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4.7.1). The same function as for codes -25 and -26, just in case one needs two terms of this type. Table 4-3 Special dielectric functions. 4.6.3. Variational (free-shape) dielectric function -29 A [cm -2 ] -30 ω 0 [cm -1 ] γ [cm -1 ] - A variational dielectric function (VDF) 19 is very different from a ‘conventional’ one in a sense, that it is not described by a single mathematical formula. Instead, the values of the dielectric function at every experimental frequency point are considered as independent parameters. The theory behind this approach is given in sections 2.2.4 and 2.2.5. A VDF can be in one of two regimes: the KK-constrained and not KK-constrained ones. In the not-KK-constrained regime both ε 1 and ε 2 are treated as independently varied parameters at every frequency point (see section 2.2.5). In the KK-constrained regime only ε 2 is treated as an independent function, while ε 1 is given by the KK-transform of ε 2 (see section 2.2.4). An extra constraint in the KK mode is that ε 2 is zero at the edges of the spectral range. It is due to avoid discontinuity of ε 2 , which causes divergent singularities in ε 1. Let N be the number of experimental frequency points. From the above it is clear that the KK-constrained VDF will have N − 2 parameters, while the non-KK-constrained one will have 2 N parameters. As the usual RefFIT parameters, the parameters, related to the VDF, can be active or inactive in fit. I beg pardon since the user interface designed to handle the variational dielectric function is rather rudimental. The reason is that the first-found ‘temporary’ interface solution is still used. It will be designed certainly more logically in future. One VDF can be optionally added to the total model dielectric function. The user can switch it on and off (if it is off, the VDF part is ignored when the total dielectric function is calculated). The frequency set ω i (see section 2.2.4) is specified when the VDF is initialized. The user can switch from the KK-constrained regime to the non-KK-constrained one and back. He can also switch on and off the VDF fitting activity (when its fitting activity is off, all parameters of the VDF are fixed). The status of the free-shape dielectric function and its parameters cannot be seen in the model window. However, it can be modified by pressing one of special buttons F4, F5, F6 and F7, while the model window is active. The action of these buttons is described in Table 4-4. Key Action F4 Switches the VDF of this model on and off. When switched off, it is not removed from the memory, but just ignored and does not contribute to the total dielectric 19 we will also refer to variational dielectric function as “free-shape” dielectric function Guide to RefFIT Page 62
function. This command cannot be used before the initialization (button F6). F5 Toggles between the KK-constrained and non KK-constrained modes. This command cannot be used before the initialization (button F6). F6 Initializes the VDF of this model. Attention: the set of the frequency points ω i is copied from the dataset #1. Make sure, that there is a dataset there! After pressing F6 the VDF is switched on in the KK-constrained regime and all its parameters are active in fit (to change that later, use F4, F5 and F7). The initial values of all parameters are zero. F7 Toggles the fitting activity of all parameters on and off simultaneously. This command cannot be used before the initialization (button F6). Table 4-4 The description of the controls of the variational dielectric function. The ‘bad news’ is that VDF is not saved together with the model (when using button F2). However, this shortcoming is easily bypassed by using macros to generate VDFs ‘on-fly’ or by exporting the model ε 1 and ε 2 to a file. It worth mentioning that to handle VDF in the KK-constrained mode requires a lot of computational work and may significantly slow down the program. Therefore one should avoid the fitting of unnecessary large datasets. On an average modern PC (at the moment of writing this manual it is Pentium 1.5-2.5 GHz) RefFIT manages easily with N ~ 1000 . Working with larger datasets would require some patience. 4.7. Special models As was mentioned in section 4.5, special models are distinguished from the “Dielectric Function” model by a ‘code’, which is stored in the parameter “Einf”. The table “Lorentzians” is used to store the model parameters, whose meaning depends solely on the model type. Also, the output quantities are different from the ones of the “Dielectric Function” model (even though the same abbreviations are used, as in Table 4-2). Special models often contain links to other models. Table 4-5 lists special models and the corresponding codes. The detailed description of special models is presented in the subsequent sections. “Einf” (Code) Special model -1 Differential dielectric function (section 4.7.1) -2 Reflection and transmission of a multi-layer sample (section 4.7.2) -3 Ellipsometry of an orthorhombic sample (section 4.7.3) -4 Ellipsometry of an orthorhombic sample (differential model) (section 4.7.4) -5 Ellipsometry of an orthorhombic film on an orthorhombic substrate (section 4.7.5) -6 Extended Drude model (section 4.7.6) Table 4-5 Special models. Guide to RefFIT Page 63
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Last updated: 20.04.2004 Guide to R
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4.8. Dataset manager ..............
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that time. The later development of
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1.4. Let’s keep in touch Please,
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2.1.1. Levenberg-Marquardt algorith
Page 11 and 12: Guess initial parameters p , , p 1
Page 13 and 14: achieve a proper ‘balance’ betw
Page 15 and 16: The third requirement is that at ve
Page 17 and 18: Equation 2-19 is useful to estimate
Page 19 and 20: The first problem is that the Loren
Page 21 and 22: The problem can be circumvented by
Page 23 and 24: In these cases the fitting of the d
Page 25 and 26: 3. Tutorial This chapter shows how
Page 27 and 28: Figure 3-3 Graph contents window is
Page 29 and 30: Figure 3-7 Click the button and in
Page 31 and 32: If you are still far from this fitt
Page 33 and 34: Figure 3-15 The model and experimen
Page 35 and 36: Figure 3-18 The “Graph properties
Page 37 and 38: Figure 3-20 Loading the reflectivit
Page 39 and 40: Figure 3-22 The general RefFIT view
Page 41 and 42: Figure 3-25 The general RefFIT view
Page 43 and 44: MainWindow(XPos = 0, YPos = 0, Widt
Page 45 and 46: emarkable ‘anomaly’, related to
Page 47 and 48: ###################################
Page 49 and 50: # restores the original application
Page 51 and 52: 4. Reference 4.1. System requiremen
Page 53 and 54: Figure 4-2 The “Parameter control
Page 55 and 56: The model file stores information a
Page 57 and 58: considering multiple (Fabri- Perot)
Page 59 and 60: optical conductivity in practical u
Page 61: Kronig friendly, so be careful! “
Page 65 and 66: Iinc Itrans ε ε ( 1) ( 2) … (n)
Page 67 and 68: In ellipsometry the complex ratio
Page 69 and 70: ` Figure 4-10 The experimental conf
Page 71 and 72: Here ω p and ∞ ε are considered
Page 73 and 74: points “#pts” and the grid type
Page 75 and 76: 4.9.2. Graph contents To set the gr
Page 77 and 78: Available ChiSq terms and click the
Page 79 and 80: At each iteration a linear equation
Page 81 and 82: Before a macro is actually executed
Page 83 and 84: Quantity Text Abbreviation of the q
Page 85 and 86: Parameters: Name Type Description W
Page 87 and 88: “Wp” - plasma frequency; “G
Page 89 and 90: ShowLine Integer =12: Chalk =13: Br
Page 91 and 92: XMin Double Minimal X (frequency) v
Page 93 and 94: always come in pairs. All commands
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