An analytical threshold-voltage model of trench-isolated MOSdevices with nonuniformly doped substrates

A simple closed-form expression of the threshold voltage is developed for trench-isolated MOS (TIMOS) devices with feature size down to the deep-submicrometer range. The analytical expression is the first developed to include the nonuniform doping effect of a narrow-gate-width device. The inverse narrow width effect can be predicted analytically from the proposed model. It was derived by modeling the gate sidewall capacitance to include the two-dimensional field-induced edge fringing effect and solving the Poisson equation to include the channel implant effect at different operating backgate biases. A two-dimensional simulation program was developed, and the simulated data were used for verification of the analytical model. Good agreements between the modeled and simulated data have been achieved for a wide range of gate widths and biases. The model is well suited for the design of the basic transistor cell in DRAM circuits using trench field oxide isolation structure