Hole mobility of strained GaN from first principles

Nitride semiconductors are ubiquitous in optoelectronic devices such as LEDs and Blu-Ray optical disks. A major limitation for further adoption of GaN in power electronics is its low hole mobility. In order to address this challenge, here we investigate the phonon-limited mobility of wurtzite GaN using the ab initio Boltzmann transport formalism, including all electron-phonon scattering processes, spin-orbit coupling, and many-body quasiparticle band structures. We demonstrate that the mobility is dominated by acoustic deformation-potential scattering, and we predict that the hole mobility can significantly be increased by lifting the split-off hole states above the light and heavy holes. This can be achieved by reversing the sign of the crystal-field splitting via strain or via coherent excitation of the $A_1$ optical phonon through ultrafast infrared optical pulses.

Figure 1

Total energy versus volume at zero temperature for the rocksalt, wurtzite, and zinc-blende phases of GaN.

Figure 2

Phase diagram of GaN. The phonon frequencies are computed using the PBE functional, without spin-orbit coupling, at 11 different volumes. The experimental values (black triangles) are from Ref. [36]. The light gray rectangle represents the maximum strain (9.8 GPa at 2% strain) and temperature (500 K) investigated in this paper.

Figure 3

Electronic band structure of wurtzite GaN using (a) the LDA functional in the optimized ground-state LDA structure, and (b) quasiparticle $G_0{W}_0+{\mathrm{\Delta }}_{\mathbf{k}}$ calculation. We indicate the effective masses at the zone center, obtained from the second derivatives of the band energy with respect to the wave vector along the $\mathrm{\Gamma }-M$ and $\mathrm{\Gamma }-A$ directions, respectively. The band gap is off scale for clarity. We indicate the naming convention for the three topmost eigenstates at $\mathrm{\Gamma }$. The energy levels have been aligned to the band edges. A schematic of the Brillouin zone of wurtzite GaN is given in the upper left corner.

Figure 4

Convergence tests for the electron and hole mobilities of wurtzite GaN. (a), (b) Electron and hole mobility vs temperature, for different sizes of the Brillouin-zone grids of electrons ($\mathbf{k}$) and phonons ($\mathbf{q}$). The calculations are performed within the SERTA using LDA and Cauchy grids. (c), (d) Electron and hole mobilities of GaN using uniform $100\times 100\times 100$ grids, calculated iteratively from the self-consistent BTE, as a function of the number of iterations.

Figure 5

Comparison between calculations of mobility using the “local approximation” to the band velocity and the “exact” velocity, which takes into account the contribution from the nonlocal part of the ionic pseudopotentials. (a), (b) Electron and hole mobility in GaN versus temperature, both in the local approximation (gray) and using exact velocities (red). Same comparison, this time for silicon, using a PBE pseudopotential (c), (d) or LDA pseudopotential (e), (f).

Figure 6

Calculated temperature-dependent Hall factor of unstrained wurtzite GaN, for electrons and holes.

Figure 7

Phonon dispersion relations (a), (c) and phonon density of states (b), (d) of wurtzite GaN at the relaxed (blue lines) or strained (gray lines) atomic positions. The experimental data are from Ref. [116] (filled disks, inelastic x-ray scattering) and from Ref. [117] (empty diamonds, Raman).

Figure 8

(a), (b) Sensitivity of the spin-orbit splitting ${\mathrm{\Delta }}_{\mathrm{so}}$ and the crystal-field splitting ${\mathrm{\Delta }}_{\mathrm{cf}}$ to the $c/a$ ratio and the internal $u$ parameter in wurtzite GaN. In (a) we fix the internal parameter to $u=0.3765$, in (b) we fix the aspect ratio to $c/a=1.6299$. (c), (d) Dependence of $c/a$ and $u$ on biaxial and uniaxial strain, respectively. (e), (f) Dependence of ${\mathrm{\Delta }}_{\mathrm{so}}$ and ${\mathrm{\Delta }}_{\mathrm{cf}}$ on the biaxial and uniaxial strain, respectively. The region outside of the dashed lines in (f) leads to a reversal of ${\mathrm{\Delta }}_{\mathrm{cf}}$.

Figure 9

(a), (b) Change in the $GW$ quasiparticle band structure of GaN upon uniaxial compression and dilation, respectively. The energy levels have been aligned to the band edges.

Figure 10

Predicted temperature-dependent Hall (a) electron and (b) hole mobility in wurtzite GaN as a function of biaxial and uniaxial strain.

Figure 11

Critical layer thickness of GaN as a function of strain, estimated using Eq. (25). The gray area represents the minimal strain required for crystal-field splitting inversion under uniaxial or biaxial strain.