Charge integration and multigrid techniques in semiconductor device simulation

• Main Author: Liddiard, C. L.
• Published: Swansea University 1987
• Subjects: 621.3
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637908

Science and technology is experiencing a period of very rapid change which is euphemistically referred to as the information technology revolution. The main impetus for the latter is born of the ability to fabricate many thousands of devices on a single slice of monolithic crystal, otherwise known as the 'chip'. The ability to do this has meant that the power of the computer touches all facets of society. It is not surprising, therefore, that a great deal of emphasis is placed upon device fabrication. As functional circuits use more and more components, device geometries get progressively smaller, so that the only realistic way of predicting the behaviour of a device is through a computer model, or a device simulation. It is in obtaining improvements in the latter that forms the motivation for this thesis. In the early part of the thesis, the essential groundwork in electronic devices is covered. It serves to introduce both devices and approximate analytic modelling, thus showing the advantages of full numerical simulation. The results obtained serve as qualitative references, giving an idea of the type of solutions to be expected. The calculation of charge integrals is investigated. A fully consistent method contrasts the simpler 'lumping', and results for both formulations are presented. These results have prompted analytic investigations, which, in one dimension, have highlighted serious stability problems in consistent charge integration. In two dimensions, consistent charge integration has also been shown to produce oscillatory results. The origin of these 'wiggles' has been demonstrated as dependent on the mesh topology, showing fully consistent integration to be impractical. This leads to the recommendation of charge 'lumping', which extends to higher dimensions also. An exposition of the 'Multigrid' method is given, with particular emphasis on application to device simulation. All algorithms utilised are described, with detailed definition of problem dependent parameters. An optimal damping factor for damped Jacobi relaxation has been developed in respect of the Pisson equation. The contraction map defined may be extended to allow a fully consistent definition of the map for a general finite element discrete system. 'Multigrid' has been shown to be viable, within the limits of the model presented, for the continuity equations. The final chapter of the thesis serves to unite the material presented. The innovative aspects of the work are highlighted, with particular reference to previously published activity in these areas. This naturally describes the significance of the thesis in device simulation literature.