Route to High Hole Mobility in GaN via Reversal of Crystal-Field Splitting

A fundamental obstacle toward the realization of GaN $p$-channel transistors is its low hole mobility. Here we investigate the intrinsic phonon-limited mobility of electrons and holes in wurtzite GaN using the ab initio Boltzmann transport formalism, including all electron-phonon scattering processes and many-body quasiparticle band structures. We predict that the hole mobility can be increased by reversing the sign of the crystal-field splitting in such a way as to lift the split-off hole states above the light and heavy holes. We find that a 2% biaxial tensile strain can increase the hole mobility by 230%, up to a theoretical Hall mobility of $120{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ at room temperature and $620{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ at 100 K.

Figure 1

Electron (a) and hole (b) mobilities of wurtzite GaN, calculated using the ab initio Boltzmann formalism, compared with the experimental data from Refs. [17, 18, 32, 33, 34]. We show both the drift mobilities computed via Eqs. (1)–(3) and the Hall mobilities obtained by applying the Hall factor taken from Ref. [25].

Figure 2

Phonon density of states in GaN (a) and spectral decomposition of the electron (b) and hole (c) scattering rates as a function of phonon energy where the piezoacoustic (red) and polar Fröhlich (green) scattering rates have been highlighted. The rates are calculated as angular averages for carriers at an energy of $k_{B}T=25\mathrm{meV}$ away from the band edge (left vertical axis). The dashed lines represent the cumulative integral of each spectrum of $\partial {\tau }^{-1}/\partial \omega$, and add up to the carrier scattering rate ${\tau }^{-1}$ (right-hand vertical axis). The shadings in (a) indicate the energy ranges shown in (b) and (c).

Figure 3

Crystal-field engineering of band structure and mobility in GaN. (a),(b) Change in the $GW$ quasiparticle band structure of GaN upon biaxial dilation and compression, respectively. The energy levels have been aligned to the conduction band minimum (CBM) and valence band maximum (VBM). (c) Electron wave function at the VBM at $\mathrm{\Gamma }$ for the undistorted wurtzite GaN structure, as well as for 2% biaxial dilation and 2% biaxial compression, respectively. (d) Crystal-field splitting ${\mathrm{\Delta }}_{\mathrm{cf}}$ versus strain and (e) corresponding hole Hall mobility at 300 K. (f) Predicted temperature-dependent hole mobility in wurtzite GaN as a function of biaxial strain.