Simulation of optically pumped mid-infrared intersubband semiconductor laser structures

Abstract

A theoretical self-consistent investigation of optically pumped mid-infrared intersubband semiconductor laser with hot electron effects is presented. Electron dynamics under optical pumping are investigated within a rate equation formulation where particle and energy flow equations are derived from Boltzmann’s equation using Fermi statistics. Electron-polar optical phonon interactions with suitable screening are calculated by using a macroscopic model with slab and interface phonon modes. Our calculations show that despite hot electron effects, population inversion between the first and second excited states can occur at low temperatures under intersubband optical excitation. It is anticipated that lasing in the mid-infrared can be achieved with asymmetric quantum well structures optimized for electron concentrations exceeding 1011/cm2.

Gain optimization in optically pumped AlGaAs unipolar quantum-well lasers

“…At the end of this section, we will briefly discuss the confidence limits of the obtained results, in view of the fact that there is a bit of a spread of values of various material parameters in the literature, e.g., [26], [33]- [35], and a considerably larger spread of the values of the transition linewidth , e.g., [17], [35], [24].…”

“…To obtain more generally applicable results, and in view of the fact that the first term in (3) is much more important than the second one, in this work we choose to optimize only the first term. The quantities in it depend on the QW profile (the transition lifetimes are only weakly dependent on the pump intensity [17], so this may be neglected), and do not depend on and . Only later, when checking the gain in the final design, will we use the exact expression (1).…”

“…Taking the refractive index (for the phase velocity) in the GaAs-AlGaAs alloy to be [15] and the transition line width meV [17], [24] at K, the transition cross section is given by cm meV Â . Therefore, the gain in the optically pumped intersubband laser is proportional to the factor (4) in which only those terms relevant for this work (i.e., which can be varied by suitable tailoring of the QW profile) are retained.…”

“…The function may be written as (16) and if has no zeros, the integral remains finite for any value of . To ensure that, under this condition, also has no zeros, the free parameter should satisfy (17) By varying the parameter in the allowed range, one gets the family of isospectral potentials (18) which all have the energy spectrum identical to that of the initial potential , with an additional real state at . To make the function , which has no zeros, we write it as the linear combination of particular solutions of the Schrödinger equation (19) satisfying the boundary conditions and .…”

“…To some extent, this problem may be overcome by optimizing the asymmetric coupled QWs (ACQW), and by increasing the spacing between the ground state and lower laser state, though this drives the electron-phonon relaxation process away from resonance [16]. In further, more advanced design considerations, the influence of interface and confined phonons on electron relaxation times, as well as on carrier heating, for a range of optical pump powers, has also been included [17], [18]. Finally, we note that the optimization of the gain/loss ratio was also considered [19], [20].…”