Application of multi-subband self-consistent energy balance method to terahertz quantum cascade lasers

Abstract

We present simulation results for two resonant phonon terahertz quantum cascade lasers using a self-consistent energy balance model, which determines the electron temperature for each conduction subband. These temperatures, along with the electron populations and scattering rates, are determined in a manner similar to previously published models. However, the presented model is able to converge through the use of an algorithm that appears to be robust. The predicted individual subband electron temperatures, population densities and scattering rates are compared to previously published Monte Carlo and experimental studies for both lasers, where subband temperature variations were observed. These quantities were chosen since they provided the only comparison to modeling results from other studies.

Modeling techniques for quantum cascade lasers

“…Since the assumption of a single effective electron temperature is not always adequate in QCLs, 175 extended approaches have been developed allowing for different effective temperatures T i in the individual subbands. 93…”

“…The most basic model of laser gain media in general is the rate equation approach, 88 which is also frequently applied to QCLs. 77,[89][90][91][92][93][94] The electron transport is simply described by transition rates between the relevant energy levels in the gain medium. In the case of the QCL, these are the electron subbands, and the corresponding transitions are referred to as intersubband transitions.…”

“…Offering a compromise between accuracy and predictive power on the one hand and relative numerical efficiency on the other hand, the self-consistent rate equation approach is widely used for the simulation of QCLs. 67,77,[91][92][93]173 Although extensions of the selfconsistent rate equation approach to include the light field have been presented, 77 the optical cavity field is neglected in most cases. Such simulations yield the unsaturated population inversion or gain, indicating if lasing can start at all, but giving no information about the actual lasing operation.…”

Temperature performance of terahertz quantum-cascade lasers with resonant-phonon active-regions

“…It is to be noted that electron temperature in various subbands is expected to be higher than the lattice temperature, and a temperature differential in the range of 0-100 K has been predicted for resonant-phonon THz QCLs, which also varies for different subbands. This was determined by both numerical calculations [37,43] as well as experimental observations [44]. The shown electrontransport mechanisms directly or indirectly lead to a reduction in the population inversion Δn ul in the QCL superlattice, and hence terahertz gain as in equation (1).…”

Temperature degradation of 2.3, 3.2 and 4.1 THz quantum cascade lasers

“…Secondly, the experimental study of the corresponding mechanisms is hampered by the fact that the temperature of the electronic subsystem differs significantly from the heat removal temperature at T 100 K [7][8][9]. Thirdly, all known studies of the thermal attenuation of the generation of pulsed lasers, as well as studies of lasers with record operating temperatures, were carried out at short pulse durations i.e.…”