H. Rodríguez-Coppola

Optical properties of (001) GaN/AlN quantum wells

Abstract The absorption coefficient and the photoluminescence of (001) GaN/AlN quantum wells are calculated for several values of the well width, with and without the excitonic effect corrections, in the usual monoelectronic approach and as a many-body problem. The calculation was performed considering separate isolated bands for electrons, heavy and light holes. The monoelectronic approach to the optical properties was performed by assuming infinite well walls and finite well walls, respectively. The calculation including the excitonic effect as a many-body problem was performed within a recent approach designed for low-dimensional systems. The different wells studied here present many localized states and a complicated absorption spectrum. The monoelectronic approach in the infinite quantum well approximation reproduces quite well the spectrum of the wide wells due to the fact that the ground states of electrons and holes are well fixed by this model of quantum well.

A general theory of matching for layered systems

The problem of matching Green functions is studied for one or more coupled interfaces for those cases of physical interest, like quantum wells or superlattices, in which differential calculus is involved, e.g. Schrodinger equations. The Green functions are related to the transfer matrices of the constituent media and these can be evaluated by efficient numerical algorithms. One can then obtain the matched Green function of the composite system without having to directly evaluate any Green function or derivative thereof. The formulae for the matched wavefunction are also derived and practical aspects are discussed.

The inverse dielectric function of a quasi-two-dimensional electron gas in a quantum well: plasmons in a thin metal layer

A formal expression for the energy-loss function of a fast electron interacting with an inhomogeneous quasi-2D electron gas in a quantum well is given in the quasiclassical approximation. It uses the non-local inverse dielectric function derived in a previous paper. As an illustrative example, the plasmon dispersion relations of a thin metal film embedded in dielectric caps are calculated, taking into consideration the influence of the empty part of the electronic spectrum, the dielectric discontinuity of the system and the influence of various occupied subbands. By following the peaks of the loss function, rather than seeking zeros of the secular determinant, one can easily obtain the plasmon branches even when these enter the domains of Landau damping. For several occupied subbands the number of acoustic plasmon branches is the same as the number of occupied subbands, and the intersubband plasmon branches at q = 0 appear at energies close to each one of the transitions allowed in the system, which we call the leading transition of the plasmon branch. The depolarization effect is shown to be strongly dependent on the population of the system and on the type of the leading transition involved, i.e. a leading transition between occupied subbands or between one occupied and one empty subband. Some regularities for this effect are observed, correlating the depolarization energy with the order of the states involved as the leading transition of the plasmon mode.

Analysis of the full matched Green function and wavefunction from the transfer matrices

The full Green function of an arbitrary medium is related to its transfer matrix. For matched systems - e.g. a single heterojunction, a quantum well or a superlattice - the full matched Green function and wavefunction can be finally expressed in terms of the transfer matrices of the constituent media. These can be evaluated by efficient numerical algorithms and one then has a method for doing practical calculation. This is demonstrated by making two physical applications. The analysis is complete for problems involving one differential equation.

A study of the matching problem using transfer matrixes

An A-B-C configuration-which corresponds to various systems of physical interest, such as a barrier or a quantum well-is studied by combining a surface Green function matching analysis of the entire system with a description of the intermediate (B) region in terms of a transfer matrix in the sense of Mora and co-workers (1985). This hybrid approach proves very useful when it is very difficult to construct the corresponding Green function GB. An application is made to the calculation of quantised sub-band levels in a parabolic quantum well. Further possibilities for the extension of this approach are pointed out.

Transfer matrix and matrix Green function: the matching problem

The connection between the Green function and the transfer matrix is extended beyond the case of one single differential equation – e.g. a one band model. The Surface Green Function Matching analysis is thus performed in terms of transfer matrices when the Green functions involved are matrices. The practical use of the formalism is demonstrated by studying two physical problems. One is the spatial analysis of proximity effects associated with elementary excitations in a superconductor in contact with a normal metal or a different superconductor. The other one is a calculation of electronic states in semiconductor superlattices made of lead salts.

Multichannel transmission of holes in a multiband problem

The hole tunneling process through a single-barrier semiconductor heterostructure, modeled by a sectionally constant potential in the 4 x 4 Kohn-Luttinger model, has been studied within an elastic multichannel-multiband scattering theory by means of the transfer matrix formalism. We derive compact expressions for the relevant scattering quantities of the system in terms of the transfer matrix elements. All the amplitudes of the incident flux were taken as non-zero at the same time. Using this approach, each channels contribution to the transmission process can be identified as a function of the incoming particles energy for each hole-propagation mixed mode. In the uncoupled-channel limit, for modes with equal effective masses and m j (eigenvalue of the total angular momentum projection), the tunneling is allowed and the other paths are forbidden as expected. In the framework of our method it is possible to study intra- and inter-band transitions of m j for non-zero transversal momentum. Several inter-band conversions of m j , between modes with the same sign of Kramer degeneracy under time reversal symmetry operation, rise with the transversal momentum.

Exchange effects in multisubband plasmons in a quantum well

Exchange effects in the intra and intersubband plasmons of a quasi-two-dimensional (Q2D) electron gas confined in a quantum well are studied by means of an extension of the 3D Hubbard dielectric function to the Q2D case. This dielectric function takes full account of the multisubband structure of the spectrum of electronic states. The theory is first tested for semiconductors with a model calculation which yields the expected pattern of behaviour for low electronic densities and then used to study a metallic quantum well. The calculations included a total of ten subbands, seven of them occupied. The main effect of exchange is a tendency to stabilize the plasmon lifetimes against Landau damping. The long wave dispersion relations of the lowest 16 normal modes included in the calculation are also substantially modified.

Surface Green function matching for symmetric structures: optical phonons in a double barrier structure

Abstract A surface Green function matching (SGFM) analysis is formally developed for planar multilayer structures having mirror image symmetry so that (i) matching is effected at only one half of the interfaces and (ii) even and odd solutions are obtained separately from different factorised SGFM problems for each parity. This may be very useful in avoiding problems of numerical resolution when eigenvalues of opposite parity are closely spaced. The practical usefulness of the factorised SGFM method is demonstrated by applying it to the study of long wave polar optical phonons in a GaAs-based A-B-A-B-A double barrier resonant tunnelling structure and this is compared with the corresponding simple quantum well B-A-B in which the B barriers are semi-infinite. The results show some interesting features and indicate that, depending on design parameters, the long range electrostatic coupling across even fairly thick barriers may have strong effects on the electrical spectral strength of the modes, which should affect significantly the electron-phonon interaction

Study of the eight-band Kane model by full transfer matrix and surface Green function matching

Full Transfer Matrix and Surface Green Function Matching are applied to the practical study of layered semiconductor systems described, within the Envelope Function Approximation, by the eight-band Kane model. A practical procedure is given to sor out the numerical difficulties often arising on integrating across thick constituent layers. A numerical application for the case of HgTe/CdTe superlattice is presented. The results agree quite well with the experimental and theoretical results obtained by other methods.