Strain/Stress Measurements at Micro/Nano-scales
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Several techniques have been developed for strain measurements at micro- and nano-scales, e.g. listed in Table 4312. The stress and strain measurements can be classified by:
         i) direct measurements, which measures the deformation in a structure, for instance:
              i.A) measure wafer curvature first and then extract the stress theoretically.
              i.B) use X-ray diffraction to measure the lattice parameter by Bragg diffraction. High-resolution X-ray diffraction can be performed with small synchrotron probes of tens to hundreds nm in diameter.
              i.C) measure the local lattice parameters by using TEM-based techniques in Å to nm spatial resolutions.
                     i.C.a) Dark-field (DF) TEM imaging is a classical technique used to map strain variation in crystals.
                     i.C.b) ADF-STEM has recently been suggested for strain analysis.
                Note that, with TEM-based techniques, surface strain relaxation of TEM sample occurs when:
                     a) the crystal in the TEM sample is highly strained,
                     b) the TEM is very thin.
         ii) indirect measurement, e.g. Raman spectroscopy can determine how the vibrations of atoms bonded together change when stress is present.

On the other hand, the sample milling direction sometimes is tricky because the incident electron beam needs to be perpendicular to the wanted strain component.

Table 4312. Techniques for strain measurements at micro- and nano-scales. (DF: Dark-field)

TEM/SEM-based techniques
X-ray diffraction
Raman spectroscopy
DF inline holography

DF off-axis electron holography (DFOH)

Information mechanism
Direct correlation between the phase and crystal potential from the electron exit wave function         Direct correlation between the phase and crystal potential from the electron exit wave function    
Optimum sample thickness
<50 nm for TEM and 50-100 nm for STEM
50-100 nm
Measurement field of view
30-200 nm
400 - 1500 nm
2-4 nm
7 for [340], 10 nm for [230] [110]
2-10 nm
4-6 nm
~500 nm to micro-scale
~500 nm to micro-scale
Stain accuracy
10-3 - 5x10-2
Lattice parameter accuracy
              10-4 - 10-5Å  
Simple experimental set-up
Clear drawback
Strain relaxation due to very thin specimen
A constant strain field, resulting in a uniform contrast, cannot be interpreted; sensitive to crystal orientation, thickness and composition
High angle sample-tilt is needed; HOLZ line
due to large strain gradient
Other drawback
Strain modification due to the extra stress induced by amorphized TEM sample surfaces and/or strain relaxation (especially for a large strain in the original materials) in very thin TEM samples    
Signal improvement
Can be significantly improved by selecting the elastic scattering with an energy filter    
Special hardware
Cs corrector for atomic
resolution strain imaging
    A small
biprism and Lorentz
Special notes
Most favorable technique for routine work
[2, 7]
[5, 6]
* The spatial resolution is determined by many factors within microscopy principle as well as the direction relative to the strain axes in the two-dimensional (2D) projection.









[1] F. Hüe, M. Hÿtch, F. Houdellier, E. Snoeck, and A. Claverie, “Strain mapping in MOSFETS by high-resolution electron microscopy and electron holography”, Materials Science and Engineering B, vol 154-155, pp. 221-224, 2008.
[2] P. Zhang, A. A. Istratov, E.R. Weber, C. Kisielowski, H. F. He, C. Nelson, and J. C. H. Spence, “Direct strain measurement in a 65 nm node strained silicon transistor by convergent-beam electron diffraction” Applied Physics Letters, vol 89, pp. 161907, 2006.
[3] K. Usuda, T. Numata, and S. Takagi, “Strain evaluation of strained-Si layers on SiGe by the nano-beam electron diffraction (NBD) method”, Materials Science in Semiconductor Processing, vol 8, pp. 155-159, 2005.
[4] C. T. Koch, V. B. Özdöl, and P. A. Van Aken, “An efficient, simple, and precise way to map strain with nanometer resolution in semiconductor devices”, vol 96, pp. 091901-3, 2010.
[5] M. J. Hÿtch, F. Houdellier, F. Hüe, and E. Snoeck, “Nanoscale holographic interferometry for strain measurements in electronic devices”, Nature, vol 453, pp. 1086-1089, 2008. 
[6] M.J. Hÿtch, F. Houdellier, A. Claverie, and L. Clément, Comparison of CBED and Dark-field Holography for Strain Mapping in Nanostructures and Devices, 2009. ESSDERC '09. Proceedings of the European Solid State Device Research Conference, (2009) 307 - 310.
[7] Jian Min Zuo, John C.H. Spence, Advanced Transmission Electron Microscopy Imaging and Diffraction in Nanoscience, 2017.