In 2005, Wartak and Weetman demonstrated a self-consistent model of a quantum-well semiconductor laser in which carrier Wigner functions obeying a quantum Boltzmann equation are coupled to the optical field, so that carrier transport, gain, and the emission spectrum are computed together. The model relied on a relaxation-time description of scattering, an ad-hoc carrier-capture term for the seven-layer separate-confinement structure, an averaged Langevin-force treatment of spontaneous emission, a simplified band structure without spin-orbit self-energy terms, and it was demonstrated only in steady state; the authors explicitly left open the reduction of these approximations, the extension to dynamical properties (modulation response, turn-on transients), the application to transport-dominated devices such as the tunneling-injection laser, and validation against experimental data for different device structures. The subsequent literature is as follows: the direct Wigner-function line ended in 2007 and was continued by the same group as steady-state nonequilibrium-Green's-function laser simulations (2012), while fully microscopic many-body models based on the semiconductor Bloch equations (coupled density-matrix equations of motion for the carrier distributions and interband polarizations) achieved microscopic scattering, realistic band structure, quantitative experimental validation, and even ultrafast laser dynamics, but without longitudinal quantum transport resolution. No published work couples quantum-transport-resolved carrier dynamics and microscopic carrier capture to dynamical lasing with a fully stochastic spontaneous-emission treatment and multi-structure experimental validation; this dynamical, transport-resolved core remains open.

Background

A quantum-well (QW) semiconductor laser confines electrons and holes in a thin semiconductor layer (the well) embedded in wider-gap material; its performance is governed by how carriers are transported through barrier and cladding layers, captured into the quantized well states, scattered among those states, and recombine radiatively. Practical laser design has therefore long relied on hierarchy levels beyond simple rate equations, since phenomenological carrier lifetimes and capture times limit predictive power for new device structures. The Wigner function is a quasi-probability distribution of quantum carriers over position and momentum; its equation of motion, often called the quantum Boltzmann equation (QBE), reduces to the classical Boltzmann transport equation in the semiclassical limit while retaining genuinely quantum effects such as tunneling through barriers and quantized subbands. Weetman and Wartak (Journal of Applied Physics 93, 9562, 2003) built a QBE model of a QW laser in which carrier Wigner functions for a seven-layer separate-confinement heterostructure (SCH, the layered structure that funnels both carriers and light toward the active well) are coupled self-consistently to the electromagnetic field, so that the optical spectrum and the carrier distribution are determined together rather than one being prescribed. To keep the coupled problem tractable, several approximations were made. Carrier-carrier and carrier-phonon scattering were collapsed into a relaxation-time approximation (RTA), in which all microscopic collision processes are represented by a single phenomenological relaxation time that drives each distribution toward quasi-equilibrium. Capture of carriers from the SCH into the well entered through an ad-hoc source/loss term rather than a microscopic scattering calculation. The band structure was an effective-mass Hamiltonian without spin-orbit self-energy terms; spin-orbit coupling mixes the valence bands, and a realistic band structure requires multi-band corrections or corresponding self-energies. Spontaneous emission was represented by an averaged Langevin force, a stochastic noise term whose fluctuation correlations are replaced by their ensemble average, rather than by a fully stochastic quantum treatment. Finally, only steady-state operation was demonstrated. The dynamical laser characteristics of interest are the modulation response (the small-signal output response to sinusoidal current modulation, which bounds the maximum data rate of a directly modulated transmitter) and turn-on transients (the large-signal switching behavior when the drive current is stepped above threshold). Transport-aware dynamical laser modeling existed only at the semiclassical level, e.g. the Monte-Carlo/Boltzmann carrier-capture study of Grupen, Kosinovsky, and Hess (IEDM 1993), which established that capture limits the modulation bandwidth. A tunneling-injection laser, in which carriers enter the well by phonon-assisted tunneling through a thin barrier so that carrier heating is reduced, was proposed as an application where a quantum-transport laser model would be most valuable, since its very operating principle is a coherent transport process that rate-equation models cannot describe from first principles.

Problem Statement

Complete the Wigner-function/quantum-Boltzmann modeling program for quantum-well semiconductor lasers that Wartak and Weetman explicitly left open: construct, and validate against experimental data, a single self-consistent quantum-transport model of an edge-emitting quantum-well laser in which (1) carrier scattering is treated microscopically rather than through a relaxation-time approximation, with band structure incorporating spin-orbit coupling via the corresponding self-energy or multi-band terms; (2) carrier capture from the separate-confinement layers into the quantum well is derived from microscopic scattering theory, replacing the ad-hoc capture term introduced for the seven-layer structure; (3) spontaneous emission is treated as a fully stochastic quantum process rather than through an averaged Langevin force, that is, without replacing the fluctuation correlations of the stochastic noise term by their ensemble average; (4) the model predicts dynamical laser properties, specifically the modulation response and turn-on transients, and not only steady-state spectra and thresholds; (5) the model is applied to a transport-dominated device, for example the tunneling-injection laser, whose carrier injection proceeds via phonon-assisted tunneling; and (6) its predictions are quantitatively compared with published experimental measurements for two device structures, a conventional edge-emitting quantum-well laser and a transport-dominated tunneling-injection device, whose measurement sources and compared observables (steady-state spectra and thresholds, and the modulation response and turn-on transients of condition (4)) are identified and justified in advance of the comparison. The unifying objective is a predictive, self-consistent quantum-transport description of the quantum-well laser in which every previously phenomenological element (scattering time, capture term, averaged spontaneous-emission noise) is replaced by a microscopic one, and whose validity is established by reproduction of both steady-state and dynamical measurements. All six conditions must hold jointly in a single model for the task to be resolved; satisfying only a subset, or matching measurements only qualitatively, does not suffice, and the comparison required by condition (6) is quantitative, that is, the model's computed steady-state and dynamical characteristics must agree with those measurements within the uncertainty stated in the corresponding source or, where no uncertainty is reported, within an explicitly stated tolerance. Achievements of the individual components in adjacent frameworks (density-matrix many-body gain and ultrafast-dynamics models without transport resolution; steady-state nonequilibrium-Green's-function laser simulations) do not by themselves constitute a solution, since none couples longitudinal quantum transport and microscopic carrier capture to dynamical lasing within a validated model.

References

  1. M. S. Wartak and P. Weetman, 'Advanced Modeling of Quantum Well Semiconductor Lasers Based on Wigner Function Approach', Proceedings of the 19th International Symposium on High Performance Computing Systems and Applications (HPCS'05), pp. 288-294, 2005. DOI: 10.1109/HPCS.2005.13, https://doi.org/10.1109/HPCS.2005.13
  2. P. Weetman and M. S. Wartak, 'Wigner function modeling of quantum well semiconductor lasers using classical electromagnetic field coupling', Journal of Applied Physics 93, 9562-9575 (2003). DOI: 10.1063/1.1574180, https://doi.org/10.1063/1.1574180
  3. M. S. Wartak and P. Weetman, 'Advanced modeling of semiconductor lasers based on quantum Boltzmann equations', Microwave and Optical Technology Letters 38, 369-371 (2003). DOI: 10.1002/mop.11063, https://doi.org/10.1002/mop.11063
  4. P. Weetman and M. S. Wartak, 'Advanced Approach to Modelling Quantum Well Semiconductor Lasers Based on the Quantum Boltzmann Equation: Green's Function Approach', Journal of Computational and Theoretical Nanoscience 3, 463-478 (2006). DOI: 10.1166/JCTN.2006.3032, https://doi.org/10.1166/JCTN.2006.3032
  5. P. Weetman and M. S. Wartak, 'Self-consistent model of a nanoscale semiconductor laser using Green and Wigner functions in two bases', Physical Review B 76, 035332 (2007). DOI: 10.1103/PhysRevB.76.035332, https://doi.org/10.1103/PhysRevB.76.035332
  6. J. M. Miloszewski and M. S. Wartak, 'Semiconductor laser simulations using non-equilibrium Green's functions', Journal of Applied Physics 111, 053104 (2012). DOI: 10.1063/1.3689324, https://doi.org/10.1063/1.3689324
  7. J. M. Miloszewski, M. S. Wartak, S. G. Wallace, and S. Fafard, 'Theoretical investigation of carrier capture and escape processes in cylindrical quantum dots', Journal of Applied Physics 114, 154311 (2013). DOI: 10.1063/1.4824469, https://doi.org/10.1063/1.4824469
  8. M. S. Wartak, 'Introduction to Simulations of Semiconductor Lasers', CRC Press (2024). DOI: 10.1201/9781003265849, https://doi.org/10.1201/9781003265849
  9. S. Steiger, R. G. Veprek, and B. Witzigmann, 'Unified simulation of transport and luminescence in optoelectronic nanostructures', Journal of Computational Electronics 7, 509-520 (2008). DOI: 10.1007/s10825-008-0261-Z, https://doi.org/10.1007/s10825-008-0261-Z
  10. A. Wacker, M. Lindskog, and D. O. Winge, 'Nonequilibrium Green's Function Model for Simulation of Quantum Cascade Laser Devices Under Operating Conditions', IEEE Journal of Selected Topics in Quantum Electronics 19, 1-11 (2013). DOI: 10.1109/JSTQE.2013.2239613, https://doi.org/10.1109/JSTQE.2013.2239613
  11. J. Hader, J. V. Moloney, and S. W. Koch, 'Microscopic evaluation of spontaneous emission- and Auger-processes in semiconductor lasers', IEEE Journal of Quantum Electronics 41, 1217-1226 (2005). DOI: 10.1109/JQE.2005.854127, https://doi.org/10.1109/JQE.2005.854127
  12. I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, 'Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking', Optica 1, 192 (2014). DOI: 10.1364/OPTICA.1.000192, https://doi.org/10.1364/OPTICA.1.000192
  13. I. Kilen, S. W. Koch, J. Hader, and J. V. Moloney, 'Fully microscopic modeling of mode locking in microcavity lasers', Journal of the Optical Society of America B 33, 75 (2016). DOI: 10.1364/JOSAB.33.000075, https://doi.org/10.1364/JOSAB.33.000075
  14. K. Böhringer and O. Hess, 'A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation', Progress in Quantum Electronics 32, 159-246 (2008). DOI: 10.1016/j.pquantelec.2008.10.002, https://doi.org/10.1016/j.pquantelec.2008.10.002
  15. H. Wenzel, M. Kantner, M. Radziunas, and U. Bandelow, 'Semiconductor Laser Linewidth Theory Revisited', Applied Sciences 11, 6004 (2021). DOI: 10.3390/app11136004, https://doi.org/10.3390/app11136004
  16. D.-S. Han and L. V. Asryan, 'Output power of a double tunneling-injection quantum dot laser', Nanotechnology 21, 015201 (2009). DOI: 10.1088/0957-4484/21/1/015201, https://doi.org/10.1088/0957-4484/21/1/015201
  17. J. Weinbub and D. K. Ferry, 'Recent advances in Wigner function approaches', Applied Physics Reviews 5, 041104 (2018). DOI: 10.1063/1.5046663, https://doi.org/10.1063/1.5046663
  18. M. Grupen, G. Kosinovsky, and K. Hess, 'The effect of carrier capture on the modulation bandwidth of quantum well lasers', Proceedings of the IEEE International Electron Devices Meeting (IEDM), pp. 609-612 (1993). DOI: 10.1109/IEDM.1993.347285, https://doi.org/10.1109/IEDM.1993.347285
  19. A. Grabowski, J. S. Gustavsson, and A. Larsson, 'Impact of Carrier Transport and Capture on VCSEL Dynamics', IEEE Journal of Quantum Electronics 59, 1-6 (2023). DOI: 10.1109/JQE.2023.3236396, https://doi.org/10.1109/JQE.2023.3236396