Quantum effects in Si n-MOS inversion layer at high substrate concentration

The charge distribution at the semiconductgor-insulator interface is calculated for electrons by solving Schrödinger's and Poisson's equations self-consistently for particles obeying Fermi-Dirac statistics at 300 K. The results are applied to carriers in the channel of a crystalline MOSFET with the (100) axis perpendicular to the gate oxide. The inversion charge density calculated quantum mechanically is smaller than that calculated classically. This affects the shift of the subthreshold curves. The shift is larger at higher substrate impurity concentrations, and is especially pronounced at more than 10¹⁷ cm⁻³, which is the concentration used in recent MOS devices. The shift is as large as 0.18 V when the substrate impurity concentration is 8.5 × 10¹⁷ cm⁻³. Comparisons with measurement are also shown and it agrees well with quantum mechanical calculations. The inversion layer depth is compared, and a new efficient method is derived by transferring the quantum mechanical effect into the classical calculation. The results of this new method agree well with the quantum mechanical calculations and with the measurements.