Raman measurements of uniaxial strain in silicon nanostructures

Abstract

The strain-shift coefficient used to convert Raman shifts to strain depends on multiple factors including phonon deformation potentials (PDPs). PDPs have been reported for silicon, which differ by 30%. This leads to varying strain-shift-coefficients. Using the wrong strain-shift coefficient affects the strain determined. The discrepancies in the reported PDPs were previously ascribed to surface stress relaxation and the opacity of the material to the laser radiation. This paper shows that surface orientation and scattering geometry are major factors behind the PDPs discrepancies. The work further demonstrates that different PDPs are required to accurately characterize transverse optical and longitudinal optical Raman modes. The effects of sample geometry and stress have also been studied. State of the art devices use nanowires and thin films under large values of uniaxial stress; however, previous experiments to determine PDPs and strain-shift coefficients in silicon have been limited to bulk material and stress only in the range 0–2 GPa. In this work, the strain-shift coefficient of silicon nanostructures is determined for a large range of geometries and applied stress values (0–4.5 GPa). Strain in the samples has been measured using three independent techniques: analytical calculations, finite element simulations, and by direct visual inspection of the samples elongation using scanning electron microscopy. Raman shifts have been measured using 458 nm and 364 nm laser radiations. The combination of these techniques and the large number of samples (up to 85) has allowed the accurate determination of the strain-shift coefficient for the technologically important (100) silicon surface.

Origin of Anomalous Piezoresistive Effects in VLS Grown Si Nanowires

“…Application of stress to the NW causes a shift of the first order optical phonon peak of Si at 520.2 cm –1 linearly dependent on the strain. 40 These typical shifts to lower wave numbers of a strained NW integrated in the TSD and, for comparison, bulk Si are shown in Figure 3 a. The inset shows the relationship between the Raman signal peak shift and thereof calculated strain values of the NW.…”

Lattice strain and tilt mapping in stressed Ge microstructures using X-ray Laue micro-diffraction and rainbow filtering

“…bulge testing) (El Kurdi et al, 2010a;Sánchez-Pérez et al, 2011;Boztug et al, 2013). Strain measurements are usually done by micro-Raman spectroscopy (El Kurdi et al, 2010a;Boztug et al, 2013;Ghrib et al, 2013;Ureña et al, 2013).…”

Roughness analysis in strained silicon-on-insulator wires and films

“…The strain levels were verified by scanning electron microscopy (SEM) and Raman spectroscopy and compared with analytical calculations and finite element simulations. 33,34 The silicon crystal structure of the samples was also analyzed and concluded that it has not been compromised. 34 Strain determined by SEM was carried out by measuring the displacement of a mobile cursor fabricated alongside the silicon beams with respect to a fixed cursor positioned at the substrate sidewalls.…”

“…33,34 The silicon crystal structure of the samples was also analyzed and concluded that it has not been compromised. 34 Strain determined by SEM was carried out by measuring the displacement of a mobile cursor fabricated alongside the silicon beams with respect to a fixed cursor positioned at the substrate sidewalls. Additional details of the fabrication process and strain characterization can be found in Refs.…”