An alternative of spectroscopic ellipsometry: The double-reference method

Abstract

We have developed a conceptually new type of ellipsometry which allows the determination of the complex refractive index by simultaneously measuring the unpolarized normal-incidence reflectivity relative to the vacuum and to another reference media. From these two quantities the complex optical response can be directly obtained without Kramers-Kronig transformation. Due to its transparency and large refractive index over a broad range of the spectrum, from the far-infrared to the soft ultraviolet region, diamond can be ideally used as a second reference. The experimental arrangement is rather simple compared to other ellipsometric techniques. PACS numbers:Determination of the complex dielectric response of a material is an everlasting problem in optical spectroscopy. Depending on the basic optical properties, whether the sample is transparent or has strong absorption in the photon-energy range of interest, its absolute reflectivity or the transmittance is usually detected with normal incidence. Both quantities are related to the intensity of the light and give no information about the phase change during either reflection or transmission. Consequently, the phase shift is generally determined by Kramers-Kronig (KK) transformation in order to obtain the complex dielectric response. However, for the proper KK analysis the reflectivity or the transmittance spectrum has to be measured in a broad energy range, ideally over the whole electromagnetic spectrum.On the other hand, there exist ellipsometric methods [1,2] which are capable to simultaneously detect both the intensity and the phase of the light reflected back or transmitted through a media. Among them the most state-of-the-art technique is the time domain spectroscopy but its applicability is mostly restricted to the far infrared region. [3,4] An other class of ellipsometric techniques, sufficient for broadband spectroscopy, requires polarization-selective detection of light. [1,2] (In the following we will discuss experimental situations in reflection geometry although most of the considerations are valid for transmission, as well.) A representative example is the so-called rotating-analyzer ellipsometry (RAE) when the reflectivity is measured at a finite angle of incidence, usually in the vicinity of the Brewster angle. [1,2] Under this condition the Fresnel coefficients are different for polarization parallel (p-wave) and perpendicular (s-wave) to the plane of incidence and the initially linearly polarized light becomes elliptically polarized upon the reflection. By rotating the analyzer the ellipsometric parameters, i.e. the phase difference and the intensity ratio for the p-wave and s-wave components of the reflected light, [5] are measured and the complex refractive index can be directly obtained. Each of the above experimental methods is far more complicated than the measurement of unpolarized reflectivity or transmittance near normal incidence.As an alternative, we describe a new type of ellipsometry, hereafter referred to as double-reference spectrosc...