Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging

2018 ◽  
Vol 24 (2) ◽  
pp. 79-92 ◽  
Author(s):  
Karl K. Sabelfeld ◽  
Anastasiya Kireeva
Keyword(s):  
Broad Class ◽  
Life Time ◽  
Stochastic Simulation Algorithm ◽  
Reaction Process ◽  
Diffusion Reaction ◽  
Threading Dislocations ◽  
Time Behavior ◽  
Drift Diffusion ◽  
Robin Boundary ◽  
Cathodoluminescence Imaging

Abstract 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 space and time. The method can be applied to a broad class of drift-diffusion-reaction problems where the time behavior of the absorbed material is of interest. The important advantage of the method suggested is the ability to incorporate local inclusions like dislocations, point defects and other singular folds and complicated structures. General Robin boundary conditions on the boundary are treated in a probabilistic way. The method is tested against exact solutions for a series of examples with bounded and unbounded domains. An application to the dislocation imaging problem, which includes thousand threading dislocations, is given.

Random walk on spheres method for solving anisotropic drift-diffusion problems

2018 ◽  
Vol 24 (1) ◽  
pp. 43-54 ◽  
Author(s):  
Irina Shalimova ◽  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Anisotropic Diffusion ◽  
Stochastic Simulation Algorithm ◽  
Local Variation ◽  
Diffusion Reaction ◽  
Drift Diffusion ◽  
Mesh Free ◽  
Electron Beam Induced Current ◽  
Defects In Semiconductors ◽  
Diffusion Problems

Abstract 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 efficient for calculation of fluxes to boundaries and the concentration of the absorbed particles inside the domain. Applications to cathodoluminescence (CL) and electron beam induced current (EBIC) methods for the analysis of dislocations and other defects in semiconductors are discussed.

Random walk on spheres method for solving anisotropic drift-diffusion problems

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Irina Shalimova ◽  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Anisotropic Diffusion ◽  
Stochastic Simulation Algorithm ◽  
Local Variation ◽  
Diffusion Reaction ◽  
Drift Diffusion ◽  
Mesh Free ◽  
Electron Beam Induced Current ◽  
Defects In Semiconductors ◽  
Diffusion Problems

AbstractWe 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 efficient for calculation of fluxes to boundaries and the concentration of the absorbed particles inside the domain. Applications to cathodoluminescence (CL) and electron beam induced current (EBIC) methods for the analysis of dislocations and other defects in semiconductors are discussed.

scholarly journals Coincident Electron Channeling and Cathodoluminescence Studies of Threading Dislocations in GaN

2013 ◽  
Vol 20 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Gunasekar Naresh-Kumar ◽  
Jochen Bruckbauer ◽  
Paul R. Edwards ◽  
Simon Kraeusel ◽  
Ben Hourahine ◽  
...  
Keyword(s):  
Structural Damage ◽  
Light Emission ◽  
Threading Dislocations ◽  
Nonradiative Recombination ◽  
Contrast Imaging ◽  
Force Microscopy ◽  
Electron Channeling ◽  
Microscopy Techniques ◽  
Cathodoluminescence Imaging ◽  
Edge Dislocations

AbstractWe combine two scanning electron microscopy techniques to investigate the influence of dislocations on the light emission from nitride semiconductors. Combining electron channeling contrast imaging and cathodoluminescence imaging enables both the structural and luminescence properties of a sample to be investigated without structural damage to the sample. The electron channeling contrast image is very sensitive to distortions of the crystal lattice, resulting in individual threading dislocations appearing as spots with black–white contrast. Dislocations giving rise to nonradiative recombination are observed as black spots in the cathodoluminescence image. Comparison of the images from exactly the same micron-scale region of a sample demonstrates a one-to-one correlation between the presence of single threading dislocations and resolved dark spots in the cathodoluminescence image. In addition, we have also obtained an atomic force microscopy image from the same region of the sample, which confirms that both pure edge dislocations and those with a screw component (i.e., screw and mixed dislocations) act as nonradiative recombination centers for the Si-doped c-plane GaN thin film investigated.

Random walk on spheres algorithm for solving transient drift-diffusion-reaction problems

2017 ◽  
Vol 23 (3) ◽  
Author(s):  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Diffusion Reaction ◽  
Drift Diffusion ◽  
Walk On Spheres Algorithm

AbstractWe 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 [

Short Time Behavior of Solutions to Linear and Nonlinear Schrödinger Equations

2008 ◽  
Vol 60 (5) ◽  
pp. 1168-1200 ◽  
Author(s):  
Michael Taylor
Keyword(s):  
Broad Class ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Time Behavior ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Pinsky Phenomenon ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear ◽  
Short Time

AbstractWe examine the fine structure of the short time behavior of solutions to various linear and nonlinear Schrödinger equations ut = iΔu+q(u) on I×ℝn, with initial data u(0, x) = f (x). Particular attention is paid to cases where f is piecewise smooth, with jump across an (n−1)-dimensional surface. We give detailed analyses of Gibbs-like phenomena and also focusing effects, including analogues of the Pinsky phenomenon. We give results for general n in the linear case. We also have detailed analyses for a broad class of nonlinear equations when n = 1 and 2, with emphasis on the analysis of the first order correction to the solution of the corresponding linear equation. This work complements estimates on the error in this approximation.

SECOND ORDER BOUNDARY CONDITIONS FOR THE DRIFT-DIFFUSION EQUATIONS OF SEMICONDUCTORS

1995 ◽  
Vol 05 (04) ◽  
pp. 429-455 ◽  
Author(s):  
A. YAMNAHAKKI
Keyword(s):  
Boundary Conditions ◽  
Test Problem ◽  
Fluid Model ◽  
Diffusion Equations ◽  
Robin Boundary Conditions ◽  
Fluid Models ◽  
Drift Diffusion ◽  
Dirichlet Conditions ◽  
Robin Boundary ◽  
Two Fluid

By an asymptotic analysis of the Boltzmann equation of semiconductors, we prove that Robin boundary conditions for drift-diffusion equations provide a more accurate fluid model than Dirichlet conditions. The Robin conditions involve the concept of the extrapolation length which we compute numerically. We compare the two-fluid models for a test problem. The numerical results show that the current density is correctly computed with Robin conditions. This is not the case with Dirichlet conditions.

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