Universal Dispersion Model for Characterization of Thin Films Over Wide Spectral Range

Franta, Daniel; Vohánka, Jiří; Čermák, Martin

doi:10.1007/978-3-319-75325-6_3

Cited by 13 publications

(27 citation statements)

References 68 publications

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“…Nevertheless, the transition strength in the resulting model still exhibits the linear dependence on the Bose-Einstein statistical factors. The details concerning this model applied to c-Si are described in our previous works [7,10].…”

Section: U L T I-p H O N O N a B S O R P T I O Nmentioning

confidence: 99%

“…The model used for the normalized transition strength function F 0 fc (E) is based on the modification of the Drude formula [7,11]. The influence of the free-carrier contribution on the transition strength function in the region of phonon absorption is visible in Fig.…”

Section: F R E E-c a R R I E R C O N T R I B U T I O Nmentioning

confidence: 99%

“…The third condition is a result of the combination of the superconvergence theorem and the asymptotic behavior of any dielectric response, ie that for high frequencies all dispersion models converge to the model of sparse plasma. The sum rule condition is important for the construction of dispersion models because it expresses the relation between the integral value of the quantity ωε i (ω) and the density of electrons N e and nuclei N n in the material [5][6][7] ω 2 p = e 2 N e ǫ 0 m e + n e 2 Z 2 n N n ǫ 0 m n ,…”

Section: Introductionmentioning

confidence: 99%

“…Note that in order to emphasize that the dielectric response is temperature dependent, we explicitly indicated the dependence on temperature T . The equations(4), (5) and (6) can be rewritten as [6,7] ε r (E,…”

Section: Introductionmentioning

confidence: 99%

“…1, where the horizontal bars indicate the spectral ranges of the individual elementary excitations. Equations (8), (9), (10) and (11) form a basis for the construction of our dispersion models [6][7][8]. In order to describe the concrete materials, it necessary to perform one more step.…”

Section: Introductionmentioning

confidence: 99%

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Temperature dependent dispersion models applicable in solid state physics

Franta

Vohánka

Čermák

et al. 2019

Journal of Electrical Engineering

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Dispersion models are necessary for precise determination of the dielectric response of materials used in optical and microelectronics industry. Although the study of the dielectric response is often limited only to the dependence of the optical constants on frequency, it is also important to consider its dependence on other quantities characterizing the state of the system. One of the most important quantities determining the state of the condensed matter in equilibrium is temperature. Introducing temperature dependence into dispersion models is quite challenging. A physically correct model of dielectric response must respect three fundamental and one supplementary conditions imposed on the dielectric function. The three fundamental conditions are the time-reversal symmetry, Kramers-Kronig consistency and sum rule. These three fundamental conditions are valid for any material in any state. For systems in equilibrium there is also a supplementary dissipative condition. In this contribution it will be shown how these conditions can be applied in the construction of temperature dependent dispersion models. Practical results will be demonstrated on the temperature dependent dispersion model of crystalline silicon.

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Section: U L T I-p H O N O N a B S O R P T I O Nmentioning

confidence: 99%

Section: F R E E-c a R R I E R C O N T R I B U T I O Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Temperature dependent dispersion models applicable in solid state physics

Franta

Vohánka

Čermák

et al. 2019

Journal of Electrical Engineering

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Optical characterization of inhomogeneity of polymer-like thin films arising in the initial phase of plasma-enhanced chemical vapor deposition

Dvořák,

Vohánka,

Buršíková

et al. 2024

Heliyon

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Determination of thicknesses and temperatures of crystalline silicon wafers from optical measurements in the far infrared region

Franta

Vohánka

et al. 2018

Journal of Applied Physics

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Optical measurements of transmittance in the far infrared region performed on crystalline silicon wafers exhibit partially coherent interference effects appropriate for the determination of thicknesses of the wafers. The knowledge of accurate spectral and temperature dependencies of the optical constants of crystalline silicon in this spectral region is crucial for the determination of its thickness and vice versa. The recently published temperature dependent dispersion model of crystalline silicon is suitable for this purpose. Because the linear thermal expansion of crystalline silicon is known, the temperatures of the wafers can be determined with high precision from the evolution of the interference patterns at elevated temperatures.

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Universal Dispersion Model for Characterization of Thin Films Over Wide Spectral Range

Cited by 13 publications

References 68 publications

Temperature dependent dispersion models applicable in solid state physics

Temperature dependent dispersion models applicable in solid state physics

Optical characterization of inhomogeneity of polymer-like thin films arising in the initial phase of plasma-enhanced chemical vapor deposition

Determination of thicknesses and temperatures of crystalline silicon wafers from optical measurements in the far infrared region

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