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Heterostructure Semiconductor Device Modelling
E.A.B. Cole
The Department has very close links with the Department of Electronic and Electrical Engineering, and with other departments, where new electronic devices with dimensions in the nanometer rang are being developed. Mathematical modelling plays a vital role in this development, along with the generation of new numerical techniques for the solution of the modelling equations. An inter-departmental research centre has been established at the University to provide a forum for research in this area. This is the Centre for Nano-Device Modelling and Dr Cole was its first Director from 1996 to 2000.
Current trends in microwave semiconductor technology take advantage of developments in low-dimensional structures using heterojunctions. These are made from very thin layers of semiconducting material, frequently less than ten nanometers thick. An example of this is the HEMT using Gallium Arsenide and Aluminium Gallium Arsenide in which electrons suffer little scattering, and consequently very fast devices with little noise can be fabricated. When source, gate and drain contacts are connected to the surface, a current flows from the source to the drain which can be controlled by varying the voltage on the gate. The purpose of this work is to model the device numerically to obtain expressions for the device behaviour, for example, its current-voltage characteristic.
There are many different ways in which semiconductor devices can be modelled, but electron transport in the device is based on equations which are mainly derived from the Boltzmann transport equation---current continuity and energy transport---together with the Poisson equation for the electrostatic potential. These are sufficient for many devices, for example, the Metal Semiconductor Field Effect Transistor (MESFET). But in the case of the High Electron Mobility Transistor (HEMT) the electrons move in potential wells caused by the layer interfaces and so the Schrödinger equation of quantum mechanics has to be solved self-consistently with the other equations.
Manufacturers of these devices are constantly trying out different layer structures in order to improve performance, and require fast and accurate solutions of the modelling equations. We are looking at this HEMT problem and others in two main ways: testing the various assumptions behind the equations using relatively simple numerical codes, and developing new numerical codes for more efficient solutions.
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