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Suprem-III User´s Manual
is to specify the input partial pressure of the dopant with the PP.DOPAN parameter. The surface concentration is
then calculated as a function of the partial pressure, time increment, growth rate, and the mass transport and kinetic
coefficients, K.a, K.p, and K.mf as specified by the SILICON statement. (See the previous reference.)
The numerical solution of the diffusion equations requires that the total step time be divided into a number
of smaller time increments, dt’s, in order to insure sufficient accuracy. There are two mechanisms that control the
choice of dt’s, one is due to a restriction on interface movement such that no interface moves more than one cell
spacing during a dt. The other time step control algorithm has been chosen to give the desired accuracy without using
excessive amounts of computation time. Unless the interface control chooses a smaller dt, it will attempt to use
a dt equal to that specified by the DTMIN parameter. Subsequent dt’s are chosen in the following manner.
1. At each point in the current structure a projected
concentration is calculated from the previous two
solutions.
Cp = C’ + (C’ - C’’)*dt/dt’
Where C’ is the previous concentration, C’’ is the
concentration before that, and dt’ is the previous dt.
2. From the current solution value, C, and the absolute
and relative truncation error parameters, an ‘error’
term at each point is then calculated.
Cerr = abs(C - Cp) / (ABS.ERR + abs(C)*REL.ERR)
3. The next dt is then calculated from the following
expression.
dtnext = dt * sqrt( (1. + dt/dt’)/Cerrmax )
Where Cerrmax is the maximum value of Cerr calculated
at each point in the structure.
4. A value of dtnext is calculated for each impurity
present with the smallest value being the one that
is ultimately used.