Surface Green Function Matching Method Research Articles

Concentration and band offset dependence of the electronic basic transition of cubic In xGa 1−xN/In yGa 1−yN quantum wells

We calculate the transition energy from the first level of holes to the first level of electrons for cubic In x Ga 1− x N/In y Ga 1− y N quantum wells. We employ the empirical tight binding approach with an sp 3s * orbital basis, nearest neighbour interactions and the spin–orbit coupling, together with the surface Green function matching method. For the alloy, we use the virtual crystal approximation. We take into account the strain in the well. We assume a value of 0.65 eV for the InN bandgap and 3.3 eV for the GaN gap. Using a value of 20% for the valence band offset, we study the transition energy behaviour varying the well width for the sets of concentrations x=0.3, y=0.02 and y=0.05; x=0.15, y=0.05; and x=0.16, y=0. For the concentrations x=0.16, y=0, we also study the influence of the band offset using values of 20%, 50% and 80% for the valence band offset. We compare our calculations with experimental data from hexagonal and cubic quantum wells, and with other theoretical calculations for cubic quantum wells. The comparison of the calculations with the experimental results from hexagonal quantum wells is good. The theoretical energy transitions are 0.35–0.5 eV higher than those obtained experimentally for cubic quantum wells.

Quasi-bound electronic states in parabolic GaAs/AlGaAs quantum wells and barriers

A full quantum-mechanical description of the quasi-bound states in parabolic quantum wells and barriers is presented. The GaAs/AlGaAs heterostructures are considered within the framework of the semi-empirical sp3s* spin dependent tight-binding model and the surface Green function matching method (SGFM). Series of equidistant energy quasi-bound states are observed in the continuous spectrum and their FWHM and mean life time are calculated. Strong energy and spatial localizations are found in correlation with the large mean life times.

Study of the electronic fundamental transition of zincblende InN/InGaN quantum wells

In this work we calculate the transition energy from the first level of holes to the first level of electrons (1h–1e) for cubic InN/InxGa1-xN quantum wells. We employ the empirical tight binding approach with a sp3s* orbital basis, nearest neighbors interactions and the spin–orbit coupling, together with the surface Green function matching method. Our tight binding parameters give a value of 0.65eV for the InN gap and 3.3eV for GaN. For the InxGa1-xN alloy we use the virtual crystal approximation. We study the transition energy behavior varying the well width for concentrations x=0.2, 0.5, and 0.8. For the calculations, we use two values of the valence band offset: 30% and 50%. We take into account the strain in the well, due to the different lattice constants between the well and the barrier.

Electronic structure of (0 0 1) AlN/GaN quantum wells by means of a sp 3s ∗d 5 empirical tight-binding Hamiltonian

We have studied the electronic band structure of (0 0 1) AlN/GaN quantum wells by means of a sp 3s ∗d 5 empirical tight-binding Hamiltonian with nearest-neighbor interactions, including spin–orbit coupling and the effects of strain together with the surface Green function matching method. We have analyzed quantum wells with a thickness in the range 2 ⩽ n ⩽ 50, n being the number of principal layers of GaN in the well region. Results are presented for the Γ ¯ point and the Γ ¯ K ¯ direction of the 2D Brillouin zone. The orbital character and the spatial localization of the different states have been also studied.

Elastic layered waves in (001) III-V nitride systems

We have studied the acoustic waves in (001) single and multielastic wells formed by AlN, GaN, and InN in the zinc-blende structure. We have used the surface Green function matching method to obtain the dispersion relations and the local density of states. The anisotropy of the materials is included and the different propagation directions ranging from the [1,0,0] to the [1,1,0] have been considered. In these symmetry directions the sagittal waves are associated with a different velocity threshold than the transverse ones, thus showing a different behavior to that found in the isotropic case. For the [1,1,0] direction the sagittal modes are confined to a different range of velocities than the transverse modes. It has been found that the anisotropy introduces a more complex picture with a different mixing of the displacement components and the existence of different characteristics for different ranges of propagation direction.

AlN, GaN and InN (0 0 1) surface electronic band structure

We have studied the electronic band structure of the ideal (0 0 1) surface of AlN, GaN and InN in the zinc-blende phase. We have employed an empirical sp 3s ∗d 5 Hamiltonian with nearest-neighbor interactions including spin-orbit coupling and the surface Green function matching method. We have obtained the different surface states together with their corresponding orbital character and localization in the different layers. A similar physical picture is obtained for the three materials.

Elastic waves at the (0 0 1) and (1 1 0) surfaces of AlN, GaN and InN

We have studied the acoustic waves in the (0 0 1) and (1 1 0) surfaces of AlN, GaN and InN. We have employed the surface Green function matching method and different sets of calculated elastic constants available in the literature for these materials, because no experimental values are available. Important differences are found for the velocities of the bulk and surface acoustic waves coming from these sets of elastic constants, in such a way that they could be easily measured by ultrasonic and Brillouin techniques. These results together with the expressions obtained here for the velocities of the acoustic waves in high symmetry directions could be used to determine the elastic coefficients of these materials.

Tight-binding calculation of the electronic band structure of GaN, AlN and BN (0 0 1) ideal surfaces

We study the electronic band structure of the zinc-blende phase (0 0 1) ideal surface of GaN, AlN and BN by means of an empirical tight binding sp 3 s * Hamiltonian with nearest-neighbour interactions plus some second-neighbour interactions and the surface Green function matching method. We have studied both anion and cation terminated surfaces and we have obtained the different surface states with their corresponding spectral localization and orbital character.

Electronic properties of Fibonacci quasi-periodic heterostructures

We study the electronic states of different GaAs–AlAs Fibonacci quasi-perodic 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 the eighth Fibonacci generation formed from different building blocks. We compare these results with those of the constituent quantum wells and with those of heterostructures containing the same number of GaAs and AlAs slabs after periodic repetition of the building blocks. No Fibonacci spectrum is found in the energy regions near the conduction and valence band edges of GaAs. A selective localization of the local density of states in the GaAs layers is found for many electronic 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.

Elastic waves in graded-composition systems

We study the transverse and sagittal elastic waves in graded-composition systems, having a parabolic or linear grading, by means of the full transfer matrix technique and the surface Green function matching method. We obtain the velocities of the different waves as a function of the thickness of the structure, and we compare the variation of the velocities of these waves for the different profiles employed in our calculations. The spatial localization of the different modes is also considered.

Effect of non-abrupt interfaces in AlAs/GaAs superlattices with embedded GaAs quantum wells

In the present paper, we investigate the effect of the non-abrupt interfaces on the electronic and optical properties of short-period AlAs/GaAs superlattices with embedded GaAs quantum wells. The lateral disorder and the component interdiffusion at the interfaces are averaged over the layer planes and are effectively represented by a diffusion concentration profile in the growth direction. The diffusion length L D is used as a parameter characterizing the degree of interface broadening. The electronic structure calculations are made using the sp 3s * spin-dependent empirical tight-binding Hamiltonian, the virtual crystal approximation, and the surface Green function matching method. The dependencies of the lowest electron (E1), heavy hole (HH1), and light hole (LH1) bound states on the diffusion length are calculated for L D from 0 to 4 monolayers. It is found that the energies of the transitions (E1-HH1) and (E1-LH1) increase as L D increases. The results obtained are compared with photoluminescence data for MBE-grown samples. It is found that the degree of interface broadening depends on the growth temperature and on the sample geometry. The diffusion lengths calculated from the experimental data follow the expected trends, revealing a good qualitative agreement between theory and experiment.

Stark effect in diffused quantum wells

We study the longitudinal Stark effect in diffused AlGaAs/GaAs quantum wells grown along the [1,0,0] direction. The energies of the ground electron and hole states and the first excited hole state are calculated for different diffusion lengths and electric field strengths. The energies of the main optical transitions and their Stark shifts are found. The intensities of the transitions are considered in terms of the bound states spatial distributions. The calculations are carried out within the semi-empirical sp3s*tight-binding model including spin and the surface Green function matching method. We compare our results with those obtained by means of other theoretical methods.

Stark shift effects in rectangular and graded gap quantum wells

We study the Stark effect in rectangular quantum wells and in quantum wells with linear variation of the composition. The energies of the bound electronic states, the transition energies and their Stark shifts are calculated when a longitudinal electric field is applied. The spatial overlap of the electron and hole states and the intensity of the main optical transitions are considered, and their dependence on the electric field strength is discussed. We compare the Stark effect characteristics of the rectangular and graded composition quantum wells. Numerical calculations are performed within the framework of a semi-empirical sp 3s∗ tight-binding model, the virtual crystal approximation and the surface Green function matching method. A comparison between the theoretical results and the experimental data available for these systems is made, and a critical discussion is presented.

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.

Transverse elastic waves in Fibonacci superlattices

We study the transverse elastic waves propagating in 6-mm class hexagonal crystals forming Fibonacci superlattices. These are formed by repetitions of CdS and ZnO slabs in A and B constituent blocks following the Fibonacci sequence. We study the periodic superlattices formed by the infinite repetition of a given Fibonacci generation together with the finite Fibonacci generations having stress-free surfaces, in order to compare the effects introduced by the different boundary conditions. We have also considered the effects of piezoelectricity when all the interfaces are metallized and kept at a fixed potential. We use the surface Green function matching method forNnonequivalent interfaces to obtain the dispersion relations and the density of states of these systems. We have studied the influence of the increasing order of the Fibonacci generations on the dispersion relation of the transverse elastic modes. The Fibonacci spectrum is clearly seen even for low-order Fibonacci generations and is almost not modified by the piezoelectric coupling when the interfaces are metallized.

Electronic structure of (001) AlAs–InAs–GaAs multilayer structures

The electronic structure of different (001) (AlAs) m (InAs) 1(GaAs) n multilayer structures is studied. We have thus seen the influence of the relative thicknesses of the constituent materials and of the positions of the InAs principal layers in the multilayer structures on the energy eigenstates and on their spatial localization. The calculations are based on an sp 3s * empirical tight-binding model and on the surface Green function matching method.

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.

Electronic properties of GaAs - AlAs Fibonacci superlattices

We study the electronic band structure and the local density of states of different GaAs - AlAs Fibonacci superlattices grown along the [001] direction. We use an empirical tight-binding Hamiltonian including spin - orbit coupling together with the surface Green function matching method. We have analysed second-to-fifth-generation superlattices with different generating layer thicknesses. A selective localization of the local density of states in the thickest GaAs slabs is found for both the highest valence and lowest conduction band states in all of the cases considered in our study.