Using self-consistent electron Monte Carlo simulations, we optimize an alloy-graded heterobarrier layer for in situ recycling of phonons emitted in $\mathrm{Ga}\mathrm{N}$ semiconductor diode devices, leading to improved electrical and thermal performance. The band offset and effective mass of $\mathrm{Al}\mathrm{In}\mathrm{Ga}\mathrm{N}$ quaternary alloying are engineered to enhance thermionic transport across the built-in potential barrier in diode devices (e.g., LEDs, Schottky diodes), leading to an increase in current and upstream phonon reabsorption compared to the same device with no heterobarrier. The simulations indicate a current gain of over 10%, which is consistent with the results of a thermionic model and demonstrates potential for integrated cooling with simultaneous current gain in semiconductor devices.

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• Energy conversion technologies
• Energy transport
• Phonons
• Solid-state refrigeration
• Thermionic emission
• Diodes
• III-V semiconductors
• Thermoelectrics