Generalized transconductance and transresistance methods for MOSFET characterization

Abstract

The concept of transconductance is generalized to include substrate and drain transconductances in addition to the usual gate transconductance. Generalized transresistances are defined as the ratio of transconductance to square of conductance, and their proportionality to channel length and reciprocal square of gate drive is exploited to develop six new analytical methods for determination of MOSFET threshold voltage and channel length. Quantitative expressions for the error components due to short channel geometry effects, asymmetry and bias dependence of source and drain series resistances, and mobility degradation are derived and related to total threshold voltage and channel length errors of various methods. In one set of methods the channel length error due to bias dependence of series resistance is eliminated by extrapolation to zero gate drive. Estimated errors agree well with measurements on submicron LDD transistors and the high precision of the gate transresistance technique is demonstrated with a channel length error of 3 nm limited by instrument resolution. Threshold voltage accuracy of 2 mV is obtained with the square-root substrate transresistance technique when series resistance is independent of substrate bias.