| Summary: | 博士 === 國立交通大學 === 電子工程學系 === 86 === In this dissertation, we have developed some physical models
and numerical techniques for stepwise Boltzmann transport
equation (BTE) simulations. They are the rational function
fitting of the nuclear scattering cross-section function, the
exact nuclear scattering cross-section calculation and the non-
uniform energy grid momentum matrix which records the ion energy
and direction angle. They are successfully applied in ion
implantation simulations including ion and recoil distributions.
The stopping power is expressed in terms of the differential
scattering cross-section. The nuclear differential scattering
cross-section is examined in great detail in this work. In order
to simplify the scattering cross-section, Lindhard, Nielson and
Scharff (LNS) had proposed a nuclear scattering cross-section
function to reduce the nuclear cross-section into one-variable.
However, current existing cross-section function equations are
too tedious or not accurate enough. A more efficient and precise
rational function fitting is devised for the LNS nuclear
scattering cross-section function. In order to describe the
nuclear stopping effects correctly, a systematic evaluation of
the exact nuclear differential scattering cross-section is
presented. It is composed of a two-dimensional table
construction and a two-dimensional divided difference
interpolation. The two-dimensional table is synthesized of the
impact parameter as a function of ion energy and scattering
angle. It is obtained by the iterative reverse magic formula
method. The integrals involving the nuclear scattering cross-
section are carefully evaluated with our interpolation. After
comparing to conventional methods, we find our new scheme can
produce a better agreement with the experiment and Monte Carlo
(MC) simulations. For example, the relative errors of projected
ranges for B in Si are reduced to be lower than 10% compared to
MC. In addition, a non-uniform energy grid momentum
matrix is proposed to replace the conventional uniform grid
matrix for heavy ion implantations. The non-uniform grid can
consider the low energy part strictly and the number of stopped
particles is obtained exactly. As an example, the relative
errors of projected ranges for 100 keV Bi in Si are reduced from
14% to 10% compared to MC. Our program is also applied to
other implantation problems, a multi-pass BTE is developed for
the calculations of the light ion and recoil distributions.
Besides, the multi-component target implantations are
considered. It is proved that our program can give a more
correct outcome, for instance, the errors of projected ranges
for Er in SiC are reduced from 15% to 11% compared to the
experiment. A parallelized BTE program for the multi-component
target implantation simulation is developed on CONVEX SPP-1000
with PVM (Parallel Virtual Machine) environment. A speed-up
factor of 3.3 has been achieved for the simulation of AZ1350 of
five components.
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