Feasibility Study to Evaluate Lattice-Space Changing of a Step-Graded SiGe/Si (110) Using STEM Moiré

A moiré between crystal lattice planes and scanning electron beam-lines formed in a scanning transmission electron microscope includes the information of the lattice spacing. We apply these phenomena to a compositionally graded SiGe thin film deposited onto a Si substrate by molecular beam epitaxy method. The results of the experiments and image analysis show the potential of this technique to analyze a slight change of the lattice spacing according to a compositional change.


Introduction
A slight change of lattice spacing around hetero-interfaces of crystalline materials has an important role for their properties in most of the cases in general. In a field of semiconductor devices, lattice strains due to hetero-structures are important to realize high-speed transistors and we also have been studying them [1] [2] [3] [4] [5]. Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) are useful to analyze this kind of local lattice spacing of crystals. However, TEM-based techniques such as high-resolution TEM/STEM images and nano-beam transmission electron diffraction techniques are not suitable for the wide range observation, for example, observation from the squared-micron order area. Recently, a very unique method to analyze lattice spacing has been reported by other researchers [6]- [12]. The essence of this How to cite this paper: Yamanaka, J., Shirakura, M., Yamamoto, C., Sato, K., Yamada, T., Hara, K.O., Arimoto, K., Nakagawa, K., Ishizuka technique is as follows: A moiré can be observed when the electron beam is focused small enough, the scan periodicity of the STEM is close to the crystal plane spacing, and the scan direction is suitable for the crystal plane. It is called STEM moiré. The STEM moiré has the information of the crystal plane spacing. A schematic illustration of the STEM moiré is shown in Figure 1.
The research group of the University of Yamanashi also reported the experimental results about STEM moiré observation of Ge/Si (100) [13]. HREM Research Inc. and CEMES-CNRS developed an image analysis method to evaluate two dimensional lattice strains from the STEM moiré [14]. In this study, we produced a compositionally step-graded SiGe thin layers onto the Si (110) substrate, observed the STEM moiré, and calculated the slight change of the {111} plane spacing of the SiGe layers.

Experimental Procedure
A Si/SiGe/Si (110) hetero-structure was produced using the molecular beam epitaxy (MBE) method. We used an E-gun for Si and a K-cell for Ge. The substrate temperature was 600˚C. The deposition rate of Si was 0.5 Å/s. When the Si-Ge was deposited, the evaporation rate of Si was kept to 0.5 Å/s, and that of Ge was adjusted to produce a certain composition of Si-Ge solid solution. (Therefore, the total growth rate of the Si-Ge was slightly higher than 0.5 Å/s.) A composi- The Ge-composition of the uniform SiGe layer was evaluated by X-ray reciprocal mapping (XRM). It was revealed that the Ge-composition was at about 22 at%. We intended to divide the Ge-composition from 2 to 20 at% by 2-at% steps as mentioned before. However, the Ge-composition of each layer might have slightly shifted to be Ge-rich. If we simply divide 22 at% into 10 layers, the          Figure 4(c) using the software sMoiré [14]. Reciprocals of scan spacing, lattice spacing, and moiré spacing are shown in this figure. In Figure 4(c), there is a twin and the moiré patterns across the twin show slightly different directions. According to this fact, the moiré spots in Figure 5 are split. Figure 6 is the enlarged image of a part of Figure 4(c). The image analysis software "sMoiré" (HREM Research Inc.) was utilized to calculate the lattice spacing from this STEM moiré. This software was developed in order to evaluate the two dimensional lattice strains from the STEM moiré [14]. In this study, we used this software to calculate one dimensional changes of the {111} crystal plane spacing. Essentially, FFT was applied to the moiré and the spacing of the {111} planes from each layer were calculated from the FFT results. Figure 7 is the result of the image analysis for the moiré shown in Figure 6.

Results and Discussion
The change of the {111} spacing with changing the positon in the specimen was plotted. We expected to detect how it is changing according to the Ge-concentration.  Figure 4(c) using the software sMoiré [14]. Three arrows can be interpreted as reciprocals of scan spacing, lattice spacing, and moiré spacing. The moiré spots are split because the moiré changes its direction across the twin in the area of Figure 4(c).

Scan spacing
Lattice spacing Moiré spacing Figure 6. An enlarged image of Figure 4(c). The {111} space in the red rectangle area was calculated using the software sMoiré [14]. The result is shown in Figure 7. Figure 7. The results of the image analysis. The horizontal axis is a distance on the specimen. The direction is perpendicular to the interface of the each layer. The vertical axis is a change of the {111} spacing calculated from the moiré spacing using the software sMoiré [14].
the accurate value of the {111} spacing could not calculated yet for this specimen and there is an uncertainty of the calculated {111} spacing. However, the tendency of the changes of the {111} spacing, that is gradually decreases toward the low-Ge-concentration area, is qualitatively consistent with the expected inclination. The reason of the uncertainty of the calculated {111} spacing in each layer might be the noise of the STEM images. We need further study to measure precise value by using this technique.

Summary
We succeeded in observing the STEM moiré of the compositionally step-graded