Using Electron Diffraction Techniques, CBED and N-PED to measure Strain with High Precision and High Spatial Resolution

Abstract

Changes in the lattice parameters, i.e., introduction of strain, can modify material properties greatly. For instance, the band structure is modified with strain and this leads to changes in the transport or optical properties. In microelectronic devices, strain has been used to improve the mobility of charge carriers since 2003, with strain as low as 0.7% improving mobility by 50% [1]. Transmission Electron Microscopy (TEM) is presently the only technique that can measure the strain in individual nano-objects with high spatial resolution (about 1 nm) and high precision (about 10 -4 ). Here we focus on recent developments we have made in two electron diffraction techniques: Off-axis Convergent Beam Electron Diffraction (CBED) and Nanobeam Precession Electron Diffraction (N-PED). Off-axis CBED can give 3D maps of the complete 3D strain tensor but it is computationally and experimentally demanding. In contrast, N-PED is a straightforward and precise technique, but it is limited to the projected 2D strain.In off-axis CBED the originality of our approach is to use both the deficient HOLZ lines of the transmitted beam and the excess HOLZ lines of the diffracted beams to measure the strain [2]. Using Bloch wave calculated CBED patterns as tests, we could retrieve 7 out of the 9 components of the deformation gradient tensor F. In particular, the volume of the cells can be determined (Fig. 1b). By using two different electron beam directions engendering an angle of 22°, we show that it is possible to determine the whole tensor F. In addition, the method can also be extended to the analysis of split HOLZ lines that allow measuring the variations of the strain tensor along the electron beam.Depending on the convergence angle (α), the diffraction spots look like more dots or disks and the diameter of the incident beam varies (Fig. 1). When α is about 2 mrad, the diffracted disks do not have a uniform intensity (Fig. 2f), which can complicate accurate determination of the position of the disks. It is why in Nanobeam Electron diffraction (NBED) α is reduced in order to have spots with more uniform intensities (Fig. 2c) [3]. As these intensity variations are very sensitive to thickness, chemical composition and orientation, it turns out that the positioning of the disk centers is not very robust. This is why we introduced the precession of the beam [4]: the incident beam is tilted by an angle α p and rotated around the original incident direction and a "descan" of the beam is applied after the sample in order to bring back the diffracted spot to their original positions (Fig. 1g-1h). The advantages of introducing precession are manifold: (i) uniformity in the disk intensity, (ii) presence of more diffracted spots, (iii) possibility to work with a relatively large convergence angle in order to reduce the beam diameter ( Fig. 1j-1k); all this leads to an improved precision with a smaller probe [4]. Classically, PED is used in crystallography problems with α p greater than 1°, in order to have diffracted intensities that appro...

Atomic‐scale strain analysis for advanced Si/SiGe heterostructure by using transmission electron microscopy

“…99 Figure 6B-E shows typical NBED and CBED mode diffraction patterns for <011> Si and provides a comparison with the PED mode. 99,100 The CBED pattern is composed of diffraction discs, but the intensity of diffraction discs is not homogeneous due to the dynamic effect that hinders the acquisition of the exact location of the diffraction discs (Figure 6B). The diffraction effect restricts the beam size, and the beam diameter (d) is inversely proportional to the α: d = 0.514 λ/α.…”

“…Nevertheless, similar to the CBED and NBED techniques, the major drawbacks of obtaining 2D strain maps are a slow speed and the high data volume. 100…”

“…The PED system means that the electron beam can be tilted and rotated by controlling the focal and objective coils and form a conical illumination of the sample; at the same time, the rotation of the diffraction electron beam can be de‐scanned and reset by controlling the objective and the projective mirror coils to compensate for the deviation of the electron beam from the original position, thus obtaining the steady and high‐resolution PED patterns 99 . Figure 6B–E shows typical NBED and CBED mode diffraction patterns for <011> Si and provides a comparison with the PED mode 99,100 . The CBED pattern is composed of diffraction discs, but the intensity of diffraction discs is not homogeneous due to the dynamic effect that hinders the acquisition of the exact location of the diffraction discs (Figure 6B).…”

“…In brief, the PED technique, with high spatial resolution and signal‐to‐noise ratio, allows reproducible and efficient strain measurement at the nanoscale and offers detailed maps of strain distribution. Nevertheless, similar to the CBED and NBED techniques, the major drawbacks of obtaining 2D strain maps are a slow speed and the high data volume 100 …”

Comprehension of peculiar local emission behavior of InGaAs quantum well by colocalized nanocharacterization combining cathodoluminescence and electron microscopy techniques

“…7(b)]. Figures 6(a)-6(e) show STEM image reconstructed, 27 N-PED results of the area of interest, and AlAs strain profiles. The GaAs buffer layer is chosen as reference for N-PED strain calculations.…”