Моделювання розподілу носіїв заряду в активній області P-I-N-діодів методами теорії збурень

• Дата: 2021
• Автори: Бомба, Андрій, Мороз, Ігор
• Формат: Стаття
• Мова: English
• Опубліковано: Kamianets-Podilskyi National Ivan Ohiienko University 2021
• Онлайн доступ: http://mcm-tech.kpnu.edu.ua/article/view/251064
• Назва журналу: Mathematical and computer modelling. Series: Technical sciences

A mathematical model of the electron-hole plasma stationary distribution in the active region (i-region) of p-i-n-diodes in the diffusion-drift approximation is proposed. The model is represented in the form of a nonlinear singularly perturbed boundary value problem for the system of equations of the electron-hole currents continuity, the Poisson equation and the corresponding boundary conditions. The decomposition of the nonlinear boundary value problem of modeling the stationary distribution of charge carriers in the plasma of p-i-n-diodes is carried out on the basis of the solutions asymptotic representation. The model problem is reduced to a sequence of the linear boundary value problems with a characteristic separation of the main (regular) components of the asymptotics and a boundary corrections. It was found that the formulation of the problem for finding the zero term of the asymptotics regular part coincides with the classical formulation of the p-i-n-diodes characteristics modeling problem, which is carried out in the approximation of the ambipolar diffusion (approximation of a self-consistent electrostatic field). The proposed mathematical model and the method of its linearization make it possible to determing the main components in the diffusion-drift process and to study their role. For example, it becomes possible to study (including by analytical methods) the behavior of plasma in the p-i-, n-i-contacts zones. The results of the study are aimed at developing methods for designing p-i-n-diode structures, used, in particular, as active elements of the signals switches of a microwave data transmission systems and the corresponding protective devices.