=================================================================================
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)
Technique |
|
X-ray diffraction |
Raman spectroscopy |
|
DF (S)TEM |
|
|
EBSD |
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
|
|
|
|
|
|
7 for [340], 10 nm for [230] [110]
|
|
|
|
|
|
|
|
|
|
10-4 |
10-3 - 5x10-2 |
|
0.01% |
10-4 |
10-4
|
|
Lattice
parameter accuracy |
|
|
|
|
|
|
|
10-4 - 10-5Å |
|
Sensitivity |
10-3 |
10-3 |
10-4 |
10-3 |
|
|
3x10-4 |
|
|
Complexity |
|
|
|
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 |
|
|
|
|
|
|
|
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
condenser
aperture |
|
Electrostatic
biprism and Lorentz
lens |
|
|
Special notes |
|
|
|
Most favorable technique for routine work |
|
|
|
|
|
References |
[1] |
|
[2, 7] |
[3] |
|
[4] |
[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.
|