Raman Spectrum Curve Fitting for Estimating Surface Stress Distribution in Single-Crystal Silicon Microstructure

Abstract

This paper describes evaluation of surface stress distribution in single-crystal silicon (SCS) microstructure using laser Raman spectroscope. An in-house uniaxial tensile tester was employed to apply the uniaxial tensile stresses to SCS (001)[100] and (001) [110] film specimens with a number of microscale convex structures. A linear relationship between the applied tensile stress and Raman peak shift increment was obtained from Raman spectroscopy at a flat section of the specimen. Raman spectroscopy was also conducted to observe nonuniform stress distribution around the convex structures under uniaxial tensile loading. In observations around a convex structure, ''twocurve fitting'' was adopted for the asymmetric spectrum, which had been observed clearly under the tensile stresses of over 1000 MPa. The two-curve fitting was able to separate information of the top corner from that of the bottom one at the edge. The stress distribution estimated by the two peak positions was much closer to finite element analysis (FEA) results than that obtained by the one peak position.

Elimination of strength degrading effects caused by surface microdefect: A prevention achieved by silicon nanotexturing to avoid catastrophic brittle fracture

“…Curve-fitting approximations using a Lorentzian function 50 (refer to the methods section and supplementary Fig. S6 ) were generated to obtain the wavenumber shift ( Δω ), which can be converted into tensile stress ( σ ) for sc-silicon using equation (3) 50 : With no load applied, both non-textured and nanotextured V-notch samples measured at the notch tip retained the Raman peak at approximately 520.6 cm −1 ( Figs. S6(a,c) ), which is similar to the reported value for a non-stressed silicon peak 51 .…”

“…The obtained Raman spectrum consisted of a very large volume of information from the stress-free silicon surface; this information was separated from the information derived from the stressed silicon regions. Two curve-fitting approximations using a Lorentzian function 50 were applied to separate the non-stressed spectra from the stressed Raman spectra, as shown in supplementary Figs. S6(a–d) .…”

Micro-scale measurement and modeling of stress in silicon surrounding a tungsten-filled through-silicon via

“…Because of the simple strain state near the surface, a scalar relation between the Raman shift and stress (-435 MPa/cm À1 ) could be used. This methodology is similar to the analytical comparisons of stress in the edge force model of Hu 32,33 or micro-dogbone-like uniaxial tension, 35 among others in published micro-Raman results. 31,36 Anastassakis et al has argued 28 that the selectivity of phonons scattering from light polarized perpendicular to a component of strain causes the Raman shift of light polarized in the y s direction to be dominated by strains in the x s direction, especially when a low N.A.…”

Mechanical Reliability of Reactively Alloyed NiAl as a Structural Material

“…The details of the equipment are published elsewhere. (13,(16)(17)(18)(19) The equipment consists of a piezoelectric actuator, an actuator case with a lever for elongation amplification, a load cell with a resolution of 2 mN, a linear variable differential transformer (LVDT) for tension stroke measurement, an image analysis system with a charge-coupled device (CCD) camera for the specimen's displacement measurement, and a specimen holder with a microheater. The image analysis system has a resolution of 13 nm/pixel for the displacement measurement.…”