Skip to main content
Log in

On the numerical aspects of deterministic multisubband device simulations for strained double gate PMOSFETs

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

In this paper numerical aspects of deterministic multisubband device simulations are presented for strained double gate PMOSFETs including magnetotransport. The simulations are based on a self-consistent solution of the multisubband Boltzmann transport equation (BTE), 6×6 kp Schrödinger equation (SE) and Poisson equation (PE). For accurate and efficient calculation of the subband structure, an efficient discretization of the 2D k-space combined with a monotonic cubic spline interpolation is employed. The multisubband BTE is solved with a deterministic method based on a Fourier expansion of the distribution function. The Fourier series is found to converge rapidly for nanoscale double gate PMOSFETs. A convergence enhancement method for the Gummel type SE-PE-BTE loop by solving the BTE-PE simultaneously is proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Engl, W.L., et al.: Device modeling. Proc. IEEE 71, 10 (1983)

    Article  Google Scholar 

  2. Thompson, S., et al.: A 90 nm logic technology featuring 50 nm strained silicon channel transistors, 7 layers of Cu interconnects, low k ILD, and 1 um2 SRAM cell. In: IEDM Tech. Dig. p. 61 (2002)

  3. Mistry, K., et al.: A 45 nm logic technology with high-k+metal gate transistors, strained silicon, 9 Cu interconnect layers, 193 nm dry patterning, and 100% Pb-free packaging. In: IEDM Tech. Dig., pp. 247–250 (2007)

  4. Krishnamohan, T., et al.: Comparison of (001), (110) and (111) Uniaxial- and biaxial-strained-Ge and strained-Si PMOS DGFETs for all channel orientations: mobility enhancement, drive current, delay and off-state leakage. In: IEDM Tech. Dig. (2008)

  5. Grasser, T., et al.: A non-parabolic macroscopic transport models for device simulation based on bulk Monte Carlo data. J. Appl. Phys. 97, 093710 (2005)

    Article  Google Scholar 

  6. Jungemann, C., et al.: Failure of moments-based transport models in nanoscale devices near equilibrium. IEEE Trans. Electron Devices 52(11), 2404 (2005)

    Article  Google Scholar 

  7. Lundstrom, M., Ren, Z.: Essential physics of carrier transport in nanoscale MOSFETs. IEEE Trans. Electron Devices 49(1), 133 (2002)

    Article  Google Scholar 

  8. Pham, A.T., et al.: Deterministic multisubband device simulations for strained double gate PMOSFETs including magnetotransport. In: IEDM Tech. Dig. (2008)

  9. Pham, A.T., et al.: Efficient simulation of hole transport in strained Si and SiGe on insulator inversion layers. Solid-State Electron. 52, 1660 (2008)

    Article  Google Scholar 

  10. Jungemann, C., et al.: Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle. J. Appl. Phys. 100, 024502-1 (2006)

    Article  Google Scholar 

  11. Ringhofer, C.: A mixed spectral—difference method for the steady state Boltzmann–Poisson system. SIAM J. Numer. Anal. 41, 64 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gnudi, A., et al.: Two-dimensional MOSFET simulation by means of a multidimensional spherical harmonics expansion of the Boltzmann transport equation. Solid-State Electron. 36, 575 (1993)

    Article  Google Scholar 

  13. Goldsman, N., et al.: Advances in the spherical Harmonic-Boltzmann-Wigner approach to device simulation. Superlattices Microstruct. 27, 159 (2000)

    Article  Google Scholar 

  14. Pham, A.T., et al.: Microscopic modeling of hole inversion layer mobility in unstrained and uniaxially stressed Si on arbitrarily oriented substrates. Solid-State Electron. 52, 1437 (2008)

    Article  Google Scholar 

  15. Meinerzhagen, B., et al.: Quasi-simultaneous solution method: a new highly efficient strategy for numerical MOST simulations. IEEE Trans. Comput.-Aided Des. 4, 575 (1985)

    Article  Google Scholar 

  16. Jungemann, C., Meinerzhagen, B.: Analysis of the stochastic error of stationary Monte Carlo device simulations. IEEE Trans. Electron Devices 48(5), 985 (2001)

    Article  Google Scholar 

  17. Widiger, D.J., et al.: Two-dimensional transient simulation of an idealized high electron mobility transistor. IEEE Trans. Electron Devices 32(6), 1092 (1985)

    Article  Google Scholar 

  18. Pham, A.T., et al.: Physics-based modeling of hole inversion layer mobility in strained SiGe on insulator. IEEE Trans. Electron Devices 54(9), 2174 (2007)

    Article  Google Scholar 

  19. Pham, A.T., et al.: Simulation of mobility variation and drift velocity enhancement due to uniaxial stress combined with biaxial strain in Si PMOS. In: Proc. IWCE, pp. 45–48 (2009)

  20. Oberhuber, R., et al.: Subband structure and mobility of two-dimensional holes in strained Si/SiGe MOSFETs. Phys. Rev. B 58, 9941 (1998)

    Article  Google Scholar 

  21. Wang, E.X., et al.: Physics of hole transport in strained silicon MOSFET inversion layers. IEEE Trans. Electron Devices 53(8), 1840 (2006)

    Article  Google Scholar 

  22. Fischetti, M.V., et al.: Six-band kp calculation of the hole mobility in silicon inversion layers: dependence on surface orientation, strain, and silicon thickness. J. Appl. Phys. 94, 1079 (2003)

    Article  Google Scholar 

  23. Pham, A.T., et al.: A fast k*p solver for hole inversion layers with an efficient 2D k-space discretization. J. Comput. Electron. 7(3), 99 (2008)

    Article  Google Scholar 

  24. Fritsch, F.N., Carlson, R.E.: Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 17(2), 238 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  25. Levenberg, K.: A method for the solution of certain problems in least squares. Q. Appl. Math. 2, 164 (1944)

    MATH  MathSciNet  Google Scholar 

  26. Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11, 431 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  27. Michielis, M.D., et al.: A new analytical model for the energy dispersion in two-dimensional hole inversion layers. Solid-State Electron. 51, 598 (2007)

    Article  Google Scholar 

  28. Michielis, M.D., et al.: A new multi subband Monte Carlo simulator for nano p-MOSFETs. In: Proc. ULIS, pp. 67–70 (2008)

  29. Jin, S., et al.: Simulation of silicon nanowire transistors using Boltzmann transport equation under relaxation time approximation. IEEE Trans. Electron Devices 55(3), 727 (2008)

    Article  Google Scholar 

  30. Jungemann, C., et al.: Simulation of linear and nonlinear electron transport in homogeneous silicon inversion layers. Solid-State Electron. 36, 1529 (1993)

    Article  Google Scholar 

  31. Varga, R.S.: Matrix Iterative Analysis. Series in Automatic Computation. Prentice-Hall, Englewood Cliffs (1962)

    Google Scholar 

  32. Ren, Z., et al.: NanoMOS 2.5: A two-dimensional simulator for quantum transport in double-gate MOSFETs. IEEE Trans. Electron Devices 50(9), 1914 (2003)

    Article  Google Scholar 

  33. Pham, A.T., et al.: A convergence enhancement method for deterministic multisubband device simulations of double gate PMOSFET. In: Proc. SISPAD, pp. 115–118 (2009)

  34. Meziani, Y.M., et al.: Magnetoresistance mobility measurements in sub 0.1 μm Si MOSFETs. In: Proc. ESSDERC, pp. 157–160 (2004)

  35. Chaisantikulwat, W., et al.: Differential magnetoresistance technique for mobility extraction in ultra-short channel FDSOI transistors. Solid-State Electron. 50(4), 637 (2006)

    Article  Google Scholar 

  36. Huet, K., et al.: Monte Carlo study of apparent magnetoresistance mobility in nanometer scale metal oxide semiconductor field effect transistors. J. Appl. Phys. 104, 044504 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anh-Tuan Pham.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pham, AT., Jungemann, C. & Meinerzhagen, B. On the numerical aspects of deterministic multisubband device simulations for strained double gate PMOSFETs. J Comput Electron 8, 242–266 (2009). https://doi.org/10.1007/s10825-009-0301-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-009-0301-3

Keywords

Navigation