Evaluation of Lattice-Spacing of SiGe/Si by NBD using Two Condenser-lens TEM, Experimental Study about the Effect of Convergence Angle

Nano-beam electron diffraction (NBD) is a useful technique to study nanometer-order crystallographic structures. If we use a high-end TEM which has three or more condenser lenses, it is possible to take sharp diffraction patters from nanometer-order area. However, if we use an ordinary TEM which has two condenser lenses, it is quite difficult to take sharp diffraction patters from nanometer-order area. Therefore, the NBD using two condenser-lens TEM has not been a popular technique to evaluate lattice spacings. Recently, the authors reported experimental works to evaluate SiGe lattice spacings using NBD taken by two condenser-lens TEM [1, 2]. The motivation was simple; we considered that the precise measurement might be possible if we could find the center of the diffraction disks correctly. The subject of this study is to elucidate the best experimental condition using two condenser-lens TEM to evaluate the lattice spacings. The specimen was 100 nm thick SiGe film grown onto Si (100) by MBE. The growth temperature was 600 C. After the MBE growth, X-ray reciprocal space mapping was carried out then it was revealed that the Ge concentration was about 30 at % and the SiGe lattice was almost relaxed (relaxation ratio: 95%). Focused ion beam (Ga+ ion type FIB, Hitachi FB-2100A) was utilized to fabricate the specimens for TEM observations followed by depositing protection layers of C, Pt-Pd, and W. The acceleration voltage of the FIB was 40 kV. FEI's TEM, tecnai Osiris, an ordinally field-emission TEM without any Cs-correctors nor monochromator, was utilized with the acceleration voltage of 200 kV. The NBD raw data were recorded using 2048×2048 CCD camera. Basic procedure to read out the center of the diffraction disks were same as we reported, i.e., binarizing the raw data to clarify the outer boundary of the disks, drawing the outer circle for each diffraction disks, then reading out the positions of the disk centers [1, 2]. After that, one new process was added in this study. We read out main seven disks including direct beam, then we re-align them by mathematical optimization considering the reciprocal vectors must be expressed by their linear combination. Then we adjusted the data by using Si data as an in-specimen standard. Figure 1 is the example of the disk-center reading out process in this study. One example how we analyzed the NBD diffraction disks. The incidental beam direction was [001]. This figure shows the raw data, binarized data to clarify the outer boundary of the diffraction disks, drawing outer circle and finding the center, the data after defining the centers for seven major diffraction disks. NBD raw data. (a): Taken from Si substrate. The diameter of the 2nd condenser aperture was 150 μm. Convergence semi angle was 4.51 mrad. (b): Taken from Si substrate. The diameter of the 2nd condenser aperture was 100 μm. Convergence semi angle was 2.12 mrad. (c): Taken from Si substrate. The diameter of the 2nd condenser aperture was 70 μm. Convergence semi angle was 1.49 mrad. (d): Taken from SiGe film. The diameter of the 2nd condenser aperture was 150 μm. Convergence semi angle was 4.51 mrad. (e): Taken from SiGe film. The diameter of the 2nd condenser aperture was 100 μm. Convergence semi angle was 2.12 mrad. (f): Taken from SiGe film. The diameter of the 2nd condenser aperture was 70 μm. Convergence semi angle was 1.49 mrad. We systematically changed the convergence angle in this study. Some of the experimental raw data is shown in Figure 2. We took the data repetitively from the same specimen, both the SiGe and Si data were taken all time and the Si data were utilized as standard data. We analyzed the data with the above-mentioned procedure, including the calibration using the Si data. The calculated d-spacing are shown in Figure 3. From the results shown in the Figure 3, we can conclude as follows: (1) We succeeded in distinguish the (400) spacing of the Si0.7Ge0.3 from that of Si, even their difference is about 0.02 nm. (2) Errata decreased in comparison with our previous reports [1, 2]. It is considered that our new calibration procedure, using in-specimen standard and mathematical optimization considering the reciprocal vectors must be expressed by their linear combination, works well. (3) Small convergence angle is not necessary. Convergence angle did not affect the results. The most important point of this method is reading out the center of the diffraction disks. This might be completely opposite to previous way of thinking. However, our experimental results exhibited that our simple method is good to evaluate the d-spacing from the nanometer-order areas [3]. The distance between the 400 and -400 diffraction disks and the direct beam, after the calibration. d-spacings in a real space are also shown. The convergence angle of the incidental beam is shown in the insertions.