Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors
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 stoc...
Gespeichert in:
| Veröffentlicht in: | Physica A Jg. 556; S. 124800 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier B.V
15.10.2020
|
| Schlagworte: | |
| ISSN: | 0378-4371, 1873-2119 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | 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–diffusion equations is proposed here for the first time. In each time step, the method calculates the solution on a cloud of points using a new global Monte Carlo random walk and Cellular Automata algorithms. The Poisson equation is solved by a global version of the Random Walk on Spheres method which calculates both the solutions and the derivatives without using finite difference approximations. The method is also able to calculate fluxes to any desired part of the boundary, from arbitrary sources. For transient drift–diffusion equations we suggest a stochastic expansion from cell to cell algorithm for calculating the whole solution field. All new global random walk algorithms developed in this paper are validated by comparing the simulation results with exact solutions. Application of the developed method to solve a system of 2D transport equations for electrons and holes in a semiconductor is given.
•A new Monte Carlo algorithm for nonlinear drift–diffusion-Poisson systems is developed.•The algorithm for drift calculation is meshless in space and time.•The accuracy and the cost of the algorithm are estimated and analyzed.•The performance of the algorithm is shown by solving transport problems in semiconductors. |
|---|---|
| AbstractList | 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–diffusion equations is proposed here for the first time. In each time step, the method calculates the solution on a cloud of points using a new global Monte Carlo random walk and Cellular Automata algorithms. The Poisson equation is solved by a global version of the Random Walk on Spheres method which calculates both the solutions and the derivatives without using finite difference approximations. The method is also able to calculate fluxes to any desired part of the boundary, from arbitrary sources. For transient drift–diffusion equations we suggest a stochastic expansion from cell to cell algorithm for calculating the whole solution field. All new global random walk algorithms developed in this paper are validated by comparing the simulation results with exact solutions. Application of the developed method to solve a system of 2D transport equations for electrons and holes in a semiconductor is given.
•A new Monte Carlo algorithm for nonlinear drift–diffusion-Poisson systems is developed.•The algorithm for drift calculation is meshless in space and time.•The accuracy and the cost of the algorithm are estimated and analyzed.•The performance of the algorithm is shown by solving transport problems in semiconductors. |
| ArticleNumber | 124800 |
| Author | Kireeva, Anastasya Sabelfeld, Karl K. |
| Author_xml | – sequence: 1 givenname: Karl K. surname: Sabelfeld fullname: Sabelfeld, Karl K. email: sabelfeld.karl@yahoo.de – sequence: 2 givenname: Anastasya surname: Kireeva fullname: Kireeva, Anastasya email: sharifulina@ssd.sscc.ru |
| BookMark | eNqFkEtuGzEMhoUiAeI8TpDNXGBcvTyPRReF0TQFDLRAk7WgoaSYxszIFeWg3uUOvWFO0rHdVRbNigDB7yf5XbKzMY6esVvB54KL6uNmvl3vyc4ll1NH6obzD2wmmlqVUoj2jM24qptSq1pcsEuiDedc1ErO2O-fOcLaUkYoCIddbzPGsbD9U0yY1wMVIaaCYv-M41Nhi2lxj6O3U29P2Q9FDIVLGPLryx-HIexowssfEYmmGP9rd8yjwxj5ASGObgc5Jrpm58H25G_-1Sv2ePflYXlfrr5__bb8vCpBcZVLq21YLKRQsnUdaKmqwEHXHQgOzjU1aN92VQVdt9BSLGzrtOaiq9uqaiyESl2x9pQLKRIlHwxgPh6Vk8XeCG4OCs3GHBWag0JzUjix6g27TTjYtH-H-nSi_PTWM_pkCNCP4B0mD9m4iP_l_wL5gZNG |
| CitedBy_id | crossref_primary_10_1515_mcma_2021_2097 crossref_primary_10_1016_j_jpdc_2021_08_006 crossref_primary_10_1515_mcma_2021_2092 |
| Cites_doi | 10.1016/S0021-9991(03)00073-1 10.1007/BF01450410 10.1007/s10825-017-1118-0 10.1002/zamm.19670470502 10.1016/j.spl.2016.10.006 10.1515/mcma-2019-2039 10.1016/j.camwa.2018.05.025 10.1007/s10910-014-0446-6 10.1515/mcma-2016-0118 10.1007/978-3-030-25636-4_27 10.1016/j.agrformet.2004.07.007 10.1134/S1064562418060108 10.1515/mcma-2019-2032 10.1214/aoap/1029962812 10.1515/rnam.1995.10.6.495 10.1515/mcma-2017-0113 10.1016/S0021-8502(00)00031-8 10.1007/BF00536914 10.1016/0167-2789(94)00093-X 10.1103/RevModPhys.15.1 10.1007/s11009-006-7292-3 |
| ContentType | Journal Article |
| Copyright | 2020 Elsevier B.V. |
| Copyright_xml | – notice: 2020 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.physa.2020.124800 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 1873-2119 |
| ExternalDocumentID | 10_1016_j_physa_2020_124800 S037843712030409X |
| GroupedDBID | --K --M -DZ -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 7-5 71M 8P~ 9JN 9JO AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAPFB AAXUO ABAOU ABMAC ABNEU ABYKQ ACAZW ACDAQ ACFVG ACGFS ACNCT ACRLP ADBBV ADEZE ADFHU ADGUI AEBSH AEKER AEYQN AFFNX AFKWA AFTJW AGHFR AGTHC AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIIAU AIKHN AITUG AIVDX AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR AXLSJ BKOJK BLXMC EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA IHE IXIXF J1W K-O KOM M38 M41 MHUIS MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SDP SES SPC SPCBC SPD SSB SSF SSQ SSW SSZ T5K TN5 TWZ WH7 XPP YNT ZMT ~02 ~G- 29O 5VS 6TJ 9DU AAFFL AAQFI AAQXK AATTM AAXKI AAYWO AAYXX ABFNM ABJNI ABWVN ABXDB ACLOT ACNNM ACROA ACRPL ADMUD ADNMO ADVLN AEIPS AFJKZ AFODL AGQPQ AIIUN AJWLA ANKPU APXCP ASPBG AVWKF AZFZN BBWZM BEHZQ BEZPJ BGSCR BNTGB BPUDD BULVW BZJEE CITATION EFKBS EJD FEDTE FGOYB HMV HVGLF HZ~ MVM NDZJH R2- SEW SPG VOH WUQ XOL YYP ZY4 ~HD |
| ID | FETCH-LOGICAL-c303t-a4af5521329dbc4236f0c47bc10cdd87c4e9b66cbb54215a9d4401b79668acf63 |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000551669500028&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0378-4371 |
| IngestDate | Sat Nov 29 07:16:50 EST 2025 Tue Nov 18 20:36:03 EST 2025 Fri Feb 23 02:47:25 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Drift–diffusion-Poisson equation Transport of electrons and holes Global random walk on spheres Stochastic expansion from cell to cell algorithm |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c303t-a4af5521329dbc4236f0c47bc10cdd87c4e9b66cbb54215a9d4401b79668acf63 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_physa_2020_124800 crossref_primary_10_1016_j_physa_2020_124800 elsevier_sciencedirect_doi_10_1016_j_physa_2020_124800 |
| PublicationCentury | 2000 |
| PublicationDate | 2020-10-15 |
| PublicationDateYYYYMMDD | 2020-10-15 |
| PublicationDate_xml | – month: 10 year: 2020 text: 2020-10-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationTitle | Physica A |
| PublicationYear | 2020 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Ito, Mckean (b1) 1965 A.P. Prudnikov, Brychkov Yu. A., O.I. Marychev, Integrals and Series, vol. 1. Elementary Functions. Vamos, Suciu, Vereecken (b26) 2003; 186 Medvedev (b16) 2010; vol. 6083 Sabelfeld (b6) 2017; 121 Buffoni, Cupini (b25) 2001; 6 Grebenkov (b8) 2014 Amann (b29) 1967; 47 Deaconu, Lejay (b7) 2006; 8 Milewski (b10) 2018; 76 Milstein, Tretyakov (b3) 1999; 9 Cheshkova (b30) 1995; 10 Polyanin (b27) 2002 Dimitrijev (b21) 2006 Khodadadian, Taghizadeh, Heitzinger (b5) 2018 Sabelfeld (b4) 1991 K. (b23) 2018; 98 Karl (b24) 2019; 25 Sabelfeld, Brandt, Kaganer (b22) 2015; 53 Chandrasekhar (b32) 1943; 15 Sabelfeld (b9) 2019; 25 Kireeva, Sabelfeld, Kireev (b19) 2019 Vesala, Rannik, Leclerc, Foken, Sabelfeld (b18) 2004; 127 Amann (b28) 1967; 8 Sabelfeld, Kireeva (b14) 2019 Karapiperis, Blankleider (b15) 1994; 78 Markowich, Ringhofer, Schmeiser (b20) 1990 Ermakov, Sipin (b2) 2009 Mikhailov, Cheshkova (b31) 1998; 38 Hertz (b34) 1909; 67 Sabelfeld (b13) 2019 Sabelfeld (b11) 2016; 22 Sabelfeld (b12) 2017; 23 Onischuk, Levykin, Strunun, Ushakova, Samoilova, Sabelfeld, Panfilov (b17) 2000; 31 Sabelfeld (10.1016/j.physa.2020.124800_b9) 2019; 25 10.1016/j.physa.2020.124800_b33 Sabelfeld (10.1016/j.physa.2020.124800_b4) 1991 Onischuk (10.1016/j.physa.2020.124800_b17) 2000; 31 Ito (10.1016/j.physa.2020.124800_b1) 1965 Milstein (10.1016/j.physa.2020.124800_b3) 1999; 9 Amann (10.1016/j.physa.2020.124800_b29) 1967; 47 Sabelfeld (10.1016/j.physa.2020.124800_b12) 2017; 23 Karapiperis (10.1016/j.physa.2020.124800_b15) 1994; 78 Deaconu (10.1016/j.physa.2020.124800_b7) 2006; 8 Sabelfeld (10.1016/j.physa.2020.124800_b6) 2017; 121 Ermakov (10.1016/j.physa.2020.124800_b2) 2009 Milewski (10.1016/j.physa.2020.124800_b10) 2018; 76 Sabelfeld (10.1016/j.physa.2020.124800_b11) 2016; 22 Hertz (10.1016/j.physa.2020.124800_b34) 1909; 67 Sabelfeld (10.1016/j.physa.2020.124800_b22) 2015; 53 Markowich (10.1016/j.physa.2020.124800_b20) 1990 Sabelfeld (10.1016/j.physa.2020.124800_b14) 2019 Polyanin (10.1016/j.physa.2020.124800_b27) 2002 Kireeva (10.1016/j.physa.2020.124800_b19) 2019 Buffoni (10.1016/j.physa.2020.124800_b25) 2001; 6 Karl (10.1016/j.physa.2020.124800_b24) 2019; 25 Khodadadian (10.1016/j.physa.2020.124800_b5) 2018 K. (10.1016/j.physa.2020.124800_b23) 2018; 98 Dimitrijev (10.1016/j.physa.2020.124800_b21) 2006 Amann (10.1016/j.physa.2020.124800_b28) 1967; 8 Vamos (10.1016/j.physa.2020.124800_b26) 2003; 186 Chandrasekhar (10.1016/j.physa.2020.124800_b32) 1943; 15 Vesala (10.1016/j.physa.2020.124800_b18) 2004; 127 Mikhailov (10.1016/j.physa.2020.124800_b31) 1998; 38 Grebenkov (10.1016/j.physa.2020.124800_b8) 2014 Sabelfeld (10.1016/j.physa.2020.124800_b13) 2019 Medvedev (10.1016/j.physa.2020.124800_b16) 2010; vol. 6083 Cheshkova (10.1016/j.physa.2020.124800_b30) 1995; 10 |
| References_xml | – volume: vol. 6083 start-page: 204 year: 2010 end-page: 211 ident: b16 article-title: Multi-particle cellular-automata models for diffusion simulation publication-title: LNCS – volume: 25 start-page: 85 year: 2019 end-page: 96 ident: b24 article-title: Sabelfeld: A global random walk on spheres algorithm for transient heat equation and some extensions publication-title: Monte Carlo Methods Appl. – volume: 15 start-page: 1 year: 1943 end-page: 89 ident: b32 article-title: Stochastic problems in physics and astronomy publication-title: Rev. Modern Phys. – year: 1990 ident: b20 article-title: Semiconductor Equations – volume: 47 start-page: 285 year: 1967 end-page: 299 ident: b29 article-title: Optimale anfangsverteilungen bei der Monte–Carlo–methode mit informationsspeicherung publication-title: Z. Angew. Math. Mech. – volume: 98 start-page: 435 year: 2018 end-page: 438 ident: b23 article-title: Sabelfeld: A mesh free stochastic algorithm for solving diffusion-convection-reaction equations on complicated domains publication-title: Dokl. Math. – volume: 31 start-page: 1263 year: 2000 end-page: 1281 ident: b17 article-title: Aggregate under homogeneous Silane thermal decomposition publication-title: J. Aerosol Sci. – year: 1991 ident: b4 article-title: Monte Carlo Methods for Boundary Value Problems – volume: 127 start-page: 111 year: 2004 end-page: 116 ident: b18 article-title: Flux and concentration footprints publication-title: Agricult. Forest Meterol. – reference: A.P. Prudnikov, Brychkov Yu. A., O.I. Marychev, Integrals and Series, vol. 1. Elementary Functions. – year: 2019 ident: b13 article-title: Meshfree stochastic algorithms for systems of diffusion-advection-reaction equations and anisotropic diffusion flux calculations publication-title: Probabilistic Eng. Mech. – year: 2014 ident: b8 article-title: Efficient Monte Carlo methods for simulating diffusion-reaction processes in complex systems publication-title: First-Passage Phenomena and their Applications – volume: 121 start-page: 6 year: 2017 end-page: 11 ident: b6 article-title: A mesh free floating random walk method for solving diffusion imaging problems publication-title: Statist. Probab. Lett. – volume: 38 start-page: 99 year: 1998 end-page: 106 ident: b31 article-title: Solution of the Dirichlet difference problem for the multidimensional Helmholtz equation by the Monte Carlo method publication-title: J. Comput. Math. Math. Phys. – volume: 8 start-page: 117 year: 1967 end-page: 130 ident: b28 article-title: Eine Monte–Carlo–methode mit informationsspeicherung zur Lösung yon elliptischen randwertproblemen publication-title: Z. Wahrscheinlichkeitstheor. Verwandte Geb. – volume: 23 start-page: 189 year: 2017 end-page: 212 ident: b12 article-title: Random walk on spheres algorithm for solving transient drift diffusion-reaction problems publication-title: Monte Carlo Methods Appl. – volume: 78 start-page: 30 year: 1994 end-page: 64 ident: b15 article-title: Cellular automation model of reaction-transport processes publication-title: Physica D – volume: 6 start-page: 9 year: 2001 end-page: 19 ident: b25 article-title: The adjoint advection-diffusion equation in stationary and time dependent problems: a reciprocity relation publication-title: Riv. Mat. Univ. Parma – year: 2006 ident: b21 article-title: Principles of Semiconductor Devices – start-page: 76 year: 2018 end-page: 89 ident: b5 article-title: Three-dimensional optimal multi-level Monte–Carlo approximation of the stochastic drift–diffusion–Poisson system in nanoscale devices publication-title: J. Comput. Electron. – volume: 10 start-page: 495 year: 1995 end-page: 510 ident: b30 article-title: Global estimate of the solution of the Dirichlet problem for the Helmholtz publication-title: Russian J. Numer. Anal. Math. Modelling – volume: 8 start-page: 135 year: 2006 ident: b7 article-title: A random walk on rectangles algorithm publication-title: Methodol. Comput. Appl. Probab. – volume: 25 start-page: 131 year: 2019 end-page: 146 ident: b9 article-title: Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems publication-title: Monte Carlo Methods Appl. – volume: 186 start-page: 527 year: 2003 end-page: 544 ident: b26 article-title: Generalized random walk algorithm for the numerical modeling of complex diffusion processes publication-title: J. Comput. Phys. – start-page: 9 year: 2009 end-page: 18 ident: b2 article-title: The Random Walk on Semi-Spheres and Applications for Solving Boundary Value Problems – volume: 9 start-page: 732 year: 1999 end-page: 779 ident: b3 article-title: Simulation of a space–time bounded diffusion publication-title: Ann. Appl. Probab. – year: 2002 ident: b27 article-title: Handbook of Linear Partial Differential Equations for Engineers and Scientists – year: 1965 ident: b1 article-title: Diffusion Processes and their Sample Paths – volume: 67 start-page: 387 year: 1909 end-page: 398 ident: b34 article-title: Über den gegenseitigen durchschnittlichen Abstand von Pukten die mit bekannter mittlerer Dichte im Raume angeordnet sind publication-title: Math. Ann. – volume: 76 start-page: 854 year: 2018 end-page: 876 ident: b10 article-title: Combination of the meshless finite difference approach with the Monte Carlo random walk technique for solution of elliptic problems publication-title: Comput. Math. Appl. – year: 2019 ident: b14 article-title: A meshless random walk on parallelepipeds algorithm for solving transient anisotropic diffusion-recombination equations and applications to cathodoluminescence imaging publication-title: Numer. Math. – volume: 53 start-page: 651 year: 2015 end-page: 669 ident: b22 article-title: Stochastic model for the fluctuation-limited reaction–diffusion kinetics in inhomogeneous media based on the nonlinear Smoluchowski equations publication-title: J. Math. Chem. – year: 2019 ident: b19 article-title: Synchronous multi-particle cellular automaton model of diffusion with self-annihilation publication-title: Lecture Notes in Comput. Sci. – volume: 22 start-page: 265 year: 2016 end-page: 281 ident: b11 article-title: Random walk on spheres method for solving drift-diffusion problems publication-title: Monte Carlo Methods Appl. – year: 2019 ident: 10.1016/j.physa.2020.124800_b13 article-title: Meshfree stochastic algorithms for systems of diffusion-advection-reaction equations and anisotropic diffusion flux calculations publication-title: Probabilistic Eng. Mech. – volume: 186 start-page: 527 year: 2003 ident: 10.1016/j.physa.2020.124800_b26 article-title: Generalized random walk algorithm for the numerical modeling of complex diffusion processes publication-title: J. Comput. Phys. doi: 10.1016/S0021-9991(03)00073-1 – volume: 67 start-page: 387 year: 1909 ident: 10.1016/j.physa.2020.124800_b34 article-title: Über den gegenseitigen durchschnittlichen Abstand von Pukten die mit bekannter mittlerer Dichte im Raume angeordnet sind publication-title: Math. Ann. doi: 10.1007/BF01450410 – start-page: 76 issue: 17 year: 2018 ident: 10.1016/j.physa.2020.124800_b5 article-title: Three-dimensional optimal multi-level Monte–Carlo approximation of the stochastic drift–diffusion–Poisson system in nanoscale devices publication-title: J. Comput. Electron. doi: 10.1007/s10825-017-1118-0 – volume: 47 start-page: 285 issue: 5 year: 1967 ident: 10.1016/j.physa.2020.124800_b29 article-title: Optimale anfangsverteilungen bei der Monte–Carlo–methode mit informationsspeicherung publication-title: Z. Angew. Math. Mech. doi: 10.1002/zamm.19670470502 – volume: 38 start-page: 99 issue: 1 year: 1998 ident: 10.1016/j.physa.2020.124800_b31 article-title: Solution of the Dirichlet difference problem for the multidimensional Helmholtz equation by the Monte Carlo method publication-title: J. Comput. Math. Math. Phys. – volume: 121 start-page: 6 year: 2017 ident: 10.1016/j.physa.2020.124800_b6 article-title: A mesh free floating random walk method for solving diffusion imaging problems publication-title: Statist. Probab. Lett. doi: 10.1016/j.spl.2016.10.006 – volume: 25 start-page: 131 issue: 2 year: 2019 ident: 10.1016/j.physa.2020.124800_b9 article-title: Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems publication-title: Monte Carlo Methods Appl. doi: 10.1515/mcma-2019-2039 – volume: 76 start-page: 854 issue: 4 year: 2018 ident: 10.1016/j.physa.2020.124800_b10 article-title: Combination of the meshless finite difference approach with the Monte Carlo random walk technique for solution of elliptic problems publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2018.05.025 – volume: 53 start-page: 651 issue: 2 year: 2015 ident: 10.1016/j.physa.2020.124800_b22 article-title: Stochastic model for the fluctuation-limited reaction–diffusion kinetics in inhomogeneous media based on the nonlinear Smoluchowski equations publication-title: J. Math. Chem. doi: 10.1007/s10910-014-0446-6 – volume: 22 start-page: 265 issue: 4 year: 2016 ident: 10.1016/j.physa.2020.124800_b11 article-title: Random walk on spheres method for solving drift-diffusion problems publication-title: Monte Carlo Methods Appl. doi: 10.1515/mcma-2016-0118 – volume: vol. 6083 start-page: 204 year: 2010 ident: 10.1016/j.physa.2020.124800_b16 article-title: Multi-particle cellular-automata models for diffusion simulation – year: 1965 ident: 10.1016/j.physa.2020.124800_b1 – year: 2019 ident: 10.1016/j.physa.2020.124800_b19 article-title: Synchronous multi-particle cellular automaton model of diffusion with self-annihilation publication-title: Lecture Notes in Comput. Sci. doi: 10.1007/978-3-030-25636-4_27 – volume: 127 start-page: 111 issue: 3–4 year: 2004 ident: 10.1016/j.physa.2020.124800_b18 article-title: Flux and concentration footprints publication-title: Agricult. Forest Meterol. doi: 10.1016/j.agrformet.2004.07.007 – year: 2006 ident: 10.1016/j.physa.2020.124800_b21 – volume: 98 start-page: 435 issue: 2 year: 2018 ident: 10.1016/j.physa.2020.124800_b23 article-title: Sabelfeld: A mesh free stochastic algorithm for solving diffusion-convection-reaction equations on complicated domains publication-title: Dokl. Math. doi: 10.1134/S1064562418060108 – volume: 6 start-page: 9 issue: 4 year: 2001 ident: 10.1016/j.physa.2020.124800_b25 article-title: The adjoint advection-diffusion equation in stationary and time dependent problems: a reciprocity relation publication-title: Riv. Mat. Univ. Parma – ident: 10.1016/j.physa.2020.124800_b33 – year: 2019 ident: 10.1016/j.physa.2020.124800_b14 article-title: A meshless random walk on parallelepipeds algorithm for solving transient anisotropic diffusion-recombination equations and applications to cathodoluminescence imaging publication-title: Numer. Math. – volume: 25 start-page: 85 issue: 1 year: 2019 ident: 10.1016/j.physa.2020.124800_b24 article-title: Sabelfeld: A global random walk on spheres algorithm for transient heat equation and some extensions publication-title: Monte Carlo Methods Appl. doi: 10.1515/mcma-2019-2032 – volume: 9 start-page: 732 issue: 3 year: 1999 ident: 10.1016/j.physa.2020.124800_b3 article-title: Simulation of a space–time bounded diffusion publication-title: Ann. Appl. Probab. doi: 10.1214/aoap/1029962812 – year: 2014 ident: 10.1016/j.physa.2020.124800_b8 article-title: Efficient Monte Carlo methods for simulating diffusion-reaction processes in complex systems – volume: 10 start-page: 495 issue: 6 year: 1995 ident: 10.1016/j.physa.2020.124800_b30 article-title: Global estimate of the solution of the Dirichlet problem for the Helmholtz n-dimensional equation by the Monte Carlo method publication-title: Russian J. Numer. Anal. Math. Modelling doi: 10.1515/rnam.1995.10.6.495 – year: 1991 ident: 10.1016/j.physa.2020.124800_b4 – start-page: 9 year: 2009 ident: 10.1016/j.physa.2020.124800_b2 – volume: 23 start-page: 189 issue: 3 year: 2017 ident: 10.1016/j.physa.2020.124800_b12 article-title: Random walk on spheres algorithm for solving transient drift diffusion-reaction problems publication-title: Monte Carlo Methods Appl. doi: 10.1515/mcma-2017-0113 – volume: 31 start-page: 1263 issue: 11 year: 2000 ident: 10.1016/j.physa.2020.124800_b17 article-title: Aggregate under homogeneous Silane thermal decomposition publication-title: J. Aerosol Sci. doi: 10.1016/S0021-8502(00)00031-8 – year: 1990 ident: 10.1016/j.physa.2020.124800_b20 – volume: 8 start-page: 117 year: 1967 ident: 10.1016/j.physa.2020.124800_b28 article-title: Eine Monte–Carlo–methode mit informationsspeicherung zur Lösung yon elliptischen randwertproblemen publication-title: Z. Wahrscheinlichkeitstheor. Verwandte Geb. doi: 10.1007/BF00536914 – volume: 78 start-page: 30 issue: 1–2 year: 1994 ident: 10.1016/j.physa.2020.124800_b15 article-title: Cellular automation model of reaction-transport processes publication-title: Physica D doi: 10.1016/0167-2789(94)00093-X – volume: 15 start-page: 1 issue: 1 year: 1943 ident: 10.1016/j.physa.2020.124800_b32 article-title: Stochastic problems in physics and astronomy publication-title: Rev. Modern Phys. doi: 10.1103/RevModPhys.15.1 – volume: 8 start-page: 135 issue: 1 year: 2006 ident: 10.1016/j.physa.2020.124800_b7 article-title: A random walk on rectangles algorithm publication-title: Methodol. Comput. Appl. Probab. doi: 10.1007/s11009-006-7292-3 – year: 2002 ident: 10.1016/j.physa.2020.124800_b27 |
| SSID | ssj0001732 |
| Score | 2.3362012 |
| Snippet | Stochastic simulation algorithms for solving transient nonlinear drift diffusion recombination transport equations are developed. The governing system of... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 124800 |
| SubjectTerms | Drift–diffusion-Poisson equation Global random walk on spheres Stochastic expansion from cell to cell algorithm Transport of electrons and holes |
| Title | Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors |
| URI | https://dx.doi.org/10.1016/j.physa.2020.124800 |
| Volume | 556 |
| WOSCitedRecordID | wos000551669500028&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-2119 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001732 issn: 0378-4371 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Nb9QwELWgBYkL4lOUL_nALaTajR07PlaoCKhUVWqR9hbZjk23WpKSZKvlxn_gH_JLGMdOsmXRih64RKvI8VqZl8mb8eQNQm8SoTiRExUrNtEx1czGItEkVjIRzMDjJ63smk3w4-NsNhP9jm7TtRPgZZmtVuLyv5oazoGx3aezNzD3MCmcgN9gdDiC2eH4T4Y_bSt9Lp38ctTMv4buXJFcfKnqeXvu9RciWEKXSZBR6bUyZC_q7NhjUc_BOYcyCOJ6qCxdUi0-qcBMMJn5thwr6BpXXl-VTje2CltDgeyeeAyM6dJTqczChp7YR7JeREf7YxFAbcyVz_KWsHzZfJfrKQmIP12FR7rmuQiEppT43iq9m03TdUcJtCLrJEo3fbhPJ1zsu9SOU4ZKnARGP_q6YvYfb7KhvrAvXbvIu0lyN0nuJ7mNdhOeCvDhuwcfD2efhtf2lBO_5RTW3ktUdcWAG2v5O41ZoyZnD9D9EFPgA4-Fh-iWKR-hu_7uN4_RakQEHhGBR0RgQAQOiMASD4jAHhG4srhDxK8fPzewgAcsuGHXsfAEfX5_ePbuQxwabsQamEwbSyptCnyOJKJQGog2sxNNudLTiS6KjGtqhGJMK5VSoIpSFBTCc8UhZM6ktow8RTuwRvMMYU6FhWiAKJIpCjGrMsYoNpXw6AstlN1DSX__ch3U6F1TlEW-xXZ76O1w0aUXY9k-nPWGyQOf9DwxB6htu_D5zf7nBbo3PgUv0U5bL80rdEdftfOmfh1w9htqHJ5D |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Stochastic+simulation+algorithms+for+solving+a+nonlinear+system+of+drift%E2%80%93diffusion-Poisson+equations+of+semiconductors&rft.jtitle=Physica+A&rft.au=Sabelfeld%2C+Karl+K.&rft.au=Kireeva%2C+Anastasya&rft.date=2020-10-15&rft.issn=0378-4371&rft.volume=556&rft.spage=124800&rft_id=info:doi/10.1016%2Fj.physa.2020.124800&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_physa_2020_124800 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0378-4371&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0378-4371&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0378-4371&client=summon |