High resistance at crystal grain boundaries in $n$-type germanium is investigated. The resistance is symmetrical with respect to the direct on of the current and resembles the characteristics of a rectifier in the blocking direction. Such barriers are also photosensitive. The barrier is eliminated when the material is converted to $p$-type by nucleon bombardment or heat treatment. A theory is developed assuming the existence of surface states at the boundary. The ability of the barriers to withstand high voltages, around 100 volts, is explained by showing that the surface charge increases with increasing voltage. The dc conductance of the barrier, measured at different temperatures, agrees with theory in the dependence on temperature as well as in the order of magnitude. At sufficiently low temperatures the barriers show a capacitance independent of the frequency, whereas at higher temperatures the barrier admittance is strongly frequency dependent. These results are in agreement with the theory, showing that at low temperatures the current across the boundary is mainly carried by electrons, the hole current becoming increasingly important as the temperature is raised. The height of the potential barrier above the Fermi level is determined and found to be independent of temperature. A small difference in the measured breakdown voltage for the two directions of current is attributed to a difference in impurity concentration on the two sides of the boundary, which is confirmed by the ac measurements. The number of electrons on the boundary states is found to be of the order ${10}^{12}$ ${\mathrm{cm}}^{-2\mathrm{}}$ at the breakdown, which may be the saturation of the boundary states. However, the field at breakdown is only a few times lower than the critical value for the onset of the Zener current, and this mechanism cannot be definitely ruled out.

• Received 21 July 1952

DOI:https://doi.org/10.1103/PhysRev.88.867