(c) Dr Paul Kinsler. [Acknowledgements & Feedback]
LOCATION: CMMP, Manchester, UK, December 1998: poster presentation.
WORK DONE AT:
Institute of Microwaves and Photonics,
University of Leeds.
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AUTHORS: P. Kinsler, P. Harrison and R.W. Kelsall.
NB: The text and figures of the poster were prepared by RWK.
Asymmetric quantum wells are of technological interest for application in far-infrared intersubband lasers. These devices have the potential to provide an enormous increase in the wavelength range of solid-state photonic sources, with emission wavelengths from 5um to over 100um anticipated.
Design of intersubband lasers requires detailed knowledge of intersubband carrier dynamics.
Attention is focused on the non-radiative processes, since these dominate carrier and energy transfer.
Schematic diagram - of the single-stepped asymmetric quantum well used in the simulations. The deep well is 65Å GaAs, the shallow well (step) layer is 157Å Al0.16Ga0.84As, and the barrier layers are both Al0.24Ga0.76As. The structure is designed for optical pumping of carriers from the 1st to the 3rd subband by a 10.6(m CO2 laser, and the subband separation E3-E2 is tuned for far-infrared emission at 58um (5.2THz). A range of structures can be designed, with different emission energies, yet the same pump energy, by varying the width and Al content of the step layer.
Non-radiative transition rates were calculated using Fermi's Golden Rule: electron-LO phonon, electron-acoustic phonon, and electron-electron scattering processes were all included.
In order to obtain accurate data on intersubband dynamics, the Boltzmann transport equation must be solved. This is done via a Monte Carlo algorithm, in which the k-space trajectories of an ensemble of carriers are simulated. Each trajectory comprises a stochastic sequence of scattering events, including momentum and energy conservation rules, and stochastic selection of scattering angle from the appropriate probability distribution in each case.
For the 3-subband system, a total of 117 distinct scattering processes must be included in the simulation.
Degneracy (Pauli exclusion) is implemented by weighting the selection of a particular scattering event according to the actual subband energy distribution functions, which must be regenerated at frequent timesteps during the simulation.
The electron-electron interaction is particularly difficult to implement in a Monte Carlo algorithm. The process is treated as a 2-particle interaction, and a scattering `partner' is selected randomly from the distribution in the required subband.
Preliminary results are shown for simulations of transient cooling from non-equilibrium distributions created from an assumed optical intersubband excitation. Optical pumping with a CO2 laser tuned to the E3-E1 energy will excite electrons into the 3rd subband with an energy distribution that is an approximate replica of that in the 1st subband.
Previous calculations of scattering rates showed two main effects:
In these simulations, we use a reduced lattice temperature of TL=30K, and a moderate doping density of 10x10e10/cm2. The initial photoexcited carrier distribution was assumed to be a Fermi-Dirac distribution with Te=TL.
Transient population relaxation - following an initial photoexcitation of 4e10/cm2 electrons into the 3rd subband. Initially, a fast exponential depopulation of the 3rd subband is observed, with a lifetime of ~0.3ps. This is followed by a slower exponential decay, characterised by a lifetime of ~9ps. Note that there is virtually no repopulation of the 2nd subband, indicating that the 3-2 electron-electron scattering processes are not significant, relative to the 3-1 intersubband transitions.
Transient energy relaxation - following an initial photoexcitation of 4e10/cm2 electrons into the 3rd subband. The graph shows the average kinetic energy of electrons in each subband, and the overall average electron energy in the 3-subband system. The sharp drop in the overall average electron energy indicates strong phonon emission in the first picosecond. The peak in the 2nd subband energy indicates injection of a small number of hot carriers via 3-2 electron-electron scattering.
Transient population relaxation - following an initial photoexcitation of 1e10/cm2 electrons into the 3rd subband. Despite the reduced excitation density, and consequent increased carrier density in the lower subband, a subband lifetime of 9ps is again obtained.
Transient energy relaxation - following an initial photoexcitation of 1e10/cm2 electrons into the 3rd subband.
Transient population relaxation. For comparison, relaxation following photoexcitation into the 2nd subband was also simulated. The initial density of excited carriers was 4e10/cm2. Depopulation is again characterised by two exponential responses, the first with a lifetime of ~1ps, and the second, with a lifetime of ~40ps.
Transient energy relaxation - following an initial photoexcitation of 4e10/cm2 electrons into the 2nd subband. The energy relaxation rate is considerably slower than for the case of photoexcitation into the 3rd subband.
A Monte Carlo simulation of intersubband electron dynamics in GaAs/AlGaAs asymmetric quantum wells (AQWs) has been developed, which includes all relevant electron-phonon and electron-electron scattering processes.
Preliminary simulation results indicate that, in a suitably designed 3-subband AQW, both 3-2 electron-phonon and electron-electron scattering can be suppressed sufficiently that a population inversion between the 2nd and 3rd subbands persists following an initial photoexcitation.
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Date=19980106 21 Author=P.Kinsler