Carrier mobility and current saturation in the MOS transistor

Consideration is given to the phenomenon of saturation of drain current in the insulated-gate field-effect transistor. The effect of limited carrier drift velocity in the transistor channel is evaluated, and a quantitative theory developed to predict behavior in such a region of current flow. It is shown that the "paradox" of complete pinch-off at the drain need not necessarily be resolved by postulating a limiting carrier velocity to explain drain-current saturation. It is found that saturation of drain current may be meaningfully ascribed to saturation of carrier velocity only for special cases, such as
n
-type germanium transistors, and, in addition, this current saturation is only to "first order." Detailed consideration is given to behavior of drain-current saturation, and the physical mechanisms controlling saturation drain resistance and voltage gain are discussed and compared. It is proposed that for high-resistivity substrates, electrostatic drain to channel feedback is dominant, whereas for low-resistivity substrates modulation of the length of the space-charge region at the drain is dominant. Experimental evidence is presented for silicon metal-oxide-semiconductor (MOS) transistors which indicates that the effect of the channel mobile charge on the field distribution in the drain space-charge region is negligible as compared to several sources of "fixed" charge. Based on this it is concluded that carrier mobility within this region does not play a significant role in determining device characteristics. Brief consideration is also given to the "constant-carrier-mobility" approximation for behavior in the source region of the channel. It is found that due to fairly strong surface region scattering in silicon units, the effects of field dependent mobility are reduced substantially below that observed in single-crystal bulk material. The constant-mobility approximation is also experimentally confirmed by the excellent "square-law behavior" demonstrated by these transistors.