Resistivity of Bulk Silicon and of Diffused Layers in Silicon

A diffused layer in silicon is generally characterized by four parameters: the concentration, C,, , of diffused donors or acceptors at the surface, the concentration, C u , of acceptors or donors originally in the material (background concentration), the depth, x j , of the resultant junction, and the sheet resistivity, ps , of the layer. A knowledge of the relationship between these parameters is essential to the establishment of device processing recipes, the evaluation of diffusion techniques, and investigations of the thermodynamic properties of silicon. The desired relationship may be readily calculated, given a knowledge of the distribution of the diffused impurities, the variation of the resistivity of n- and p-type silicon with donor or acceptor density, and a fast electronic computer. The results of such a computation were first 387 388 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1962 made generally available three years ago, in the form of curves relating C,, to 1/psXj for a given CB , for 11- and for p-type layers in silicon, and for several common distributions. 1 Recent calculations, however, based on new and more extensive silicon resistivity data, have indicated considerable error in the earlier results. Thus a comprehensive recomputation has been undertaken, the outcome of which is presented herewith. A necessary adjunct to the calculation is an accurate knowledge of the resistivity of n- and p-type silicon with varying dopant concentration. To this end, most of the extant data have been reviewed and supplemented here and there with some new determinations.