The determination of the carrier diffusion length of semiconductors such as $\mathrm{Ga}\mathrm{N}$ and $\mathrm{Ga}\mathrm{As}$ by cathodoluminescence imaging requires accurate knowledge about the spatial distribution of generated carriers. To obtain the lateral distribution of generated carriers for sample temperatures between 10 and 300 K, we utilize cathodoluminescence intensity profiles measured across single quantum wells embedded in thick $\mathrm{Ga}\mathrm{N}$ and $\mathrm{Ga}\mathrm{As}$ layers. Thin ($\mathrm{Al}$,$\mathrm{Ga}$)$\mathrm{N}$ and ($\mathrm{Al}$,$\mathrm{Ga}$)$\mathrm{As}$ barriers respectively prevent carriers diffusing in the $\mathrm{Ga}\mathrm{N}$ and $\mathrm{Ga}\mathrm{As}$ layers to reach the well, which would broaden the profiles. The experimental cathodoluminescence profiles are found to be systematically wider than the energy loss distributions calculated by means of the Monte Carlo program casino, with the width monotonically increasing with decreasing temperature. This effect is observed for both $\mathrm{Ga}\mathrm{N}$ and $\mathrm{Ga}\mathrm{As}$ and becomes more pronounced for higher acceleration voltages. We discuss this phenomenon in terms of both the electron-phonon interaction controlling the energy relaxation of hot carriers and the shape of the initial carrier distribution. Finally, we present a phenomenological approach to simulate the carrier generation volume that can be used for the investigation of the temperature dependence of carrier diffusion.

• Received 4 December 2020
• Revised 24 November 2021
• Accepted 18 January 2022

DOI:https://doi.org/10.1103/PhysRevApplied.17.024017