Effect of free-carrier absorption on the threshold current density of GaAs/(Al,Ga)As quantum-cascade lasers

GaAs/Al0.33Ga0.67As quantum-cascade lasers with plasmon-assisted waveguides exhibit a decreasing threshold current density j(th) with increasing wave number nu(0) of the laser line, which changes as a function of the injector doping density. We have developed an analytical approach based on the effective dielectric tensor component for the p-polarized light emitted from a quantum-cascade laser, which explains the observed dependence of j(th)(nu(0)) in terms of losses due to free-carrier absorption predominantly in the doped waveguides alpha(WG)(nu(0)). A contribution to the losses by free-carrier absorption in the quantum-cascade structure itself and subsequently to j(th) can be neglected except for very high injector doping densities. The calculated values for alpha(WG)(nu(0)) are in good agreement with the experimental data. Our approach quantitatively predicts the observed decrease of j(th) from 17 to 7 kA cm(-2) with increasing nu(0) between 900 and 1100 cm(-1). In addition to achieving a direct physical insight into the influence of free-carrier absorption on the laser performance, the proposed analytical approach provides a simple tool for the determination of the waveguide losses for any quantum-cascade laser without adopting a numerical solver. (C) 2004 American Institute of Physics.