Numerical analysis of nonlinear model of excited carrier decay

• Autorzy: Natalija Tumanova , Raimondas Čiegis , Mečislavas Meilūnas
• Języki publikacji: EN

Abstrakty

EN

This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.

Słowa kluczowe

EN

Nonlinear ODE; Numerical approximation; A priori estimates; Convergence; Model identification

Kategorie tematyczne

• 65L12: Finite difference methods
• 65Z05: Applications to physics
• 65L20: Stability and convergence of numerical methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 6
• Strony: 1140-1152

Daty

wydano

2013-06-01

online

2013-03-28

Twórcy

autor

Natalija Tumanova

• Department of Mathematical Modeling, Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Saulėtekio av. 11, 10223, Vilnius, Lithuania

autor

Raimondas Čiegis

• Department of Mathematical Modeling, Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Saulėtekio av. 11, 10223, Vilnius, Lithuania

autor

Mečislavas Meilūnas

• Department of Mathematical Modeling, Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Saulėtekio av. 11, 10223, Vilnius, Lithuania

Bibliografia

• [1] Ascher U.M., Petzold L.R., Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, Philadelphia, 1998 http://dx.doi.org/10.1137/1.9781611971392[Crossref]
• [2] Carnevale N.T., Hines M.L., The NEURON Book, Cambridge University Press, Cambridge, 2006 http://dx.doi.org/10.1017/CBO9780511541612[Crossref]
• [3] Chegis R.Yu., A study of difference schemes for a class of models of excitability, Comput. Math. Math. Phys., 1992, 32(6), 757–767
• [4] Chis O.-T., Banga J.R., Balsa-Canto E., Structural identifiability of systems biology models: a critical comparison of methods, PLoS ONE, 6(11), #e27755
• [5] Čiegis R., Tumanova N., Finite-difference schemes for parabolic problems on graphs, Lith. Math. J., 2010, 50(2), 164–178 http://dx.doi.org/10.1007/s10986-010-9077-1[Crossref]
• [6] Enns R.H., It’s a Nonlinear World, Springer Undergrad. Texts Math. Technol., Springer, New York, 2011 http://dx.doi.org/10.1007/978-0-387-75340-9[Crossref]
• [7] Gerisch A., Chaplain M.A.J., Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems, Math. Comput. Modelling, 2006, 43(1-2), 49–75 http://dx.doi.org/10.1016/j.mcm.2004.05.016[Crossref]
• [8] Goudon T., Miljanovic V., Schmeiser C., On the Shockley-Read-Hall Model: generation-recombination in semiconductors, SIAM J. Appl. Math., 2007, 67(4), 1183–1201 http://dx.doi.org/10.1137/060650751[WoS][Crossref]
• [9] Hairer E., Nørsett S.P., Wanner G., Solving Ordinary Differential Equations I, Springer Ser. Comput. Math., 8, Springer, Berlin, 1993
• [10] Hairer E., Wanner G., Solving Ordinary Differential Equations II, Springer Ser. Comput. Math., 14, Springer, Berlin, 1996 http://dx.doi.org/10.1007/978-3-642-05221-7[Crossref]
• [11] Hall R.N., Electron-hole recombination in Germanium, Physical Review, 1952, 87(2), 387–387 http://dx.doi.org/10.1103/PhysRev.87.387[Crossref]
• [12] Hanslien M., Karlsen K.H., Tveito A., A maximum principle for an explicit finite difference scheme approximating the Hodgkin-Huxley model, BIT, 2005, 45(4), 725–741 http://dx.doi.org/10.1007/s10543-005-0023-2[Crossref]
• [13] Hauser J.R., Numerical Methods for Nonlinear Engineering Models, Springer, Berlin, 2009 http://dx.doi.org/10.1007/978-1-4020-9920-5[Crossref]
• [14] Hodgkin A., Huxley A., A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, 1952, 117(4), 500–544
• [15] Horváth Z., Positivity of Runge-Kutta and diagonally split Runge-Kutta methods, Appl. Numer. Math., 1998, 28(2–4), 309–326 http://dx.doi.org/10.1016/S0168-9274(98)00050-6[Crossref]
• [16] Hundsdorfer W., Verwer J.G., Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Ser. Comput. Math., 33, Springer, Berlin-Heidelberg-New York-Tokyo, 2003
• [17] Ichimura M., Temperature dependence of a slow component of excess carrier decay curves, Solid-State Electronics, 2006, 50(11–12), 1761–1766 http://dx.doi.org/10.1016/j.sse.2006.10.001[Crossref]
• [18] Macdonald D., Cuevas A., Validity of simplified Shockley-Read-Hall statistics for modeling carrier lifetimes in crystalline silicon, Phys. Rev. B, 2003, 67(7), #075203 http://dx.doi.org/10.1103/PhysRevB.67.075203[Crossref]
• [19] Mascagni M., The backward Euler method for numerical solution of the Hodgkin-Huxley equations of nerve conduction, SIAM J. Numer. Anal., 1990, 27(4), 941–962 http://dx.doi.org/10.1137/0727054[Crossref]
• [20] Miao H., Xia X., Perelson A.S., Wu H., On identifiability of nonlinear ODE models and applications in viral dynamics, SIAM Rev., 2011, 53(1), 3–39 http://dx.doi.org/10.1137/090757009[Crossref][WoS]
• [21] Mitra S., Mitra A., Kundu D., Genetic algorithm and M-estimator based robust sequential estimation of parameters of nonlinear sinusoidal signals, Commun. Nonlinear Sci. Numer. Simul., 2011, 16(7), 2796–2809 http://dx.doi.org/10.1016/j.cnsns.2010.10.005[Crossref][WoS]
• [22] Pincevičius A., Meilūnas M., Tumanova N., Numerical simulation of the conductivity relaxation in the high resistivity semiconductor, Math. Model. Anal., 2007, 12(3), 379–388 http://dx.doi.org/10.3846/1392-6292.2007.12.379-388[Crossref][WoS]
• [23] Schmerler S., Hahn T., Hahn S., Niklas J., Gründig-Wendrock B., Explanation of positive and negative PICTS peaks in SI-GaAs, Journal of Materials Science: Materials in Electronics, 2008, 19(S1), 328–332 http://dx.doi.org/10.1007/s10854-007-9564-2[Crossref]
• [24] Shockley W., Read W.T., Statistics of the recombinations of holes and electrons, Phys. Rev., 1952, 87(5), 835–842 http://dx.doi.org/10.1103/PhysRev.87.835[Crossref]
• [25] Sivanandam S.N., Deepa S.N., Introduction to Genetic Algorithms, Springer, Berlin, 2010
• [26] Starikovičius V., Čiegis R., Iliev O., A parallel solver for the design of oil filters, Math. Model. Anal., 2011, 16(2), 326–341 http://dx.doi.org/10.3846/13926292.2011.582591[Crossref][WoS]
• [27] Sundnes J., Lines G.T., Cai X., Nielsen B.F., Mardal K.-A., Tveito A., Computing the Electrical Activity in the Heart, Monogr. Comput. Sci. Eng., 1, Springer, Berlin, 2006
• [28] Tikidji-Hamburyan R.A., Genetic algorithm modification to speed up parameter fitting for a multicompartment neuron model, BMC Neuroscience, 2008, 9(S1), #P90 [Crossref]
• [29] Tumanova N., Čiegis R., Predictor-corrector domain decomposition algorithm for parabolic problems on graphs, Math. Model. Anal., 2012, 17(1), 113–127 http://dx.doi.org/10.3846/13926292.2012.645891[WoS][Crossref]
• [30] Van Geit W., De Schutter E., Achard P., Automated neuron model optimization techniques: a review, Biol. Cybernet., 2008, 99(4–5), 241–251 http://dx.doi.org/10.1007/s00422-008-0257-6[Crossref]
• [31] Yao L., Sethares W.A., Nonlinear parameter estimation via the genetic algorithm, IEEE Trans. Signal Process., 1994, 42(4), 927–935 http://dx.doi.org/10.1109/78.285655[Crossref]

Identyfikatory

DOI

10.2478/s11533-013-0226-8