Detailed formulation of energy balance equations in single quantum well devices

Abstract

An energy balance equation model coupled with drift-diffusion transport equations are solved in heterojunction p-i-n diodes with embedded single quantum well to model hot electron effects. A detailed formulation of hot electron transport is presented. In the well, the carrier energy levels are estimated from the analytical expressions applied to a quantum well with finite height. Both bound and free carriers are modeled by Fermi-Dirac statistics. Both size quantization and the two dimensional density of states in the well are considered. Thermionic emission is applied to the heterojunctions and quantum wells boundary. Energy transfer among the charge carriers and crystal lattice is modeled by an energy relaxation lifetime. Two sets of devices are simulated. First, the simulated kinetic energy and carrier density profiles were compared with published Monte Carlo results on an GaAs n þ /n/n þ diode. Second, the current-voltage characteristics of an embedded single quantum well AlGaAs/GaAs p-i-n structure was compared with measured data. Both comparisons are satisfactory and demonstrate the usefulness of the model for studying quantum well structures.

Design and Simulation of Multiquantum-Well AlGaAs/GaAs Single Junction Solar Cell with Back Surface Reflector

“…The expression for the direct kinetic energy exchange among the electron and hole carriers is based on the effective mass approximation due to optical generation for electron and holes in the bulk described in detail in articles [14,15]. The details of the device modeling and the formulations are also discussed in our previous work published in [16,17]. order to reflect unabsorbed photons from the GaAs/AlGaAs QW junction.…”