Elastic Constants Of Silicon Research Articles

Contactless excitation of acoustic resonance in insulating wafers

Contactless excitation and detection of high harmonic acoustic overtones in a thin insulator single crystal are described using radio frequency spectroscopy techniques. Single crystal [001] silicon wafer samples were investigated, one side covered with a Nb thin film, the common starting point for the fabrication of quantum devices. The coupling between electromagnetic signals and mechanical oscillation is achieved from the Lorentz force generated by an external magnetic field. This method is suitable for any sample with a metallic surface or covered with a thin metal film. High resolution measurements of the temperature dependence of the sound velocity and elastic constants of silicon are reported and compared with known results.

ATOMISTIC STUDY OF THE STRENGTH AND ELASTIC CONSTANTS OF PERFECT AND DEFECTED SILICON

The effects of vacancies on the strength and elastic constants of silicon, such as Young's modulus and Poisson's ratio are investigated using the molecular dynamics simulations with the Stillinger–Weber potential. The defected crystalline cells contain randomly generated defect distributions in the simulation models. The ideal strength is found to be 33.6 GPa at the strain 0.26. The Young's modulus and Poisson's ratio is 148 GPa and 0.252, respectively. It is found that the strength decreases as the point defect fraction increases, and the variation of the strength versus the point defect fraction coincides with a decaying exponential function. In addition, vacancies are shown to reduce the elastic constants. In general, the elastic constants of silicon vary linearly versus the defect fraction.

Elastic constants of defected and amorphous silicon with the environment-dependent interatomic potential

The elastic constants of a wide range of models of defected crystalline and amorphous silicon are calculated, using the environment-dependent interatomic potential (EDIP). The defected crystalline simulation cells contain randomly generated defect distributions. An extensive characterization of point defects is performed, including structure, energy and influence on elastic constants. Three important conclusions are drawn. (1) Defects have independent effects on the elastic constants of silicon up to (at least) a defect concentration of 0.3%. (2) The linear effect of Frenkel pairs on the ⟨110⟩ Young's modulus of silicon is $\ensuremath{-}1653\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ per defect fraction. (3) 17 different point defect types cause a very similar decrease in the ⟨110⟩ Young's modulus: $\ensuremath{-}(0.28\ifmmode\pm\else\textpm\fi{}0.05)%$ when calculated in isolation using a 1728-atom cell. These principles will be very useful for predicting the effect of radiation damage on the elastic modulus of silicon in the typical case in which point-defect concentrations can be estimated, but the exact distribution and species of defects is unknown. We also study amorphous samples generated in quenching the liquid with EDIP, including an ideal structure of perfect fourfold coordination, samples with threefold and fivefold coordinated defects, one with a nanovoid, and one with an amorphous inclusion in a crystalline matrix. In the last case, a useful finding is that the change in the Young's modulus is simply related to the volume fraction of amorphous material, as has also been observed by experiment.

Defect-Induced Shifts in the Elastic Constants of Silicon

ABSTRACTAs MEMS devices become ever more sensitive, even slight shifts in materials properties can be detrimental to device performance. Radiation-induced defects can change both the dimensions and mechanical properties of MEMS materials, which will be of concern to designers of MEMS for applications involving radiation exposure, such as those in a reactor environment or in space. We have performed atomistic simulations of the effect that defects and amorphous regions, such as could be produced by radiation damage, have on the elastic constants of silicon. We have then applied the results of the elastic constant shift calculations to a hypothetical MEMS device, and calculated the difference that would be generated by this effect.

811 シリコンの表面応力と表面弾性定数

811 シリコンの表面応力と表面弾性定数

Device Implications of the Electronic Effect in the Elastic Constants of Silicon

Device Implications of the Electronic Effect in the Elastic Constants of Silicon

Temperature variation of some combinations of third-order elastic constants of silicon between 300 and 3 °K

The ultrasonic harmonic generation technique has been used to determine the nonlinearity parameters of silicon between room temperature and 3 °K. By measuring the amplitude of the second harmonic of an initially sinusoidal longitudinal ultrasonic wave propagating along the three principal directions, the temperature dependence of three linear combinations of third-order elastic (TOE) constants of silicon have been studied. Between room temperature and 77 °K, the magnitude of the TOE constants does not vary much as a function of temperature. Between 77 and 3 °K, C111 changes by 3.5%, C112+4C166 changes by 11.7%, and C123+6C144+8C456 changes by −207%. All these combinations are negative at room temperature as well as at low temperatures except C123+6C144+8C456 which is positive below 8 °K. Room-temperature values of the strain generalized Grüneisen parameters of silicon have been calculated from measured nonlinearity parameters and are compared with existing values. Complete sets of third-order elastic constants at 298, 77, and 4 °K have been calculated by combining our nonlinearity parameters with pressure derivatives of elastic constants measured by Beattie and Schirber [Phys. Rev. B 1, 1548 (1970)].

Effect of Doping on the Elastic Constants of Silicon

Keyes' theory of the dependence of the shear elastic constants of degenerate $p$-type Ge on hole concentration has been extended to degenerate $p$-type Si by including in the theory the light-hole band and the split-off band. It is shown that the total effect in the elastic constants is the sum of effects arising from the light-hole, heavy-hole, and split-off bands and originates in a change of the Fermi level with strain. Using the ultrasonic pulse-echo technique, measurements were made at 78\ifmmode^\circ\else\textdegree\fi{}K of the elastic constant ${C}^{\ensuremath{'}}=\frac{1}{2}({C}_{11}\ensuremath{-}{C}_{12})$ of Si samples containing: (a) 7.0\ifmmode\times\else\texttimes\fi{}${10}^{15}$, (b) 3.2\ifmmode\times\else\texttimes\fi{}${10}^{18}$, (c) 1.4\ifmmode\times\else\texttimes\fi{}${10}^{19}$, and (d) 1.1\ifmmode\times\else\texttimes\fi{}${10}^{20}$ B atoms ${\mathrm{cm}}^{\ensuremath{-}3}$. Relative to the purest sample (a), the change in ${C}^{\ensuremath{'}}$ is -12, -42, and -193 (in units of ${10}^{8}$ dyne ${\mathrm{cm}}^{\ensuremath{-}2}$), respectively. Equating these values with the calculated changes in ${C}^{\ensuremath{'}}$ and using effective masses from the top of the various valence bands, the values of 5.8, 8.5, and 11.8 eV were obtained for the deformation potential constant ${{\ensuremath{\Xi}}_{s}}^{\ensuremath{'}}$. These values were corrected to 4.9, 7.1, and 9.94 eV by estimating the dependence on the wave vector of the effective masses as inferred from Kane's work on the band structure of Si. Possible sources of the dependence of ${{\ensuremath{\Xi}}_{s}}^{\ensuremath{'}}$ on doping are discussed.