Avalanche breakdown in silicon diffused junctions

Abstract

In silicon erfc or gaussian diffused junctions, as well as in linearly graded and step junctions, avalanche breakdown voltage is given approximately by V B = (5.8 × 10 4) X T 0.84 where X T is total depletion-layer thickness in cm and V B is breakdown voltage in volts. This expression holds to ±9 per cent for plane junctions in the range 15 V to 1 kV, as indicated in Fig. 6, and should be useful to the practical device designer. The quantity X T for a diffused junction of the erfc type can be obtained from Fig. 3, which extends the range of previously published curves and is somewhat easier to read as well. This chart and Fig. 4, which gives peak field E M , can be used to estimate quantitatively the departure of such a diffused junction from pure step or pure graded behavior. The generalized V B - X T relationship is based in part on the results of Sze and Gibbons. When their expressions for V B in step and linearly graded junctions are recast in terms of X T (instead of doping N B and gradient a, respectively) these reduce to power-law expressions differing only in numerical coefficient (∼ 10 per cent difference). The expression's upper range, 300–1000 V, is based upon the recent diffused-junction data of van Overstraeten and de Man, and the lower range, 15–300 V, is also consistent with the experimental data of Miller on step junctions and Carlson on diffused junctions. Carlson's observations were made in about 1959 on large numbers of commercial diodes and have not previously been generally available. These sets of experimental data are compared with the calculated results of the workers mentioned above, plus the diffused-junction results of Kennedy and O'Brien.