C–V index of hyperabrupt p-n junctions

C–V index n for hyperabrupt p⁺-n junctions with exponentially retrograded n-region has been computed numerically for different values of parameters characterizing the impurity profile and the results have been plotted graphically. Although n is found to vary with the bias across the junction for any given impurity distribution, the maximum value nmax of n is determined only by the ratio of the background concentration to the crossover concentration in the retrograded region. By making this ratio R₀ smaller and smaller, values of n substantially larger than unity can be obtained. Practical considerations, however, limit the maximum value of n to about 10. An empirical relation expressing nmax as a function of the ratio R₀ has been obtained. Calculated results are compared with the values of n measured on hyperabrupt junctions fabricated by a double diffusion process.