Theory of the carrier-density fluctuations in an IGFET near threshold

Abstract

A three‐dimensional perturbation‐theory treatment of the carrier‐density fluctuations in the insulated‐gate field‐effect transistor (IGFET) above threshold and their effect upon the source‐drain current is presented. The fluctuations are considered to be generated by interface charge nonuniformities. It is shown that such fluctuations reduce the source‐drain current over that for a uniform device with the same average carrier density. It is found that the fluctuations increase with decreasing carrier density, that they are larger in a shallow channel than in a deep channel, and that the increase in fluctuations with decreasing carrier density is quite abrupt. The critical carrier density below which carrier‐density fluctuations are important is found to be ?10¹¹ carriers/cm² at 300 °K and ?10¹² carriers/cm² at 0 °K for ordinary‐device charge densities. The difference in the threshold for the onset of fluctuations at the two temperatures is attributable to the smaller amplitude of fluctuations at high temperatures. For interface charge densities in the neighborhood of 10¹⁰/cm² or lower no effect of fluctuations upon the IGFET current at 300 °K is expected, but there will still be an effect at low temperatures. These results are expected to be important in interpreting dc IGFET mobility measurements.