Electron temperature and mechanisms of hot carrier generation in quantum cascade lasers

Abstract

A technique for calculating the temperature of the nonequilibrium electron distribution functions in general quantum well intersubband devices is presented. Two recent GaAs/Ga1−xAlxAs quantum cascade laser designs are considered as illustrative examples of the kinetic energy balance method. It is shown that at low current densities the electron temperature recovers the expected physical limit of the lattice temperature, and that it is also a function of current density and the quantised energy level structure of the device. The results of the calculations show that the electron temperature Te can be approximated as a linear function of the lattice temperature Tl and current density J, of the form Te=Tl+αe−lJ, where αe−l is a coupling constant (∼6–7 K/kA cm−2 for the devices studied here) which is fixed for a particular device.

Towards automated design of quantum cascade lasers

“…[13][14][15][16][17] However, the output characteristics of these devices are still poor in comparison to InP based mid-infrared QCLs, demanding further optimization of layer structures and investigations of the influences of relevant physical and technological parameters. 18,19 As the GaAs/ AlGaAs system is lattice matched, the alloy composition and layer width can be varied independently. In midinfrared devices, the separations between the energy states in the active region are set by the desired emission wavelength ͑between the active laser levels͒ and the longitudinal optical ͑LO͒ phonon energy ͑between the ground and lower laser level͒, which facilitates the population inversion by allowing the fast emptying of the lower laser state by means of nonradiative transitions.…”

Quantum Transport Simulation of High-Power 4.6-μm Quantum Cascade Lasers

“…The lower lasing level is considerably hotter than average, with electron temperatures in the range 2200 to 2400 K; the extractor states (not shown) have comparable temperatures to the lower lasing level. The high electron temperature in the lower lasing level is intuitively plausible: this level is populated by electrons that scattered from the upper to the lower lasing level and thus possess approximately 240 meV of excess kinetic energy (240 meV corresponds to a temperature of ∼ 2800 K) [45]. Solid horizonal lines denote the lattice temperature.…”

Design and simulation of InGaAs∕AlAsSb quantum-cascade lasers for short wavelength emission

“…The wavefunctions were then used to evaluate all the principal electron-electron and electron-LO phonon intra-and inter-period scattering rates [7]. An energy balance equation was also included in the self-consistent procedure [8] from which the electron temperature (T e ) can be evaluated. The self-consistent solution yields the nonequilibrium electron density in each of the subbands, from which the total current density J, the local gain g and the modal gain G M can be calculated.…”

“…4 at lattice temperatures of 77 and 300 K. At 77 K a linear dependence was obtained although at the higher lattice temperature there is evidence of an exponential increase in electron temperature with current density, but this can be reasonably approximated as quasi-linear. The electron-lattice coupling constants (α e-l ) were deduced from straight line fits to the data [8]. At the lower sheet doping density (N s = 2.4×10 11 cm −2 ) α e-l was calculated to be equal to 49.1 and 58.5 K/kA cm −2 at 77 and 300 K respectively.…”