software to fit optical spectra - Quantum Materials Group

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4.7.1. Differential dielectric function This model is intended to fit differential spectra of any quantity that can be generated by the “Dielectric function” model (section 4.6). The theoretical description of differential spectra is presented in section 2.3. A model of the “Differential dielectric function” type combines the two models of the “Dielectric function” type. The first dielectric function is treated as a base model and the second one – as a differential model. The description of the parameters is given in Table 4-6. # Wo Wp G 1 Base model # - - 2 Differential model # - - Table 4-6 The meaning of the parameters of the “Differential dielectric function” model. The output quantities of this model are the differential analogs of the quantities, generated by the “Dielectric function” model (see Table 4-2). For instance, the quantity “S1” is the differential conductivity. The Figure 4-5 presents an example of the “Differential dielectric function” model. It is assumed here that the base DF is stored in the “Model2” and the differential DF is in “Model3”. Note that all parameters of the “Model1” are fixed. The output quantity “R” of the “Model1” will correspond to the differential reflectivity ∆ R , “T” will correspond to the differential transmission ∆ T and so forth. Figure 4-5 An example of the “Differential dielectric function” model. Usually the fitting of differential spectra is done in two steps. On the first step the base model is adjusted to fit the base spectra. On the second step all the parameters of the base model are fixed and the differential model is adjusted to fit the differential spectra. Note that the internal parameters of the base model should be fixed on the second step. 4.7.2. Reflection and transmission of a multi-layer sample This model has been designed to fit the normal-incidence reflection and transmission spectra of samples that consist of an arbitrary number of layers (Figure 4-6). Each layer is supposed to be isotropic and described by its own complex dielectric functionε , thickness d and thickness spread δ d . Guide to RefFIT Page 64
Iinc Itrans ε ε ( 1) ( 2) … (n) ε Iref d1±δd1 d2±δd2 dn±δdn Figure 4-6 The experimental configuration of the model “Reflection and transmission of a multi-layer sample”. The sample reflectivity is defined as R = I ref / I inc , transmission is defined as T = I trans / I inc , where I inc is the intensity of the incident light, I ref - intensity of the reflected light and I trans - intensity of the transmitted light. The exact formulas for R and T are rather cumbersome; they can be found, for instance, in Ref. [14]. The parameters of this model are described in Table 4-7. The number of layers is given by the number of rows in the “Lorentzians” table. Each row corresponds to a particular layer. # Wo Wp G 1 DF model (layer #1) Thickness d (layer #1) [cm] Relative thickness spread δd/d (layer #1) 2 DF model (layer #2) Thickness d (layer #2) [cm] Relative thickness spread δd/d (layer #2) … … … … N DF model (layer #n) Thickness d (layer #n) [cm] Relative thickness spread δd/d (layer #n) Table 4-7 The parameters of the model “Reflection and transmission of a multi-layer sample”. An example of this of kind of model window is shown in Table 4-6. Here a two-layer system (film-substrate) is modeled. The top layer (film) is described by the dielectric function from “Model2”; it has a thickness of 1.76e-6 cm (17.6 nm) and relative thickness spread of 1%. The substrate is described by the dielectric function from “Model3” and it is 0.057 cm (570 micron) thick with a relative spread of 3%. Note that the film thickness is treated as a variable parameter (marked blue). Guide to RefFIT Page 65
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software to fit optical spectra - Quantum Materials Group

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