C. R. Bennett

MULTISUBBAND HOT-ELECTRON TRANSPORT IN GAN-BASED QUANTUM WELLS

A simple rigorous analytical theory of two-dimensional (2D) nonequilibrium electrons occupying an arbitrary number of subbands in a quantum well is developed. The electric-field dependence of electron mobility and the average kinetic energy for AlN/GaN quantum wells are presented. At temperatures below 200 K the electron mobility is controlled mainly by the acoustic phonon scattering and it is a nonmonotonous function of the electric field, which has a maximum. At room and higher temperatures the interaction with both acoustic and polar optical phonons determine the hot-electron mobility and it depends very weakly on the electric field. Both the mobility and average energy of 2D electrons are smaller than that for three-dimensional (3D) electrons in the bulk semiconductor. Our theory provides a self-consistent transition from the 2D to the 3D regime of electron transport with increasing electric field accompanied by the occupation of an increasingly large number of subbands by the electrons.

Effects of a monolayer on the electron-phonon scattering rates in a quantum well: Dielectric continuum versus hybrid model

Recent publications have suggested that a reduction in the total electron-phonon scattering rate in a quantum well can be achieved by the inclusion of a monolayer of a different material. The predictions have been based upon two distinct models: the dielectric continuum (DC) model and the hybrid model. In the DC model the symmetric phonon modes are modified upon introducing the monolayer (via the electromagnetic boundary conditions) and hence a reduction in the intrasubband electron-phonon scattering rate is expected. In the hybrid model it is the antisymmetric modes that are modified and a reduction in the intersubband scattering rate is thus expected. It is shown here, however, that when the calculations are done correctly the calculated rates are approximately the same for both models if the thickness of the monolayer is vanishingly small and the electron wave functions are assumed to be unchanged. This implies that the inclusion of a monolayer of a finite thickness in a quantum well will only have a m...

The interaction of electrons with optical phonons in embedded circular and elliptical GaAs quantum wires

We consider electronic intrasubband transitions involving the confined and interface optical phonons of circular and elliptical GaAs quantum wires. Detailed treatments are given for a GaAs wire embedded in AlAs where the electrons are confined via an infinite potential barrier. The optical phonons are described using the dielectric continuum (DC) model, which for the GaAs/AlAs system compares favourably with more sophisticated macroscopic models and ab initio microscopic calculations in its prediction for the total scattering rates. The DC model has been applied previously to the circular case, bur here we evaluate the rates analytically. It is shown that the behaviour of the electrons and phonons in elliptical wires is both quantitatively and qualitatively different from that in circular wires, especially as regards angular properties.

THE BLOCH-GRUNEISEN MOBILITY OF TWO-DIMENSIONAL ELECTRON GAS IN ALGAN/GAN HETEROSTRUCTURES

We present calculations of the Bloch–Gruneisen electron mobility in zincblende (ZB) and wurtzite (WZ) AlGaN/GaN quantum-well heterostructures. Within the Boltzmann equation approach, we derive an expression for the momentum relaxation time which explicitly takes into account the Pauli principle restrictions, and show that these are comparable in importance to a screening effect at temperatures up to 150 K provided that the electron density is high. This is of particular importance for GaN-based quantum wells for which very high electron densities initiated by the strain-induced and spontaneous polarization fields have been recently reported. Dependences of the mobility on the lattice temperature and the electron density for both ZB and WZ GaN are presented, and it is shown that the WZ mobility is higher than the ZB mobility.

Quantum Capture of Injected Electrons in GaN-Based Laser Heterostructures

A theoretical analysis of the electron capture process in double quantum well heterostructures is presented. It is argued that it is necessary to distinguish between the two physically different cases of a wide separate confinement region and a narrow one. The capture parameters are investigated as a function of the quantum well width and the electron temperature of injected electrons using different models for the polar optical phonons in double heterostructures. A comparison of the electron capture is made between GaN/AlN and GaAs/AlAs structures. We show that there exist both quantitative and qualitative differences in the behaviour of the capture parameters in these heterostructures.

Electron temperature and cooling of 2D hot electron gas in deep quantum wells

Abstract The non-equilibrium kinetics of the two-dimensional electron gas in a deep quantum well is studied for qualitatively different physical situations, which are distinguished by the different strength of the electron–electron interaction. The electron temperature and the electron mobility dependences on the electric field, electron density, and the lattice temperature are presented. It is shown that at high electron density the electron temperature is a non-monotonous function of the electric field, which has a segment where the electron temperature decreases with increasing electric field. We also predict a new physical effect – the absolute cooling of the electrons whereby the electron temperature of the two-dimensional electron gas is lower than the lattice temperature.

Influences of asymmetric quantum wells on electron-phonon interactions

We calculate the electron capture rates for electrons at the bottom of the first subband above a CdSe quantum well surrounded by ZnSe and ZnS barrier layers. The electron capture mechanism is defined as the transition of an electron at the bottom of the first subband above the quantum well into all possible subbands within the quantum well by the emission of optical phonons, described here by the dielectric continuum model. The asymmetry of the structure influences the shape of the interface modes which must be taken into account together with the confined modes in each material. It is found that the capture rates depend on the width of the quantum well. At regular intervals of well width sharp peaks appear which correspond to electron and phonon resonances. Furthermore the asymmetry of the structure does not allow the capture rates to drop to very small values unlike the symmetric quantum well (e.g. GaN/AlN).

Band-gap renormalization in quantum wire systems: dynamical correlations and multi-subband effects

We study the band-gap renormalization in a model semiconductor quantum wire due to the exchange-correlation effects among the charge carriers. We construct a two-subband model for the quantum wire, and employ the GW -approximation to obtain the renormalized quasi-particle energies at the optical band edge. The renormalization is calculated as a function of electron-hole plasma density and the wire radius. Our results show that the very presence of the second subband affects the renormalization process even in the absence of occupation by the carriers. We compare the fully dynamical random-phase approximation results to the quasi-static case in order to emphasize the dynamical correlation effects. Effects of electron-phonon interaction within the two-subband model are also considered.

Confined optical phonon effects on the band gap renormalisation in quantum wire structures

Abstract We consider the different approximations for the bandgap renormalisation (BGR) within the random phase approximation (RPA), the quasi-static limit and the plasmon-pole approximation, and compare with the full result. We then include bulk optical phonons and also the phonon confinement using the phonons from the dielectric continuum (DC) model. We show that the results are very similar except at low densities where the quasi-static results overestimate the renormalisation.

The hybrid model for optical phonon confinement in AlN/GaN quantum wells

Abstract The confined optical phonons of the AlN/GaN quantum well system are described for an extended version of a continuum theory. The need for the extension is because the reststrahl bands of the two materials overlap and hence a dispersive mode from one material can propagate in the other, weakening the confinement. There is also a problem as to which mechanical boundary conditions should be used in this case. We compare total electron–phonon scattering rates in a quantum well structure for different mechanical boundary conditions and show that, because all of the phonons modes are included, the results are very similar.