On the extraction of oxide thickness and sub-band energy shift in thin oxide MOS capacitors with permeable gates

Accurate extraction of the gate dielectric thickness of MOS devices (t_ox) by electrical means is becoming increasingly difficult because quantum mechanical (QM) effects complicate the modeling of the free carrier charge and differential capacitance, hence the derivation of analytical expressions relating t_ox to easily measurable parameters. A simple and promising technique to locally extract t_ox and other quantization parameters from measured C-V curves was recently proposed, based on an empirical charge model. This technique was shown to provide reasonably accurate estimates of t_ox down to ≈ 4 nm. In this paper we exploit the above mentioned technique as a vehicle to investigate the impact of carrier quantization and wave function penetration in ultra-thin oxides on the accuracy of oxide thickness extraction procedures. To this purpose the vehicle procedure is applied to simulated C-V curves obtained from an accurate quantum mechanical model of the MOS stack