Inhomogeneous laser cooling of AlGaAs/GaAs semiconductor quantum well and lattice thermal diffusion

A four-step laser cooling model according to time sequence is proposed for AlGaAs/GaAs semiconductor quantum wells. The four steps are: (i) cold electrons are pumped coherently by a laser beam close to the edge of the conduction band; (ii) the photo-induced cold carriers are heated to higher energy levels via inelastic phonon scattering; (iii) the hot electrons spontaneously recombine with the hot holes, releasing photons that escape out of the system, thus subtracting from the quantum-well layer a power larger than that gained by the pumping process; (iv) phonons thermally diffuse from the barrier regions into the well region, thereby cooling the entire lattice structure. Based on this physical model, a quantum thermal-diffusion equation which includes the carrier-phonon energy exchange and the thermal radiation from environment as source terms is derived to determine the lattice temperature evolution. This gives rise to both temporal and spatial dependences of the lattice and carrier temperatures in the quantum-well structure. An energy balance equation is simultaneously derived to determine the carrier temperature adiabatically due to ultrafast carrier-phonon scattering for a given lattice temperature at any position and moment.