Characterization of ultrathin metal–oxide–semiconductor structures using coupled current and capacitance–voltage models based on quantum calculation

Abstract

We have developed a capacitance–voltage (C–V) and a current–voltage (I–V) quasistatic quantum model of ultrathin metal–oxide–semiconductor (MOS) structures based on the self-consistent solution of the Schrödinger and Poisson equations. The direct tunneling current takes into account the carrier distribution in energy subbands and uses the notions of corrected tunnel transparency and of impact frequency at the injecting electrode. These models are used to obtain the main physical parameters of n+-polysilicon/SiO2/〈100〉 p-Si MOS structures, with oxide thickness ranging from 1.2 to 3.5 nm. The extracted parameters are the oxide thickness (TOX), the substrate doping, both at the Si/SiO2 interface [NS(0)] and deep in the bulk [NS(∞)], and the polysilicon gate doping (NP) near the polysilicon/SiO2 interface. For this range of oxide thickness, the direct tunneling current strongly perturbs the C–V measurements, which must be corrected. Down to 1.5 nm oxide thickness, these parameters are obtained by C–V characterization. Below 1.5 nm oxide thickness, the C–V correction fails and TOX is obtained by a coupled C–V and I–V characterization procedure, based on the adjustment of the effective mass of the electrons in the oxide (mOX) with the oxide thickness. The whole characterization procedure provides TOX values with associated errors very close to the ellipsometric measurements. The information obtained on the substrate doping seems to correspond well with advanced MOS technologies. The C–V and I–V simulation results are in good agreement with measurements for all the samples and a good consistency is found between the C–V and I–V models. Finally, we show that the extracted TOX obtained with the variation of mOX with TOX provide a better agreement than those with a constant mOX value, compared to the ellipsometric measurements.