Abrupt p-n junctions at arbitrary injection levels

By introducing an injection level factor it is possible to obtain an approximate solution to the one-dimensional transport equations through an abrupt p-n junction. Within its approximations, this solution is valid at levels of injection including the medium and high level cases. It is shown that this general solution yields the accepted forms for the limiting cases of low and high injection and is accurate to better than 20 per cent in the medium injection region. It is also demonstrated that an expression for the I–V characteristic of a p-n junction at arbitrary injection levels can be obtained by an analogue approach. These two expressions are compared using representative bulk parameters for silicon, germanium and indium antimonide and it is shown that the latter approach is generally accurate to better than 8 per cent. A complete analytic expression for the current voltage characteristic of a p+−n junction is derived and shown to describe experimental observations within the error of measurement.