Analytical solutions for avalanchebreakdown voltages of singlediffused gaussian junctions
Abstract
Closedform solutions of the potential difference between the 2 edges of the depletion layer of a single diffused Gaussian p n junction are obtained by integrating Poisson's equation and equating the magnitudes of the positive and negative charges in the depletion layer. By using the closed form solution of the static Poisson's equation and Fulop's average ionization coefficient, the ionization integral in the depletion layer is computed, which yields the correct values of avalanche breakdown voltage, depletion layer thickness at breakdown, and the peak electric field as a function of junction depth. Newton's method is used for rapid convergence. A flowchart to perform the calculations with a programmable handheld calculator, such as the TI59, is shown.
 Publication:

Solid State Electronics
 Pub Date:
 March 1983
 DOI:
 10.1016/00381101(83)900850
 Bibcode:
 1983SSEle..26..211S
 Keywords:

 Electron Avalanche;
 Electron Diffusion;
 Ionization Coefficients;
 PN Junctions;
 Poisson Equation;
 Surface Diffusion;
 Computerized Simulation;
 Convergence;
 Depletion;
 Impurities;
 Newton Methods;
 NewtonRaphson Method;
 Normal Density Functions;
 Numerical Stability;
 Performance Prediction;
 Electronics and Electrical Engineering