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SUMMARYThis paper reports the results of a study of an error parameter, m, which has been proposed as a measure for determining the effects on accuracy of the basic assumptions upon which TLM modelling of diffusion and heat flow has been founded. The nature of the m parameter is studied in detail by using a two-dimensional thermal diffusion problem. The use of rn in the implementation of automatic timestepping is discussed in a practical three-dimensional engineering problem.

Thin film metal-insulator-semiconductor devices have been prepared on n-type InP substrates. The metal used was aluminium and the insulating oxide film was produced using an anodisation technique. Diodes were made with oxide thicknesses of 40 AA and 110 AA and were evaluated using current-voltage measurements over the temperature range 150-350K and also capacitance-voltage techniques. Both sets of measurements were compared with current metal-insulator-semiconductor theory and values were obtained for the barrier height in the semiconductor. Reasonable agreement was found but an anomaly previously observed in the Richardson plot in Al-InP Schottky barriers was again evident in the devices. The capacitance-voltage results indicated a surface-state density in the region of 1012 cm-2 eV-1. Values were also obtained for the barrier height presented to electrons by the insulating layer. This proved to be rather smaller than expected, which suggests that the mechanism of current flow through the layer is not simple tunnelling.

SUMMARYThe difference equations of the scalar linear transmission-line matrix (TLM) routine as introduced by Johns for numerically solving the diffusion equation are shown to be isomorphic to Goldstein's correlated random walk model of diffusion. For the infinite homogeneous bar their exact solution is derived algebraically and given in the form of Jacobi polynomials. This puts the TLM algorithm on a sounder mathematical and physical basis. The accuracy in solving the diffusion equation is investigated in general form and thus its astonishing efficiency explained. Several other basic questions of this numerical technique are also discussed.

Transmission line matrix (TLM) schemes for the Laplace equation exhibit some curious features. There exist values of TLM parameters where convergence towards the analytical values is very rapid. This phenomenon is first examined using a binary scattering approach. A Fourier analysis of the equivalently bounded diffusion equation does not reveal any features that would account for these observations. However, a similar analysis using the Telegraphers' equation suggests that a TLM model under optimum conditions is operating at the transition between real and imaginary solutions. Small differences between the optimized parameters predicted by the two approaches are probably due to inaccuracies in the Fourier description of the heat-injecting boundary condition that is used in TLM models