Modulus Of Single Crystal Silicon Research Articles

Temperature Dependent Internal Friction Behavior of Single Crystal Germanium Studied by the Impulse Excitation Technique

The anelastic relaxation process in crystalline solids is influenced by various mechanisms including diffusion of atoms and point defects, grain boundary viscosity, dislocation, phase transformation, etc. To analyze the type and concentration of relaxing units participating in a particular activated process, measuring the internal friction is a well-known approach. A fundamental measure of internal friction can be defined as the ratio between the mechanical energy dissipated during one cycle in a unit volume and the maximum stored elastic energy per unit volume during that cycle [1]. The impulse excitation technique (IET) is a well-established mechanical spectroscopic technique analyzing the internal friction and Young’s modulus behaviour of materials as function of temperature [2]. IET measures the resonant frequency of a specimen by exciting it mechanically with an impulse tool. The resonance frequencies are characteristic for the sample material and are related to its stiffness, mass and geometry. The amplitude decay of a free vibration can be related to the internal friction, i.e. the dissipation of the vibration energy or damping. Measurement of the resonance frequency allows the calculation of Young's modulus E. This technique has been previously applied to determine the temperature dependent Young's modulus of single crystal silicon and germanium in the <100>, <110> and <111> crystallographic directions [3,4,5]. More and more, single crystal germanium and silicon layers and substrates are used together to process advanced nano-eletronic devices. The thermal stresses during crystal growth and device processing have an important impact on generation and diffusion of point defects and in the worst case also can lead to dislocation generation. Although the temperature dependent mechanical properties of silicon are well known, this is much less the case for germanium.In the present study, the impulse excitation technique was used to analyze the temperature dependence of the internal friction in single crystal Ge in the <111>, <100> and <110> directions between room and melting temperatures. A similar set-up was used as in [6] but equipped with a specimen chamber and specimen suspension system allowing heating the samples in an inert atmosphere up to the Ge melt temperature. Between room temperature and melt temperature, three internal friction peaks were observed for each crystallographic orientation after internal friction spectrum analysis, a typical spectrum is shown in the figure. The mechanism leading to these peaks is thermally activated. To interpret the observed internal friction peaks, various aspects such as activation energy of peaks, peak positions and relaxation time will be discussed. The origin of the relaxation peaks is associated with intrinsic point defect processes and/or extended defect formation.

An experimental method for studying Young’s modulus of single crystal silicon at high temperature

This article reports a novel indirect experimental method to measure Young’s modulus of single crystal silicon at high temperature. Young’s modulus at high temperature is estimated by measuring the elastic deformation of single crystal silicon microstructure at room temperature and high temperature. Since it is difficult to measure the elastic deformation directly at high temperature, a novel indirect method is presented in this study. In order to prevent plastic deformation at high temperature, the Von Mises yield criterion is applied to predict the onset of plastic deformation. The resulting Young’s modulus of single crystal silicon is about 110 ± 17 GPa at 900 °C in the &lt;100&gt; direction from the present experiment.

Measurement of the temperature coefficient of Young's modulus of single crystal silicon and 3C silicon carbide below 273 K using micro-cantilevers

This paper reports on the measurement of the thermal coefficient of Young's modulus of both single crystal silicon and 3C silicon carbide over the temperature range spanning 200–290K. The thermal coefficients were determined by monitoring the change of resonance frequency of micro-cantilevers as their temperature was reduced. The thermal coefficient of Young's modulus, 1/E·δE/δT was measured to be −52.6±3.45ppm/K for silicon and −39.8±5.99ppm/K for 3C silicon carbide, agreeing well with theoretical predictions, and also with experimental values that have been previously published for temperatures above 273K. This work has therefore expanded the temperature range over which the thermal coefficient of Young's modulus has been measured to below 273K and towards the temperatures required for low-temperature military and space applications.

In situ thermomechanical testing for micro/nanomaterials

Abstract

From Atomic-Level Lattice Structure to Estimate the Silicon Mechanical Bulk Behaviour Using the Atomistic-Continuum Mechanics

This paper proposes a novel atomistic-continuum mechanics (ACM) based on the finite element method (FEM) to investigate the mechanical bulk behavior of atomic-level single crystal silicon under uniaxial tensile loading. The ACM could be reduced efficiently the computational time and maintained the simulation accuracy. A general form of Stillinger-Weber potential function was used for interaction between the silicon atoms in the ACM simulations. Simulation results shows that the Young’s modulus of single crystal silicon were 121.8, 153 and 174.6 GPa along the (100), (110) and (111) crystallographic plane, respectively. These results are in reasonable agreement with the experiment and simulation results reported in the literature.

Mechanical characterization of single crystal silicon and UV-LIGA nickel thin films using tensile tester operated in AFM

This paper describes the mechanical characteristics of microscale single crystal silicon (SCS) and UV-LIGA nickel (Ni) films used for microelectromechanical systems (MEMS). A compact tensile tester, operated in an atomic force microscope (AFM), was developed for accurate evaluation of Young's modulus, tensile strain and tensile strength of microscale SCS and UV-LIGA Ni specimens. SCS specimens with nominal dimensions of 20 μm in thickness, 50 μm in width and 600 μm in length were prepared by a conventional photolithography and etching process. UV-LIGA Ni specimens, with a thickness of 15 μm, a width of 50 μm and a length of 600 μm in nominal dimensions, were also fabricated by electroplating using a UV thick photoresist mould. All specimens have line patterns on their specimen gauge section to measure axial elongation under tensile loading. The SCS specimens showed a linear stress–strain response and fractured in a brittle manner, whereas the UV-LIGA Ni specimens showed elastic–inelastic deformation behaviour. Young's modulus of SCS and UV-LIGA Ni specimens obtained from tensile tests averaged 169.2 GPa and 183.6 GPa, respectively, close to those of bulk materials. However, the tensile strength of both materials showed a larger value than the bulk materials: 1.47 GPa for the SCS and 0.98 GPa for the Ni specimens. Yield stress and breaking elongation of UV-LIGA Ni specimens were also quite different from those of the bulk Ni because of the specimen size effect on inelastic properties.