Direct measurement of electron channeling in a crystal using scanning transmission electron microscopy

Self-focusing of an atomic-scale high-energy electron wave packet by channeling along a zone axis in crystalline silicon is directly measured by scanning transmission electron microscopy using thin epitaxial SrTiO${}_3$(100) islands grown on Si(100) as test objects. As the electron probe propagates down a silicon atom column, it is progressively focused onto the column, resulting in a fourfold increase in the scattered signal at the channeling maximum. This results in an enhancement of the visibility of the SrTiO${}_3$ islands, which is lost if the sample is flipped upside down and the channeling occurs only after the probe scatters off the SrTiO${}_3$ layer. The evolution of the probe wave function calculated by the multislice method accurately predicts the trends in the channeling signal on an absolute thickness scale. We find that while electron channeling enhances the visibility of on-column atoms, it suppresses the contribution from off-column atoms. It can therefore be used as a filter to selectively image the atoms that are most aligned with the atomic columns of the substrate. By using this technique, coherent islands can be distinguished from relaxed islands. For SrTiO${}_3$ films formed in a topotactic reaction on Si(100), we show that only $\sim$55$\%$ of the SrTiO${}_3$ is aligned with the Si atom columns. The fraction of coherent SrTiO${}_3$ islands on Si(100) can be increased by choosing growth conditions away from equilibrium.

Figure 1

(a) and (b) Plan-view and (c) cross-sectional ADF-STEM images of a nominally 2.5-uc-thick epitaxial SrTiO${}_3$(100) film grown on Si(100) and capped with 15 nm of amorphous Si showing the formation of SrTiO${}_3$ islands and nonuniform coverage. (a) and (b) are viewed along a substrate $\langle 001\rangle$ zone axis and (c) along a $\langle 110\rangle$ zone axis. For more details, see Ref. 11.

Figure 2

Channeling signal $dI/dz$ determined by simulating the ADF intensity after each slice and taking the derivative with respect to the sample thickness $z$. The channeling signal was computed for two probe positions, the first one on the atomic column and the second one in-between atomic columns, propagating down Si$\langle 001\rangle$. Phonon scattering was taken into account using the frozen-phonon approximation and following the Einstein model for thermal vibrations, averaging over 20 phonon configurations.

Figure 3

Focusing of the electron probe in crystalline Si due to electron channeling along ${\langle 100\rangle }_{\text{Si}}$. Probe profiles at the entrance and at the exit surface of a 10-nm-thick Si crystal, respectively.

Figure 4

Plan-view imaging of a thin epitaxial SrTiO${}_3$ film grown on crystalline Si and capped with amorphous Si in areas of the sample where the crystalline Si is increasingly thicker. The sample was oriented so that the electron probe first propagates through the crystalline Si substrate before reaching the SrTiO${}_3$ layer. The thickness of the crystal was determined by matching the experimentally recorded convergent beam electron diffraction (CBED) patterns [left half of (a)–(f)] with simulated CBED patterns of crystalline Si at various thicknesses [right half of (a)–(f)]. Low-angle annular dark field imaging of the epitaxial SrTiO${}_3$ film [(g)–(l)] reveals the change in the visibility of the SrTiO${}_3$ islands with sample thickness.

Figure 5

Process of extracting the average ADF intensity of the SrTiO${}_3$ islands from plan-view ADF images. (a) Original ADF image, (b) background of (a) determined using a singular value decomposition routine, and (c) the background-subtracted image. The average intensity from the SrTiO${}_3$ islands is determined by fitting two Gaussians to the histogram of (c) and taking the difference between the centers of the two Gaussians.

Figure 6

Comparison of the theoretical and the experimentally measured channeling signal in Si(100). For the experimental results, the orientation of the sample is labeled by substrate/SrTiO${}_3$ when the electron probe propagates through the substrate before scattering off the SrTiO${}_3$ layer, and by SrTiO${}_3$/substrate when the sample is flipped upside down. The error bars reflect the uncertainty in the determination of the crystal thickness by matching the experimental CBED patterns with simulations and the standard deviation of the intensity of the SrTiO${}_3$ islands determined for different parts of the ADF image by the procedure described in the text.

Figure 7

Visibility of a single Sr atom placed on the side through which the electron beam exits of a (a) 10-nm- and (b) 40-nm-thick crystalline Si substrate. As the Sr atom is moved off an atomic column, the visibility decreases and drops below the detection limit when displaced by less than 1 Å. The visibility is calculated using a simple model (convolution of the incident probe intensity with the projected position of all the atoms in the sample weighted by $Z$${}^{1.7}$) and multislice for two detector geometries corresponding to the LAADF and the HAADF signal. At a Si substrate thickness of 10 nm, the Sr visibility for HAADF imaging closely follows the shape of the electron probe at that thickness.

Figure 8

Plan-view ADF-STEM images of a nominally 2.5-uc-thick epitaxial SrTiO${}_3$(100) film grown on Si(100) using a 1-ML-thick Sr template and capped with 15 nm of amorphous Si viewed along a substrate $\langle 001\rangle$ zone axis. The sample is oriented so that (a) the Si substrate and (b) the a-Si layer constitute the entrance surface. When electron channeling is used to enhance the visibility of the SrTiO${}_3$ layer, the SrTiO${}_3$ that is aligned with the Si columns is preferentially imaged and the apparent coverage decreases.