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

Franta, Daniel; Franta, Pavel; Vohánka, Jiří; Čermák, Martin; Ohlı́dal, Ivan

doi:10.1063/1.5026195

Cited by 3 publications

(4 citation statements)

References 23 publications

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“…2F), using the rigorous coupled-wave analysis method. For optical simulation of bioresorbable temperature sensor responses, the S 4 package also accounted for optical dispersion relations of silicon ( 49 ) and silicon dioxide ( 50 ), as well as the thermal expansion properties of each material ( 51 ).…”

Section: Methodsmentioning

confidence: 99%

Bioresorbable optical sensor systems for monitoring of intracranial pressure and temperature

et al. 2019

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Continuous measurements of pressure and temperature within the intracranial, intraocular, and intravascular spaces provide essential diagnostic information for the treatment of traumatic brain injury, glaucoma, and cardiovascular diseases, respectively. Optical sensors are attractive because of their inherent compatibility with magnetic resonance imaging (MRI). Existing implantable optical components use permanent, nonresorbable materials that must be surgically extracted after use. Bioresorbable alternatives, introduced here, bypass this requirement, thereby eliminating the costs and risks of surgeries. Here, millimeter-scale bioresorbable Fabry-Perot interferometers and two dimensional photonic crystal structures enable precise, continuous measurements of pressure and temperature. Combined mechanical and optical simulations reveal the fundamental sensing mechanisms. In vitro studies and histopathological evaluations quantify the measurement accuracies, operational lifetimes, and biocompatibility of these systems. In vivo demonstrations establish clinically relevant performance attributes. The materials, device designs, and fabrication approaches outlined here establish broad foundational capabilities for diverse classes of bioresorbable optical sensors.

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Section: Methodsmentioning

confidence: 99%

Bioresorbable optical sensor systems for monitoring of intracranial pressure and temperature

et al. 2019

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“…These values are in a From the values of the quantity χ describing the quality of the fit it is evident that the obtained fit is worse than the fits in the first two columns. This is especially true for the fit of the Watan-abe et al data (χ = 0.275 for the 4-th fit in [12] and χ = 1.231 for the 2-nd fit). For this reason we added the fourth ABESF term in to the formula (20).…”

Section: Thermal Expansion Effectmentioning

confidence: 93%

“…Therefore it can be calculated by means of the integration over the Brillouin zone. As it was shown in [12,15,16], the temperature dependence of the linear thermal expansion can be modeled using the average Bose-Einstein statistical factors (ABESF). In this model the continuous distribution of phonons is represented by a small number of average phonons, and the linear thermal expansion is given as follows…”

Section: Thermal Expansion Effectmentioning

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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Optical properties of the crystalline silicon wafers described using the universal dispersion model

Franta

Vohánka

Branecky

et al. 2019

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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The optical properties of a slightly boron doped float-zone crystalline silicon wafer are studied using ellipsometry and spectrophotometry in a wide spectral range from far IR to vacuum UV. One side of the wafer was cleaned in an argon plasma, which influenced the optical properties of silicon near the surface. The dielectric response of silicon was modeled using a simplified universal dispersion model which is constructed on the basis of parameterization of the joint density of states describing both the electronic and phonon excitations. Several variants of models describing phonon absorption and interband transitions are discussed. It was possible to accurately determine the optical constants of bulk silicon and the optical constants near the perturbed surface over a wide spectral range. These optical constants agree well with those found in other works. From the optical measurements, it was also possible to determine the thickness of the wafer and the static value of resistivity, and the determined values agreed with nominal values specified for the wafer.

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

Cited by 3 publications

References 23 publications

Bioresorbable optical sensor systems for monitoring of intracranial pressure and temperature

Bioresorbable optical sensor systems for monitoring of intracranial pressure and temperature

Temperature dependent dispersion models applicable in solid state physics

Optical properties of the crystalline silicon wafers described using the universal dispersion model

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