Stochastic simulation of exciton transport in semiconductor heterostructures
-
Karl Sabelfeld
and
Ivan Aksyuk
Abstract
Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z. The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.
Funding statement: The research was performed within the framework of the state assignment of ICMMG SB RAS FWNM-2022-0002.
References
[1] R. K. Ahrenkiel, Minority Carriers In III-V Semiconductors: Physics and Applications, Ch. 2 (Eds. R. K. Ahrenkiel and M. S.Lundstrom). Ser. Semicondunctors and Semimetals, Vol. 39. Academic Press, Boston, 1993.10.1016/S0080-8784(08)62594-6Search in Google Scholar
[2] O. Brandt, V. M. Kaganer, J. Lähnemann, T. Flissikowski, C. Pfüller, K. K. Sabelfeld, A. E. Kireeva, C. Cheze, R. Calarco, H. Grahn, and U. Jahn, Carrier diffusion in GaN: A cathodoluminescence study. II: Ambipolar versus exciton diffusion. Phys. Rev. Applied 17 (2022), No. 2, 024018.10.1103/PhysRevApplied.17.024018Search in Google Scholar
[3] L. Devroye, Non-Uniform Random Variate Generation. Springer, New York, 1986.10.1007/978-1-4613-8643-8Search in Google Scholar
[4] U. Jahn, V. M. Kaganer, K. K. Sabelfeld, A. E. Kireeva, J. Lähnemann, C. Pfüller, C. Cheze, K. Biermann, R. Calarco, and O. Brandt, Carrier diffusion in GaN: A cathodoluminescence study. I: Temperature-dependent generation volume. Phys. Rev. Applied 17 (2022), No. 2, 024017.10.1103/PhysRevApplied.17.024017Search in Google Scholar
[5] E. Kablukova, K. Sabelfeld, D. Protasov, and K. Zhuravlev, Stochastic simulation of electron transport in a strong electrical field in low-dimensional heterostructures. MCMA 29 (2023), No. 4.10.1515/mcma-2023-2019Search in Google Scholar
[6] V. M. Kaganer, Lähnemann, C. Pfüller, K. K. Sabelfeld, A. E. Kireeva, and O. Brandt, Determination of the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations: Fallacies and opportunities. Phys. Rev. Appl. 12 (2019), 054038.10.1103/PhysRevApplied.12.054038Search in Google Scholar
[7] A. Kireeva, K. K. Sabelfeld, and S. Kireev, Parallel simulation of drift–diffusion–recombination by cellular automata and global random walk algorithm. The Journal of Supercomputing 77 (2021), 6889–6903.10.1007/s11227-020-03529-ySearch in Google Scholar
[8] J. Lähnemann, V. M. Kaganer, K. K. Sabelfeld, A. E. Kireeva, U. Jahn, C. Cheze, R. Calarco, and O. Brandt, Carrier diffusion in GaN: A cathodoluminescence study. III: Nature of nonradiative recombination at threading dislocations. Phys Rev. Applied 17 (2022), No. 2, 024019.10.1103/PhysRevApplied.17.024019Search in Google Scholar
[9] W. Liu, J.-F. Carlin, N. Grandjean, B. Deveaud, and G. Jacopin, Exciton dynamics at a single dislocation in GaN probed by picosecond time-resolved cathodoluminescence. Applied Physics Letters 109 (2016), 042101.10.1063/1.4959832Search in Google Scholar
[10] E. Malic, R. Perea-Causin, R. Rosati, D. Erkensten, and S. Brem, Exciton transport in atomically thin semiconductors. Nature Communications 14 (2023), 3430.10.1038/s41467-023-38556-9Search in Google Scholar PubMed PubMed Central
[11] N. Mengel, L. Gümbel, Ph. Klement, M. Fey, C. Fuchs, K. Volz, S. Chatterjee, and M. Stein, The influence of internal interfaces on charge-carrier diffusion in semiconductor heterostructures. Phys. Status Solidi B 260 (2023), 2300103.10.1002/pssb.202300103Search in Google Scholar
[12] A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists. Charman & Hall/CRC, Boca Raton, 2002.10.1201/9781420035322Search in Google Scholar
[13] K. K. Sabelfeld, Monte Carlo Methods in Boundary Value Problems. Springer Verlag, New York–Heidelberg–Berlin, 1991.10.1007/978-3-642-75977-2Search in Google Scholar
[14] K. K. Sabelfeld, Random Fields and Stochastic Lagrangian Models: Analysis and Applications in Turbulence and Porous Media. Walter de Gruyter, Berlin, 2012.10.1515/9783110296815Search in Google Scholar
[15] K. K. Sabelfeld, Random walk on spheres algorithm for solving transient drift–diffusion–reaction problems. MCMA 23 (2017), No. 3, 189–212.10.1515/mcma-2017-0113Search in Google Scholar
[16] K. Sabelfeld, V. Kaganer, C. Pfüller, and O. Brandt, Dislocation contrast in cathodoluminescence and electron-beam induced current maps on GaN(0001). Journal of Physics D: Applied Physics 50 (2017), No. 40, 405101.10.1088/1361-6463/aa85c8Search in Google Scholar
[17] A. J. Walker, New fast method for generating discrete random numbers with arbitrary frequency distributions. Electr. Lett. 10 (1974), No. 8, 127–128.10.1049/el:19740097Search in Google Scholar
[18] K. Wei, X. Liu, G. Du, and R. Han, Simulation of carrier transport in heterostructures using the 2D self-consistent full-band ensemble Monte Carlo method. Journal of Semiconductors 31 (2010), No. 8, 084004.10.1088/1674-4926/31/8/084004Search in Google Scholar
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Articles in the same Issue
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- Simulation algorithms for stationary sequences with distributions in the form of a mixture of Gaussian distributions
- Monte Carlo simulation of polarized lidar returns for atmospheric clouds sensing
- Stochastic simulation of exciton transport in semiconductor heterostructures
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Articles in the same Issue
- Frontmatter
- Simulation algorithms for stationary sequences with distributions in the form of a mixture of Gaussian distributions
- Monte Carlo simulation of polarized lidar returns for atmospheric clouds sensing
- Stochastic simulation of exciton transport in semiconductor heterostructures
- Semi-Lagrangian approximations of the transfer operator in divergent form
- Numerical modelling of large elasto-plastic multi-material deformations on Eulerian grids
