Ellipsometry complex refractive index

Finally, n was determined by spectroscopic ellipsometry. The main drawback with this technique when applied to anisotropic samples is that the measured ellipsometric functions tanlF and cos A are related both to the incidence angle and the anisotropic reflectance coefficient for polarizations parallel and perpendicular to the incidence plane. The parameters thus have to be deconvolved from a set of measurements performed with different orientations of the sample [see (2.15) and (2.16)]. The complex refractive index determined by ellipsometry is reliable only in the spectral region where the sample can be considered as a bulk material. In fact, below the absorption... 

Another reason for its relative neglect may be that it deals with properties that are rather unfamiliar, such as complex refractive index and the nature of polarised light, and has a mathematical basis that can seem obscure. To some extent this is the fault of ellipsometrists who have sometimes been content to talk only to other specialists in the field and have not devoted much effort to popularising the technique. Understanding what ellipsometry is and what it can do does require some acquaintance with the basic concepts, and, in particular, with three important parameters that are often ignored. 

Ellipsometry is a useful method if a consistent set of optical parameters k, n) can be determined. Then a measurement of the complex refraction index allows the determination of d and k. 

An obvious attractive feature of ellipsometry is that two parameters are obtained in a single measurement. If there is only one perfectly homogeneous surface with a complex refractive index, the real and complex part of the refractive index can be calculated from the two ellipsometric angles. The situation becomes more complicated if the assumed system becomes more complicated every thin film has a thickness and a complex refractive index, which means three additional parameters. 

Fig. 4.1-164 ZnTe. Numerically calculated spectral dependence of the complex refractive index ( andk) solid lines). The circles are measured ellipsometry data [1.130]. The triangles are experimental data taken from [1.131]...

In addition to measurement of the dielectric constant at frequencies ranging from 10 kHz to 1 MHz through capacitance measurement using evaporated dot contacts, it is possible to use spectroscopic ellipsometry to evaluate its refractive index. The complex refractive index is the square root of the product of the complex relative dielectric constant and the complex relative permeability. Since ULK films are nonmagnetic, the permeabUity can be approximated by unity. While it is true that the eUipsometry... 

Structure of porous silicon (Astrova and Tolmachev 2000). A serial-parallel model for the porosity and oxidation dependence of dielectrics for porous silicon has thus been reported. Predictions agree with experimental results, which enable us to measure the extent of oxidation (Pan et al. 2005). An ab initio quantum mechanical study of the effects of oxidation process in porous silicon using an interconnected supercell structure and its complex refractive index was also reported and compared with experimental data obtained from spectroscopic ellipsometry (Cisneros et al. 2007). 

In order to calculate the optical generation rates in the organic absorbers (see appendix 1), it is necessary to determine the complex refractive index n = n + ik of all layers. The most useful method to obtain this data is spectroscopic ellipsometry, which allows us to determine the real part n and imaginary part k of the refractive index. The general measurement principle of ellipsometry is to measure the polarization of an output beam after the polarized input beam has interacted with the sample. From the change in polarization we derive the optical properties of the layer by fitting the measured output polarization to a model of the optical response of the material [144]. 

The complex dielectric function, e = i — ie2, which describes the material properties is connected to the complex refractive index N for discussing optical propagation through e = N, vhth e = n — and = Ink. Eor absorbing media, k and 2 are positive. Ellipsometry allows direct measurements to be made of the refractive index (n) and the extinction coefficient (k). 

Constructing an optical model. In the data analysis procedure in ellipsometry, an optical model corresponding to the investigated sample structures must be constructed firstly. An optical model is represented by the complex refractive index and layer thickness of each layer, normally, it consists of an air/thin film/ substrate structure. It should be decided if any layer is anisotropac at this stage, and whether or not interface layers are to be modeled as a single effective medium approximation, or is a more complicated graded interface to be used for the sample. 

Figure 24. Spectra of complex refractive index, 7 2 = 2 j 2 for th passive oxide formed at 1.43 V vs. RHE in pH 8.4 borate and pH 3.1 phosphate solution for 1 h. The Ni was calculated from multi-wavelength ellipsometry with the film thickness. Reprint from T. Ohtsuka, K. Azumi, and N. Sato , A spectroscopic Property of the Passive Film on Iron by 3-parameter Reflectometry , Denki Kagaku, 51 (1983) 155, Copyright 1983 with permission from The Electrochemical Soc. of Japan.

Light is an electromagnetic wave and all its features relevant for ellipsometry can be described within the framework of Maxwell s theory [1]. The relevant material properties are described by the complex dielectric function e or alternatively by the corresponding refractive index n. 

In ellipsometry monochromatic light such as from a He-Ne laser, is passed through a polarizer, rotated by passing through a compensator before it impinges on the interface to be studied [142]. The reflected beam will be elliptically polarized and is measured by a polarization analyzer. In null ellipsometry, the polarizer, compensator, and analyzer are rotated to produce maximum extinction. The phase shift between the parallel and perpendicular components A and the ratio of the amplitudes of these components, tan are related to the polarizer and analyzer angles p and a, respectively. The changes in A and when a film is present can be related in an implicit form to the complex index of refraction and thickness of the film. 

Thus, in principle, one can obtain the complex index of refraction from the upper left-hand quarter of the optical tensor M= [My, (i,j = 1,..., 3)]. We now explain how these optical constants can be derived from ellipsometry. 

As the molecular-scale heterogeneity of the active layer greatly influences the power conversion efficiency, it is fundamentally important to identify and control the structural and optical properties and their relation to the function of a photovoltaic device. Ellipsometry is especially useful in determining the complex index of refraction and layer thickness, as well as structural details in thin-film geometry [69-72]. This information is needed to calculate the internal optical electric field distribution and the resulting photocurrent action spectra with respect to the efficiency of thin-film devices [66]. 

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