Determination of the gate dielectric capacitance of ultrathin high-k layers

A technique is proposed for extraction of the capacitance of ultrathin high-k gate dielectrics. The only assumptions made in deriving the mathematical relations for the extraction plots are that both the space charge and the interface trap capacitances are exponential functions of betaphi, where cps is the surface potential. Deviation of the value of the constant beta from that of q/2kT may be considered an indication of the extent of quantization. The proposed technique, and for the sake of comparison, some existing gate dielectric capacitance extraction techniques, were applied to different high-k gate dielectrics with varying band offsets and equivalent oxide (SiO2) thickness (EOT) varying between 0.5 and 1.5 nm. The experimental capacitance-voltage data were taken from the literature, after carefully selecting the high-k gate dielectrics, to obtain varying band offsets and EOTs. Very satisfactory linear fits to the data points in the extraction plots were consistently obtained in the case of the proposed technique, and the values of the gate dielectric capacitance, Cdi, appear to be reasonable and consistent with the experimental values of beta. The McNutt, Maserjian, and Ricco techniques were found to have serious problems.