Quantum kinetics approach to calculation of the low field mobility in the hole inversion layers of silicon MOSFET’s

  • K. L. Kovalenko
  • S. I. Kozlovskiy
  • N. N. Sharan


Analytic expressions for low field mobility have been obtained in the quantized p-type inversion layers. The confining potential is approximated by a triangular quantum well. Main attention is paid to study the dependence of the hole mobility on transverse effective field at different temperatures and concentrations of the ionized impurities. Acoustic and optical phonons, charged impurities, and surface roughness have been adopted as scattering system. Theoretical considerations are based on the quantum kinetic equation and special form of the non-equilibrium distribution function (shifted Fermi distribution). Calculations show that the acoustic phonon limited mobility does not depend on the transverse effective electrical field \(E_\mathrm{eff} \) and has a temperature dependence closer to experiment than known expression for the universal mobility. At the same time, the mobility limited by scattering with optical phonons and surface roughness is proportional to \(E_\mathrm{eff} ^{-1/3}\) and \(E_\mathrm{eff} ^{-2}\), respectively. The mobility limited by scattering by ionized impurities is a weak function of the transverse effective field. Results of the calculations are compared with known experimental data.


Low field mobility P-type quantized inversion layers Silicon 



Authors thank to Dr. M. Lisianskiy for valuable help.


  1. 1.
    Remashan, K., Wong, N.A., Chan, K., Sim, S.P., Yang, C.Y.: Modeling inversion-layer carrier mobilities in all regions of MOSFET operation. Solid-State Electron. 46(1), 153–156 (2002).  https://doi.org/10.1016/S0038-1101(01)00285-4 CrossRefGoogle Scholar
  2. 2.
    Gaubert, P., Teramoto, A.: Carrier mobility in field-effect transistors. In: Pejovic, M.M., Pejovic, M.M. (eds.) Different Types of Field-Effect Transistors: Theory and Applications, pp. 2–25. InTech, Rijeka (2017).  https://doi.org/10.5772/65626 Google Scholar
  3. 3.
    Vasilesca, D.: Mobility modeling. Arizona State University. http://manualzz.com/doc/6506074/moblity
  4. 4.
    Stern, F., Howard, W.E.: Properties of semiconductor surface inversion layers in the electric quantum limit. Phys. Rev. 163(3), 816 (1967).  https://doi.org/10.1103/PhysRev.163.816 CrossRefGoogle Scholar
  5. 5.
    Gámiz, F., Lopez-Villanueva, J.A., Banqueri, J., Carceller, J.E., Cartujo, P.: Universality of electron mobility curves in MOSFETs: a Monte Carlo study. IEEE Trans. Electron. Devices 42(2), 258–265 (1995).  https://doi.org/10.1109/16.370071 CrossRefGoogle Scholar
  6. 6.
    Fischetti, M.V., Ren, Z., Solomon, P.M., Yang, M., Rim, K.: Six-band k\(\cdot \)p calculation of the hole mobility in silicon inversion layers: dependence on surface orientation, strain, and silicon thickness. J. Appl. Phys. 94(2), 1079–1095 (2003).  https://doi.org/10.1063/1.1585120 CrossRefGoogle Scholar
  7. 7.
    Donetti, L., Gamiz, F., Rodriguez, N.: Simulation of hole mobility in two-dimensional systems. Semicond. Sci. Technol. 24(3), 035016 (2009).  https://doi.org/10.1088/0268-1242/24/3/035016 CrossRefGoogle Scholar
  8. 8.
    Vasileska, D., Ferry, D.K.: Scaled silicon MOSFET’s: universal mobility behavior. IEEE Trans. Electron Devices 44(4), 577–583 (1997).  https://doi.org/10.1109/16.563361 CrossRefGoogle Scholar
  9. 9.
    Duster, J.S., Liu, Z.H., Ko, P.K, Hu, C.: Temperature effects of the inversion layer electron and hole mobility of MOSFETs from 85 K to 500 K. In: International Conference on Solid State Devices and Materials, Makuhari, pp. 835–837 (1993)Google Scholar
  10. 10.
    Chaudhry, A., Sangwan, S., Roy, J.N.: Mobility models for unstrained and strained silicon MOSFET’s: a review. Contemp. Eng. Sci. 4, 229–247 (2011)Google Scholar
  11. 11.
    Lee, K., Choi, J., Sim, S., Kim, C.: Physical understanding of low-field carrier mobility in silicon MOSFET inversion layer. IEEE Trans. Electron Devices 38(8), 1905–1912 (1991).  https://doi.org/10.1109/16.119032 CrossRefGoogle Scholar
  12. 12.
    Takagi, S., Toriumi, A., Iwase, M., Tango, H.: On the universality of inversion layer mobility in Si MOSFET’s: Part I—Effects of substrate impurity concentration. IEEE Trans. Electron. Devices 41(12), 2357–2362 (1994).  https://doi.org/10.1109/16.337449 CrossRefGoogle Scholar
  13. 13.
    Gamiz, F., Lopez-Villanueva, J., Banqueri, J., Carceller, J., Cartujo, P.: A comparison of models for phonon scattering in silicon inversion layers. J. Appl. Phys. 77(8), 4128–4129 (1995).  https://doi.org/10.1063/1.359500 CrossRefGoogle Scholar
  14. 14.
    van Langevelde, R., Klaassen, F.M.: Effect of gate-Field dependent mobility degradation on distortion analysis in MOSFET’s. IEEE Trans. Electron. Devices 44(11), 2044–2052 (1997).  https://doi.org/10.1109/16.641382 CrossRefGoogle Scholar
  15. 15.
    Takagi, S.: Two-dimensional carrier transport in Si MOSFETs. VLSI Des. 8(1–4), 1–11 (1998).  https://doi.org/10.1155/1998/53272 CrossRefGoogle Scholar
  16. 16.
    Cheng, B., Woo, J.: Measurement and modeling of the n-channel and p-channel MOSFET’s inversion layer mobility at room and low temperature operation. J. Phys. IV 6(C3), C3–43 (1996).  https://doi.org/10.1051/jp4:1996306 Google Scholar
  17. 17.
    Pirovano, A., Lacaita, A.L., Zandler, G., Oberhuber, R.: Explaining the dependences of the hole and electron mobilities in Si inversion layers. IEEE Trans. Electron. Devices 47(4), 718–724 (2000).  https://doi.org/10.1109/16.830985 CrossRefGoogle Scholar
  18. 18.
    Lundstrom, M.: Fundamentals of Carrier Transport, 2nd edn. Cambridge University Press, Cambridge (2000)CrossRefGoogle Scholar
  19. 19.
    Lim, K.Y., Zhou, X.: A physically-based semi-empirical effective mobility model for MOSFET compact I–V modeling. Solid-State Electron. 45(1), 193–197 (2001).  https://doi.org/10.1016/S0038-1101(00)00190-8 CrossRefGoogle Scholar
  20. 20.
    Tsague, H.D., Twala, B.: Investigation of carrier mobility degradation effects on MOSFET leakage simulations. Int. J. Comput. 15, 237–247 (2016)Google Scholar
  21. 21.
    Cristoloveanu, S., Rodriguez, N., Gamiz, F.: Why the universal mobility is not. IEEE Trans. Electron. Devices 57(6), 1327–1333 (2010).  https://doi.org/10.1109/TED.2010.2046109 CrossRefGoogle Scholar
  22. 22.
    Thomas, S.M.: Electrical characterization of novel silicon MOSFETs and finFETs. Ph.D. Thesis, University of Warwick (2011). https://warwick.ac.uk/fac/sci/physics/research/condensedmatt/silicon/papers/theses/stephen_thomas_phd_thesis.pdf
  23. 23.
    Oberhuber, R., Zandler, G., Vogl, P.: Sub-band structure and mobility of two-dimensional holes in strained Si/SiGe MOSFET’s. Phys. Rev. B 58(15), 9941 (1998).  https://doi.org/10.1103/PhysRevB.58.9941 CrossRefGoogle Scholar
  24. 24.
    Takagi, S., Takayanagi, M., Toriumi, A.: Characterization of inversion-layer capacitance of holes in Si MOSFET’s. IEEE Trans. Electron. Devices 46(7), 1446–1450 (1999).  https://doi.org/10.1109/16.772489 CrossRefGoogle Scholar
  25. 25.
    Jungemann, C.: Improved modified local density approximation for modeling of size quantization in pMOSFETs/C. In: Jungemann, C.D., Nguyen, B., Neinhus, S., Decker, B., Meinerzhagen (eds.) Institute of Electrodynamics and Microelectronics, Bremen, Germany, 4p (2001)Google Scholar
  26. 26.
    Wang, E.X., Matagne, Ph, Shifren, L., Obradovic, B., Kotlyar, R., Cea, S., Stettler, M., Giles, M.D.: Physics of hole transport in strained silicon MOSFET inversion layers. IEEE Trans. Electron. Devices 53(8), 1840–1851 (2006).  https://doi.org/10.1109/TED.2006.877370 CrossRefGoogle Scholar
  27. 27.
    Saito, S., Hisamoto, D., Kimura, Y., Sugii, N., Tsuchiya, R., Torii, K., Kimura, S.: Origin of drivability enhancement in scaled pMOSFETs with 45 degree rotated \(\langle 100\rangle \) channels. In: Symposium on VLSI Technology, Tech. Dig. (2006).  https://doi.org/10.1109/VLSIT.2006.1705261
  28. 28.
    Donetti, L., Gámiz, F., Thomas, S., Whall, T.E., Leadley, D.R., Hellström, P.-E., Malm, G.D., Östling, M.: Hole effective mass in silicon inversion layers with different substrate orientations and channel directions. J. Appl. Phys. 110(6), 063711 (2011).  https://doi.org/10.1063/1.3639281 CrossRefGoogle Scholar
  29. 29.
    Hou, Y.-T., Li, M.-F.: A simple and efficient model for quantization effects of hole inversion layers in MOS devices. IEEE Trans. Electron. Devices 48(12), 2893–2898 (2001).  https://doi.org/10.1109/16.974723 CrossRefGoogle Scholar
  30. 30.
    Ando, T., Fowler, A.B., Stern, F.: Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54(2), 437 (1982).  https://doi.org/10.1103/RevModPhys.54.437 CrossRefGoogle Scholar
  31. 31.
    Ferry, D.K., Goodnick, S.M., Bird, J.: Transport in Nanostructures, 2nd edn. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  32. 32.
    Sze, S.M., Ng, K.K.: Physics of Semiconductor Devices, 3rd edn. Wiley, London (2007)Google Scholar
  33. 33.
    Boiko, I.I.: Kinetics of Electron Gas Interacting with Fluctuating Potential. Naukova Dumka, Kiev (1993). (in Russian)Google Scholar
  34. 34.
    Boiko, I.I., Sirenko, Y.M., Vasilopoulos, P.: Dielectric formalism for a quasi-one-dimensional electron gas. I. Quantum transport equation. Phys. Rev. B 43(9), 7216 (1991).  https://doi.org/10.1103/PhysRevB.43.7216 CrossRefGoogle Scholar
  35. 35.
    Boiko, I.I., Sirenko, Y.M., Vasilopoulos, P.: Dielectric formalism for a quasi-one-dimensional electron gas. II. Dielectric functions and potential correliators. Phys. Rev. B 14(3), 788–797 (1991).  https://doi.org/10.1103/PhysRevB.43.7224 Google Scholar
  36. 36.
    Boiko, I.I.: Transport of Carriers in Semiconductors. V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, Kyiv (2009). (in Russian)Google Scholar
  37. 37.
    Kozlovskiy, S.I., Sharan, N.N.: Dilatation deformation potential, drift mobility and piezoresistance in p-type silicon (quantum kinetic approach). J. Comput. Electron. 14(3), 788–797 (2015).  https://doi.org/10.1007/s10825-015-0716-y CrossRefGoogle Scholar
  38. 38.
    Kozlovskiy, S.I., Sharan, N.N.: Piezoresistance effect in n-type silicon: from bulk to nanowires. J. Comput. Electron. 13(2), 515–528 (2014).  https://doi.org/10.1007/s10825-014-0563-2 CrossRefGoogle Scholar
  39. 39.
    Yu, P.Y., Cardona, M.: Fundamentals of Semiconductors: Physics and Material Properties, 4th edn. Springer, Heidelberg (2010)CrossRefMATHGoogle Scholar
  40. 40.
    Takagi, S.A., Iwase, M., Tango, H.: On the universality of inversion layer mobility in Si MOSFET’s: Part II—effects of surface orientation. IEEE Trans. Electron. Dev. 41(12), 2363–2368 (1994).  https://doi.org/10.1109/16.337450 CrossRefGoogle Scholar
  41. 41.
    Schroder, D.K.: Semiconductor Material and Device Characterization. Wiley, London (2006)Google Scholar
  42. 42.
    Watt, J.T., Plummer, J.D.: Universal mobility-field curves for electrons and holes in MOS inversion layers. In: Symposium on VLSI Technology, pp. 81–82 (1987)Google Scholar
  43. 43.
    Chen, K., Wann, H.C., Ko, P.K., Hu, C.: The impact of device scaling and power supply change on cmos gate performance. IEEE Electron. Device Lett. 17(5), 202–204 (1996).  https://doi.org/10.1109/55.491829 CrossRefGoogle Scholar
  44. 44.
    Knezevic, I., Ramayya, E.B., Vasileska, D., Goodnick, S.M.: Diffusive transport in quasi-2D and quasi-1D electron systems. J. Comput. Theor. Nanosci. 6(8), 1725–1753 (2009).  https://doi.org/10.1166/jctn.2009.1240 CrossRefGoogle Scholar
  45. 45.
    Jin, S., Fischetti, M.V., Tang, T.-W.: Modeling of surface-roughness scattering in ultrathin-body SOI MOSFETs. IEEE Trans. Electron. Devices 54(9), 2191–2203 (2007).  https://doi.org/10.1109/TED.2007.902712 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.V. Lashkaryov Institute of Semiconductor PhysicsNational Academy of Sciences of UkraineKievUkraine

Personalised recommendations