Internal Field Emission at Narrow Silicon and Germanium $p-n$ Junctions

A detailed study has been made of the reverse characteristics of several silicon and germanium alloyed $p-n$ junctions with breakdown voltages in the range of about 0.1 to 0.8 volt. In these junctions the reverse current is generated almost entirely by internal field emission (tunneling). The reverse bias characteristics are insensitive to the dislocation density present so that the tunneling current occurs mainly in undistorted material. From capacitance studies it is established that these narrow junctions are very close to being ideal step junctions. The room-temperature reverse characteristics are analyzed in terms of the usual tunneling probability expressions and in particular, good agreement, both qualitative and quantitative, is found between experiment and theory. The tunneling probability $\exp (-\frac{\alpha {\epsilon }^{\frac{3}{2}}}{E})$, when compared with experiment, yields values for $\alpha {\epsilon }^{\frac{3}{2}}$ in agreement with the theoretical ones to within a factor of less than 2 for both silicon and germanium.

The critical voltage (the reverse bias voltage necessary to maintain a constant tunneling current) was measured as a function of temperature from 4.2°K up to temperatures as high as 700°K. In germanium, the critical voltage drops monotonically as the temperature increases whereas in silicon, there is considerable structure in the curve. This is shown to be consistant with the tunneling being by direct transitions in germanium and by indirect transitions (involving phonon emission and absorption) in silicon. In germanium, the temperature dependence of the critical voltage arises from that of the direct energy gap while in silicon, it is determined, primarily, by the available phonon density. From an analysis of the temperature data for silicon that invokes the transverse acoustic phonons, the estimate of $\alpha {\epsilon }^{\frac{3}{2}}$ that is obtained is in excellent agreement with that found, independently, from the analysis of the reverse characteristics.