Karl Sabelfeld

Karl Sabelfeld
Russian Academy of Sciences | RAS

Prof., Dr.

About

240
Publications
99,847
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
2,645
Citations
Citations since 2017
64 Research Items
1060 Citations
2017201820192020202120222023050100150
2017201820192020202120222023050100150
2017201820192020202120222023050100150
2017201820192020202120222023050100150
Introduction
Karl Sabelfeld currently works at Russian Academy of Sciences. His current research iinterests are in stochastic simulation, PDEs, semiconductor simulations, nucleation, nanowire growth, randomization, iintegral equations.
Additional affiliations
January 1976 - present
Russian Academy of Sciences
Position
  • Principal Investigator, Head of a group

Publications

Publications (240)
Article
In this paper, we address a long-standing open problem in stochastic simulation: construction of a random walk on spheres (RWS) algorithm for solving a system of elasticity equations, known as the Lamé equation. Many attempts to generalize the classic probabilistic representations like the Kac formula for parabolic and scalar elliptic equations fai...
Article
A combined kinetic Monte Carlo algorithm and continuous thermodynamically based model for simulation of heterogeneous nucleation of GaN islands on a substrate under burst regime when a long incubation time is followed by a rapid nucleation of stable nuclei is developed. In this model the kinetics of GaN islands nucleation on a substrate during thei...
Article
The global random walk on grid method (GRWG) is developed for solving two-dimensional nonlinear systems of equations, the Navier–Stokes and Burgers equations. This study extends the GRWG which we have earlier developed for solving the nonlinear drift-diffusion-Poisson equation of semiconductors (Physica A 556 (2020), Article ID 124800). The Burgers...
Article
In this paper, we address the problem of flow simulation at high Péclet numbers by the random walk on spheres (RWS) method. Conventional deterministic methods here face difficulties related to high solution gradients near the boundary in the region known as the boundary layer. In the finite-difference methods, this leads to introduction of very fin...
Preprint
Full-text available
The results of a parallel implementation of a randomized vector algorithm for solving systems of linear equations are presented in the paper. The solution is represented as a Neumann series. The stochastic method computes this series by sampling only random columns, avoiding matrix-by-matrix and matrix-by-vector multiplications. We consider the cas...
Article
In this paper, we study the multiple recombination exciton–photon–exciton process governed by a coupled system of the drift-diffusion-recombination equation and the integral radiative transfer equation. We develop a random walk on spheres algorithm for solving this system of equations. The algorithm directly simulates the transient drift-diffusion...
Article
Full-text available
A meshless Random Walk on arbitrary parallelepipeds simulation algorithm is developed and implemented for solving transient anisotropic diffusion-reaction equations. In contrast to the conventional Feynman-Kac based algorithm the suggested method does not use small time step simulations of the relevant diffusion processes. Instead, exact simulation...
Article
The present study addresses the sensitivity analysis of particle concentration dispersion in the turbulent flow. A stochastic spectral model of turbulence is used to simulate the particle transfer. Sensitivity analysis is performed by estimations of Morris and Sobol indices. This study allows to define the significant and nonsignificant model param...
Article
Randomized scalable vector algorithms for calculation of matrix iterations and solving extremely large linear algebraic equations are developed. Among applications presented in this paper are randomized iterative methods for large linear systems of algebraic equations governed by M-matrices. The crucial idea of the randomized method is that the ite...
Article
The determination of the carrier diffusion length of semiconductors such as GaN and GaAs by cathodoluminescence imaging requires accurate knowledge about the spatial distribution of generated carriers. To obtain the lateral distribution of generated carriers for sample temperatures between 10 and 300 K, we utilize cathodoluminescence intensity prof...
Article
Full-text available
A Global Random Walk on Spheres (GRWS) algorithm for calculating the solution and its derivatives of drift‐diffusion‐reaction equations in any desired set of points is suggested. The GRWS algorithm is able to find the solution and derivative fields in any family of points simultaneously, using only one ensemble of random walks which drastically dec...
Article
In this paper, we present and study highly efficient stochastic methods, including optimal super convergent methods for multidimensional sensitivity analysis of large-scale ecological models and digital twins. The computational efficiency (in terms of relative error and computational time) of the stochastic algorithms for multidimensional numerical...
Article
In this letter we suggest a new randomized scalable stochastic-matrix-based algorithms for calculation of large matrix iterations. Special focus is on positive or irreducible nonnegative class of matrices. As an application, a new randomized vector algorithm for iterative solution of large linear systems of algebraic equations governed by M-matrice...
Article
A stochastic model of nanocrystals clusters formation is developed and applied to simulate an aggregation of cadmium sulfide nanocrystals upon evaporation of the Langmuir–Blodgett matrix. Simulations are compared with our experimental results. The stochastic model suggested governs mobilities both of individual nanocrystals and its clusters (arrays...
Article
We further develop in this study the Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion-recombination equations first suggested in our recent article [K. Sabelfeld, First passage Monte Carlo algorithms for solving coupled systems of diffusion–reaction equations, Appl. Math. Lett. 88 2019, 141–148]. The random...
Article
In this paper we develop stochastic simulation methods for solving large systems of linear equations, and focus on two issues: (1) construction of global random walk algorithms (GRW), in particular, for solving systems of elliptic equations on a grid, and (2) development of local stochastic algorithms based on transforms to balanced transition matr...
Article
A parallel implementation of a three-dimensional cellular automaton (CA) model of electron — hole transport in a semiconductor is presented. Carriers transport is described by a nonlinear system of drift-diffusion-Poisson equations. This system includes the drift-diffusion equations in divergence form for electrons and holes and the Poisson equatio...
Article
We suggest in this paper a global random walk on grid (GRWG) method for solving second order elliptic equations. The equation may have constant or variable coefficients. The GRWS method calculates the solution in any desired family of m prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman–Kac for...
Article
Full-text available
We suggest in this paper a parallel implementation of cellular automation and global random walk algorithms for solving drift–diffusion–recombination problems which in contrast to the classical random walk on spheres (RWS) methods calculate the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to...
Article
Monte Carlo algorithms are developed to simulate the electron transport in semiconductors. In particular, the drift velocity in GaN semiconductors is calculated, and a comparison with experimental measurements is discussed. Explicit expressions for the scattering probabilities and distributions of the scattering angle of electrons on polar optical...
Article
Full-text available
A random walk based stochastic simulation algorithm for solving a nonlinear system of transient drift-diffusion-Poisson equations for semiconductors with random doping profile is developed. The method is then applied to simulate and analyze the stochastic dynamics of the transport of electrons and holes in doped semiconductor material. This analysi...
Article
A Random Walk on Ellipsoids (RWE) algorithm is developed for solving a general class of elliptic equations involving second- and zero-order derivatives. Starting with elliptic equations with constant coefficients, we derive an integral equation which relates the solution in the center of an ellipsoid with the integral of the solution over an ellips...
Preprint
We investigate the impact of threading dislocations with an edge component (a or a+c-type) on carrier recombination and diffusion in GaN(0001) layers close to the surface as well as in the bulk. To this end, we utilize cathodoluminescence imaging of the top surface of a GaN(0001) layer with a deeply buried (In,Ga)N quantum well. Varying the acceler...
Preprint
We determine the diffusion length of excess carriers in GaN by spatially resolved cathodoluminescence spectroscopy utilizing a single quantum well as carrier collector or carrier sink. Monochromatic intensity profiles across the quantum well are recorded for temperatures between 10 and 300 K. A classical diffusion model accounts for the profiles ac...
Article
This study deals with a narrow escape problem, a well-know difficult problem of evaluating the probability for a diffusing particle to reach a small part of a boundary far away from the starting position of the particle. A direct simulation of the diffusion trajectories would take an enormous computer simulation time. Instead, we use a different ap...
Chapter
The paper presents parallel implementation of a stochastic model of electron and hole transport in a semiconductor. The transfer process is described by a nonlinear system of drift-diffusion-Poisson equations, which is solved by combining different stochastic global algorithms. The nonlinear system includes drift-diffusion equations for electrons a...
Article
Stochastic simulation algorithms for solving transient nonlinear drift diffusion recombination transport equations are developed. The governing system of equations includes two drift diffusion equations coupled with a Poisson equation for the potential whose gradient forms the drift velocity. A stochastic algorithm for solving nonlinear drift-diffu...
Article
A new random walk based stochastic algorithm for calculation of the solution and its derivatives of high-dimensional second order elliptic equations with constant coefficients in any desired set of points is suggested. In contrast to the conventional random walk methods the new Global Random Walk (GRW) algorithm is able to find the solution in many...
Article
We suggest in this paper a new stochastic simulation algorithm for solving narrow escape problems governed by drift-diffusion-reaction equations of high dimension. The developed method drastically improves the efficiency of the diffusion trajectory tracking algorithm by introducing an artificial drift directed to the target position. The method is...
Article
We suggest in this paper two new random walk based stochastic algorithms for solving high-dimensional PDEs for domains with complicated geometrical structure. The first one, a Random Walk on Spheres (RWS) algorithm is developed for solving systems of coupled drift-diffusion-reaction equations where the random walk is living both on randomly sampled...
Preprint
The determination of the carrier diffusion length of semiconductors such as GaN and GaAs by cathodoluminescence imaging requires accurate knowledge about the spatial distribution of generated carriers. To obtain the lateral distribution of generated carriers for sample temperatures between 10 and 300 K, we utilize cathodoluminescence intensity prof...
Article
Full-text available
The paper presents a three-dimensional cellular automaton model of electrochemical oxidation of the carbon. The sample of the electro-conductive carbon black “Ketjenblack EC-600JD” consisting of granules of carbon is simulated. The electrochemical oxidation of the carbon granules occurs through a few successive stages. Parallel implementation of th...
Article
Full-text available
We investigate, both theoretically and experimentally, the drift, diffusion, and recombination of excitons in the strain field of an edge threading dislocation intersecting the GaN{0001} surface. We calculate and measure hyperspectral cathodoluminescence maps around the dislocation outcrop for temperatures between 10 and 200 K. Contrary to common b...
Article
A meshless stochastic algorithm for solving anisotropic transient diffusion problems based on an extension of the classical Random Walk on Spheres method is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have derived approximations of the probability densities...
Chapter
This paper is devoted to supercomputer simulations of transient anisotropic diffusion processes with recombination in GaN semiconductors containing a set of threading dislocations. The random walk on arbitrary parallelepipeds and cubes based on a Monte Carlo algorithm suggested by K. K. Sabelfeld is here applied to a cathodoluminescence imaging pro...
Chapter
In this paper a synchronous multi-particle cellular automaton model of diffusion with self-annihilation is developed based on the multi-particle cellular automata suggested previously by other authors. The models of pure diffusion and diffusion with self-annihilation are described and investigated. The correctness of the models is tested separately...
Preprint
We investigate, both theoretically and experimentally, the drift, diffusion, and recombination of excitons in the strain field of an edge threading dislocation intersecting the GaN{0001} surface. We calculate and measure hyperspectral cathodoluminescence maps around the dislocation outcrop for temperatures between 10 to 200 K. Contrary to common be...
Article
In this paper a random walk on arbitrary rectangles (2D) and parallelepipeds (3D) algorithm is developed for solving transient anisotropic drift-diffusion-reaction equations. The method is meshless, both in space and time. The approach is based on a rigorous representation of the first passage time and exit point distributions for arbitrary rectang...
Article
A new random walk based stochastic algorithm for solving transient diffusion equations in domains where a reflection boundary condition is imposed on a plane part of the boundary is suggested. The motivation comes from the field of exciton transport and recombination in semiconductors where the reflecting boundary is the substrate plane surface whi...
Article
We suggest in this paper a global Random Walk on Spheres (gRWS) method for solving transient boundary value problems, which, in contrast to the classical RWS method, calculates the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to mN trajectories in the conventional RWS algorithm. The idea is...
Article
We suggest in this letter a new Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion–reaction equations where the random walk is living both on the randomly walking spheres and inside the relevant balls. The method is mesh free both in space and time, and is well applied to solve high-dimensional problems with...
Article
A mesh free stochastic algorithm for solving transient diffusion–convection–reaction problems on domains with complicated structure is suggested. For the solutions of this kind of equations exact representations of the survival probabilities, the probability densities of the first passage time and position on a sphere are obtained. Based on these r...
Chapter
The article deals with the implementation of the Monte Carlo method for simulation of cathodoluminescence transients in the vicinity of threading dislocations in semiconductors. The Monte Carlo algorithm is based on the random-walk-on-spheres method proposed by K. K. Sabelfeld for solving drift-diffusion-reaction parabolic equations. The cathodolum...
Article
We develop in this paper a hybrid kinetic Monte Carlo and continuous thermodynamically based model for the simulation of homogeneous nucleation under burst regime when a long incubation time is followed by rapid nucleation of stable nuclei. In this model we assume that the kinetics of particle nucleation and disaggregation is governed by a Smolucho...
Article
Exact representations for the probability density of the life time and survival probability for a sphere and a disc are derived for a general drift-diffusion-reaction process. Based on these new formulas, we suggest an extremely efficient stochastic simulation algorithm for solving transient cathodoluminescence (CL) problems without any mesh in spa...
Article
We suggest a random walk on spheres based stochastic simulation algorithm for solving drift-diffusion-reaction problems with anisotropic diffusion. The diffusion coefficients and the velocity vector vary in space, and the size of the walking spheres is adapted to the local variation of these functions. The method is mesh free and extremely efficien...
Article
We suggest a new efficient and reliable random walk method, continuous both in space and time, for solving high-dimensional diffusion–advection–reaction equations. It is based on a discovered intrinsic relation between the von Mises–Fisher distribution on a sphere with this type of equations. It can be formulated as follows: the von Mises–Fisher di...
Article
We suggest a random walk on spheres based stochastic simulation algorithm for solving drift-diffusion-reaction problems with anisotropic diffusion. The diffusion coefficients and the velocity vector vary in space, and the size of the walking spheres is adapted to the local variation of these functions. The method is mesh free and extremely efficien...
Article
The strain field of a dislocation emerging at a free surface is partially relaxed to ensure stress free boundary conditions. We show that this relaxation strain at the outcrop of edge threading dislocations in GaN{0001} gives rise to a piezoelectric volume charge. The electric field produced by this charge distribution is strong enough to dissociat...
Article
The stochastic model of the growth of an ensemble of GaN nanowires (NW) in a plasma-assisted molecular beam epitaxy suggested in our recent paper (Sabelfeld and Kablukova, 2016) is here further developed to include coalescence caused by bundling of nanowires. Moreover, in the extended model the Ga and N atoms are simulated separately to mimic nucle...
Conference Paper
We suggest a parallel implementation of a Monte Carlo method for cathodoluminescence contrast maps simulation based on a random walk on spheres algorithm developed by K. K. Sabelfeld for solving drift-diffusion problems. The method for cathodoluminescence imaging in the vicinity of external forces is based on the explicit representation of the exit...
Conference Paper
In the paper we present a cellular automaton model of electrochemical oxidation of the carbon. A two-dimensional sample of the electro-conductive carbon black “Ketjenblack ES DJ 600” is simulated. In the model the sample consists of a ring-formed granules of carbon. The carbon granules under the influence of the electrochemical oxidation are destro...
Article
This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity o...
Article
Full-text available
Stochastic models and simulation algorithms for spatially separated reactants in the vicinity of traps were developed. The methods were applied to simulate electron–hole recombination in inhomogeneous semiconductors. Continuous kinetic Monte Carlo methods were compared with a discrete cellular automata algorithm. Recombination kinetics for pure dif...
Article
A probabilistic collocation based polynomial chaos expansion method is developed for simulation of particle transport in porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure. The flow is modeled in a two-dimensional domain with mixed Dirichlet-Neumann boundary conditions. The relevant Karhunen-L...
Article
In this paper, a stochastic model of nanowire growth by molecular beam epitaxy based on probability mechanisms of surface diffusion, mutual shading, rescattering of adatoms, and survival probability is proposed. A direct simulation algorithm based on this model is constructed. A comprehensive study of kinetics of the growth of a family of nanowires...
Article
We investigate the radiative and nonradiative recombination processes in planar (In,Ga)N/GaN(0001) quantum wells and (In,Ga)N quantum disks embedded in GaN$(000\bar{1})$ nanowires using photoluminescence spectroscopy under both continuous-wave and pulsed excitation. The photoluminescence intensities of these two samples quench only slightly between...
Article
This paper describes the stochastic models of electron-hole recombination in inhomogeneous semiconductors in two-dimensional and three-dimensional cases, which were developed on the basis of discrete (cellular automaton) and continuous (Monte Carlo method) approaches. The particle recombination kinetics in pure diffusion and diffusion with tunnelin...
Article
We suggest a new mesh free random walk method for solving boundary value problems in semi-infinite domains with mixed boundary conditions. The method is based on a probabilistic interpretation of the diffusion processes. Our simulations show that the suggested algorithm is extremely efficient for solving diffusion imaging problems, in particular, f...
Article
We suggest in this paper a Random Walk on Spheres (RWS) method for solving transient drift-diffusion-reaction problems which is an extension of our algorithm we developed recently [26] for solving steady-state drift-diffusion problems. Both two-dimensional and three-dimensional problems are solved. Survival probability, first passage time and the e...
Article
A probabilistic collocation based polynomial chaos expansion method is developed to solve stochastic boundary value problems with random coefficients and randomly distributed initial data. In this paper we deal with two different boundary value problems with random data: the Darcy equation with random lognormally distributed hydraulic conductivity,...
Article
This paper describes the stochastic models of electron-hole recombination in inhomogeneous semiconductors in two-dimensional and three-dimensional cases, which were developed on the basis of discrete (cellular automation) and continuous (Monte Carlo method) approaches. The mathematical model of electron-hole recombination, constructed on the basis...
Article
A stochastic model of the growth of an ensemble of nanowires (NW) in a plasma-assisted molecular beam epitaxy is suggested. The model is based on a probabilistic description of surface diffusion, shading, multiple rescattering of atoms, and survival probability. The model is implemented in a form of a direct simulation Monte Carlo algorithm. We pre...
Article
Stochastic models of electron-hole recombination in 2D and 3D inhomogeneous semiconductors based on a discrete cellular automata approach are presented in the paper. These models are derived from a Monte Carlo algorithm based on spatially inhomogeneous nonlinear Smoluchowski equations with the random initial distribution density used to simulate th...
Article
We theoretically analyze the contrast observed at the outcrop of a threading dislocation at the GaN(0001) surface in cathodoluminescence and electron-beam induced current maps. We consider exciton diffusion and recombination including finite recombination velocities both at the planar surface and at the dislocation. Formulating the reciprocity theo...
Article
We suggest a new mesh free random walk method for solving boundary value problems in semi-infinite domains with mixed boundary conditions. The method is based on a probabilistic interpretation of the diffusion processes. Our simulations show that the suggested algorithm is extremely efficient for solving diffusion imaging problems, in particular, f...
Article
In this short paper we present a stochastic projection based Monte Carlo algorithm for solving a nonlinear ill-posed inverse problem of recovering the phase of a complex-valued function provided its absolute value is known, under some additional information. The method is developed here for retrieving the step structure of the epitaxial films from...
Article
The well-known random walk on spheres method (RWS) for the Laplace equation is here extended to drift-diffusion problems. First we derive a generalized spherical mean value relation which is an extension of the classical integral mean value relation for the Laplace equation. Next we give a probabilistic interpretation of the kernel. The distributio...
Article
We investigate the nucleation, growth and coalescence of spontaneously formed GaN nanowires in molecular beam epitaxy combining the statistical analysis of scanning electron micrographs with Monte Carlo growth models. We find that (i) the nanowire density is limited by the shadowing of the substrate from the impinging fluxes by already existing nan...
Article
In this short article we suggest randomized scalable stochastic matrix-based algorithms for large linear systems. The idea behind these stochastic methods is a randomized vector representation of matrix iterations. In addition, to minimize the variance, it is suggested to use stochastic and double stochastic matrices for efficient randomized calcul...
Article
To simulate spatially inhomogeneous bimolecular reactions driven by diffusion and tunneling we suggest a new stochastic algorithm which combines the well known Random Walk on Spheres (RWS) method and the kinetic Monte Carlo algorithm. This drastically decreases the computer time in the case of diffusion, and especially for low concentrations. This...
Article
We suggest a series of extremely fast stochastic algorithms based on exact representations we derive in this paper for the first passage time and exit point probability densities, splitting and survival probabilities. We apply the developed algorithms to the following three classes of problems: (1) simulation of epitaxial nanowire growth, (2) diffu...
Article
We suggest random walk on semi-infinite cylinders methods for solving interior and exterior diffusion problems with different types of boundary conditions which include mixed Dirichlet, Neumann, and Robin boundary conditions on different parts of the boundary. Based on probabilistic interpretation of the diffusion process, stochastic simulation alg...
Book
This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in...
Conference Paper
An asynchronous CA model of annihilation of electrons and holes in an inhomogeneous semiconductor is presented. The model is based on the Monte Carlo algorithm of electron-hole annihilation. CA model allows us to study the dynamics of electron-hole spatial distribution. The annihilation process is simulated for different values of the modeling para...
Data
Елена Пащенко собирает измеритель радона в атмосфере после смены фильтра Olena Pashchenko collects the measuring of radon in the atmosphere after changing the filter
Data
The location of the detector of the daughter products of radon decay on the 6th floor in Siberia ( minus 40 degrees to plus 35 degrees Celsius). The rate of flow of external air 10 liters per minute, the mode of operation - continuous. The main thing in life is not to be lazy
Data
Measurement of the concentration of daughter products of radon decay on the 6th floor in Akademgorodok (Novosibirsk) for two weeks continuously. Without changing the filter, since there was no smoky winter situation in the city. The accumulation time of the signal is one minute. This chart is still not averaged by the method of the running average...
Article
A stochastic algorithm for simulation of fluctuation-induced kinetics of H$_2$ formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is bas...
Conference Paper
Based on a stochastic algorithm for simulation of annihilation of spatially separate electrons and holes in a disordered semiconductor, we present numerical results for the photon flux and luminescence in semiconductors. The model is based on the spatially inhomogeneous, nonlinear Smoluchowski equations with random initial distribution density. In...
Article
We suggest stochastic simulation techniques for solving two classes of linear and nonlinear inverse and ill-posed problems: (1) recovering the particle nanosize distribution from diffusion battery measurements, and (2) retrieving the step structure of the epitaxial films from the x-ray diffraction analysis. To solve these problems we develop three...
Article
The paper deals with a stochastic analysis of random displacements governed by isotropic elasticity equations. The elasticity constants are assumed to be random fields with gaussian distribution. Under the assumption of small fluctuations of elasticity constants but not ignoring their distribution and correlation structure, we derive the spectral t...
Article
The coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand–Levitan equation. We obtain the estimation of the solution of the Gelfand–Levitan equat...
Article
An inverse problem of reconstructing the two-dimensional coefficient of the wave equation is solved by a stochastic projection method. We apply the Gel'fand–Levitan approach to reduce the nonlinear inverse problem to a family of linear integral equations. The stochastic projection method is applied to solve the relevant linear system. We analyze th...
Article
A stochastic algorithm for simulation of fluctuation-induced reaction-diffusion kinetics is presented and further developed following our previous study [J. Math. Chem. (2015), DOI 10.1007/s10910-014-0446-6] where this method was used to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. This model is...
Article
To describe the annihilation of spatially separate electrons and holes in a disordered semiconductor, we suggest the use of a model based on the spatially inhomogeneous, nonlinear Smoluchowski equations with random initial distribution density. Furthermore, we present a Monte Carlo algorithm for solving this equation. Our approach provides a genera...
Article
A generalization of a polynomial chaos-based algorithm for solving PDEs with random input data is suggested. The input random field is assumed to be defined by its mean and correlation function. The method uses the Karhunen–Loève expansion, in its analytical form, for the input random field. Potentially, however, if desired, the Karhunen–Loève expa...
Article
Diffraction profiles for different models of dislocation arrangements are calculated directly by the Monte Carlo method and compared with the strain distributions for the same arrangements, which corresponds to the Stokes–Wilson approximation. It is shown that the strain distributions and the diffraction profiles are in close agreement as long as l...
Article
We present in this paper a further development of the stochastic spectral method for solving boundary value problems in domains which are composed by a set of overlapped discs first suggested by the first author in Appl. Math. Comput. 219 (2013), no. 10, 5123–5139]. We study statistical characteristics of the solution to isotropic diffusion problem...
Article
Full-text available
We investigate the origin of the fast recombination dynamics of bound and free excitons in GaN nanowire ensembles by temperature-dependent photoluminescence spectroscopy using both continuous-wave and pulsed excitation. The exciton recombination in the present GaN nanowires is dominated by a nonradiative channel between 10 and 300 K. Furthermore, b...

Network

Cited By

Projects