Surface Green Function Matching Research Articles

Green’s function matching method for one- and zero-dimensional heterostructures

A method for the calculation of the Green's function of one-dimensional (wirelike) and zero-dimensional (boxlike) heterostructures is developed. The method is based on the formalism of surface Green's function matching (SGFM) for discrete media. The matching formulas are derived for structures consisting of an infinite ``external'' medium with an embedded array of wires (boxes), periodic in two (three) dimensions, for an arbitrary shape of the matching surface. Efficient algorithms to calculate the domain Green's functions are also proposed. Unlike the supercell methods widely used to compute the electronic structure of one- and zero-dimensional systems that scale with the supercell size, the developed approach scales with the interface size, which makes it extremely efficient to study systems such as disordered alloys, clusters of defects, and nanoscale materials. We employ it to calculate the localized and extended electronic states of a periodic array of $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{As}$ (001) nanowires using an $s{p}^{3}{s}^{*}$ tight-binding Hamiltonian with spin-orbit coupling.

SGFM and the new FISIM states

The Surface Green's Function Matching (SGFM) method is useful to distinguish the bulk effects from the surface ones since it calculates the two Green's functions separately in a neat and direct way. We have used this feature of the method to establish the correct interpretation of the Frontier Induced Semi-Infinite Medium (FISIM) states. We discuss the valence band electronic structure of the (001) oriented II–VI wide band gap zinc-blende semiconductor compounds. We have found three characteristic surface resonances besides the known bulk bands. Two of these resonances correspond to the anion-terminated surface and the third one to the cation terminated one. Further, we have shown that three non-dispersive (001)-surface-induced bulk states are also characteristic of these systems. These are neither surface nor Bloch states. These are states localized in planes perpendicular to the surface with non-vanishing spectral weight inside the bulk. They are not Bloch states since they are the consequence of the surface-boundary condition and their characteristics depend on the direction of the surface, they are therefore, surface-induced bulk states. In this talk, I briefly review our description of these systems. I also quote that similar states are present in other systems as calcopirites and at interfaces and superlattices, as well. These states are, actually, a general wave property and appear as the consequence of the boundary condition set by the presence of any frontier. For that reason, we have decided to call them Frontier Induced Semi-infinite Medium (FISIM) states.

A general-purpose approach for calculating transport in contact–molecule–contact systems: TARABORD implementation and application to a polythiophene-based nanodevice

We present a general-purpose approach for calculating quantum transport properties of contact–molecule–contact systems, based on nonequilibrium surface Green's function matching. The method is quite general and may be applied to systems described at different levels of accuracy, e.g., tight binding and ab initio. The computer program TARABORD that implements the general formalism is applied to various nanoscale systems. Our results for infinite carbon chain and porphyrin tapes are shown to be in good agreement with previous studies. We further apply the method to a polythiophene-based nanodevice and explain the main features of transport characteristics in terms of the molecular energy levels and coupling to gold nanocontacts.

Mean lifetimes of quasi‐bound electronic states in single rectangular quantum wells

A detailed theoretical study of quasi-bound electronic states in single AlGaAs/GaAs quantum wells is presented. The dependence of the full width at half maxima (FWHM) of the virtual states and their mean lifetime on the well width is revealed for quantum well widths from 10 to 500 monolayers (MLs). Series of strongly localized electronic states are found in the continuum spectra of wide quantum wells and the energy and spatial localizations of these states are investigated. The numerical calculations are performed within the frame-work of a semi-empirical sp3s* tight-binding model including spin. The Surface Green-Function Matching (SGFM) method is applied and a new numerical scheme is proposed to determine the energy position and the line shape of the quasi-bound states. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Why green functions for matching?

Work on Surface Green Function Matching (SGFM) has been the subject of extensive collaborations with members of the Iberoamerican community of solid state physicists. The conceptual frame, the basic general results and their meaning, form and generality of scope are discussed. The practical aspects of SGFM calculations are discussed, with attention to formal arguments which prove useful in practice and to computational transfer matrix techniques. A wide range of selected applications are presented. The approach taken is a historical—not strictly chronological—perspective with emphasis on the significance of the results in their own time, as well as a reflection of the collaborations with many members of this community.

Electronic structure of (001) GaN/AlN quantum wells

Abstract The electronic structure of (0 0 1) GaN/AlN quantum wells at the Γ ¯ point of the Brillouin zone is studied for 2 ⩽ n ⩽ 50, where n is the number of principal layers of GaN in the well region. The calculations are based on a surface Green-function matching analysis together with two different empirical tight-binding models. We study the influence of the strain and the spin–orbit coupling on the quantum well states.

Electronic properties of quasiperiodic heterostructures

We study the electronic states of different GaAs-AlAs Fibonacci, Thue-Morse and Rudin-Shapiro quasiperiodic heterostructures grown along the [001] direction. We employ an empirical tight-binding Hamiltonian including spin-orbit coupling together with the surface Green-function matching method. We present results for different generations of the quasiperiodic heterostructures, formed by different building blocks. We compare these results with those of the constituent quantum wells and with those of heterostructures containing the same total number of GaAs and AlAs slabs after periodic repetition of the building blocks. The states in the energy regions near the conduction- and valence-band edges of GaAs do not exhibit any spectrum fragmentation. They show a strong localization of the local density of states in the GaAs layers, and they can be traced to the states of the isolated quantum wells.

Elastic waves in quasiperiodic structures

We study the transverse and sagittal elastic waves in different quasiperiodic structures by means of the full transfer-matrix technique and surface Green-function matching method. The quasiperiodic structures follow Fibonacci, Thue-Morse and Rudin-Shapiro sequences, respectively. We consider finite structures having stress-free bounding surfaces and different generation orders, including up to more than 1000 interfaces. We obtain the dispersion relations for elastic waves and spatial localization of the different modes. The fragmentation of the spectrum for different sequences is evident for intermediate generation orders, in the case of transverse elastic waves, whereas, for sagittal elastic waves, higher generation orders are needed to show clearly the spectrum fragmentation. The results of Fibonacci and Thue-Morse sequences exhibit similarities not present in the results of Rudin-Shapiro sequences.

Electronic properties of near-surface GaAs/Al xGa 1− xAs quantum wells

Two-dimensional systems such as quantum wells confined on one side by a quasi-infinite barrier and on the other by a very thin variable barrier layer show interesting features. Experimental results show a strong red-shift [1] and, a opposing blue-shift [2] on the transition energy. In order to determine which of the two results is correct, here we study theoretically the electronic properties of near-surface GaAs/Ga x Al 1− x As quantum wells using an empirical Tight-Binding Hamiltonian together with the Surface Green Function Matching (SGFM) method. We study the effect of the width of the variable barrier on the energy values and the spatial localization of the different states on this heterostructure.

Surface Waves at the Interface Between two ViscousFluids

The Surface Green Function Matching analysis (SGFM) is used tostudy the normal modes of the interface oscillations between twonon-mixed fluids by considering the difference in their densities andviscosities. The limiting case of viscous–inviscid system isused for comparison. The role of the viscosity and the density ratioson the momentum exchange and on the polarization of the surface modesis analyzed.

Thomas-Fermi approximation in a tight-binding calculation ofδ-doped quantum wells in GaAs

We present a tight-binding calculation of the electronic structure of $\ensuremath{\delta}$-doped quantum wells in GaAs. A self-consistent potential obtained in the Thomas-Fermi approximation is considered as an external potential in our tight-binding model. A spin-dependent ${\mathrm{sp}}^{3}{s}^{*}$ basis is used and nearest neighbors are considered to treat GaAs bulk crystals doped with Si or Be. We change the semiempirical Hamiltonian matrix of the (001) direction in each atomic layer, adding the value of the self-consistent external potential in this layer to all diagonal elements of the matrix. The inhomogeneous $\ensuremath{\delta}$-doped finite region is matched with two semi-infinite homogeneous GaAs barriers within the framework of the surface Green-function matching method. We compare the tight-binding results with the results obtained in the envelope-function approximation and with the experimental data available for the Si- and Be-doped GaAs.

Sagittal elastic waves in Fibonacci superlattices

We study the sagittal elastic waves propagating along the [100] direction in Fibonacci superlattices, formed by the repetition of GaAs and AlAs slabs in $A$ and $B$ constituent blocks following the Fibonacci sequence.We consider infinite repetition of a given Fibonacci generation and the finite Fibonacci generation with free surfaces, as a comparison. We have considered in our study systems ranging from the second to the eighth generation. We employ the surface Green-function matching for $N$ nonequivalent interfaces to obtain the dispersion relation and the density of states of the different systems. In this way it is possible to obtain the spatial localization of the different modes. We have studied the influence of the increasing Fibonacci generations on the dispersion relation of the sagittal elastic modes.

Electronic surface configuration of thePt3Mn(111)and layered2×2Pt/Pt3Mn(111)compounds

The (111) surface electronic structure of stable intermetallic compounds of diluted Mn concentration within a Pt matrix is studied by means of a surface Green-function matching method, based on an empirical tight-binding parametrization scheme. From the calculated density of states, enhanced values of the giant Mn magnetic moments are found at the surface: $3.5{\ensuremath{\mu}}_{B}$ and $3.2{\ensuremath{\mu}}_{B}$ for the ${\mathrm{Pt}}_{3}\mathrm{Mn}$ and ${\mathrm{P}\mathrm{t}/\mathrm{P}\mathrm{t}}_{3}\mathrm{Mn}$ structures, respectively.

Efficient method for the simulation of STM images. I. Generalized Green-function formalism

We present a theoretical formalism specially suited for the simulation of scanning tunneling microscopy (STM) images. The method allows for a realistic description of the STM system, taking fully into account its three-dimensional nature. Bias effects may also be considered since the theory is not restricted to the low-bias limit. The starting point is the previously applied Landauer-B\"uttiker formula, which expresses the current at the STM junction as a sum of transmission coefficients linking eigenstates at each electrode. The transmission coefficients are directly obtained from the scattering matrix which is, in our approach evaluated through Green-function techniques; in particular, we employ the surface Green-function matching (SGFM) method to find the Green function at the interface, and explicitly derive simple expressions for the current. Additionally, the formalism goes beyond the elastic-scattering limit by considering inelastic effects via an optical potential. We also present a method to analyze the current in terms of contributions arising from individual atomic orbital interactions and their interference with other interactions. To this end, the SGFM method is replaced by a first-order expansion of the interface Green function.

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

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

Simultaneous surface Green's-function matching for discrete systems with N interfaces

The surface Green's-function matching (SGFM) method for discrete systems is extended to the case of arbitrary multilayer structures, so that matching is simultaneously effected at an arbitrary number N of interfaces. In this way all the SGFM formulas are obtained in a compact 2 N × 2 N supermatrix form, ready for practical calculations. As an illustration, the vibrational properties of multilayer one-dimensional systems are considered.

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.

Electronic states of a semi-infinite superlattice with an embedded quantum well

We study the electronic states at the Gamma point of a heterostructure, formed by a semiinfinite substrate (AlAs), a well material (GaAs) and a semi-infinite superlattice (AlAs/GaAs), grown along the (001) direction. We employ an empirical tight binding (ETB) Hamiltonian together with the surface Green function matching (SGFM) method. We study the effect of the well layer width and the relative thicknesses of the layers forming the superlattice on the energy values and spatial localization of the different states (near the main gap at the Gamma point) of this heterostructure.

Simultaneous surface Green function matching for N interfaces

The method of surface Green function matching (SGFM) is extended to the case of an arbitrary number N of interfaces so that all the SGFM formulae are obtained in a compact N*N matrix (or supermatrix) form ready for practical calculations. As an example, shear (surface horizontal) waves in a Ni-W-Al-Ni structure are studied by a straightforward application of the general formulae. The range of applications of physical interest is stressed.

Polar optical phonons at semiconductor interfaces

We study long wave polar optical modes at semiconductor surfaces (GaAs) and interfaces (GaAs/AlAs). We have considered also the cases in which the surface or interface is kept at a fixed electrostatic potential. The spectrum of excitations then shows significant differences. The existence of localized and resonant modes has been obtained by studying the spectral strength through the surface Green function matching (SGFM) method.