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Book cover Deterministic Solvers for the Boltzmann Transport Equation

Part of the book series: Computational Microelectronics ((COMPUTATIONAL))

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Abstract

For a Si hole inversion layer the parameters for phonon and surface roughness scattering, which are shown in Table  12.1, have been obtained by matching the simulation results to the long-channel low-field mobility measurements for bulk Si PMOSFETs from Takagi [5] at three lattice temperatures 223, 300, and 443 K shown in Fig. 12.1 (top). As in [3, 4], a phonon energy of ℏω = 61. 2 meV was used and kept fixed in this work. The other four scattering parameters were considered as adjustable parameters and their values were extracted by the fitting procedure. The Levenberg-Marquardt least square fitting algorithm [6, 7] was employed and the parameter set of Fischetti in [2] was chosen for initial values. The optimum scattering parameters after fitting are still in good agreement with the ones of Fischetti in [2]. After calibration, all scattering parameters are kept fixed for all simulations. Figure 12.1 (top) shows that the calculated channel mobility fits well the long channel low-field mobility measurements of Takagi [5].

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Notes

  1. 1.

    The results based on the classical DD model shown here are simulated with the GALENE device simulator [26] based on the self-consistent solutions of the constitutive equation for current density, the current continuity equation, and Poisson equation. Quantum corrections are excluded from these simulations. The gate work function difference is adjusted such that the threshold voltage is the same as the one in the multisubband device simulations. A constant mobility of 93 cm2/Vs, which is consistent with the homogenous channel low-field mobility for N inv = 1. 3 ×1013 cm − 2, is assumed. For the mobility reduction due to a limiting drift velocity, the saturated drift velocity of holes in bulk Si (v sat = 9. 5 ×106 cm s − 1) is assumed. The band gap narrowing due to the heavy doping is assumed to be negligible.

  2. 2.

    The average hole drift velocity is defined as: v x (x) = 1 ∕ N inv(x)1 ∕ (2π)2 ∑ν ∫v x ν(x, k)f ν(x, k)d2 k where v x ν is the subband group velocity in the channel direction x and f ν the subband distribution function.

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Authors and Affiliations

  1. Device Laboratory, Samsung Information Systems America, Inc., 75 West Plumeria Drive, San Jose, CA, 95134, USA

    Sung-Min Hong

  2. Institut für Elektronische Bauelemente und Schaltungstechnik, TU Braunschweig, 3329, 38023, Braunschweig, Germany

    Anh-Tuan Pham

  3. Institut für Theoretische Elektrotechnik, RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany

    Christoph Jungemann

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  1. Sung-Min Hong
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Hong, SM., Pham, AT., Jungemann, C. (2011). Results. In: Deterministic Solvers for the Boltzmann Transport Equation. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0778-2_12

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  • DOI: https://doi.org/10.1007/978-3-7091-0778-2_12

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