1998, Vol. 8, Nos. (1-4), pp. 515-520
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Calibration of a One Dimensional Hydrodynamic
Simulator with Monte Carlo Data
O. MUSCATO a,,, S. RINAUDOband P. FALSAPERLA
Dipartimento di Matematica, Viale Andrea Doria, 95125 Catania (Italy)"
bSGS-THOMSON Microelectronics, Stradale Primo Sole 50, 95121 Catania (ltaly)
In this paper we use the code Exemplar for matching a hydrodynamic 1D, time-
dependent simulator and the transport coefficients obtained by the Monte Carlo
simulator Damocles. This code is based on the Least Square method and it does not
require any a priori knowledge about the simulator (analytical form of the equations
etc.). The stationary electron flow in a one dimensional n+-n-n+submicron silicon
diode is simulated.
Keywords." TCAD, VLSI, BTE, transport theory, fluid mechanics, electronic devices
Electronic transport in semiconductors can be
described by hydrodynamic models (hereafter
HM), obtained by taking the moments of the
Boltzmann transport equation (hereafter BTE):
the resulting mathematical model consists of an
infinite hierarchy of Partial Differential Equations
expressing balance laws for the particle number n,
velocity,total energy E, deviatoric stress tensor
(0"), energy flux
coupled with the Poisson equation.
Recently Anile and Muscato  presented an
Extended Hydrodynamic model where the closure
of the moment hierarchy is obtained by exploiting
the entropy principle:
(or heat flux h ) and so on,
this system, which is
hyperbolic, consists of 13 scalar equations in the
determines the description of the stress and of
the heat flux, at variance with the other models.
Such a model has been tested successfully with
Monte Carlo (hereafter MC) simulations in Silicon
. The Left H and Side of the balance equations,
called production terms, represent the average rate
of change of carrier total energy Qw, momentum
Qp, energy-flux Qs and stress Q</j> due to the
scattering of carriers with the lattice. Usually they
are approximated with ad hoe empirical formula
 or as relaxation terms : this last approxima-
tion leads to a serious inconsistency with one of
the fundamental principles of Linear Irreversible
Thermodynamics, the Onsager Reciprocity Princi-
(n,,E,( ij),) and completely
O. MUSCATO et al.
Salvatore Rinaudo is research staff member at
ST. His research interests include process and
devices numerical simulations and technology
Paolo Falsaperla is Graduade student at Catania
University. His research interests include numer-
ical simulations and mathematical models for