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Macroscopic Transport Models for Classical Device Simulation

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Springer Handbook of Semiconductor Devices

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Abstract

We review macroscopic transport models as used in classical device simulation such as drift-diffusion, hydrodynamic, and energy transport models. Using a systematic approach, these transport models are derived from the semiclassical Boltzmann equation by applying the method of moments. The drift-diffusion model is based on the first two moments of the Boltzmann equation, while hydrodynamic and energy transport models consider three or four moments. Within the framework of the diffusion approximation, the convective terms in the hydrodynamic models can be neglected, resulting in the much simpler diffusive energy transport models. A discussion of the physical assumptions needed for the validity of these models is given.

In cases where the energy distribution is insufficiently described by a heated Maxwellian distribution, energy transport models give poor results. Based on the diffusion approximation, a six-moment model generalizing the energy transport model is presented. All model parameters can be extracted from fullband bulk Monte Carlo simulations. The six-moment model is applied for the simulation of devices with channel length in the deca-nanometer regime. Short-channel and hot-carrier effects for which the heated Maxwellian assumption introduces particularly large errors are studied. Comparing all models, it is demonstrated that the six-moment model can improve on the drift-diffusion and energy transport models.

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References

  1. International Technology Roadmap for Semiconductors 2012: Sheet 2012_MS3 in Modeling_2012Tables.xlsx. http://www.itrs2.net/2012-itrs.html

  2. VanRoosbroeck, W.V.: Theory of flow of electrons and holes in germanium and other semiconductors. Bell Syst. Tech. J. 29, 560–607 (1950)

    Article  Google Scholar 

  3. Selberherr, S.: Analysis and Simulation of Semiconductor Devices. Springer, Wien–New York (1984)

    Book  Google Scholar 

  4. Wachutka, G.K.: Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling. IEEE Trans. Comput. Aided Des. 9(11), 1141–1149 (1990)

    Article  Google Scholar 

  5. Windbacher, T., Sverdlov, V., Selberherr, S.: Nano-Electronic Devices, pp. 1–96. Springer New York (2011)

    Google Scholar 

  6. Gummel, H.K.: A self-consistent iterative scheme for one-dimensional steady state transistor calculations. IEEE Trans. Electron Dev. 11(10), 455–465 (1964)

    Article  Google Scholar 

  7. Scharfetter, D.L., Gummel, H.K.: Large-signal analysis of a silicon read diode oscillator. IEEE Trans. Electron Dev. 16(1), 64–77 (1969)

    Article  Google Scholar 

  8. Stratton, R.: Diffusion of hot and cold electrons in semiconductor barriers. Physical Review 126(6), 2002–2014 (1962)

    Article  Google Scholar 

  9. Bløtekjær, K.: Transport equations for electrons in two-valley semiconductors. IEEE Trans. Electron Dev. ED-17(1), 38–47 (1970)

    Article  Google Scholar 

  10. Grasser, T., Tang, T., Kosina, H., Selberherr, S.: A review of hydrodynamic and energy-transport models for semiconductor device simulation. Proc. IEEE 91(2), 251–274 (2003)

    Article  Google Scholar 

  11. Vasicek, M., Cervenka, J., Esseni, D., Palestri, P., Grasser, T.: Applicability of macroscopic transport models to decananometer MOSFETs. IEEE Trans. Electron Dev. 59(3), 639–646 (2012)

    Article  Google Scholar 

  12. Markowich, P., Ringhofer, C., Schmeiser, C.: Semiconductor Equations. Springer, Wien, New York (1990)

    Book  MATH  Google Scholar 

  13. Jüngel, A.: Transport Equations for Semiconductors. Springer, Berlin, Heidelberg (2009)

    Book  Google Scholar 

  14. Sverdlov, V., Ungersboeck, E., Kosina, H., Selberherr, S.: Current transport models for nanoscale semiconductor devices. Mater. Sci. Eng. R Rep. 58(6), 228–270 (2008)

    Article  Google Scholar 

  15. Gritsch, M.: Numerical Modeling of Silicon-on-Insulator MOSFETs. Dissertation, Technische Universität Wien (2002). http://www.iue.tuwien.ac.at/phd/gritsch

    Google Scholar 

  16. Dirks, H.K.: Quasi-stationary fields for microelectronic applications. Electrical Engineering 79(2), 145–155 (1996)

    Article  Google Scholar 

  17. Steinmetz, T., Kurz, S., Clemens, M.: Domains of validity of quasistatic and quasistationary field approximations. COMPEL Int. J. Comput. Math. Electr. Electron. Eng. 30(4), 1237–1247 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Koch, S., Weiland, T.: Different types of quasistationary formulations for time domain simulations. Radio Science 46(5), (2011)

    Google Scholar 

  19. Meinerzhagen, B., Engl, W.L.: The influence of the thermal equilibrium approximation on the accuracy of classical two-dimensional numerical modeling of silicon submicrometer MOS transistors. IEEE Trans. Electron Dev. 35(5), 689–697 (1988)

    Article  Google Scholar 

  20. Baccarani, G., Rudan, M., Guerrieri, R., Ciampolini, P.: Physical models for numerical device simulation. In: W.L. Engl (ed.) Process and Device Modeling. Advances in CAD for VLSI, vol. 1, pp. 107–158. North-Holland (1986)

    Google Scholar 

  21. Caughey, D.M., Thomas, R.E.: Carrier mobilities in silicon empirically related to doping and field. Proc. IEEE 52, 2192–2193 (1967)

    Article  Google Scholar 

  22. Simlinger, T., Brech, H., Grave, T., Selberherr, S.: Simulation of submicron double-heterojunction high electron mobility transistors with MINIMOS-NT. IEEE Trans. Electron Dev. 44(5), 700–707 (1997)

    Article  Google Scholar 

  23. ISE Integrated Systems Engineering AG, Zurich, Switzerland.: DESSIS-ISE, ISE TCAD Release 10. ISE, Zürich, Switzerland (2004)

    Google Scholar 

  24. Quay, R.: Analysis and Simulation of High Electron Mobility Transistors. Dissertation, Technische Universität Wien Fakultät für Elektrotechnik (2001). http://www.iue.tuwien.ac.at/phd/quay

    Google Scholar 

  25. Shockley, W., Read, W.T.: Statistics of the recombinations of holes and electrons. Physical Review 87(5), 835–842 (1952)

    Article  MATH  Google Scholar 

  26. Hall, R.N.: Electron-hole recombination in germanium. Physical Review 87(2), 387–387 (1952)

    Article  Google Scholar 

  27. Ferry, D.K.: Semiconductors. Macmillan, New York (1991)

    Google Scholar 

  28. Azoff, E.M.: Generalized energy-momentum conservation equation in the relaxation time approximation. Solid State Electron. 30(9), 913–917 (1987)

    Article  Google Scholar 

  29. Thoma, R., Emunds, A., Meinerzhagen, B., Peifer, H.J., Engl, W.L.: Hydrodynamic equations for semiconductors with nonparabolic band structure. IEEE Trans. Electron Dev. 38(6), 1343–1353 (1991)

    Article  Google Scholar 

  30. Kane, E.O.: {Band structure of indium antimonide}. J. Phys. Chem. Solids 1, 249–261 (1957)

    Google Scholar 

  31. Lundstrom, M.: Fundamentals of carrier transport. Cambridge University Press (2000)

    Google Scholar 

  32. Nag, B.R.: Electron Transport in Compound Semiconductors. Springer Series in Solid-State Sciences, vol. 11. Springer (1980)

    Google Scholar 

  33. Grasser, T., Kosina, H., Selberherr, S.: Influence of the distribution function shape and the band structure on impact ionization modeling. J. Appl. Phys. 90(12), 6165–6171 (2001)

    Article  Google Scholar 

  34. Lee, S.C., Tang, T.: Transport coefficients for a silicon hydrodynamic model extracted from inhomogeneous Monte-Carlo calculations. Solid State Electron. 35(4), 561–569 (1992)

    Article  Google Scholar 

  35. Souissi, K., Odeh, F., Tang, H.H.K., Gnudi, A.: Comparative studies of hydrodynamic and energy transport models. COMPEL 13(2), 439–453 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  36. Gardner, C.L.: Numerical simulation of a steady-state electron shock wave in a submicrometer semiconductor device. IEEE Trans. Electron Dev. 38(2), 392–398 (1991)

    Article  Google Scholar 

  37. Anile, A.M., Maccora, C., Pidatella, R.M.: Simulation of n+-n-n+ devices by a hydrodynamic model: Subsonic and supersonic flows. COMPEL 14(1), 1–18 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  38. Fatemi, E., Jerome, J., Osher, S.: Solution of the hydrodynamic device model using high-order nonoscillatory shock capturing algorithms. IEEE Trans. Comput. Aided Des. 10(2), 232–244 (1991)

    Article  Google Scholar 

  39. Thomann, E., Odeh, F.: On the well-posedness of the two-dimensional hydrodynamic model for semiconductor devices. COMPEL 9(1), 45–57 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  40. Tang, T.: Extension of the Scharfetter-Gummel algorithm to the energy balance equation. IEEE Trans. Electron Dev. 31(12), 1912–1914 (1984)

    Article  Google Scholar 

  41. Gnudi, A., Odeh, F.: An efficient discretization scheme for the energy-continuity equation in semiconductors. In: Baccarani, G., Rudan, M. (eds.) Proc. Simulation of Semiconductor Devices and Processes, vol. 3, pp. 387–390. Tecnoprint, Bologna (1988)

    Google Scholar 

  42. Tang, T., Ieong, M.K.: Discretization of flux densities in device simulations using optimum artificial diffusivity. IEEE Trans. Comput. Aided Des. 14(11), 1309–1315 (1995)

    Article  Google Scholar 

  43. McAndrew, C.C., Singhal, K., Heasell, E.L.: A consistent nonisothermal extension of the Scharfetter-Gummel stable difference approximation. IEEE Electron Dev. Lett. EDL-6(9), 446–447 (1985)

    Article  Google Scholar 

  44. Forghieri, A., Guerrieri, R., Ciampolini, P., Gnudi, A., Rudan, M., Baccarani, G.: A new discretization strategy of the semiconductor equations comprising momentum and energy balance. IEEE Trans. Comput. Aided Des. 7(2), 231–242 (1988)

    Article  Google Scholar 

  45. Choi, W.S., Ahn, J.G., Park, Y.J., Min, H.S., Hwang, C.G.: A time dependent hydrodynamic device simulator SNU-2D with new discretization scheme and algorithm. IEEE Trans. Comput. Aided Des. 13(7), 899–908 (1994)

    Article  Google Scholar 

  46. Rudan, M., Odeh, F.: Multi-dimensional discretization scheme for the hydrodynamic model of semiconductor devices. COMPEL 5(3), 149–183 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  47. Benvenuti, A., Coughran, W.M., Pinto, M.R.: A thermal-fully hydrodynamic model for semiconductor devices and applications to III-V HBT simulation. IEEE Trans. Electron Dev. 44(9), 1349–1359 (1997)

    Article  Google Scholar 

  48. Xu, D., Tang, T., Kucherenko, S.S.: Time-dependent solution of a full hydrodynamic model including convective terms and viscous effects. VLSI Design 6(1-4), 173–176 (1998)

    Article  Google Scholar 

  49. Aluru, N.R., Law, K.H., Pinsky, P.M., Dutton, R.W.: An analysis of the hydrodynamic semiconductor device model – Boundary conditions and simulations. COMPEL 14(2/3), 157–185 (1995)

    Article  MATH  Google Scholar 

  50. Bløtekjær, K.: High-frequency conductivity, carrier waves, and acoustic amplification in drifted semiconductor plasmas. Ericsson Technics 2, 126–183 (1966)

    Google Scholar 

  51. Grasser, T., Kosina, H., Gritsch, M., Selberherr, S.: Using six moments of Boltzmann’s transport equation for device simulation. J. Appl. Phys. 90(5), 2389–2396 (2001)

    Article  Google Scholar 

  52. Ringhofer, C., Schmeiser, C., Zwirchmayer, A.: Moment methods for the semiconductor Boltzmann equation in bounded position domains. SIAM J. Numer. Anal. 39(3), 1078–1095 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  53. Baccarani, G.: Private communication (2020)

    Google Scholar 

  54. Hess, K.: Advanced Theory of Semiconductor Devices. Prentice-Hall (1988)

    Google Scholar 

  55. Azoff, E.M.: Energy transport numerical simulation of graded AlGaAs/GaAs heterojunction bipolar transistors. IEEE Trans. Electron Dev. 36(4), 609–616 (1989)

    Article  Google Scholar 

  56. Lundstrom, M.: Fundamentals of Carrier Transport, Modular Series on Solid State Device, vol. X. Addison-Wesley (1990)

    Google Scholar 

  57. Baccarani, G., Wordeman, M.R.: An investigation of steady-state velocity overshoot in silicon. Solid State Electron. 28(4), 407–416 (1985)

    Article  Google Scholar 

  58. Hänsch, W.: The Drift Diffusion Equation and Its Application in MOSFET Modeling. Springer, Wien–New York (1991)

    Book  Google Scholar 

  59. Lee, S.C., Tang, T., Navon, D.H.: Transport Models for MBTE. In: Miller, J.J.H. (Ed.) NASECODE VI - Numerical Analysis of Semiconductor Devices and Integrated Circuits, pp. 261–265. Boole Press, Dublin (1989)

    Google Scholar 

  60. Tang, T., Gan, H.: Two formulations of semiconductor transport equations based on spherical harmonic expansion of the Boltzmann transport equation. IEEE Trans. Electron Dev. 47(9), 1726–1732 (2000)

    Article  Google Scholar 

  61. Ieong, M.K.: A multi-valley hydrodynamic transport model for GaAs extracted from self-consistent Monte Carlo data. Master’s thesis, University of Massachusetts Amherst (1993)

    Google Scholar 

  62. Tang, T., Ramaswamy, S., Nam, J.: An improved hydrodynamic transport model for silicon. IEEE Trans. Electron Dev. 40(8), 1469–1476 (1993)

    Article  Google Scholar 

  63. Stratton, R.: Semiconductor current-flow equations (diffusion and degeneracy). IEEE Trans. Electron Dev. 19(12), 1288–1292 (1972)

    Article  Google Scholar 

  64. Landsberg, P.T., Hope, S.A.: Two formulations of semiconductor transport equations. Solid State Electron. 20, 421–429 (1977)

    Article  Google Scholar 

  65. Landsberg, P.T.: D grad ν or grad(Dν)? J. Appl. Phys. 56(4), 1119–1122 (1984)

    Article  Google Scholar 

  66. Apanovich, Y., Lyumkis, E., Polsky, B., Shur, A., Blakey, P.: Steady-state and transient analysis of submicron devices using energy balance and simplified hydrodynamic models. IEEE Trans. Comput. Aided Des. 13(6), 702–711 (1994)

    Article  MATH  Google Scholar 

  67. Ramaswamy, S., Tang, T.: Comparison of semiconductor transport models using a Monte Carlo consistency check. IEEE Trans. Electron Dev. 41(1), 76–83 (1994)

    Article  Google Scholar 

  68. Vecchi, M.C., Reyna, L.G.: Generalized energy transport models for semiconductor device simulation. Solid State Electron. 37(10), 1705–1716 (1994)

    Article  Google Scholar 

  69. Ieong, M., Tang, T.: Influence of hydrodynamic models on the prediction of submicrometer device characteristics. IEEE Trans. Electron Dev. 44(12), 2242–2251 (1997)

    Article  Google Scholar 

  70. Tang, T., Wang, X., Gan, H., Leong, M.K.: An analytic expression of thermal diffusion coefficient for the hydrodynamic simulation of semiconductor devices. VLSI Design 13(1-4), 131–134 (2000)

    Article  Google Scholar 

  71. Tomizawa, M., Yokoyama, K., Yoshii, A.: Nonstationary carrier dynamics in quarter-micron Si MOSFET’s. IEEE Trans. Comput. Aided Des. 7(2), 254–258 (1988)

    Article  Google Scholar 

  72. Banoo, K., Lundstrom, M.S.: Electron transport in a model Si transistor. Solid State Electron. 44, 1689–1695 (2000)

    Article  Google Scholar 

  73. Grasser, T., Kosik, R., Jungemann, C., Kosina, H., Selberherr, S.: Nonparabolic macroscopic transport models for device simulation based on bulk Monte Carlo data. J. Appl. Phys. 97(12), 093710.1–12 (2005)

    Google Scholar 

  74. Vasicek, M.: Advanced Macroscopic Transport Models. Dissertation, Technische Universität Wien (2009). http://www.iue.tuwien.ac.at/phd/vasicek

    Google Scholar 

  75. Pejčinović, B., Tang, H.H.K., Egley, J.L., Logan, L.R., Srinivasan, G.R.: Two-dimensional tensor temperature extension of the hydrodynamic model and its applications. IEEE Trans. Electron Dev. 42(12), 2147–2155 (1995)

    Article  Google Scholar 

  76. Cook, R.K., Frey, J.: An efficient technique for two-dimensional simulation of velocity overshoot effects in Si and GaAs devices. COMPEL 1(2), 65–87 (1982)

    Article  Google Scholar 

  77. Stettler, M.A., Alam, M.A., Lundstrom, M.S.: A critical examination of the assumptions underlying macroscopic transport equations for silicon devices. IEEE Trans. Electron Dev. 40(3), 733–740 (1993)

    Article  Google Scholar 

  78. Laux, S., Fischetti, M.: Transport models for advanced device simulation-truth or consequences? In: Proc. Bipolar/BiCMOS Circuits and Technology Meeting the 1995 (1995), pp. 27–34. https://doi.org/10.1109/BIPOL.1995.493859

    Google Scholar 

  79. Schenk, A.: Halbleiterbauelemente–Physikalische Grundlagen und Simulation. ETH Zurich, Integrated Systems Laboratory (2001)

    Google Scholar 

  80. Ruch, J.G.: Electron dynamics in short channel field-effect transistors. IEEE Trans. Electron Dev. ED-19(5), 652–654 (1972)

    Article  Google Scholar 

  81. Chen, D., Kan, E., Ravaioli, U., Shu, C., Dutton, R.: An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects. IEEE Electron Dev. Lett. 13(1), 26–28 (1992). https://doi.org/10.1109/55.144940

    Article  Google Scholar 

  82. Chen, D., Sangiorgi, E., Pinto, M., Kn, E., Ravaioli, U., Dutton, R.: Analysis of spurious velocity overshoot in hydrodynamic simulations. In: Proc. NUPAD IV Numerical Modeling of Processes and Devices for Integrated Circuits Workshop on (1992), pp. 109–114

    Google Scholar 

  83. Tang, T., Ramaswamy, S., Nam, J.: An improved hydrodynamic transport model for silicon. IEEE Trans. Electron Dev. 40(8), 1469–1477 (1993). https://doi.org/10.1109/16.223707

    Article  Google Scholar 

  84. Geurts, B.J.: An extended Scharfetter-Gummel scheme for high order momentum equations. COMPEL 10(3), 179–194 (1991)

    Article  MATH  Google Scholar 

  85. Liotta, S.F., Struchtrup, H.: Moment equations for electrons in semiconductors: Comparison of spherical harmonics and full moments. Solid State Electron. 44, 95–103 (2000)

    Article  Google Scholar 

  86. Nekovee, M., Geurts, B.J., Boots, H.M.J., Schuurmans, M.F.H.: Failure of extended moment equation approaches to describe ballistic transport in submicron structures. Phys. Rev. B 45(10), 6643–6651 (1992)

    Article  Google Scholar 

  87. Grasser, T., Kosina, H., Heitzinger, C., Selberherr, S.: Characterization of the hot electron distribution function using six moments. J. Appl. Phys. 91(6), 3869–3879 (2002)

    Article  Google Scholar 

  88. Reik, H.G., Risken, H.: Distribution functions for hot electrons in many-valley semiconductors. Physical Review 124, 777–784 (1961)

    Article  MATH  Google Scholar 

  89. Sonoda, K., Dunham, S.T., Yamaji, M., Taniguchi, K., Hamaguchi, C.: Impact ionization model using average energy and average square energy of distribution function. Jpn. J. Appl. Phys. 35(2B), 818–825 (1996)

    Article  Google Scholar 

  90. Struchtrup, H.: Extended moment method for electrons in semiconductors. Physica A 275, 229–255 (2000)

    Article  Google Scholar 

  91. Kosik, R., Grasser, T., Entner, R., Dragosits, K.: On the highest order moment closure problem. In: Proceedings IEEE International Spring Seminar on Electronics Technology 27th ISSE 2004, pp. 118–120. IEEE (2004)

    Google Scholar 

  92. Kosik, R.: Numerical Challenges on the Road to NanoTCAD. Dissertation, TU Wien (2004). http://www.iue.tuwien.ac.at/phd/kosik

    Google Scholar 

  93. Jungemann, C., Meinerzhagen, B.: Hierachical Device Simulation – The Monte Carlo Perspective. Springer, Wien, New York (2003)

    Book  MATH  Google Scholar 

  94. Vasicek, M., Cervenka, J., Wagner, M., Karner, M., Grasser, T.: A 2D non-parabolic six-moments model. Solid State Electron. 52, 1606–1609 (2008)

    Article  Google Scholar 

  95. Tang, T.: Hydrodynamic transport modeling of semiconductor devices – Issues and some solutions. In: Semiconductor TCAD Workshop & Exhibition, pp. 1–19. Hsinchu, Taiwan (1999)

    Google Scholar 

  96. Agostino, F., Quercia, D.: Short-channel effects in MOSFETs. Tech. rep., Introduction to VLSI design (EECS 467) (2000)

    Google Scholar 

  97. Bordelon, T.J., Wang, X.L., Maziar, C., Tasch, A.F.: An efficient non-parabolic formulation of the hydrodynamic model for silicon device simulation. In: Proc. Intl. Electron Devices Meeting (IEDM) (1990), pp. 353–356

    Google Scholar 

  98. Wolokin, G., Frey, J.: Overshoot effects in the relaxation time approximation. In: Proc. NASECODE VIII (Vienna, 1992), pp. 107–108

    Google Scholar 

  99. Grasser, T., Kosina, H., Selberherr, S.: Investigation of spurious velocity overshoot using Monte Carlo data. Appl. Phys. Lett. 79, 1900–1902 (2001)

    Article  Google Scholar 

  100. Bude, J.D.: MOSFET modeling into the ballistic regime. In: Proc. Simulation of Semiconductor Processes and Devices, pp. 23–26. Seattle, Washington, USA (2000)

    Google Scholar 

  101. Lundstrom, M.: Drift-diffusion and computational electronics - Still going strong after 40 years! In: 2015 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD). IEEE (2015)

    Google Scholar 

  102. Baccarani, G., Gnani, E., Gnudi, A., Reggiani, S.: Theoretical analysis and modeling for nanoelectronics. Solid State Electron. 125, 2–13 (2016)

    Article  Google Scholar 

  103. Yu, Z., Dutton, R.W., Kiehl, R.A.: Circuit/device modeling at the quantum level. IEEE Trans. Electron Dev. 47(10), 1819–1825 (2000)

    Article  Google Scholar 

  104. Pourfath, M., Sverdlov, V., Selberherr, S.: Transport modeling for nanoscale semiconductor devices. In: 2010 10th IEEE International Conference on Solid-State and Integrated Circuit Technology, pp. 1737–1740 (4, 2010)

    Google Scholar 

  105. Keldysh, L.: Concerning the theory of impact ionization in semiconductors. Sov. Phys. JETP 21, 1135–1144 (1965)

    Google Scholar 

  106. Grasser, T., Kosina, H., Selberherr, S.: Hot carrier effects within macroscopic transport models. Int. J. High Speed Electron. Syst. 13, 973–901 (2003)

    Article  Google Scholar 

  107. Grasser, T., Kosina, H., Heitzinger, C., Selberherr, S.: Accurate impact ionization model which accounts for hot and cold carrier populations. Appl. Phys. Lett. 80(4), 613–615 (2002). https://doi.org/10.1063/1.1445273

    Article  Google Scholar 

  108. Gehring, A., Grasser, T., Kosina, H., Selberherr, S.: Simulation of hot-electron oxide tunneling current based on a non-Maxwellian electron energy distribution function. J. Appl. Phys. 92(10), 6019–6027 (2002). https://doi.org/10.1063/1.1516617

    Article  Google Scholar 

  109. Tyaginov, S.E., Starkov, I., Enichlmair, H., Park, J., Jungemann, C., Grasser, T.: In: Sah, R. (Ed.) Silicon Nitride, Silicon Dioxide, and Emerging Dielectrics 11, pp. 321–352. ECS Transactions (2011)

    Google Scholar 

  110. Grasser, T. (ed.): Hot Carrier Degradation in Semiconductor Devices. Springer International Publishing (2014). https://doi.org/10.1007/978-3-319-08994-2

  111. Sharma, P., Tyaginov, S., Wimmer, Y., Rudolf, F., Rupp, K., Bina, M., Enichlmair, H., Park, J.M., Minixhofer, R., Ceric, H., Grasser, T.: Modeling of hot-carrier degradation in nLDMOS devices: Different approaches to the solution of the Boltzmann transport equation. IEEE Trans. Electron Dev. 62(6), 1811–1818 (2015)

    Article  Google Scholar 

  112. Jech, M., Sharma, P., Tyaginov, S.E., Rudolf, F., Grasser, T.: On the limits of applicability of drift-diffusion based hot carrier degradation modeling. Jpn. J. Appl. Phys. 55(4S), 1–6 (2016). https://doi.org/10.7567/JJAP.55.04ED14

    Article  Google Scholar 

  113. Sharma, P., Tyaginov, S.E., Rauch, S.E., Franco, J., Makarov, A., Vexler, M.I., Kaczer, B., Grasser, T.: Hot-carrier degradation modeling of decananometer nMOSFETs using the drift-diffusion approach. IEEE Electron Dev. Lett. 38(2), 160–163 (2017). https://doi.org/10.1109/LED.2016.2645901

    Article  Google Scholar 

  114. Jech, M., Ullmann, B., Rzepa, G., Tyaginov, S.E., Grill, A., Waltl, M., Jabs, D., Jungemann, C., Grasser, T.: Impact of mixed negative bias temperature instability and hot carrier stress on MOSFET characteristics-part II: Theory. IEEE Trans. Electron Dev. 66(1), 241–248 (2019). https://doi.org/10.1109/TED.2018.2873421

    Article  Google Scholar 

  115. Bina, M., Tyaginov, S.E., Franco, J., Rupp, K., Wimmer, Y., Osintsev, D., Kaczer, B., Grasser, T.: Predictive hot-carrier modeling of n-channel MOSFETs. IEEE Trans. Electron Dev. 61(9), 3103–3110 (2014)

    Article  Google Scholar 

  116. Sharma, P., Tyaginov, S.E., Wimmer, Y., Rudolf, F., Rupp, K., Enichlmair, H., Park, J., Ceric, H., Grasser, T.: Comparison of analytic distribution function models for hot-carrier degradation in nLDMOSFETs. Microelectronics Reliability 55(9-10), 1427–1432 (2015). https://doi.org/10.1016/j.microrel.2015.06.021

    Article  Google Scholar 

  117. IμE, MINIMOS-NT 2.1 User’s Guide.: Institut für Mikroelektronik, Technische Universität Wien, Austria (2004). http://www.iue.tuwien.ac.at/software

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Acknowledgements

Many of the results shown in the previous sections were computed with software developed by the Institute for Microelectronics at TU Wien in the course over many years. The authors are indebted to Andreas Gehring, Martin Wagner, Oliver Triebl, Thomas Windbacher, Prateek Sharma, Gerhard Rzepa, Stanislav Tyaginov, and Markus Kampl for their contributions to the development and implementation of the six-moment model or for applications thereof. We thank Viktor Sverdlov, Josef Weinbub, and especially Hans Kosina for numerous discussions during the preparation of this manuscript.

Special thanks go to Prof. David Esseni, who helped with Monte Carlo code and simulations. We are indebted to Prof. Christoph Jungemann who provided a spherical harmonic code and numerous fullband Monte Carlo simulation results.

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Authors and Affiliations

  1. Technical University Vienna, Institute for Microelectronics, Vienna, Austria

    Johann Cervenka, Robert Kosik, Markus Jech, Martin Vasicek, Markus Gritsch & Tibor Grasser

  2. Institute for Microelectrocnics, Technische Universitat Wien, Vienna, Austria

    Siegfried Selberherr

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  4. Martin Vasicek
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  7. Tibor Grasser
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Correspondence to Johann Cervenka or Tibor Grasser .

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Editors and Affiliations

  1. Department of Electrical, Electronic and Information Engineering and Advanced Research Center on Electronic Systems, University of Bologna, Bologna, Italy

    Massimo Rudan

  2. Department of Physics, Informatics and Mathematics - FIM, University of Modena and Reggio Emilia, Modena, Italy

    Rossella Brunetti

  3. Department of Electrical, Electronic and Information Engineering and Advanced Research Center on Electronic Systems, University of Bologna, Bologna, Italy

    Susanna Reggiani

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Cervenka, J. et al. (2023). Macroscopic Transport Models for Classical Device Simulation. In: Rudan, M., Brunetti, R., Reggiani, S. (eds) Springer Handbook of Semiconductor Devices . Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-79827-7_37

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  • DOI: https://doi.org/10.1007/978-3-030-79827-7_37

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