Nanoscale Measurements of Strain and Stress

The ability to measure strain (or stress, the two are related by material elastic constants) at the nanoscale significantly effects development in a number of advanced device technologies including microelectronics, photonics, and microelectromechanical systems. For example, stress-engineered transistor channels with increased carrier mobility have been in use since the 90 nm semiconductor technology node and are expected to play a large role in improving the performance of microelectronic devices as dimensions shrink even further. NIST Nanomechanical Properties Group scientists have recently measured strains in indented silicon as small as 10-4 (providing stress resolution of about 10 MPa) using both electron back scattered diffraction (EBSD), with spatial resolution of the order of 10 nm, and confocal Raman microscopy (CRM), with spatial resolution of about 100 nm. Analysis of several hundred high-quality EBSD patterns recorded along a line crossing the midpoint of a 20-µm wedge-indentation in Si allowed the deformation of the Si crystal to be measured at each point along the line. From the deformation tensor, the full strain and stress tensor profiles across the indentation were determined. 
Equivalent experiments were performed using an in-house CRM system to measure Raman line shifts at each point on a similar scan-line across the indentation, thus determining the profile of compressive stress normal to the indentation. Comparison of the EBSD and CRM results showed extremely good agreement except very close to the indentation, where (decreasing) stress gradients normal to the surface are large. Hence, close to the indentation, the EBSD measurements, which sample closer to the surface than CRM, indicated greater stresses. Decreasing the wavelength of the Raman excitation to probe smaller sample depths indicated that the two sets of results converged as the wavelength and depth probed were decreased. The stress profiles were well fit by an inverse square law as predicted from an Eshelby analysis for an expanding cylindrical cavity.

These results demonstrate that one of the "holy grails" of nanocharacterization is being realized and was published: "Comparison of Nanoscale Measurements of Strain and Stress using Electron Back Scattered Diffraction and Confocal Raman Microscopy," M.D. Vaudin, Y.B. Gerbig, S.J. Stranick, and R.F. Cook, Appl. Phys. Letters 93 (2008) 193116.

Applications include measurements of indentation stress field anisotropy in Si: "Effect of crystallographic orientation on phase transformations during indentation of silicon," Y.B Gerbig, S.J. Stranick, D.J. Morris, M.D. Vaudin, and R.F. Cook, J. Mater. Res., 24 (2009) 1172-1183

Contact: Mark Vaudin, x5799 and Yvonne Gerbig, x6130


Created May 26, 2010, Updated August 25, 2016