Simulation of Semiconductor Rate Equations Using MATLAB's ODE45 Solver

In this study, we employ MATLAB's ODE45 tool to simulate semiconductor rate equations. These equations describe the time-dependent evolution of electron and hole concentrations in semiconductor devices. Through numerical simulation of semiconductor rate equations, we can gain deeper insights into carrier behavior within semiconductors and predict device performance characteristics. The ODE45 solver is MATLAB's adaptive Runge-Kutta method implementation for solving ordinary differential equations (ODEs). In our implementation, we formulate the rate equations as a system of coupled ODEs where carrier generation, recombination, and transport mechanisms define the differential terms. The solver uses variable step-size control to maintain numerical accuracy while efficiently computing concentration profiles over time. Key MATLAB functions include defining the differential equations in a function file, setting initial concentrations, specifying time span, and processing the output matrices containing time-evolution data. This approach provides numerical solutions for electron and hole concentration dynamics, enabling comprehensive analysis of semiconductor device behavior under various operating conditions.