In this thesis an attempt is made to formulate closed sets of transport equations which are applicable to inhomogeneous and time-dependent situations in semiconductor hot electron transport problems. The basis of the formalism is the Boltzmann Transport Equation from which macroscopic, phenomenological transport . Equations are generated by the Moments Balance Method. The equations describe the behaviour of the electron distribution function in terms of the spatial and time-dependence of its moments. When the behaviour of the electron system is assumed to be typified by that of a finite number of its moments, the components of momentum and energy being the most important members of the set, then closed systems of transport equations are obtained. In the regime of small and slowly-varying density gradients, a theory of electronic diffusion has been developed. For isotropic, single valleys it is possible to derive a set of generalised Einstein relations which express the diffusion coefficients of the electrons in terms of their mobility, differential mobility and temperature. For many valley, ellipsoidal band structures, the results cannot in general be expressed in terms of simple relations such as the generalised Einstein relations although the theory does provide a semi-analytical' framework within which diffusion may be understood in terms of macroscopic quantities. The theory is applied to n-type gallium,arsenide and silicon. The effects of anisotropic electron-phonon scattering and electron-electron scattering in silicon have also been examined in some detail and were found to be small in determining the values of the velocity characteristic and diffusion coefficients. The transport equations derived from the Moment Balance formalism may be modified to form the basic of constitutive equations for the Gunn Effect. These equations are able to give a unified account for the roles of diffusion, intervalley scattering and energy transport in the propagation properties of Gunn Domains, in a manner that is consistent with the Boltzmann Equation. The dynamics of domain propagation are studied. by a simulation technique. It is found that heat currents and intervalley scattering have a crucial effect on domain shapes and propagation velocity.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:594983 |
| Date | January 1972 |
| Creators | Cheung, Philip Siu-Yu |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/71882/ |
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