The lattice parameter of high‐purity silicon is measured as a function of temperature between 300 and 1500 K, and the linear thermal expansion coefficient is accurately determined. Precise measurements are made by the high‐temperature attachment for Bond’s x‐ray method to a few parts per million. It is found that the temperature dependence of the linear thermal expansion coefficient α(t) is empirically given by α(t)=(3.725{1−exp[−5.88×10−3{(t−124)} +5.548×10−4t)×10−6 (K−1), where t is the absolute temperature ranging from 120 to 1500 K. It is shown that the lattice parameter in the above temperature range can be calculated using α(t) and the lattice parameter at 273.2 K (0.5430741 nm). Measured values of the lattice parameter and the thermal expansion coefficient for high‐purity float‐zoned (100 kΩ cm) and Czochralski‐grown (30 Ω cm) single crystals are uniformly distributed within ±1×10−5 nm and ±2×10−7 K−1 with respect to the values obtained from the above empirical formula.

Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K

In 1985, the CODATA Bulletin published a Report of its Task Group on Thermophysical Properties of Solids which analyzed available data on, and gave recommended values for, the heat capacity of Cu, Fe, W, and Al2O3, the thermal expansion of Cu, Si, W, and Al2O3, the electrical resistivity of Cu, Fe, Pt, and W, the thermal conductivity of Al, Cu, Fe, and W, and the absolute thermopower of Pb, Cu, Pt, and W. The analysts for the different properties were R. B. Castanet, S. J. Collocott, P. D. Desai, C. Y. Ho, J. G. Hust, R. B. Roberts, C. A. Swenson, and G. K. White. The present paper is an updated version of the earlier report and includes more recent data which change some of the recommended values. notably the heat capacity of Cu and W and the thermal expansion of Si and W.

Thermophysical properties of some key solids: An update

The coefficient of thermal expansion (CTE), biaxial modulus, and stress of some amorphous semiconductors (a-Si:H, a-C:H, a-Ge:H, and a-GeCx:H) and metallic (Ag and Al) thin films were studied. The thermal expansion and the biaxial modulus were measured by the thermally induced bending technique. The stress of the metallic films, deposited by thermal evaporation (Ag and Al), is tensile, while that of the amorphous films deposited by sputtering (a-Si:H, a-Ge:H, and a-GeCx:H) and by glow discharge (a-C:H) is compressive. We observed that the coefficient of thermal expansion of the tetrahedral amorphous thin films prepared in this work, as well as that of the films reported in literature, depend on the network strain. The CTE of tensile films is smaller than that of their corresponding crystalline semiconductors, but it is higher for compressive films. On the other hand, we found out that the elastic biaxial modulus of the amorphous and metallic films is systematically smaller than that of their crystalline counterparts. This behavior stands for other films reported in the literature that were prepared by different techniques and deposition conditions. These differences were attributed to the reduction of the coordination number and to the presence of defects, such as voids and dangling bonds, in amorphous films. On the other hand, columnar structure and microcrystallinity account for the reduced elasticity of the metallic films.

Coefficient of thermal expansion and elastic modulus of thin films

In this work, we report the synthesis and characterization of highly ordered mesoporous CeO2 thin films with crystalline walls. While this article focuses on electrochemical studies of CeO2 with periodic nanoscale porosity, we also examine the mechanical properties of these films and show how pore flexing can be used to facilitate intercalation of lithium ions. Mesoporous samples were prepared by dip-coating using the large diblock copolymer KLE as the organic template. We establish that the films have a mesoporous network with a biaxially distorted cubic pore structure and are highly crystalline at the atomic scale when heated to temperatures above 500 °C. Following a previously reported approach, we were able to use the voltammetric sweep rate dependence to determine quantitatively the capacitive contribution to electrochemical charge storage. The net result is that mesoporous CeO2 films exhibit reasonable levels of pseudocapacitive charge storage and much higher capacities than samples prepared without...

On the Correlation between Mechanical Flexibility, Nanoscale Structure, and Charge Storage in Periodic Mesoporous CeO2 Thin Films

A blow molding method based on thermoplastic forming of bulk metallic glasses (BMGs) is used to fabricate 3-D microshells. The 3-D microshells are attached to the Si wafer through mechanical locking, which is achieved in the same processing step. Versatile sizes and shapes of the 3-D shells can be precisely controlled. High strength ( >; 1 GPa), elasticity (~ 2%), and controlled surface roughness (<; 2 nm), which are achievable for BMGs, suggest their potential use in devices, including resonators, microlenses, microfluidic, and packaging.

Three-Dimensional Shell Fabrication Using Blow Molding of Bulk Metallic Glass

Measurements of the coefficient of linear thermal expansion of pure polycrystalline silicon were made with a polarization interferometer and a platinum resistance thermometer with an estimated error of less than 0.01 × 10-6 K-1.

https://iopscience.iop.org/article/10.1088/0022-3727/14/10/003/pdf

R B Roberts

Papers

Thermal expansion reference data: silicon 300-850 K