Dispersion of MOS capacitance-voltage characteristics resulting from the random channel dopant ion distribution

The random nature of the channel dopant ion distribution in silicon MOS devices is shown to cause a stretch-out of the capacitance-voltage characteristics. This nonideal behavior is caused by surface potential fluctuations which can be accurately modeled by assuming that the threshold voltage varies laterally over the area of the device with a normal distribution. The standard deviation of the threshold voltage distribution extracted from n- and p-channel MOS devices is presented for a wide range of substrate doping levels at both room and liquid-nitrogen temperature. The observed standard deviation of the threshold voltage is accurately predicted by a three-dimensional model based on the method of images which includes only the contribution from a random distribution of dopant ions in the depletion region. The contribution to the surface potential fluctuations from other sources is shown to be insignificant at high channel doping levels