Tham khảo tài liệu 'micro electronic and mechanical systems 2009 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Comparative Analysis of High Frequency Characteristics of DDR and DAR IMPATT Diodes 271 The boundary conditions for the system 1 can be written as follows n 0 t Nd 0 p l0 t Na 4 J lo t J ns Jp 0 t Jps. where Jns Jps are electron current and hole current for inversely biased p-n junction Nd o Na l0 are concentrations of donors and acceptors at two space points x 0 and x l0 where l0 is the length of the active layer of semiconductor structure. Electrical field distribution into semiconductor structure can be obtained from Poisson equation. As electron and hole concentrations are functions of the time therefore this equation is time dependent too and time is the equation parameter. Poisson equation for this problem has the following form dE x t Ỡ2U x t . . . . ------ Nd x -Na x p x t -n x t 3 d x Ữ x where Nd x Na x are the concentrations of the donors and acceptors accordingly U x t is the potential E x t is the electric field. The boundary conditions for this equation are follows M U 0 t 0 U l0 t U0 ỴU m sin Us Illi Pm 4 m 1 where U0 is the DC voltage on diode contacts Um is the amplitude of the harmonic number m a is the fundamental frequency pm is the phase of harmonic number m M is the number of harmonics. Equations 1 - 4 adequately describe the physical processes in the IMPATT diode in a wide frequency band. However numerical solution of this system is very difficult because of the sharp dependence of equation coefficients on electric field. The evident numerical schemes have poor stability and require a lot of computing time for the good calculation accuracy obtaining. It is more advantageous to use an implicit numerical scheme that has a significant property of absolute stability. The computational efficiency and the numerical algorithm accuracy are improved by applying space and time coordinates symmetric approximation. After the approximation of the functions and its differentials the system 1 is transformed to the implicit modified Crank-Nicholson numerical
