Semiconductor Superlattice Negative Differential Conductance And Nonlinear Characteristics Of The Study

In the first part we review the properties, methods of solution and applications of Fokker-Planck equation, as well as some intepretations on the negative differential conductivity (NDC) and oscillation properties in superlattice. In the meantime, we discuss the nonlinear properties in semiconductor and choas theory. Take the circle map as a example, we analyse the roads to choas through double-period bifurcation, quasiperiod,and describe the phase-locking phenomenon in detail.In view of the phonon-electron, impurity-electron and electron-electron scattering, we treat the electron as Brownian motion particle in rectangle period potential. By using matrix continued fraction method we solve the corresponding Fokker-Planck equation of electron, and obtain the V-E relation on electricity transportion. It coincide with the emperical relation V =μE/1+(E/E_C)~2 very well. Through adapting the width or depth of period potential, we discuss the influence of temperature on NDC property. At high temperature, we can hardly observe the NDC property.Based on the relation V =μE/1+(E/E_C)~2 we probe the choas, phase-locking properties in superlattice by macro-transportion theory. Starting with the equation of high field domain motion, on certain approximation condition, we obtain a four dimension constant differential equations. By using numerical integration and FFT methods, we analyse the motion character in various parameters. Our result is similar to that in semiconductor, and prove the predictions of circle map.