Laser cooling of semiconductor quantum wells: Theoretical framework and strategy for deep optical refrigeration by luminescence upconversion

Abstract

Optical refrigeration has great potential as a viable solution to thermal management for semiconductor devices and microsystems. We have developed a first-principles-based theory that describes the evolution of thermodynamics---i.e., thermokinetics---of a semiconductor quantum well under laser pumping. This thermokinetic theory partitions a well into three subsystems: interacting electron-hole pairs (carriers) within the well, the lattice (thermal phonons), and the ambient (a thermal reservoir). We start from the Boltzmann kinetic equations and derive the equations of motion for carrier density and temperature, and lattice temperature, under the adiabatic approximation. A simplification is possible as a result of ultrafast energy exchange between the carriers and phonons in semiconductors: a single-temperature equation is sufficient for them, whereas the lattice cooling is ultimately driven by the much slower radiative recombination (upconverted luminescence) process. Our theory microscopically incorporates photogeneration and radiative recombination of the interacting electron-hole pairs. We verify that Kubo-Martin-Schwinger relation holds for our treatment, as a necessary condition for consistency in treatment. The current theory supports steady-state solutions and allows studies of cooling strategies and thermodynamics. We show by numerical investigation of an exemplary GaAs quantum well that higher power cools better when the laser is detuned from the band edge between a critical negative value and the ambient thermal energy. We argue for the existence of such a counterintuitive lower bound. Most importantly, we show that there exists an actual detuning, $3\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ above the band edge in the simulated free-carrier case and expected to be pinned at the excitonlike absorption peak owing to Coulomb many-body effects, for optimal laser cooling. Significant improvement in cooling efficacy and theoretical possibility of deep refrigeration are verified with such a fixed optimal actual detuning. In essence, this work provides a consistent microscopic framework and an optimization strategy for achieving net deep cooling of semiconductor quantum wells and related microsystems.