Theoretical modeling of multiple quantum well lasers with tunneling injection and tunneling transport between quantum wells

Abstract

Multiple quantum well lasers with tunneling transport of carriers represent a new class of semiconductor lasers. Tunneling can be utilized twofold: as an injection mechanism which drives electrons from a separate confinement heterostructure into active well and also as a mechanism facilitating transport between quantum wells. Since tunneling is normally a very fast process, one can expect that employing the tunneling mechanism for transport of electrons can result in an improvement of modulation bandwidth of multiple quantum well semiconductor lasers. This assertion is justified by an analysis based on the rate equation model (analysis of the tunneling injection) and by determining differential gain (to analyze transport between wells). The analysis, done for 0.98 and 1.55 μm semiconductor lasers, suggests that in tunneling injection lasers it is possible to obtain a substantial increase of intrinsic modulation bandwidth. For the tunneling transport between wells it is shown here within a realistic model including band mixing, that an optimum range of barrier thickness exists for which the differential gain is enhanced and, consequently, the modulation bandwidth improved. A rate equation model, the choice of parameters for the model, as well as the effect of band mixing and well coupling on the optical and differential gain are described. A new formalism for the calculation of optical gain, based on work of Aversa and Iizuka [Aversa and Iizuka, IEEE J. Quantum Electron. 28, 1864 (1992)] is developed. It employs the subband energies and envelope functions determined from the Luttinger–Kohn effective mass equation including band mixing. The study performed for a system of two wells shows that the well coupling substantially shifts the spectral gain peak. The band mixing, in turn, reduces the gain peak as compared to that obtained in the parabolic model. The well coupling enhancement of the differential gain calculated with band mixing is more noticeable than that obtained in the parabolic model. It is true especially for large carrier concentrations and for barrier widths between 20 and 40 Å. Since the relaxation-oscillation frequency depends on the differential gain as fr∝G′, the predicted enhancement of G′ indicates an increase of fr, as well.

Field dependence of the carrier occupation in double-quantum-well superlattices

“…Based on kinetic equations for the density matrix, the relaxation kinetics of QCL's has been studied by emphasizing the important role of nonequilibrium phonons at the threshold current. 5,6 Other theoretical approaches relied on coupled rate equations, 7,8 calculated characteristic carrier relaxation times, [9][10][11] or focused on important peculiarities such as the energy-band nonparabolicity. 12 Recently, a kinetic treatment based on the Monte Carlo method has been reported, [13][14][15] which allows the consideration of a large variety of scattering mechanisms in a realistic manner.…”

Wigner function modeling of quantum well semiconductor lasers using classical electromagnetic field coupling

“…The original inspiration of this model arose out of an attempt to model the tunneling injection laser, [31][32][33][34] and specifically the mechanism of phonon-assisted tunneling. In future work, the QBE will be derived from Dyson's equation for nonequilibrium Greens functions.…”

Field‐induced carrier redistribution in double‐quantum‐well superlattices

“…The implementation of the respective so-called quantum-cascade laser (QCL) succeeded more than two decades later [2]. The transport properties of these periodic multiple-quantum-well structures with a large number of different layers per period have been studied theoretically both by numerical Monte Carlo simulations [3][4][5][6][7] and approximate rate equations [8][9][10][11]. Most numerical Monte Carlo results compare well with experiments.…”