M. Cruz

Tight-binding description of disordered nanostructures : An application to porous silicon

Abstract We present the calculations of the coefficient of light (photo) absorption in porous silicon (por-Si) using the supercell tight-binding sp3s* model, in which the pores are columns digged in crystalline silicon. The disorder in the pore sizes and the undulation of the silicon wires are taken into account by considering nonvertical interband transitions. The results obtained for 8- and 32-atom supercells show a strong dependence on the pore morphology, i.e., the absorption coefficient changes with the shape and size of the silicon wires even at constant porosity. The absorption spectrum of this model for por-Si is defined by the interplay between the decrease in the indirectness of the material (connected to the absorption processes assisted by the scattering on the pores), which effectively reduces the direct gap, and the increase of the gap due to the quantum confinement.

Power law scaling of lateral deformations with universal Poisson's index for randomly folded thin sheets

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poisson’s index = 0.17 0.01, which does not depend neither the paper kind and sheet sizes thickness, edge length nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poisson’s ratio e = 0.33 0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.

Topological crossovers in the forced folding of self-avoiding matter

We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of three-dimensional plates to the folding of two-dimensional sheets, and further to the packing of one-dimensional strings, are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force–diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry, we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.

Electronic and optical properties of ordered porous germanium

The electronic band structure and dielectric function of ordered porous Ge are studied by means of a sp3s* tight-binding supercell model, in which periodical pores are produced by removing columns of atoms along [001] direction from a crystalline Ge structure and the pore surfaces are passivated by hydrogen atoms. The tight-binding results are compared with ab-initio calculations performed in small supercell systems. Due to the existence of periodicity in these systems, all the electron states are delocalized. However, the results of both electronic band structure and dielectric function show clear quantum confinement effects.

Quasi-confinement, localization and optical properties in porous silicon

Abstract The quasi-confinement concept, where electrons can find ways out through the necks between the pores, is discussed and its consequences in the localization and optical properties of porous silicon are analyzed. The polarized light absorption is studied by observing the oscillator strength behaviour. The localization is quantified using the inverse participation ratio (IPR), which gives the number of sites occupied by the wave function. The pore structure is simulated by a supercell model, where a tight-binding Hamiltonian with an sp 3 s * basis is used and empty columns of atoms are produced in an otherwise perfect silicon structure. These columns are passivated with hydrogen atoms. The results show that the bandgap broadens and the conduction band minimum shifts towards the gamma point, as the porosity increases. Likewise, the oscillator strength analysis reveals a significant enlargement of the optically active zone in the k-space, due to the localization of the wavefunction, which has been analyzed by looking at the IPR.

Vibrational states in low-dimensional structures: An application to silicon quantum wires

The Raman scattering in Si nanowires is studied by means of the local bond-polarization model based on the displacement-displacement Greens function within the linear response theory. In this study, the Born potential, including central and non-central interatomic forces, and a supercell model are used. The results show a notable shift of the main Raman peak towards lower energies, in comparison with the bulk crystalline Si case. This shift is compared with the experimental data and discussed within the quantum confinement framework.

Effect of Heterogeneity in Initial Geographic Distribution on Opinions’ Competitiveness

Spin dynamics on networks allows us to understand how a global consensus emerges out of individual opinions. Here, we are interested in the effect of heterogeneity in the initial geographic distribution of a competing opinion on the competitiveness of its own opinion. Accordingly, in this work, we studied the effect of spatial heterogeneity on the majority rule dynamics using a three-state spin model, in which one state is neutral. Monte Carlo simulations were performed on square lattices divided into square blocks (cells). Accordingly, one competing opinion was distributed uniformly among cells, whereas the spatial distribution of the rival opinion was varied from the uniform to heterogeneous, with the median-to-mean ratio in the range from 1 to 0. When the size of discussion group is odd, the uncommitted agents disappear completely after 3.30 ± 0.05 update cycles, and then the system evolves in a two-state regime with complementary spatial distributions of two competing opinions. Even so, the initial heterogeneity in the spatial distribution of one of the competing opinions causes a decrease of this opinion competitiveness. That is, the opinion with initially heterogeneous spatial distribution has less probability to win, than the opinion with the initially uniform spatial distribution, even when the initial concentrations of both opinions are equal. We found that although the time to consensus , the opinion’s recession rate is determined during the first 3.3 update cycles. On the other hand, we found that the initial heterogeneity of the opinion spatial distribution assists the formation of quasi-stable regions, in which this opinion is dominant. The results of Monte Carlo simulations are discussed with regard to the electoral competition of political parties.

Optical Absorption in Porous Silicon

The optical properties of porous silicon (p-Si) are calculated from the electronic band structure obtained by means of an sp3s* tight-binding Hamiltonian and a supercell model, in which the pores are columns detched in crystalline silicon (c-Si). The disorder in the pore sizes and the undulation of the silicon wires are considered by the existence of arandom perturbative potential, which produces non-vertical interband transitions, otherwise forbidden. A typical interval around each k-vector (optical window), where non-vertical transitions make an important contribution, depends on the value of the disorder and its order of magnitude is given by l−1, where l is the localization length. The calculated absorption spectra are compared with experiments, showing good agreement.

Quantum Effects on the Dielectric Function of Porous Silicon

In this work, the imaginary part of the dielectric function of porous silicon is studied by means of both the tight-binding and the effective medium approaches, in the latter exact result is obtained for the case of 50% porosity. Within the tight-binding approximation, the dielectric function is calculated by using the interconnected and chessboard-like supercell models for the Si skeleton. These microscopic models give quantitatively similar results, which are by a factor of three larger than those from the effective medium theory.

Computation of the Porous Silicon Dielectric Function in the Supercell Model and Comparison with Experiment

We present the results for the imaginary part of the dielectric function of porous silicon, which were obtained with the tight-binding 128–atom supercell model for different porosities. The supercells have been chosen to allow the interconnection of the Si skeleton. We have analyzed also the effects of pore morphology. We have found that, at a fixed porosity, the developing of the surface, resulting in the increase of saturating hydrogen atoms, leads to a noticeable blueshift of the absorption edge.