Variable Angle Spectroscopic Ellipsometry 
Between known ellipsometric methods the socalled Variable Angle Spectroscopic Ellipsometry (VASE) [46, 47] has been recently recognized as most useful and highly accurate method of calculating material parameters from the data of optical measurements. Whilst it does not directly measure the complex permittivity, the mathematical model it uses to deduce this and other such parameters gives a precise and reliable output without the need for referential measurements. Standard spectroscopic ellipsometry methods measure the Fresnel reflection coefficients as a function of wavelength only. Where VASE retrieval differs is that it measures the sample’s coefficients in sand ppolarized light (where sis electric field perpendicular to and pis in to the plane of incidence) as a function of wavelength and angle of incidence [48]. Measurements are obtained using several incident angles of light which results in an improvement in sensitivity and precision because the received data is taken using a variety of optical path lengths. Light is first passed through a monochromator to narrow its spectral band to a desired range before passing through a polarizer. It then strikes the specimen at an oblique angle, reflects onto a second, sometimes rotating polarizer known as an analyzer and is received by a detector. The angle of incidence, which is controlled by computer, generally varies between 50â—¦ and 80â—¦ in a rotating analyzer ellipsometer (RAE, showing Figure2) but thisis dependent onthe sample type[48]. Figure 2: A block diagram of a VASE retrieval system in the Rotating Analyser Ellipsometer (RAE )configuration[48]
Variable Angle Spectroscopic Ellipsometer [7,8] is an excellent tool to indirectly measure the complex permittivity of a layer with both known and unknown thickness. For the case when the layer thickness is known VASE instruments can measure the complex permittivity of a uniaxially anisotropic layers. Since a nanostructured layer must be previously geometrically characterized and its thickness should be already known, this review is concentrate on the possibility to measure both components of the permittivity tensor.
The VASE setup shines linearly polarized light on the sample surface with different angles of incidence. The electric field vector is oriented obliquely with respect to the plane of the light incidence. Then the ellipticity of the reflected light from the sample surface (which obviously appears in the case of the oblique incidence as one can see from the FresnelAiry formulas) is analyzed for the spolarized component of the electric field vector (component in the plane of incidence) and ppolarized component(that orthogonal to the incidence plane). The spectrometer measures the ratio of the s and p components for different angles and the existing softwares[19] fit the angular dependence of these results to the mathematically generated model of this angular dependence expected for a uniaxial layer of given thickness. This fitting deliversthe most suitable values of both components of the complex permittivity tensor at a given wavelength. Since the data is measured over the entire wavelength range the analysis of the frequency dispersion of the permittivity allows one to judge on the applicability of the VASE technique to the given nanostructure. If the dispersion turns out to be nonphysical,i.e. violates physical limitations[4], the method is not applicable. For natural films it was checked that the VASE retrievalis very accurate even near the absorption peaks where the dispersion of permittivity appears[20]. Therefore it should be applicable also for electromagnetic characterization of isotropic and uniaxial nanostructured layers beyond the resonance of its constitutive elements. Instructions of the usage can be found in the Internet [21].
There are numerous configurations available for variable angle ellipsometers, each with their own advantages, disadvantages and range of optimal incident angles. These are detailed in the literature. The resultant ratio of s and p reflectance coefficients is calculated for each angle and then compared with an assumed mathematical model detailing the physical structure of the specimen. The mathematical model of the oblique reflection of the wave from a layer of anisotropic medium with unknown tensor permittivity located on a known substrate is then used to derive the unknown permittivity. Although this overview is primarily interested in optical parameters, the layer thickness and surface and layer junction roughness can also be obtained using VASE retrieval. The high sensitivity and consequent high accuracy of VASE retrieval techniques are their strongest advantage. Their ability to be constructed in a variety of configurations also means that the system can be setup and used in a way that is optimal for each sample being tested. However care must be taken to ensure that the nanostructure under examinationis suitable for VASE retrieval. Because measurements are performed using a large wavelength range the suitability of a nanostructure must be scrutinized by analyzing the frequency dispersion of the permittivity. Samples that produce nonphysical dispersion that defy tangible limitations are not suitable for VASE retrieval techniques.
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