Abstract
The diffusion coefficient of holes can provide knowledge about carrier localization in ($\mathrm{In}$,$\mathrm{Ga}$)$\mathrm{N}$, where the carrier dynamics are altered by randomly fluctuating potential landscape. In group-III nitrides, the diffusivity of holes is difficult to measure by electrical methods but it can be studied using optical techniques. Here, we investigate the dependence of the hole diffusion coefficient on direction and carrier density in $c$-plane and $m$-plane ($\mathrm{In}$,$\mathrm{Ga}$)$\mathrm{N}$ structures by employing the light-induced transient-grating technique. We show that the hole diffusion coefficient is anisotropic in the $m$-plane structure, where it is several times larger along the $a$ crystallographic direction than along the $c$ direction. Such anisotropy is observed within the broad range of carrier densities from ${10}^{18}$ to ${10}^{20}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The diffusivity changes nonmonotonously with increasing photoexcitation, this dependence being different in thick and thin layers. We argue that an unexpectedly high diffusion coefficient at low carrier densities in thick quantum wells can be a signature of efficient hole transport via percolative paths occurring due to compositional disorder. In turn, a decrease of diffusivity with the excitation can reflect the effect of Coulomb blockade of these paths. Finally, we demonstrate that disorder impacts carrier diffusivity even at carrier densities above ${10}^{19}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, where the overflow of localized states must be included to explain the observed increase of the diffusion coefficient with the carrier density.
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