The pictures we construct for the properties of materials significantly depend upon the length scales that interest us, the specific properties in which we are interested, and the compromise between speed and accuracy that we are willing to accept. In this module, students will be taken from the basic principles of bonding at the atomic scale, through molecular and crystalline systems, arriving at the macroscopic system in terms of elastic properties, implantation damage and electronic devices. Through a combination of theory presented in a lecture context and practical applications of computational simulation, the students will review the most commonly used theoretical approaches to modelling materials, and develop an understanding of the advantages and disadvantages of each method. In particular, contrast between empirical and quantum-chemical models for bonds will be epitomised by application of LAMPS and AIMPRO codes to similar chemical systems, examining the quantitative accuracy of a range of experimentally observable properties. Following on from the atomic scale, TRIM and TCAD packages will be used to explore the implantation damage in the context of doping, with the subsequent evaluation of simple device performance, centred around a basic p-n junction.
Principal Learing Outcomes
- To be able to express the core principles underpinning computational modelling at multiple length and time scales, including implicit and explicit inclusion of atoms.
- To be able to distinguish the diverse sources of quantitative and qualitative error in simulations, based upon both the core errors at the mathematical model level, and errors introduced at the level of the model of the structure (be it a crystalline sample or an electronic device) approximating the system of interest.
- To become familiar with a number of computer packages, and be able to use them to determine the appropriate quantities, such as molecular structures, vibrational frequencies, field lines, device characteristics, and implantation profiles, from them.
- To be able to examine an experimental observation and design a computational simulation to complement the it, such as construct a model of a crystal defect and determine whether the computed properties confirm or refute the structure inferred from the experimental data.
Lectures 1-2 (Jon Goss)
Forces and energies; Empirical inter-atomic forces and types of bond; Equations of motion; Modelling vibrations; Determining transition states
Lectures 3-4 (Jon Goss)
Introductory quantum mechanical principles for electronic structure; Density
Lectures 5-6 (Jon Goss)
Modelling observables: optical transitions and the dielectric function, electrical
levels, hyperfine interactions
Lectures 7-8 (Jon Goss)
Advanced QM modelling techniques; Case studies
Lectures 9-10 (Jon Goss)
Ion implantation: themotivation, role of energy and mass, channelling, damage
Lectures 11-12 (James Kermode)
Finite element modelling (FEM)
FEM Workshop 1 (James Kermode)
Practical application of FEM: Mechanical modelling
FEM Workshop 2 (Jenny Webb)
Practical application of FEM: Mass transport
FEM Workshop 3 (Ben Green)
Practical application of FEM: Thermal