Electron interferometry techniques for strain analysis using a multibiprism microscope

Electron interferometric techniques have progressed in the last years thanks to the development of multiple biprisms microscopes. Here, we will discuss some recent developments in the field of strain measurement carried out with the I2TEM microscope (In-situ Interferometry Transmission Electron Microscope) installed in Toulouse in 2012. The I2TEM is a Hitachi HF-3300 equipped with one pre-specimen electrostatic biprism, three post-specimen biprisms, an image corrector (CEOS B-COR for correcting off-axial aberrations) and two stages (objective stage and Lorentz stage above the objective lens). In the dark-field off-axis scheme [1], electron beams diffracted by an epitaxially grown region are interfered with beams diffracted by the substrate thanks to a post-specimen biprism (Fig. 1(a)). Fig. 1(b-d) is an example obtained on a p-MOSFET like transistor with SiGe source/drain. The deformation is recorded as a frequency modulation (FM) in the hologram (Fig. 1(c)) and it can be calculated from the gradient of the reconstructed phase image (Fig 1(d)). In a recently proposed variant called differential phase contrast dark-field holography (DPCDFEH) [2], a pre-specimen biprism is used to create two overlapping waves on the sample (Fig. 1(e)). The interference of beams diffracted by slightly distant regions is acquired in a defocused plane. The deformation is recorded as a phase modulation (PM) in the hologram (Fig. 1(f)) and the DPC phase is directly proportional to the deformation (Fig. 1(g)). Another option is the 4-wave dark-field setup where two biprisms oriented perpendicularly are used to interfere three reference waves and one object wave (Fig. 1(h-j)). The holographic fringes are modulated in amplitude (AM) and each amplitude contour corresponds to a given displacement of the lattice planes. It can provide live information if a sufficient fringe contrast is achieved. In any case, strain measurement requires a reference wave diffracted by a region of known lattice parameter (usually the substrate). One solution is the “tilted reference wave” (TRW) where a pre-specimen biprism and the condenser system are used to create an object-independent reference wave with an adjustable tilt angle [3]. Fig 2(a,b) is an example acquired in the vacuum and Fig. 2(c,d) shows the dark-field configuration for strain measurement. Finally, a pre-specimen biprism can also be useful for electron diffraction techniques. For instance, one can create two parallel half cones on a specimen (SCBED) with a controllable distance (Fig. 3(a)) [4]. Each spot in the diffraction pattern contains two lobes related to the regions crossed by the two probes. Fig. 1(b) shows an example of SCBED pattern series where the left and right lobes are related to unstrained and increasingly strained regions respectively.

[1] MJ Hÿtch et al, Nature 453 (2008), 1086–1089.
[2] T Denneulin et al, Ultramicroscopy 160 (2016), 98–109.
[3] F Röder et al, Ultramicroscopy 161 (2016), 23–40.
[4] F Houdellier et al, Ultramicroscopy 159, Part 1 (2015), 59–66.

Acknowledgments
This work was funded through the European Metrology Research Programme (EMRP) Project
IND54 Nanostrain. The EMRP is jointly funded by the EMRP participating countries within
EURAMET and the European Union. The authors acknowledge the European Union under the
Seventh Framework Programme under a contract for an Integrated Infrastructure Initiative
Reference 312483-ESTEEM2.