scholarly journals Spherical Harmonic Modeling of a 0.05 μm Base BJT: A Comparison with Monte Carlo and Asymptotic Analysis

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 147-151 ◽  
Author(s):  
C.-H. Chang ◽  
C.-K. Lin ◽  
N. Goldsman ◽  
I. D. Mayergoyz
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Band Structure ◽  
Asymptotic Analysis ◽  
Energy Distribution ◽  
Transport Equation ◽  
Spherical Harmonic ◽  
Boltzmann Transport Equation ◽  
System Of Equations ◽  
Boltzmann Transport

We perform a rigorous comparison between the Spherical Harmonic (SH) and Monte Carlo (MC) methods of solving the Boltzmann Transport Equation (BTE), on a 0.05 μm base BJT. We find the SH and the MC methods give very similar results for the energy distribution function, using an analytical band-structure, at all points within the tested devices. However, the SH method can be as much as seven thousand times faster than the MC approach for solving an identical problem. We explain the agreement by asymptotic analysis of the system of equations generated by the SH expansion of the BTE.

scholarly journals Monte Carlo Analysis of Anisotropy in the Transport Relaxation Times for the Hydrodynamic Model

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 161-165 ◽  
Author(s):  
Rossella Brunetti ◽  
Maria Cristina Vecchi ◽  
Massimo Rudan
Keyword(s):  
Monte Carlo ◽  
Band Structure ◽  
Hydrodynamic Model ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Monte Carlo Analysis ◽  
Collision Term ◽  
Monte Carlo Code ◽  
Boltzmann Transport ◽  
Transport Relaxation

This paper investigates the anisotropy properties of the relaxation times used in the hydrodynamic model. To this purpose a calculation of the collision term of the Boltzmann Transport Equation is performed by means of a Monte Carlo code accounting for the proper band structure and scattering features. Numerical results for electrons in silicon are shown at 77 and 300 K for E ║ <100> and E ║ <111>.

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