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Journal of Computational Electronics

, Volume 14, Issue 2, pp 398–408 | Cite as

Multiscale approaches for the simulation of InGaN/GaN LEDs

  • Matthias Auf der MaurEmail author
Article

Abstract

In this work we review basic aspects of multiscale approaches for combining atomistic with continuous media descriptions and quantum mechanical with semiclassical drift–diffusion transport models for LED simulations. We show how hybrid coupling of the Green’s function formalism with drift–diffusion simulations can give additional insight into device behaviour without compromising too much computational efficiency, and that the inclusion of atomistic tight-binding calculations in a multiscale framework can help in understanding specific features related to alloy fluctuations.

Keywords

LED simulation GaN Multiscale modeling Atomistic models Random alloy 

Notes

Acknowledgments

The author gratefully acknowledges A. Pecchia, G. Penazzi, F. Sacconi and A. Di Carlo for fruitful discussions, and the FP7-ICT Project NEWLED, No. FP7-318388, for financial support.

Conflict of interest

The author declares to have no conflict of interest.

References

  1. 1.
    Nakamura, S., Senoh, M., Mukai, T.: P-GaN/N-InGaN/N-GaN double-heterostructure blue-light-emitting diodes. Jpn. J. Appl. Phys. 32(1A), L8 (1993)CrossRefGoogle Scholar
  2. 2.
    Narukawa, Y., Ichikawa, M., Sanga, D., Sano, M., Mukai, T.: White light emitting diodes with super-high luminous efficacy. J. Phys. D 43(35), 354002 (2010)CrossRefGoogle Scholar
  3. 3.
    Piprek, J.: Efficiency droop in nitride-based light-emitting diodes. Phys. Status Solidi A 207, 2217 (2010)CrossRefGoogle Scholar
  4. 4.
    O’Donnell, K.P., Auf der Maur, M., Di Carlo, A., Lorenz, K.: It’s not easy being green: strategies for all-nitrides, all-colour solid state lighting. Phys. Status Solidi 6(2), 49 (2012)Google Scholar
  5. 5.
    Cho, J., Schubert, E.F., Kim, J.K.: Efficiency droop in light-emitting diodes: challenges and countermeasures. Laser Photonics Rev. 7(3), 408 (2013)CrossRefGoogle Scholar
  6. 6.
    Verzellesi, G., Saguatti, D., Meneghini, M., Bertazzi, F., Goano, M., Meneghesso, G., Zanoni, E.: Efficiency droop in InGaN/GaN blue light-emitting diodes: physical mechanisms and remedies. J. Appl. Phys. 114(7), 071101 (2013)CrossRefGoogle Scholar
  7. 7.
    Karpov, S.: ABC-model for interpretation of internal quantum efficiency and its droop in III-nitride LEDs. In: Proceedings of the International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD, pp. 17–18 (2014)Google Scholar
  8. 8.
    Piprek, J.: III-Nitride LED efficiency droop models: a critical status review. In: 13th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2013, pp. 107–108 (2013)Google Scholar
  9. 9.
    Calciati, M., Goano, M., Bertazzi, F., Vallone, M., Zhou, X., Ghione, G., Meneghini, M., Meneghesso, G., Zanoni, E., Bellotti, E., Verzellesi, G., Zhu, D., Humphreys, C.: Correlating electroluminescence characterization and physics-based models of InGaN/GaN LEDs: pitfalls and open issues. AIP Adv. 4(6), 067118 (2014)CrossRefGoogle Scholar
  10. 10.
    Karpov, S.: Modeling of III-nitride light-emitting diodes: progress, problems, and perspectives. In: Proceedings of SPIE—The International Society for Optical Engineering, 7939 (2011)Google Scholar
  11. 11.
    McBride, P., Yan, Q., Van De Walle, C.: Effects of in profile on simulations of InGaN/GaN multi-quantum-well light-emitting diodes. Appl. Phys. Lett. 105(8), 083507 (2014)CrossRefGoogle Scholar
  12. 12.
    Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge University Press, Cambridge (1995)CrossRefGoogle Scholar
  13. 13.
    Di Carlo, A.: Microscopic theory of nanostructured semiconductor devices: beyond the envelope-function approximation. Semicond. Sci. Technol. 18, 1 (2003)CrossRefGoogle Scholar
  14. 14.
    Yam, C., Meng, L., Chen, G., Chen, Q., Wong, N.: Multiscale quantum mechanics/electromagnetics simulation for electronic devices. Phys. Chem. Chem. Phys. 13, 14365 (2011)CrossRefGoogle Scholar
  15. 15.
    Steiger, S., Povolotskyi, M., Park, H.H., Kubis, T., Klimeck, G.: Nemo5: a parallel multiscale nanoelectronics modeling tool. IEEE Trans. Nanotechnol. 10(6), 1464 (2011)CrossRefGoogle Scholar
  16. 16.
    Auf der Maur, M., Pecchia, A., Penazzi, G., Sacconi, F., Di Carlo, A.: Coupling atomistic and continuous media models for electronic device simulation. J. Comput. Electron. 12(4), 553 (2013)CrossRefGoogle Scholar
  17. 17.
    Guo, J., Datta, S., Lundstrom, M., Anantram, M.P.: Towards multi-scale modeling of carbon nanotube transistors. eprint arXiv:cond-mat/0312551 (2003)
  18. 18.
    Klimeck, G.: Quantum and semi-classical transport in nemo 1-d. J. Comput. Electron. 2(2–4), 177 (2003)CrossRefGoogle Scholar
  19. 19.
    Arnold, A., Jüngel, A.: In: Mielke, A. (ed.) Analysis, Modeling and Simulation of Multiscale Problems. Springer, Berlin (2006)Google Scholar
  20. 20.
    Xu, Y., Aluru, N.R.: Multiscale electrostatic analysis of silicon nanoelectromechanical systems (NEMS) via heterogeneous quantum models. Phys. Rev. B 77, 075313 (2008)CrossRefGoogle Scholar
  21. 21.
    Auf der Maur, M., Sacconi, F., Penazzi, G., Povolotskyi, M., Romano, G., Pecchia, A., Di Carlo, A.: Coupling atomistic and finite element approaches for the simulation of optoelectronic devices. Opt. Quantum Electron. 41(9), 671 (2009)CrossRefGoogle Scholar
  22. 22.
    Leiner, C., Schweitzer, S., Schmidt, V., Belegratis, M., Wenzl, F.P., Hartmann, P., Hohenester, U., Sommer, C.: Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and fdtd. In: Proceedings of SPIE 8781, Integrated Optics: Physics and Simulations, pp. 87810Z–87810Z-9 (2013)Google Scholar
  23. 23.
    Bellotti, E., Schuster, J., Pinkie, B., Bertazzi, F.: Multiscale modeling of photon detectors from the infrared to the ultraviolet. In: Proceedings of SPIE - The International Society for Optical Engineering, vol. 8868, p. 88680R (2013)Google Scholar
  24. 24.
    Pecchia, A., Auf der Maur, M., Di Carlo, A.: Coupling length-scale from drift-diffusion to non equilibrium green’s functions. In: 15th International Workshop on Computational Electronics (IWCE), pp. 45–46 (2012)Google Scholar
  25. 25.
    Pecchia, A., Penazzi, G., Salvucci, L., Di Carlo, A.: Non-equilibrium green’s functions in density functional tight binding: method and applications. New J. Phys. 10(6), 065022 (2008)CrossRefGoogle Scholar
  26. 26.
    Aeberhard, U.: Simulation of nanostructure-based and ultra-thin film solar cell devices beyond the classical picture. J. Photonics Energy 4(1), 042099 (2014)CrossRefGoogle Scholar
  27. 27.
    Aeberhard, U.: Theory and simulation of quantum photovoltaic devices based on the non-equilibrium green’s function formalism. J. Comput. Electron. 10(4), 394 (2011)CrossRefGoogle Scholar
  28. 28.
    Aeberhard, U.: Quantum-kinetic theory of defect-mediated recombination in nanostructure-based photovoltaic devices. In: Materials Research Society Symposium Proceedings, vol. 1493, pp. 91–96 (2013)Google Scholar
  29. 29.
    Steiger, S., Veprek, R., Witzigmann, B.: Electroluminescence from a quantum-well led using negf. In: Proceedings of 2009 13th International Workshop on Computational Electronics, IWCE 2009, 5091112 (2009)Google Scholar
  30. 30.
    Vogl, P., Hjalmarson, H.P., Dow, J.D.: A semi-empirical tight-binding theory of the electronic structure of semiconductors. J. Phys. Chem. Solids 44(5), 365 (1983)CrossRefGoogle Scholar
  31. 31.
    Jancu, J.M., Scholz, R., Beltram, F., Bassani, F.: Empirical \(spds^\star \) tight-binding calculation for cubic semiconductors; general method and material parameters. Phys. Rev. B 57(11), 6493 (1998)CrossRefGoogle Scholar
  32. 32.
    Boykin, T.: Recent developments in tight-binding approaches for nanowires. J. Comput. Electron. 8(2), 142 (2009)CrossRefGoogle Scholar
  33. 33.
    Oyafuso, F., Klimeck, G., Bowen, R., Boykin, T.B.: Atomistic electronic structure calculations of unstrained alloyed systems consisting of a million atoms. J. Comput. Electron. 1(3), 317 (2002)CrossRefGoogle Scholar
  34. 34.
    Niquet, Y.M., Delerue, C.: Band offsets, wells, and barriers at nanoscale semiconductor heterojunctions. Phys. Rev. B 84, 075478 (2011)CrossRefGoogle Scholar
  35. 35.
    Camacho, D., Niquet, Y.M.: Application of keating’s valence force field model to non-ideal wurtzite materials. Phys. E 42, 1361 (2010)CrossRefGoogle Scholar
  36. 36.
    Watson-Parris, D., Godfrey, M., Dawson, P., Oliver, R., Galtrey, M., Kappers, M., Humphreys, C.: Carrier localization mechanisms in InxGa1-xN/GaN quantum wells. Phys. Rev. B 83(11), 115321 (2011)CrossRefGoogle Scholar
  37. 37.
    Bennett, S.E., Saxey, D.W., Kappers, M.J., Barnard, J.S., Humphreys, C.J., Smith, G.D., Oliver, R.A.: Atom probe tomography assessment of the impact of electron beam exposure on In\(_x\)Ga\({1x}\)N/GaN quantum wells. Appl. Phys. Lett. 99(2), 021906 (2011)CrossRefGoogle Scholar
  38. 38.
    Wu, Y.R., Shivaraman, R., Wang, K.C., Speck, J.S.: Analyzing the physical properties of ingan multiple quantum well light emitting diodes from nano scale structure. Appl. Phys. Lett. 101(8), 083505 (2012)CrossRefGoogle Scholar
  39. 39.
    Yang, T.J., Speck, J., Wu, Y.R.: Influence of nanoscale indium fluctuation in the InGaN quantum-well LED to the efficiency droop with a fully 3D simulation model. In: Proceedings of SPIE - The International Society for Optical Engineering, vol. 8986, p. 89861I (2014)Google Scholar
  40. 40.
    Lin, Y.Y., Chuang, R.W., Chang, S.J., Li, S., Jiao, Z.Y., Ko, T.K., Hon, S.J., Liu, C.H.: GaN-based LEDs with chirped multiquantum barrier structure. IEEE Photonics Technol. Lett. 24, 1600 (2012)CrossRefGoogle Scholar
  41. 41.
    Piprek, J., Simon Li, Z.: Origin of InGaN light-emitting diode efficiency improvements using chirped AlGaN multi-quantum barriers. Appl. Phys. Lett. 102(2), 023510 (2013)CrossRefGoogle Scholar
  42. 42.
    TiberCAD simulation package. http://www.tibercad.org
  43. 43.
    Vurgaftman, I., Meyer, J., Ram-Mohan, L.: Band parameters for nitrogen-containing semiconductors. Appl. Phys. Rev. 94, 3675 (2003)Google Scholar
  44. 44.
    Yan, Q., Rinke, P., Scheffler, M., Van de Walle, C.G.: Strain effects in group-iii nitrides: deformation potentials for aln, gan, and inn. Appl. Phys. Lett. 95(12), 121111 (2009)CrossRefGoogle Scholar
  45. 45.
    Li, S.X., Wu, J., Haller, E.E., Walukiewicz, W., Shan, W., Lu, H., Schaff, W.J.: Hydrostatic pressure dependence of the fundamental bandgap of inn and in-rich group iii nitride alloys. Appl. Phys. Lett. 83(24), 4963 (2003)CrossRefGoogle Scholar
  46. 46.
    Pecchia, A., Penazzi, G., Salvucci, L., Di Carlo, A.: Non-equilibrium green’s functions in density functional tight binding: method and applications. New J. Phys. 10, 065022 (2008)CrossRefGoogle Scholar
  47. 47.
    Schulz, T., Nirschl, A., Drechsel, P., Nippert, F., Markurt, T., Albrecht, M., Hoffmann, A.: Recombination dynamics in InxGa1-xN quantum wells–Contribution of excited subband recombination to carrier leakage. Appl. Phys. Lett. 105(18), 181109 (2014)Google Scholar
  48. 48.
    Nippert, F., Nirschl, A., Pietzonka, I., Schulz, T., Albrecht, M., Westerkamp, S., Kure, T., Nenstiel, C., Callsen, G., Strassburg, M., Hoffmann, A.: Influence of blue luminescence and QCSE in green InGaN QWs. Appl. Phys. Lett. (submitted)Google Scholar
  49. 49.
    Binder, M., Nirschl, A., Zeisel, R., Hager, T., Lugauer, H.J., Sabathil, M., Bougeard, D., Wagner, J., Galler, B.: Identification of nnp and npp auger recombination as significant contributor to the efficiency droop in (gain)n quantum wells by visualization of hot carriers in photoluminescence. Appl. Phys. Lett. 103(7), 071108 (2013)CrossRefGoogle Scholar
  50. 50.
    Bertazzi, F., Zhou, X., Goano, M., Ghione, G., Bellotti, E.: Auger recombination in InGaN/GaN quantum wells: a full-Brillouin-zone study. Appl. Phys. Lett. 103(8), 081106 (2013)CrossRefGoogle Scholar
  51. 51.
    Kioupakis, E., Rinke, P., Delaney, K.T., Van de Walle, C.G.: Indirect auger recombination as a cause of efficiency droop in nitride light-emitting diodes. Appl. Phys. Lett. 98, 161107 (2011)CrossRefGoogle Scholar
  52. 52.
    Iveland, J., Martinelli, L., Peretti, J., Speck, J.S., Weisbuch, C.: Direct measurement of auger electrons emitted from a semiconductor light-emitting diode under electrical injection: identification of the dominant mechanism for efficiency droop. Phys. Rev. Lett. 110, 177406 (2013)CrossRefGoogle Scholar
  53. 53.
    López, M., Pecchia, A., Auf der Maur, M., Sacconi, F., Penazzi, G., Di Carlo, A.: Atomistic simulations of InGaN/GaN random alloy quantum well LEDs. Phys. Status Solidi (c) 11(3–4), 632 (2014)CrossRefGoogle Scholar
  54. 54.
    Auf der Maur, M., Barettin, D., Pecchia, A., Sacconi, F., Di Carlo A.: Effect of alloy fluctuations in InGaN/GaN quantum wells on optical emission strength. In: 14th International Conference on (IEEE, 2014) Numerical Simulation of Optoelectronic Devices (NUSOD), pp. 11–12 (2014)Google Scholar
  55. 55.
    Caro, M.A., Schulz, S., O’Reilly, E.P.: Theory of local electric polarization and its relation to internal strain: impact on polarization potential and electronic properties of group-iii nitrides. Phys. Rev. B 88, 214103 (2013)CrossRefGoogle Scholar
  56. 56.
    Schiavon, D., Binder, M., Peter, M., Galler, B., Drechsel, P., Scholz, F.: Wavelength-dependent determination of the recombination rate coefficients in single-quantum-well GaInN/GaN light emitting diodes. Phys. Status Solidi (B) 250(2), 283 (2013)CrossRefGoogle Scholar
  57. 57.
    Foreman, B.A.: Consequences of local gauge symmetry in empirical tight-binding theory. Phys. Rev. B 66(16), 165212 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Electronic EngineeringUniversity of Rome “Tor Vergata”RomeItaly

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