Optical Properties of Thin-Film SrTiO 3 on Si Grown by MBE
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analysis of the ellipsometric data. The crystallinity and orientation of the films were analyzed using x-ray diffraction. Only the (100) and (200) Bragg reflections were found, indicating good epitaxial alignment with the Si (001) substrate. The FWHM of the (200) Bragg reflection was about 1.3', which corresponds to a thickness ("grain height") of 65 A, about half the average film thickness measured by ellipsometry. There could be some contributions to the x-ray diffraction linewidths from lattice strain fields. The ellipsometry measurements described here were performed on a vertical deep-UV VASE ellipsometer equipped with a MgF 2 Berek waveplate.6 All measurements were carried out at three angles of incidence (65', 700, 750) in 0.02 eV steps from 0.7 to 6.6 eV. At each wavelength and angle of incidence, ten data points with different polarizer and compensator settings were taken to increase the accuracy of the ellipsometric angles N' and A. These ellipsometric angles were analyzed in a three-phase (substrate/film/ambient) model. The optical constants of Si and air are known and those of the film were parametrized using the Herzinger-Johs parametric oscillator
model.' This procedure ignores the amorphous interfacial layer. It reports an effective thickness t and an effective refractive index n approximately related to the true thicknesses and refractive indices of the SrTiO 3 (subscript 1) and the interfacial layer (2) by t = tI + t 2,
and
(1) (2)
nt = nt, +n 2t2 .
Equation (1) states that the total thickness is equal to the sum of the interfacial layer and epitaxial SrTiO 3 layer thicknesses. Equation (2) approximates the total optical density nt with the sum of the individual optical densities. This approximation is valid if the wavelength is much larger than the thickness,5 which is reasonable in our case. Our procedure leads to reliable results for the thickness and the optical constants, at least for the thicker films. For the thinnest films, there is some correlation between the thickness t and the effective refractive n. RESULTS The measured ellipsometric angles5 W and A for one film are shown in Fig. 1 by the dotted lines. The solid and dashed lines show V and A, respectively, calculated as described above, resulting in a film thickness of 199 A. The average difference between the data and model is about five times larger than the statistical errors, which is very good. We conclude that the threephase model gives an excellent description of the ellipsometric data. Any attempt to describe the data with a four phase model (treating the amorphous interfacial layer and the SrMiO 3 as separate layers) primarily fits the noise and does not lead to reproducible results. We therefore claim that spectroscopic ellipsometry in our energy range (0.6 to 6.6 eV) and for a 200 A thick film is not capable of resolving the amorphous interfacial layer. We can only describe the data with an effective three-phase model using Eqs. (1)-(2). Following this procedure for SrTiO 3 films with thicknesses between 63 and 200 A, w
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