Fourier series expansion method in the study of Gunn effect: a comparison between periodic and non-periodic basis functions

The method of Fourier series expansion is used to treat the spatial dependence of the electric field in the theory of the Gunn effect. Physical consequences of using the frequently used Born-von Karman periodic basis functions are discussed. It is shown that periodic basis functions impose rather unrealistic conditions on the electric field at the boundaries, therefore these basis functions are not appropriate in the study of finite systems. Non-periodic basis functions should be used in this study. Physical meaning and significances of using non-periodic basis functions are discussed in detail. Fourier series expansion method is particularly useful in studying n-type GaAs with a sample length of the order of ten micrometers or less. Some numerical results for domain formation and propagation are given, in which the boundary conditions (for the dynamical equation) chosen for the study are briefly discussed. It is suggested that it is more appropriate to impose both of the two boundary conditions at the cathode than to impose one at the cathode and the other at the anode.