaxial compressive stress along the current channel and the uniaxial tensile stress perpendicular to the current channel can increase the hole mobility significantly. Under the combined effect of these two 8 GPa non-exclusive mechanisms, a sevenfold mobility enhancement can be obtained, up to the theoretical value of 190 cm $^{\text{2}}$ /Vs at room temperature.

The influence of uniaxial compressive stress with different orientations to the current channel on the physical and transport properties of the wurtzite GaN heterojunction quantum well is investigated in this work. By using the six-band stress-dependent k × p Hamiltonian, accurate two-dimensional physical pictures are given for the quantized valence subband under the uniaxial compressive stress on the (0001) transport plane. The low-field hole mobility is obtained by the Kubo–Greenwood formula, taking the scattering rates for acoustic phonon, polar optical phonon, and surface roughness into account. Using these methods, the microscopic relationship between the orientation of uniaxial compressive stress and low-field hole mobility is obtained according to the variations of valence subband dispersion and hole effective mass. Results show that for temperatures around and above room temperature, the acoustic phonon scattering is predominant. We find that the mobility gain is mostly contributed from effective mass, and there is an increasing trend under uniaxial compressive stress with all orientations due to the effective mass reduction. For the same stress value, the mobility decreases monotonically as the stress orientation changes from 0° to 90° with respect to the current channel. At room temperature, the calculated low-field hole mobility is 182 cm²/V s under 8 GPa uniaxial compressive stress parallel to the current channel, with the hole density of 5.5 × 10¹³ cm⁻² and the effective electric field of 0.93 MV/cm.