THE OPTIMIZATION OF THE SHAPE AND SIZE OF THE INJECTION CONTACTS OF THE INTEGRATED P-I-N-STRUCTURES ON THE BASE OF USING THE CONFORMAL MAPPING METHOD
Authors: Bomba A. Ya. , Moroz I. P. , Boichura M. V. 
Published: April 2021

Context. P-i-n-diodes are widely used in a microwave technology to control the electromagnetic field. The field is controlled by the formation of an electron-hole plasma in the region of an intrinsic semiconductor (i-region) under the influence of a control current. The development of control devices on p-i-n-diodes has led to the emergence of integral p-i-n-structures of various types, the characteristics of which (for example, switching speed, switched power level, etc.) exceed the similar characteristics of volume diodes. The properties of p-i-n-structures are determined by a number of processes: the diffusion-drift charge transfer process, the recombination-generation, thermal, injection, and the so on. Obviously, these processes should be taken into account (are displayed) in the mathematical model of the computer-aided design system for control devices of a microwave systems. Integrated process accounting leads to the formulation of complex tasks. One of them is the task of optimizing the shape, geometric dimensions and placement of the injected contacts (an active region).
Objective. The goal of the work is the development of a mathematical model and the corresponding software of the process of a microwave waves interaction with electron-hole plasma in an active region of the surface-oriented integral p-i-n-structures with ribbon-type freeform contacts to optimize an active region shape and its geometric dimensions.
Method. The main idea of the developed algorithm is to use the conformal mapping method to bring the physical domain of the problem to canonical form, followed by solving internal boundary value problems in this area for the ambipolar diffusion equation and the wave equation using numerical-analytical methods (the finite difference method; partial domains method using projection boundary conditions similar to the Galerkin method). The optimization algorithm is based on a phased solution of the following problems (the shape and geometric dimensions of the active region are specified at each stage): a computational grid of nodes for the physical regions of the problem is being found, in an active region the carriers concentration distribution is being determined and the energy transmitted coefficient in the system under study is being calculated, which is used in the proposed optimization functional. The extreme values of the functional are found by the uniform search method.
Results. The proposed mathematical model and the corresponding algorithm for optimizing the shape and geometric dimensions of the active region (i-region) of integrated surface-oriented p-i-n-structures expands the tool base for the design of semiconductor circuits of microwave frequencies (for example, similar to CST MICROWAVE STUDIO).
Conclusions. An algorithm has been developed to optimize the shape and geometrical dimensions of the active region of integrated surface-oriented p-i-n-structures with in-depth contacts intended for switching millimeter-wave electromagnetic signals. The universality of the algorithm is ensured by applying the method of conformal transformations of spatial domains. The example of the application of the proposed algorithm to search for the optimal sizes of wedge-shaped (in cross-section) contacts of silicon structures is considered.