Moderately-doped Schottky barriers: a description using thermionic emission over a wide temperature range

We report on a low temperature study of Schottky barriers between Au, Cr or Al electrodes deposited directly onto moderately-doped Si or GaAs substrates with doping densities in the range 1 x 10(15)-3 x 10(16) cm(-3) and find the unexpected result that for temperatures 5 < T <= 150 K both the zero-voltage Schottky barrier height, Phi(0)(SB)(T) and the reciprocal ideality factor, eta(T)(-1), have linear temperature dependences that extrapolate to zero at T = 0. Accordingly, the thermionic emission equation with these modified temperature-dependent parameters gives a good description of the current-voltage (I-V) characteristics at temperatures where thermionic field emission and field emission (direct tunneling) in addition to thermionic emission are known to be important. Our analysis utilizes a barrier inhomogeneity model to show that the temperature-independent product Phi(0)(SB)(T)eta(T) determined from forward bias characteristics defines a flat band voltage which is shown to be equivalent to the built-in voltage separately determined by extrapolation of capacitance versus voltage measurements made in the reverse bias region.