Ion Implantation Simulation Using Stepwise Boltzmann Transport Equation-Physical Models and Numerical Techniques

• Main Authors: Wang, Shyh-Wei, 王世維
• Other Authors: Shung-Fa Guo
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/83529562202123874582

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.