Localization of non-interacting electrons in thin layered disordered systems

Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov exponent. The results support the one-parameter scaling hypothesis for disorder strengths W studied and b=1,...,6. The obtained results for the localization length are in good agreement with both the analytical results of the self-consistent theory of localization and the numerical scaling studies of the two-dimensional Anderson model. The localization length near the band center grows exponentially with b for fixed W but no localization-delocalization transition takes place.Comment: 6 pages, 5 figure

Possibility of two types of localized states in a two-dimensional disordered lattice

We report results of our numerical calculations, based on the equation of motion method, of dc electrical conductivity, and of density of states for up to 40×40 two-dimensional square lattices modeling a tight-binding Hamiltonian for a binary (AB) compound, disordered by randomly distributed B vacancies up to 10%. Our results indicate strongly localized states away from band centers separated from the relatively weakly localized states towards midband. This is in qualitative agreement with the idea of a "mobility edge" separating exponentially localized states from the power-law localized states as suggested by the two-parameter scaling theory of Kaveh in two dimensions. An alternative explanation, consistent with one-parameter scaling theory, is that the observed numerical effects may arise as a consequence of the variation of the localization length over the band

Modeling of the process of spherical form correction for rotors of electrostatically suspended gyros

Improvement of the manufacturing technology for gyroscopic devices, which autonomously generate motion parameters of moving objects, has strategic importance and priority for various industries. The object of current research is a spherical rotor of an electrostatically suspended gyroscope which geometric parameters determine the accuracy characteristics of the device. The paper presents results of the process modeling of spherical form correction for rotors of electrostatically suspended gyroscopes at the stage of its manufacture during the coating deposition process. The proposed mathematical model of the deposition process is based on the placement of a movable screen with a hole between a rotor and a spray source. The axis of the hole lies on the dynamic axis of the rotor and it provides a formation of a spherical segment on the coating rotor surface. During deposition of an additional layer, the screen or rotor moves along the dynamic axis of the rotor changing the distance between the rotor and the screen, and there is additional rotation of the rotor around its dynamic axis. It allows adjusting the curvature of the formed coating on the rotor surface. An analytical model of the technological process for correcting the shape of spherical rotors of electrostatically suspended gyroscopes has been developed. A mathematical description, control factors and significant parameters of the process are given. The results of practical testing of the developed model are presented. The presented mathematical model makes it possible to correct the shape of the rotors during the deposition of a functional coating expanding the technological possibilities and increasing the accuracy of rotors

Optical properties of structurally-relaxed Si/SiO2_2 superlattices: the role of bonding at interfaces

We have constructed microscopic, structurally-relaxed atomistic models of Si/SiO$_2$ superlattices. The structural distortion and oxidation-state characteristics of the interface Si atoms are examined in detail. The role played by the interface Si suboxides in raising the band gap and producing dispersionless energy bands is established. The suboxide atoms are shown to generate an abrupt interface layer about 1.60 \AA thick. Bandstructure and optical-absorption calculations at the Fermi Golden rule level are used to demonstrate that increasing confinement leads to (a) direct bandgaps (b) a blue shift in the spectrum, and (c) an enhancement of the absorption intensity in the threshold-energy region. Some aspects of this behaviour appear not only in the symmetry direction associated with the superlattice axis, but also in the orthogonal plane directions. We conclude that, in contrast to Si/Ge, Si/SiO$_2$ superlattices show clear optical enhancement and a shift of the optical spectrum into the region useful for many opto-electronic applications.Comment: 11 pages, 10 figures (submitted to Phys. Rev. B

Electronic structure and the minimum conductance of a graphene layer on SiO2 from density-functional methods.

The effect of the SiO$_2$ substrate on a graphene film is investigated using realistic but computationally convenient energy-optimized models of the substrate supporting a layer of graphene. The electronic bands are calculated using density-functional methods for several model substrates. This provides an estimate of the substrate-charge effects on the behaviour of the bands near $E_F$, as well as a variation of the equilibrium distance of the graphene sheet. A model of a wavy graphene layer is examined as a possible candidate for understanding the nature of the minimally conducting states in graphene.Comment: 6 pages, 5 figure

Theory of band gap bowing of disordered substitutional II-VI and III-V semiconductor alloys

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.Comment: 14 pages, 10 figure

Electric fields and valence band offsets at strained [111] heterojunctions

[111] ordered common atom strained layer superlattices (in particular the common anion GaSb/InSb system and the common cation InAs/InSb system) are investigated using the ab initio full potential linearized augmented plane wave (FLAPW) method. We have focused our attention on the potential line-up at the two sides of the homopolar isovalent heterojunctions considered, and in particular on its dependence on the strain conditions and on the strain induced electric fields. We propose a procedure to locate the interface plane where the band alignment could be evaluated; furthermore, we suggest that the polarization charges, due to piezoelectric effects, are approximately confined to a narrow region close to the interface and do not affect the potential discontinuity. We find that the interface contribution to the valence band offset is substantially unaffected by strain conditions, whereas the total band line-up is highly tunable, as a function of the strain conditions. Finally, we compare our results with those obtained for [001] heterojunctions.Comment: 18 pages, Latex-file, to appear in Phys.Rev.

Localization length in a random magnetic field

Kubo formula is used to get the d.c conductance of a statistical ensemble of two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between minus one half and plus one half of the flux quantum. The localization length is obtained from the exponential decay of the averaged conductance as a function of the cluster side. Standard results are recovered when this numerical approach is applied to Anderson model of diagonal disorder. The localization length of the complex non-diagonal model of disorder remains well below 10 000 (in units of the lattice constant) in the main part of the band in spite of its exponential increase near the band edges.Comment: 12 two-column pages including 10 figures (epsfig), revtex, to appear in PR

Linear and Second-order Optical Response of the III-V Mono-layer Superlattices

We report the first fully self-consistent calculations of the nonlinear optical properties of superlattices. The materials investigated are mono-layer superlattices with GaP grown on the the top of InP, AlP and GaAs (110) substrates. We use the full-potential linearized augmented plane wave method within the generalized gradient approximation to obtain the frequency dependent dielectric tensor and the second-harmonic-generation susceptibility. The effect of lattice relaxations on the linear optical properties are studied. Our calculations show that the major anisotropy in the optical properties is the result of strain in GaP. This anisotropy is maximum for the superlattice with maximum lattice mismatch between the constituent materials. In order to differentiate the superlattice features from the bulk-like transitions an improvement over the existing effective medium model is proposed. The superlattice features are found to be more pronounced for the second-order than the linear optical response indicating the need for full supercell calculations in determining the correct second-order response.Comment: 9 pages, 4 figures, submitted to Phy. Rev.

Multiband tight-binding theory of disordered ABC semiconductor quantum dots: Application to the optical properties of alloyed CdZnSe nanocrystals

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