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Simudo: a device model for intermediate band materials

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Abstract

We describe Simudo, a free Poisson/drift-diffusion steady state device model for semiconductor and intermediate band materials, including self-consistent optical absorption and generation. Simudo is the first freely available device model that can treat intermediate band materials. Simudo uses the finite element method (FEM) to solve the coupled nonlinear partial differential equations in two dimensions, which is different from the standard choice of the finite volume method in essentially all commercial semiconductor device models. We present the continuous equations that Simudo solves, show the FEM formulations we have developed, and demonstrate how they allow robust convergence with double-precision floating point arithmetic. With a benchmark semiconductor pn junction device, we show that Simudo has a higher rate of convergence than Synopsys Sentaurus, converging to high accuracy with a considerably smaller mesh. Simudo includes many semiconductor phenomena and parameters and is designed for extensibility by the user to include many physical processes.

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Notes

  1. In the BDM space, the normal fluxes are shared by adjacent elements. The flux exiting the perimeter of a collection of cells exactly equals the sum of fluxes out of each of the cells, with exact arithmetic.

  2. relative to \(|w_{k}|/(\text {mesh size})\)

References

  1. Bank, R.E., Rose, D.J., Fichtner, W.: Numerical methods for semiconductor device simulation. IEEE Trans. Electron Devices 30(9), 1031 (1983)

    Article  MATH  Google Scholar 

  2. Fichtner, W., Rose, D., Bank, R.: Semiconductor device simulation. IEEE Trans. Electron Devices 30(9), 1018 (1983)

    Article  MATH  Google Scholar 

  3. Markowich, P.A.: The Stationary Semiconductor Device Equations. Computational Microelectronics. Springer, Vienna (1986)

    Book  Google Scholar 

  4. Piprek, J. (ed.): Handbook of Optoelectronic Device Modeling & Simulation. CRC Press, Boca Raton (2018)

    Google Scholar 

  5. Schenk, A.: Advanced Physical Models for Silicon Device Simulation. Springer, Wien (1998)

    Book  MATH  Google Scholar 

  6. Luque, A., Martí, A.: Increasing the efficiency of ideal solar cells by photon induced transitions at intermediate levels. Phys. Rev. Lett. 78(26), 5014 (1997)

    Article  Google Scholar 

  7. Okada, Y., Ekins-Daukes, N.J., Kita, T., Tamaki, R., Yoshida, M., Pusch, A., Hess, O., Phillips, C.C., Farrell, D.J., Yoshida, K., Ahsan, N., Shoji, Y., Sogabe, T., Guillemoles, J.F.: Intermediate band solar cells: recent progress and future directions. Appl. Phys. Rev. 2(2), 021302 (2015)

    Article  Google Scholar 

  8. Mailoa, J.P., Akey, A.J., Simmons, C.B., Hutchinson, D., Mathews, J., Sullivan, J.T., Recht, D., Winkler, M.T., Williams, J.S., Warrender, J.M., Persans, P.D., Aziz, M.J., Buonassisi, T.: Room-temperature sub-band gap optoelectronic response of hyperdoped silicon. Nat. Commun. 5, 3011 (2014)

    Article  Google Scholar 

  9. Berencén, Y., Prucnal, S., Liu, F., Skorupa, I., Hübner, R., Rebohle, L., Zhou, S., Schneider, H., Helm, M., Skorupa, W.: Room-temperature short-wavelength infrared Si photodetector. Sci. Rep. 7, 43688 (2017)

    Article  Google Scholar 

  10. Wang, M., Berencén, Y., García-Hemme, E., Prucnal, S., Hübner, R., Yuan, Y., Xu, C., Rebohle, L., Böttger, R., Heller, R., Schneider, H., Skorupa, W., Helm, M., Zhou, S.: Extended infrared photoresponse in Te-hyperdoped Si at room temperature. Phys. Rev. Appl. 10(2), 024054 (2018)

    Article  Google Scholar 

  11. Brown, A.S., Green, M.A.: Impurity photovoltaic effect: fundamental energy conversion efficiency limits. J. Appl. Phys. 92(3), 1329 (2002)

    Article  Google Scholar 

  12. Martí, A., Antolín, E., Stanley, C.R., Farmer, C.D., López, N., Díaz, P., Cánovas, E., Linares, P.G., Luque, A.: Production of photocurrent due to intermediate-to-conduction-band transitions: a demonstration of a key operating principle of the intermediate-band solar cell. Phys. Rev. Lett. 97(24), 247701 (2006)

    Article  Google Scholar 

  13. Wang, W., Lin, A.S., Phillips, J.D.: Intermediate-band photovoltaic solar cell based on ZnTe:O. Appl. Phys. Lett. 95(1), 011103 (2009)

    Article  Google Scholar 

  14. López, N., Reichertz, L.A., Yu, K.M., Campman, K., Walukiewicz, W.: Engineering the electronic band structure for multiband solar cells. Phys. Rev. Lett. 106(2), 028701 (2011)

    Article  Google Scholar 

  15. Sullivan, J.T., Simmons, C.B., Buonassisi, T., Krich, J.J.: Targeted search for effective intermediate band solar cell materials. IEEE J. Photovolt. 5(1), 212 (2015)

    Article  Google Scholar 

  16. der Maur, M.A.: A multiscale simulation environment for electronic and optoelectronic devices. Ph.D. thesis, Universita’ degli Studi di Roma Tor Vergata (2008)

  17. Birner, S., Zibold, T., Andlauer, T., Kubis, T., Sabathil, M., Trellakis, A., Vogl, P.: Nextnano: General purpose 3-D simulations. IEEE Trans. Electron Devices 54(9), 2137 (2007)

    Article  Google Scholar 

  18. Clugston, D.A., Basore, P.A.: PC1D version 5: 32-bit solar cell modeling on personal computers. In: Twenty Sixth IEEE Photovoltaic Specialists Conference, pp. 207–210 (1997)

  19. Haug, H., Greulich, J.: PC1Dmod 6.2-improved simulation of c-Si devices with updates on device physics and user interface. Energy Procedia 92(1876), 60 (2016)

    Article  Google Scholar 

  20. Varache, R., Leendertz, C., Gueunier-Farret, M., Haschke, J., Muñoz, D., Korte, L.: Investigation of selective junctions using a newly developed tunnel current model for solar cell applications. Sol. Energy Mater. Sol. Cells 141, 14 (2015)

    Article  Google Scholar 

  21. Burgelman, M., Nollet, P., Degrave, S.: Modelling polycrystalline semiconductor solar cells. Thin Solid Films 361–362, 527 (2000)

    Article  Google Scholar 

  22. Alonso-Álvarez, D., Wilson, T., Pearce, P., Führer, M., Farrell, D., Ekins-Daukes, N.: Solcore: a multi-scale, Python-based library for modelling solar cells and semiconductor materials. J. Comput. Electron. 17(3), 1099 (2018)

    Article  Google Scholar 

  23. Shockley, W., Read, W.T.: Statistics of the recombinations of holes and electrons. Phys. Rev. 87(5), 835 (1952)

    Article  MATH  Google Scholar 

  24. Marti, A., Cuadra, L., Luque, A.: Quasi-drift diffusion model for the quantum dot intermediate band solar cell. IEEE Trans. Electron Devices 49(9), 1632 (2002)

    Article  Google Scholar 

  25. Strandberg, R., Reenaas, T.W.: Drift-diffusion model for intermediate band solar cells including photofilling effects. Prog. Photovolt.: Res. Appl. 19(1), 21 (2011)

    Article  Google Scholar 

  26. Tobías, I., Luque, A., Martí, A.: Numerical modeling of intermediate band solar cells. Semicond. Sci. Technol. 26(1), 014031 (2011)

    Article  Google Scholar 

  27. Yoshida, K., Okada, Y., Sano, N.: Device simulation of intermediate band solar cells: effects of doping and concentration. J. Appl. Phys. 112(8), 084510 (2012)

    Article  Google Scholar 

  28. Cuadra, L., Martí, A., Luque, A.: Influence of the overlap between the absorption coefficients on the efficiency of the intermediate band solar cell. IEEE Trans. Electron Devices 51(6), 1002 (2004)

    Article  Google Scholar 

  29. Levy, M.Y., Honsberg, C.: Intraband absorption in solar cells with an intermediate band. J. Appl. Phys. 104(11), 113103 (2008)

    Article  Google Scholar 

  30. Hu, W.G., Inoue, T., Kojima, O., Kita, T.: Effects of absorption coefficients and intermediate-band filling in InAs/GaAs quantum dot solar cells. Appl. Phys. Lett. 97(19), 193106 (2010)

    Article  Google Scholar 

  31. Strandberg, R.: Analytic \({JV}\)-characteristics of ideal intermediate band solar cells and solar cells with up and downconverters. IEEE Trans. Electron Devices 64(5), 2275 (2017)

    Article  Google Scholar 

  32. Strandberg, R.: The \({JV}\)-characteristic of intermediate band solar cells with overlapping absorption coefficients. IEEE Trans. Electron Devices 64(12), 5027 (2017)

    Article  Google Scholar 

  33. Lin, A.S., Wang, W., Phillips, J.D.: Model for intermediate band solar cells incorporating carrier transport and recombination. J. Appl. Phys. 105(6), 064512 (2009)

    Article  Google Scholar 

  34. Navruz, T., Saritas, M.: Determination of the optimum material parameters for intermediate band solar cells using diffusion model. Prog. Photovolt: Res. Appl. 22(5), 593 (2014) 

    Article  Google Scholar 

  35. Krich, J.J., Trojnar, A.H., Feng, L., Hinzer, K., Walker, A.W.: Modeling intermediate band solar cells: a roadmap to high efficiency. In: Proceedings SPIE 8981, Physics, Simulation, and Photonic Engineering of Photovoltaic Devices III, p. 89810O (2014)

  36. Yoshida, K., Okada, Y., Sano, N.: Self-consistent simulation of intermediate band solar cells: effect of occupation rates on device characteristics. Appl. Phys. Lett. 97(13), 133503 (2010)

    Article  Google Scholar 

  37. Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The FEniCS project version 1.5. Arch. Numer Softw. 3(100), 9–23 (2015)

    Google Scholar 

  38. Eymard, R., Gallouët, T., Herbin, R.: Handbook of Numerical Analysis, vol. 7, pp. 713–1018. Elsevier, Amsterdam (2000)

    Google Scholar 

  39. He, Y., Cao, G.: A generalized Scharfetter–Gummel method to eliminate crosswind effects (semiconduction device modeling). IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 10(12), 1579 (1991)

    Article  Google Scholar 

  40. Nachaoui, A.: Iterative solution of the drift-diffusion equations. Numer. Algorithms 21, 323 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  41. Bochev, P., Peterson, K., Perego, M.: A multiscale control volume finite element method for advection-diffusion equations. Int. J. Numer. Methods Fluids 77(11), 641 (2015)

    Article  MathSciNet  Google Scholar 

  42. Cockburn, B., Karniadakis, G.E., Shu, C.W. (eds.): Discontinuous Galerkin Methods: Theory, Computation, and Applications. Lecture Notes in Computational Science and Engineering, vol. 11. Springer, Berlin (2000)

    Google Scholar 

  43. Kumar, G., Singh, M., Bulusu, A., Trivedi, G.: A framework to simulate semiconductor devices using parallel computer architecture. In: Journal of Physics: Conference Series, vol. 759, p. 012098. IOP Publishing, Bristol (2016)

  44. Kumar, G., Singh, M., Ray, A., Trivedi, G.: An FEM based framework to simulate semiconductor devices using streamline upwind Petrov–Galerkin stabilization technique. In: 2017 27th International Conference Radioelektronika, pp. 1–5 (2017)

  45. Poupaud, F., Schmeiser, C.: Charge transport in semiconductors with degeneracy effects. Math. Methods Appl. Sci. 14(5), 301 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  46. Marshak, A.H., Van Vliet, C.: Electrical current and carrier density in degenerate materials with nonuniform band structure. Proc. IEEE 72(2), 148 (1984)

    Article  Google Scholar 

  47. Nelson, J.: The Physics of Solar Cells. Imperial College Press, London (2003)

    Book  Google Scholar 

  48. McIntosh, K.R., Black, L.E.: On effective surface recombination parameters. J. Appl. Phys. 116(1), (2014)

  49. Zhao, J., Tan, J., Liu, L.: A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media. J. Comput. Phys. 232(1), 431 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  50. Johnson, C.: Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press, Cambridge (1987)

    MATH  Google Scholar 

  51. Gockenbach, M.S.: Understanding and Implementing the Finite Element Method. SIAM, New Delhi (2006)

    Book  MATH  Google Scholar 

  52. Jean Donea, A.H.: Finite Element Methods for Flow Problems. Wiley, Hoboken (2003)

    Book  MATH  Google Scholar 

  53. Gaury, B., Sun, Y., Bermel, P., Haney, P.M.: Sesame: a 2-dimensional solar cell modeling tool. Sol. Energy Mater. Sol. Cells 198, 53 (2019)

    Article  Google Scholar 

  54. Brezzi, F., Douglas, J., Marini, L.D.: Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47(2), 217 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  55. Roberts, J., Thomas, J.M.: In Finite Element Methods (Part 1), Handbook of Numerical Analysis, vol. 2, pp. 523–639. Elsevier, Hoboken (1991)

  56. Cummings, D.J., Law, M.E., Cea, S., Linton, T.: Comparison of discretization methods for device simulation. Int. Conf. Simul. Semicond. Process. Devices 2009, 1–4 (2009)

    Google Scholar 

  57. Synopsys Inc.: Sentaurus Device User Guide, vK-2015. Synopsys Inc., Mountain View (2015)

    Google Scholar 

  58. Logg, A., Mardal, K.A., Wells, G.N., et al.: Automated Solution of Differential Equations by the Finite Element Method. Springer, Berlin (2012)

    Book  MATH  Google Scholar 

  59. Marti, A., Cuadra, L., Luque, A.: Quasi-drift diffusion model for the quantum dot intermediate band solar cell. IEEE Trans. Electron Devices 49, 1632 (2002)

    Article  Google Scholar 

  60. Strandberg, R., Reenaas, T.W.: Photofilling of intermediate bands. J. Appl. Phys. 105(12), 124512 (2009)

    Article  Google Scholar 

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Acknowledgements

We acknowledge funding from US Army Research Laboratory (W911NF-16-2-0167), the Natural Sciences and Engineering Research Council of Canada TOP-SET training program, and computing resources from Compute Canada. We thank Emily Zinnia Zhang for alpha testing Simudo, contributing the first code implementing trapping processes, and valuable conversations.

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Authors and Affiliations

  1. Department of Physics, University of Ottawa, Ottawa, ON, Canada

    Eduard C. Dumitrescu, Matthew M. Wilkins & Jacob J. Krich

  2. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Matthew M. Wilkins & Jacob J. Krich

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  1. Eduard C. Dumitrescu
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  2. Matthew M. Wilkins
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  3. Jacob J. Krich
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Correspondence to Jacob J. Krich.

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Dumitrescu, E.C., Wilkins, M.M. & Krich, J.J. Simudo: a device model for intermediate band materials. J Comput Electron 19, 111–127 (2020). https://doi.org/10.1007/s10825-019-01414-3

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