arXiv subjects
Publications and source records attributed to Daniel Mourad.
The lefthanded Lov\'asz local lemma (LLLL) is a generalization of the Lov\'asz local lemma (LLL), a powerful technique from the probabilistic method. We prove a computable version of the LLLL and use it to effectivize a collection of results on the existence of certain types of non-repetitive sequences via the LLL and LLLL. This represents the first constructive proof of these results.
We show that, in general, there is no degree corresponding to the composition of two problems in the computable reducibility lattice.
We investigate how external screening shapes excitons in two-dimensional (2d) semiconductors embedded in laterally structured dielectric environments. An atomic scale view of these elementary excitations is developed using models which apply to a variety of materials including transition metal dichalcogenides (TMDCs). We find that structured dielectrics imprint a peculiar potential energy landscape on excitons in these systems: While the ground-state exciton is least influenced, higher excitations are attracted towards regions with high dielectric constant of the environment. This landscape is "inverted" in the sense that low energy excitons are less strongly affected than their higher energy counterparts. Corresponding energy variations emerge on length scales of the order of a few unit cells. This opens the prospect of trapping and guiding of higher excitons by means of tailor-made dielectric substrates on ultimately small spatial scales.
We argue that the experimentally easily accessible optical absorption spectrum can often be used to distinguish between a random alloy phase and a stoichiometrically equivalent core/shell realization of ensembles of monodisperse colloidal semiconductor quantum dots without the need for more advanced structural characterization tools. Our proof-of-concept is performed by conceptually straightforward exact-disorder tight-binding calculations. The underlying stochastical tight-binding scheme only parametrizes bulk band structure properties and does not employ additional free parameters to calculate the optical absorption spectrum, which is an easily accessible experimental property. The method is applied to selected realizations of type-I Cd(Se,S) and type-II (Zn,Cd)(Se,S) alloyed quantum dots with an underlying zincblende crystal structure and the corresponding core/shell counterparts.
We report on a combined theoretical and experimental determination of the Fermi level position in wurtzite Ga$_{1-x}$Mn$_{x}$N films with $x=4\%$ and $x=10\%$ as grown by molecular beam epitaxy. By means of ellipsometric measurements the real part of the frequency-dependent conductivity is determined. An electronic model in the framework of the effective bond-orbital model is parameterized in order to theoretically reproduce the measured transport properties. Predictions for the long-wavelength behaviour as a function of the Fermi level are made. The corresponding density of states obtained in this model is in qualitative agreement with first-principle calculations. The absence of a significant experimental peak in the AC conductivity for small frequencies indicates that the Fermi level lies in a gap between two Mn-related impurity bands in the host band gap.
Starting with empirical tight-binding band structures, the branch-point (BP) energies and resulting valence band offsets (VBOs) for the zincblende phase of InN, GaN and AlN are calculated from their k-averaged midgap energy. Furthermore, the directional dependence of the BPs of GaN and AlN is discussed using the Green's function method of Tersoff. We then show how to obtain the BPs for binary semiconductor alloys within a band-diagonal representation of the coherent potential approximation (CPA) and apply this method to cubic AlGaN alloys. The resulting band offsets show good agreement to available experimental and theoretical data from the literature. Our results can be used to determine the band alignment in isovalent heterostructures involving pure cubic III-nitrides or AlGaN alloys for arbitrary concentrations.
We present a combined experimental and theoretical approach for the determination of the low-temperature valence band offset (VBO) at CdSe/ZnTe heterojunctions with underlying zincblende crystal structure. On the experimental side, the optical transition of the type II interface allows for a precise measurement of the type II band gap. We show how the excitation-power dependent shift of this photoluminescence (PL) signal can be used for any type II system for a precise determination of the VBO. On the theoretical side, we use a refined empirical tight-binding parametrization in order to accurately reproduce the band structure and density of states around the band gap region of cubic CdSe and ZnTe and then calculate the branch point energy (also known as charge neutrality level) for both materials. Because of the cubic crystal structure and the small lattice mismatch across the interface, the VBO for the material system under consideration can then be obtained from a charge neutrality condition, in good agreement with the PL measurements.
For a wide class of technologically relevant compound III-V and II-VI semiconductor materials AC and BC mixed crystals (alloys) of the type A(x)B(1-x)C can be realized. As the electronic properties like the bulk band gap vary continuously with x, any band gap in between that of the pure AC and BC systems can be obtained by choosing the appropriate concentration x, granted that the respective ratio is miscible and thermodynamically stable. In most cases the band gap does not vary linearly with x, but a pronounced bowing behavior as a function of the concentration is observed. In this paper we show that the electronic properties of such A(x)B(1-x)C semiconductors and, in particular, the band gap bowing can well be described and understood starting from empirical tight binding models for the pure AC and BC systems. The electronic properties of the A(x)B(1-x)C system can be described by choosing the tight-binding parameters of the AC or BC system with probabilities x and 1-x, respectively. We demonstrate this by exact diagonalization of finite but large supercells and by means of calculations within the established coherent potential approximation (CPA). We apply this treatment to the II-VI system Cd(x)Zn(1-x)Se, to the III-V system In(x)Ga(1-x)As and to the III-nitride system Ga(x)Al(1-x)N.
Zero-dimensional nanocrystals, as obtained by chemical synthesis, offer a broad range of applications, as their spectrum and thus their excitation gap can be tailored by variation of their size. Additionally, nanocrystals of the type ABC can be realized by alloying of two pure compound semiconductor materials AC and BC, which allows for a continuous tuning of their absorption and emission spectrum with the concentration x. We use the single-particle energies and wave functions calculated from a multiband sp^3 empirical tight-binding model in combination with the configuration interaction scheme to calculate the optical properties of CdZnSe nanocrystals with a spherical shape. In contrast to common mean-field approaches like the virtual crystal approximation (VCA), we treat the disorder on a microscopic level by taking into account a finite number of realizations for each size and concentration. We then compare the results for the optical properties with recent experimental data and calculate the optical bowing coefficient for further sizes.
Compound semiconductor alloys of the type ABC find widespread applications as their electronic bulk band gap varies continuously with x, and therefore a tayloring of the energy gap is possible by variation of the concentration. We model the electronic properties of such semiconductor alloys by a multiband tight-binding model on a finite ensemble of supercells and determine the band gap of the alloy. This treatment allows for an intrinsic reproduction of band bowing effects as a function of the concentration x and is exact in the alloy-induced disorder. In the present paper, we concentrate on bulk CdZnSe as a well-defined model system and give a careful analysis on the proper choice of the basis set and supercell size, as well as on the necessary number of realizations. The results are compared to experimental results obtained from ellipsometric measurements of CdZnSe layers prepared by molecular beam epitaxy (MBE) and photoluminescence (PL) measurements on catalytically grown CdZnSe nanowires reported in the literature.
A multiband empirical tight-binding model for group-III-nitride semiconductors with a wurtzite structure has been developed and applied to both bulk systems and embedded quantum dots. As a minimal basis set we assume one s-orbital and three p-orbitals, localized in the unit cell of the hexagonal Bravais lattice, from which one conduction band and three valence bands are formed. Non-vanishing matrix elements up to second nearest neighbors are taken into account. These matrix elements are determined so that the resulting tight-binding band structure reproduces the known Gamma-point parameters, which are also used in recent kp-treatments. Furthermore, the tight-binding band structure can also be fitted to the band energies at other special symmetry points of the Brillouin zone boundary, known from experiment or from first-principle calculations. In this paper, we describe details of the parametrization and present the resulting tight-binding band structures of bulk GaN, AlN, and InN with a wurtzite structure. As a first application to nanostructures, we present results for the single-particle electronic properties of lens-shaped InN quantum dots embedded in a GaN matrix.
In this work we present a comparison of multiband k.p-models, the effective bond-orbital approach, and an empirical tight-binding model to calculate the electronic structure for the example of a truncated pyramidal GaN/AlN self-assembled quantum dot with a zincblende structure. For the system under consideration, we find a very good agreement between the results of the microscopic models and the 8-band k.p-formalism, in contrast to a 6+2-band k.p-model, where conduction band and valence band are assumed to be decoupled. This indicates a surprisingly strong coupling between conduction and valence band states for the wide band gap materials GaN and AlN. Special attention is paid to the possible influence of the weak spin-orbit coupling on the localized single-particle wave functions of the investigated structure.