In the electronics industry, the main application of silicon dioxide (SiO₂) is used as the gate oxide in the manufacture of semiconductor devices (MOSFETs) and as an insulation layer. With fast progress in integration density, the importance of thin-gate oxides with thicknesses less than 7 nm increases (1). Moreover, transistors are expected to use a gate dielectric with capacitance equivalent to 2–3 nm of SiO₂. These trends require thickness and optical constants measurement techniques for such thin SiO₂ films.

Techniques suitable for measuring thin insulating films on semiconductors are ellipsometry, X-ray photoemission spectroscopy (XPS), transmission electron microscopy (TEM), Rutherford backscattering, and electrical methods of capacitance-voltage (C-V). The electronic structure, properties of ultrathin gate oxides, and imaging of individual dopant atoms and clusters in bulk Si at the atomic scale have been investigated with TEM (2–4). Ellipsometry also has been used to determine the optical properties of SiO₂ (5). It has a very high resolution and accuracy like C-V among these techniques. Moreover, the ellipsometric technique has been the most sensitive to oxide thickness as thin as 2 nm or less. When films are very thin, the optical pathlength is very small compared to the wavelength, so it becomes difficult to determine the index. In most work (6,7), bulk SiO₂ index values are used and only the thickness is fit while considering that is difficult to determine simultaneously thickness and index. Existence of correlation between index and thickness for very thin films makes it not reasonable to use the refractive index of SiO₂ bulk for a film with a thickness less than 10 nm, because it was known that the optical properties including the refractive index of ultrathin SiO₂ films were different from those of thick films (8–10).

Errors in the fixed SiO₂ index values translate into errors in film thickness, but these thickness errors are usually only a fraction of a monolayer for native oxides. This level of error traditionally has been acceptable in semiconductor manufacturing. However, in modern circuits, the oxide films are becoming very thin, so effects of oxide index and interface layers are becoming important. How to model these thin layers and determine simultaneously the refractive index and thickness for more accurate results should be considered. However, the difference of ellipsometric parameters between two ultrathin films was so little that the deduced values of the refractive index and thickness were very sensitive to errors within ellipsometric parameters. In this article, we propose a scheme to simultaneously obtain more accurate refractive index and thickness of natural SiO₂ films.

Variable angle spectroscopic ellipsometry (VASE) measures the changes in the polarization state of light as a function of the angle of incidence and wavelength when light is reflected from or transmitted through a sample. Details of the VASE technique are described elsewhere (11–13). In this article, VASE was used to determine the thickness and the refractive index of natural SiO₂ thin films and also investigate the effectiveness of various optical models.

Experimental

Sample Preparation: The silicon substrates were silicon wafers with a <100> orientation. They were boron-doped, p-type with resistivity in the range 2~4 Ωcm. The oxides were naturally grown, "native" oxide films on the Si substrates. The films were assumed isotropic and homogenous for the ellipsometric analysis.