Self-consistent solutions to the intersubband rate equations in quantum cascade lasers: Analysis of a GaAs/AlxGa1-xAs device

The carrier transition rates and subband populations for a GaAs/AlGaAs quantum cascade laser operating in the mid-infrared frequency range are calculated by solving the rate equations describing the electron densities in each subband self-consistently. These calculations are repeated for a range of temperatures from 20 to 300 K. The lifetime of the upper laser level found by this self-consistent method is then used to calculate the gain for this range of temperatures. At a temperature of 77 K, the gain of the laser is found to be 34 cm(-1)/(kA/cm(-2)), when only electron–longitudinal-optical phonon transitions are considered in the calculation. The calculated gain decreases to 19.6 cm(-1)/(kA/cm(-2)) when electron–electron transition rates are included, thus showing their importance in physical models of these devices. Further analysis shows that thermionic emission could be occurring in real devices. © 2001 American Institute of Physics

Monte Carlo simulations of hole transport and relaxation in the valence bands of a semiconductor quantum well

This thesis describes the development, from first principles, of a set of Monte Carlo programs to simulate the transport and relaxation of quantum confined holes. We have examined the particular case of hole dynamics in a lOOAGaAs/AlAs single quantum well. Information on the valence band energy dispersions and hole wavefunctions in the quantum well is obtained from a 4-band k.p calculation. We derive expressions for the quantum confined hole-phonon matrix elements and scattering rates which incorporate the 4-band k.p bandstructure, and present detailed results for intra- and inter-band scattering in the first four valence subbands of the quantum well. We consider scattering by acoustic (deformation potential), non-polar optical, polar optical and piezoelectric phonons. The scattering matrix elements in all cases show marked variations with the wavevectors of the scattering states, due to strong heavy - light hole mixing in the valence subbands. The phonon scattering rates show additional structure related to the regions of extremely large densities of states which exist in subband energy minimalocated away from the Brillouin zone centre. We have carried out simulations of steady state electric field heating of the quantum confined holes. The structure in the scattering rates is reflected in the low energy portions of the carrier energy distributions, and large carrier populations are found in the off-zone-centre band minima. Using the high energy tails of these distributions, we have been able to define effective temperatures for carriers in each subband. The similarity of these temperatures indicates that intersubband scattering is important in carrier thermalisation. We have obtained values for the hole energy loss rates in the steady state, which we are able to compare with experimental results. We have also undertaken a detailed study of the transient cooling of quantum confined holes, for a range of initial conditions. We use an approximate model of inelastic acoustic scattering, and include, in our results, the time dependent energy loss rates resolved into components due to intra- and inter-band scattering by optical and acoustic phonons. The relative efficiency of cooling via different numbers of subbands is compared, and the possibility of carrier trapping in the subband energy minima is critically investigated. The influence of features peculiar to the quantum well valence bandstructure, in particular, the presence of off-zone-centre energy minima, is also examined

Electron temperature and mechanisms of hot carrier generation in quantum cascade lasers

A technique for calculating the temperature of the nonequilibrium electron distribution functions in general quantum well intersubband devices is presented. Two recent GaAs/Ga(1–x)Al(x)As quantum cascade laser designs are considered as illustrative examples of the kinetic energy balance method. It is shown that at low current densities the electron temperature recovers the expected physical limit of the lattice temperature, and that it is also a function of current density and the quantised energy level structure of the device. The results of the calculations show that the electron temperature T(e) can be approximated as a linear function of the lattice temperature T(l) and current density J, of the form T(e) = T(l) + a(e–l)J, where a(e–l) is a coupling constant (~6–7 K/kA cm(–2) for the devices studied here) which is fixed for a particular device. © 2002 American Institute of Physics

Complex permittivity measurements at Ka-Band using rectangular dielectric waveguide

The rectangular dielectric waveguide (RDWG) technique has been developed for the determination of the dielectric constant of materials from effective refractive index measurements in the Q andWbands. This paper describes the use of an optimization method in conjunction with the RDWG technique for the determination of both the dielectric constant and loss tangent of materials at Ka-Band. The effect of the uncertainty in the measured sample thickness is presented

Intersubband terahertz lasers using four-level asymmetric quantum wells

We demonstrate the potential for laser operation at far-infrared wavelengths (30–300 µm, 1–10 THz) by using intersubband emission in four-level GaAs/AlGaAs asymmetric (stepped) quantum wells. Achieving population inversion in these devices depends critically on the lifetimes of the nonradiative intersubband transitions, and so we have performed detailed calculations of electron–electron and electron–phonon scattering rates. Our four-subband structures show potential for the realization of room temperature lasing, unlike previously considered three-subband structures which did not give population inversions except at impractically low electron densities and temperatures. Auger-type electron–electron interactions involving the highly populated ground subband effectively destroyed the population inversion in three level systems, but in these four subband structures the inversion is maintained by strong phonon-mediated depopulation of the lower laser level. The largest population inversions are calculated at low temperatures (< 30 K), but for the structures with higher emission energies, room temperature (300 K) operation is also predicted. © 1999 American Institute of Physics

Electric field domains in p-Si/SiGe quantum cascade structures

The formation of domains in quantum cascade structures is one of the mechanisms strongly affecting the operation of quantum cascade lasers, quantum-well infrared detectors, and other devices. In this paper, we consider the problem of domain formation in p-doped Si/SiGe quantum cascades, using a carrier scattering transport framework. In effect, the hole flow along the cascade is described via scattering between quantized states belonging to neighboring periods, caused by phonons, alloy disorder, and carrier-carrier interactions. The generation of either periodic or of nonperiodic domains is studied in uniformly doped cascades, as well as the influence of modulation doping of cascades on the domain formation

Self-consistent scattering model of carrier dynamics in GaAs-AlGaAs terahertz quantum-cascade lasers

Intersubband electron scattering transport in terahertz GaAs–AlGaAs quantum cascade lasers is analyzed, using a full 13-level self-consistent rate equation model. The approach includes all relevant scattering mechanisms between injector–collector and active region states in the cascade structures. Employing an energy balance equation which includes the influence of both electron longitudinal optical phonon and electron–electron scattering, the method also enables evaluation of the average electron temperature of the nonequilibrium carrier distributions in the device. The electron temperature is found to give a strong influence on the output characteristics, particularly at very low temperatures. The threshold currents and electric field-current density characteristics are in very good agreement with experiment, implying that the model has a strong predictive capability

Substrate orientation and alloy composition effects in n-type SiGe quantum cascade structures

We show using a theoretical self-consistent effective mass/rate equation approach that n-type SiGe-based quantum cascade lasers are potentially made viable by either using the (111) orientation or a Ge-rich substrate

Surface plasmon waveguides with gradually doped or NiAl intermetallic compound buried contact for terahertz quantum cascade lasers

mproved designs of surface plasmon waveguides for use in GaAs/AlGaAs terahertz quantum cascade lasers are presented. Modal losses and confinement factors are calculated for TM modes in metal-variably doped multilayer semiconductor and metal-intermetallic compound layer clad structures and compared with those obtained in recently realized metal-highly doped semiconductor clad layer structures. Considerable improvements of the mode confinement factors are predicted, and guidelines for choosing the confinement layer parameters are given

On the coherence/incoherence of electron transport in semiconductor heterostructure optoelectronic devices

This paper compares and contrasts different theoretical approaches based on incoherent electron scattering transport with experimental measurements of optoelectronic devices formed from semiconductor heterostructures. The Monte Carlo method which makes no a priori assumptions about the carrier distribution in momentum or phase space is compared with less computationally demanding energy-balance rate equation models which assume thermalised carrier distributions. It is shown that the two approaches produce qualitatively similar results for hole transport in p-type Si1-xGex/Si superlattices designed for terahertz emission. The good agreement of the predictions of rate equation calculations with experimental measurements of mid- and far-infrared quantum cascade lasers, quantum well infrared photodetectors and quantum dot infrared photodetectors substantiate the assumption of incoherent scattering dominating the transport in these quantum well based devices. However, the paper goes on to consider the possibility of coherent transport through the density matrix method and suggests an experiment that could allow coherent and incoherent transport to be distinguished from each other