Semi-classical calculation of charge distributions in ultra-narrow inversion lines

An increasing interest in submicrometer-scale electronic systems has prompted study of the achievable charge confinement in ultra-narrow inversion lines. This paper describes the modeling and resultant charge distributions obtained via semi-classical calculations for the silicon grating-gate field-effect transistor. Since the gate structure of this device is periodic, a relatively small simulation region with well-defined boundary conditions could be employed. Using a finite-element technique, the charge and electrostatic potential is calculated numerically and self-consistently, as a function of electrode biases. Results are presented for charge confinement both directly underneath and between grating electrodes, and an effective capacitance is extracted for the strongest confinement regime.