Experimental determination of equivalent oxide thickness of gate insulators

We propose an experimental method of determining the equivalent oxide thickness (EOT) of gate insulators based on the principle that the capacitance associated with the bandbendings in the Si substrate and the gate (Si capacitance) depends only on the Si surface field. To do this we experimentally obtained the Si surface field by using the capacitance-voltage (CV) integration method, and we used x-ray reflectometry to measure the physical thickness of thermal oxides. We then determined the relationship between the Si capacitance and the Si surface field. The relationship among the Si capacitance, the Si surface field, the EOT, and gate voltage minus the flatband voltage was also experimentally obtained. From these two relationships, we produce ideal CV curves for any given EOT and determined EOTs in such a way that the ideal CV curves fit best with the experimental results. Accordingly, our method is free of errors that accompany modeling the quantum mechanics of the gate electrode and Si substrate, and any errors that it does contain are independent of the film thickness. We further simplified the method for practical application by approximating the above relationships using rational polynomials. The results obtained by this simplified method were in good agreement with the experiments for the whole range of thicknesses. In contrast, the conventional quantum mechanical simulators produced CV curves that showed no small difference from the measured ones in the case of thin oxides in the 1-nm-thick range, and led to an overestimate of the EOT. Our method of EOT derivation provides an important basis for developing high-performance metal-oxide-semiconductor transistors.