Chumin Wang

An exact method to solve the diluted extended Hubbard model

Abstract In this paper, we report a new method to find an exact solution of the extended Hubbard Hamiltonian for systems with a low electronic density. This method is based on mapping the original problem onto a tight-binding case in a higher dimensional space, which can be solved exactly. For one- and two-dimensional systems, the local pairing problem of two electrons with anti-parallel spins is analyzed by looking at the binding energy and the coherence lenght for different interaction regimes. This method can be applied to study the electronic correlation in non-periodic systems.

Oxygen Absorption in Free-Standing Porous Silicon: A Structural, Optical and Kinetic Analysis

Porous silicon (PSi) is a nanostructured material possessing a huge surface area per unit volume. In consequence, the adsorption and diffusion of oxygen in PSi are particularly important phenomena and frequently cause significant changes in its properties. In this paper, we study the thermal oxidation of p+-type free-standing PSi fabricated by anodic electrochemical etching. These free-standing samples were characterized by nitrogen adsorption, thermogravimetry, atomic force microscopy and powder X-ray diffraction. The results show a structural phase transition from crystalline silicon to a combination of cristobalite and quartz, passing through amorphous silicon and amorphous silicon-oxide structures, when the thermal oxidation temperature increases from 400 to 900 °C. Moreover, we observe some evidence of a sinterization at 400 °C and an optimal oxygen-absorption temperature about 700 °C. Finally, the UV/Visible spectrophotometry reveals a red and a blue shift of the optical transmittance spectra for samples with oxidation temperatures lower and higher than 700 °C, respectively.

d-Wave hole superconductivity in low-dimensional Hubbard systems

Abstract Superconducting states with d symmetry in anisotropic hole systems are investigated within a generalized Hubbard model and the BCS framework. The results reveal a key participation of the next-nearest-neighbor correlated-hopping interaction (Δt3) in the appearance of cos k x − cos k y superconducting gap, in spite of its small strength in comparison with other terms of the model. This interaction favors the superconducting state over the phase separation, which is an important obstacle when the d-wave superconducting state is originated from an attractive nearest-neighbor density–density interaction. Furthermore, the superconducting critical temperature is highly enhanced by the low-dimensionality of the system and the gap ratio exhibits a non-BCS behavior.

Surface relaxation effects on the properties of porous silicon

In this article, surface relaxation and its effects on the electronic and structural properties of porous silicon are studied by using the total-energy pseudopotential formalism within the density-functional theory. Our model is based on a 32-atom supercell, where columns of atoms are removed and saturated with hydrogen atoms. Samples with 4.4%, 13.6%, 16.8%, 28.9%, and 41.3% porosity are analyzed in detail. The results show a clear expansion of the system along the pore direction as the porosity increases. Moreover, this expansion is very sensitive to the hydrogen-atom concentration and a linear dependence is observed. The dependence of the band gap and the effective mass on the porosity are also analyzed. Here, the hydrogen-atom number and pore shapes are observed to play a fundamental role.

A first-principles model of birefringent porous silicon

Optical properties of birefringent porous silicon (b‐PSi) layers are studied by means of the density functional theory (DFT) within the local density approximation (LDA). A systematic study of crystalline silicon (c‐Si) is performed in order to validate this DFT-LDA calculation of optical properties of semiconductors. In order to simulate b‐PSi, elliptical columns of 1–4 atoms are removed from a c‐Si supercell of 16 atoms in the [100] and [010] directions. The dangling bonds are saturated with hydrogen atoms. A geometry optimization is carried out to get the minimum energy configuration. The results of the refractive index (n) show an enhanced anisotropy and the difference Δn=n[11¯0]−n[001] agrees well with experimental data. In particular, measurements in p+ and p++ doped b‐PSi samples are consistent with the results obtained in the limit cases of pore branches along the [001] direction and the perfectly straight pores, respectively.

Ellipsometry and ab initio approaches to the refractive index of porous silicon

Spectroscopic ellipsometry is used to determine the complex refractive index (n−ik), porosity, and thickness of porous silicon (PSi) films. These films are obtained by anodizing p-type crystalline silicon in a hydrofluoric acid bath. After etching, PSi samples are heated to 750 °C in a controlled oxygen environment. A detailed analysis of the ellipsometry data is performed in order to determine the complex refractive index of PSi thin film. This frequency dependence of n and k is compared with the results of ab initio quantum mechanical calculations carried out by means of CASTEP codes within the density functional theory. The theoretical results show a diminution of the lattice constant as the oxygen content grows, in contrast to the hydrogen-saturated surface case.

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.

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.

dx2-y2 pairing in the generalized Hubbard square-lattice model

The pairing between holes in a square lattice and the two-particle wave-function symmetry are studied within a generalized Hubbard model. The key participation of the next-nearest-neighbor correlated-hopping interaction in the appearance of d-wave two-hole ground state is found, which is enhanced by the on-site repulsive Coulomb interaction. There is a clear pairing asymmetry between electrons and holes, where the hole pairing occurs in a realistic regime of interactions. The two-particle states are analyzed by looking at the binding energy, the coherence length, and the effective mass of the pairs. Finally, the case of a hole-singlet in an antiferromagnetic background is also studied.

Renormalization Plus Convolution Method for Atomic-Scale Modeling of Electrical and Thermal Transport in Nanowires

Based on the Kubo-Greenwood formula, the transport of electrons and phonons in nanowires is studied by means of a real-space renormalization plus convolution method. This method has the advantage of being efficient, without introducing additional approximations and capable to analyze nanowires of a wide range of lengths even with defects. The Born and tight-binding models are used to investigate the lattice thermal and electrical conductivities, respectively. The results show a quantized electrical dc conductance, which is attenuated when an oscillating electric field is applied. Effects of single and multiple planar defects, such as a quasi-periodic modulation, on the conductance of nanowires are also investigated. For the low temperature region, the lattice thermal conductance reveals a power-law temperature dependence, in agreement with experimental data.