Anderson transition and thermal effects on electron states in amorphous silicon

I discuss the properties of electron states in amorphous Si based on large scale calculations with realistic several thousand atom models. A relatively simple model for the localized to extended (Anderson) transition is reviewed. Then, the effect of thermal disorder on localized electron states is considered. It is found that under readily accessible conditions, localized (midgap or band tail) states and their conjugate energies may fluctuate dramatically. The possible importance of non-adiabatic atomic dynamics to doped or photo-excited systems is briefly discussed.Comment: Was presented at ICAMS18, Snowbird UT, August 1999. Submitted to J. of Non-Cryst. Solid

Inversion of Diffraction Data for Amorphous Materials

The general and practical inversion of diffraction data–producing a computer model correctly representing the material explored–is an important unsolved problem for disordered materials. Such modeling should proceed by using our full knowledge base, both from experiment and theory. In this paper, we describe a robust method to jointly exploit the power of ab initio atomistic simulation along with the information carried by diffraction data. The method is applied to two very different systems: amorphous silicon and two compositions of a solid electrolyte memory material silver-doped GeSe3. The technique is easy to implement, is faster and yields results much improved over conventional simulation methods for the materials explored. By direct calculation, we show that the method works for both poor and excellent glass forming materials. It offers a means to add a priori information in first-principles modeling of materials and represents a significant step toward the computational design of non-crystalline materials using accurate interatomic interactions and experimental information

Computer simulation of low-energy excitations in amorphous silicon with voids

We use empirical molecular dynamics technique to study the low-energy vibrations in a large 4096 atom model for pure amorphous silicon and a set of models with voids of different size based on it. Numerical vibrational eigenvalues and eigenvectors for our models are obtained by exact diagonalization of their dynamical matrices. Our calculations show that localized low-energy vibrational excitations of rather complex structure are present in amorphous silicon models with voids. According to their spatial localization patterns we make an attempt to classify these excitations as modes associated with the void and "mixed" modes associated with the interaction of the void with strained regions of silicon network.Comment: Was presented at ICAMS18 conference, Snowbird UT, August 1999. Submitted to J. of Non-Cryst. Solid

Electrons and Phonons in Amorphous Semiconductors

The coupling between lattice vibrations and electrons is one of the central concepts of condensed matter physics. The subject has been deeply studied for crystalline materials, but far less so for amorphous and glassy materials, which are among the most important for applications. In this paper, we explore the electron-lattice coupling using current tools of a first-principles computer simulation. We choose three materials to illustrate the phenomena: amorphous silicon (a-Si), amorphous selenium (a-Se) and amorphous gallium nitride (a-GaN). In each case, we show that there is a strong correlation between the localization of electron states and the magnitude of thermally induced fluctuations in energy eigenvalues obtained from the density-functional theory (i.e. Kohn-Sham eigenvalues). We provide a heuristic theory to explain these observations. The case of a-GaN, a topologically disordered partly ionic insulator, is distinctive compared to the covalent amorphous examples. Next, we explore the consequences of changing the charge state of a system as a proxy for tracking photoinduced structural changes in the materials. Where transport is concerned, we lend insight into the Meyer-Neldel compensation rule and discuss a thermally averaged Kubo-Greenwood formula as a means to estimate electrical conductivity and especially its temperature dependence. We close by showing how the optical gap of an amorphous semiconductor can be computationally engineered with the judicious use of Hellmann-Feynman forces (associated with a few defect states) using molecular dynamics simulations. These forces can be used to close or open an optical gap, and identify a structure with a prescribed gap. We use the approach with plane-wave density functional methods to identify a low-energy amorphous phase of silicon including several coordination defects, yet with a gap close to that of good quality a-Si models

Optimal query complexity for estimating the trace of a matrix

Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum physics, machine learning, and pattern matching. Two metrics are commonly used for evaluating the estimators: i) variance; ii) a high probability multiplicative-approximation guarantee. Almost all the known estimators are of the form $\frac{1}{k}\sum_{i=1}^k x_i^T A x_i$ for $x_i\in \mathbb{R}^n$ being i.i.d. for some special distribution. Our main results are summarized as follows. We give an exact characterization of the minimum variance unbiased estimator in the broad class of linear nonadaptive estimators (which subsumes all the existing known estimators). We also consider the query complexity lower bounds for any (possibly nonlinear and adaptive) estimators: (1) We show that any estimator requires $\Omega(1/\epsilon)$ queries to have a guarantee of variance at most $\epsilon$. (2) We show that any estimator requires $\Omega(\frac{1}{\epsilon^2}\log \frac{1}{\delta})$ queries to achieve a $(1\pm\epsilon)$-multiplicative approximation guarantee with probability at least $1 - \delta$. Both above lower bounds are asymptotically tight. As a corollary, we also resolve a conjecture in the seminal work of Avron and Toledo (Journal of the ACM 2011) regarding the sample complexity of the Gaussian Estimator.Comment: full version of the paper in ICALP 201

Network structure and dynamics of hydrogenated amorphous silicon

In this paper we discuss the application of current it ab initio computer simulation techniques to hydrogenated amorphous silicon (a-Si:H). We begin by discussing thermal fluctuation in the number of coordination defects in the material, and its temperature dependence. We connect this to the ``fluctuating bond center detachment" mechanism for liberating H bonded to Si atoms. Next, from extended thermal MD simulation, we illustrate various mechanisms of H motion. The dynamics of the lattice is then linked to the electrons, and we point out that the squared electron-lattice coupling (and the thermally-induced mean square variation in electron energy eigenvalues) is robustly proportional to the localization of the conjugate state, if localization is measured with inverse participation ratio. Finally we discuss the Staebler-Wronski effect using these methods, and argue that a sophisticated local heating picture (based upon reasonable calculations of the electron-lattice coupling and molecular dynamic simulation) explains significant aspects of the phenomenon.Comment: 10 pages, 5 figures, accepted in J. Non. Cryst. So

Ab initio study of Cu diffusion in alpha-cristobalite

We have studied the geometries, formation energies, migration barriers and diffusion of a copper interstitial with different charge states with and without an external electric field in the α-cristobalite crystalline form of SiO2 using ab initio computer simulation. The most stable state almost throughout the band gap is charge q = + 1. The height of the migration barrier depends slightly on the charge state and varies between 0.11 and 0.18 eV. However, the charge has a strong influence on the shape of the barrier, as metastable states exist in the middle of the diffusion path for Cu with q = + 1. The heights and shapes of barriers also depend on the density of SiO2, because volume expansion has a similar effect to increase the positive charge on Cu. Furthermore, diffusion coefficients have been deduced from our calculations according to transition-state theory and these calculations confirm the experimental result that oxidation of Cu is a necessary condition for diffusion. Our molecular dynamics simulations show a similar ion diffusion, and dependence on charge state. These simulations also confirm the fact that diffusion of ions can be directly simulated using ab initio molecular dynamics.Peer reviewe

Topological and topological-electronic correlations in amorphous silicon

In this paper, we study several structural models of amorphous silicon, and discuss structural and electronic features common to all. We note spatial correlations between short bonds, and similar correlations between long bonds. Such effects persist under a first principles relaxation of the system and at finite temperature. Next we explore the nature of the band tail states and find the states to possess a filamentary structure. We detail correlations between local geometry and the band tails.Comment: 7 pages, 11 figures, submitted to Journal of Crystalline Solid

Systematic Study of Electron Localization in an Amorphous Semiconductor

We investigate the electronic structure of gap and band tail states in amorphous silicon. Starting with two 216-atom models of amorphous silicon with defect concentration close to the experiments, we systematically study the dependence of electron localization on basis set, density functional and spin polarization using the first principles density functional code Siesta. We briefly compare three different schemes for characterizing localization: information entropy, inverse participation ratio and spatial variance. Our results show that to accurately describe defect structures within self consistent density functional theory, a rich basis set is necessary. Our study revealed that the localization of the wave function associated with the defect states decreases with larger basis sets and there is some enhancement of localization from GGA relative to LDA. Spin localization results obtained via LSDA calculations, are in reasonable agreement with experiment and with previous LSDA calculations on a-Si:H models.Comment: 16 pages, 11 Postscript figures, To appear in Phys. Rev.

Anisotropic optical response of the diamond (111)-2x1 surface

The optical properties of the 2$\times$1 reconstruction of the diamond (111) surface are investigated. The electronic structure and optical properties of the surface are studied using a microscopic tight-binding approach. We calculate the dielectric response describing the surface region and investigate the origin of the electronic transitions involving surface and bulk states. A large anisotropy in the surface dielectric response appears as a consequence of the asymmetric reconstruction on the surface plane, which gives rise to the zigzag Pandey chains. The results are presented in terms of the reflectance anisotropy and electron energy loss spectra. While our results are in good agreement with available experimental data, additional experiments are proposed in order to unambiguously determine the surface electronic structure of this interesting surface.Comment: REVTEX manuscript with 6 postscript figures, all included in uu file. Also available at http://www.phy.ohiou.edu/~ulloa/ulloa.html Submitted to Phys. Rev.