Capacitance and Barrier Height in Grain Boundaries

It is shown that the capacitance of a grain boundary depends on the height of the potential barrier φ only if φ is smaller than 2kT ln (Nd/ni) (ev). For higher barrier potentials the capacitance is in good approximation a function of the bulk properties only. The capacitance as a function of applied bias and temperature (100–250°K) has been measured on tilt boundaries of 4°, 6°, and 25°, with donor concentrations ranging from 1014 to 1016 per cm3. It was found that in all cases the barrier height was larger than 2kT ln (Na/ni). This gives for the highest doped samples at 100°K a lower limit for the barrier height of 0.66(ev).