Atomic-resolution three-dimensional imaging of germanium self-interstitials near a surface: Aberration-corrected transmission electron microscopy

We report the formation and direct observation of self-interstitials in surface proximity of an elemental semiconductor by exploiting subthreshold effects in a new generation of aberration-corrected transmission electron microscopes. We find that the germanium interstitial atoms reside close to hexagonal, tetragonal, and $S$-interstitial sites. Using phase-contrast microscopy, we demonstrate that the three-dimensional position of interstitial atoms can be determined from contrast analysis, with subnanometer precision along the electron-beam direction. Comparison with a first-principles study suggests a strong influence of the surface proximity or a positively charged interstitial. More generally, our investigation demonstrates that imaging of single atom can now be utilized to directly visualize single-defect formation and migration. These high-resolution electron microscopy studies are applicable to a wide range of materials since the reported noise level of the images even allows the detection of single-light atoms.

Figure 1

(Color online) (a) Aberration-corrected images of a thin Ge crystal oriented along the [110] direction [black arrows show occupied interstitial sites, red arrows (dark gray) show column vibrations occurring during the acquisition time]. Magnified areas where an interstitial atom is observed, (b) and (c) In $T$ sites, (d) In an $H$ site that overlaps with a bond-centered site when the crystal is oriented along the [110] zone axis, (e) In an off-center site. Electron dose: $4.0\times {10}^4\text{electrons}/{\text{nm}}^2$. Range of focus from $-1$ to $-8\text{nm}$.

Figure 2

(Color online) Cs-corrected HRTEM images of a Ge crystal oriented along the [110] direction. (a) Thin area near the sample edge, where excitation of column oscillations and ${\text{Ge}}_i$ formation are observed. (b) Thicker area where we do not observe any disturbances of the crystal lattice. (c) Histograms of the measured distance between the projected atomic columns and the projected hexagonal position in the center of a unit cell (as indicated in the insert). The Gaussian fits show the wider distribution of the measurement in the thin area, highlighting the higher excitation of the column oscillation.

Figure 3

(Color online) (a) Positions of ${\text{Ge}}_i$’s extracted with subpixel precision from TEM images. The origin of the axis is the central geometrical hexagonal site defined by the surrounding atom columns. Squares with error bar: mean position of the atomic column; Squares: ${\text{Ge}}_i$’s close to the $H$ sites; Triangles: ${\text{Ge}}_i$’s close to the $T$ sites; Stars: ${\text{Ge}}_i$’s in an off-center position. (b) Model of the new $S$ configuration calculated by DFT in a passivated (110) slab of thickness 1.4 nm.

Figure 4

(Color online) (a) Simulated PMC of Ge atom columns of different heights as a function of focus (curves). The red (dark gray) and black squares present the mean PMC of the atomic columns surrounding the interstitials 1 and 2, respectively, extracted from the experiment. The blue square is the mean PMC of the ${\text{Ge}}_i$’s observed in the micrograph acquired using a focus of $-6.6\text{nm}$. (b) Contrast of the interstitials 1 and 2 [red (dark gray) and black squares, respectively] compared to the simulated contrast of an interstitial atom located at different $z$ positions. Error bars are given by noise levels: $\pm 4\%$. (c) 3D representation of the ${\text{Ge}}_i$’s $z$ position in a five-atom high crystal along the [110] direction. The blue cigar shapes represent the position of the interstitials 1 (right cigar) and 2 (left cigar). The elongation of the cigars represents the noise-limited precision of the measurement $\left(\pm 0.9\text{nm}\right)$ and scales shaded in blue (gray) gives the probability for the presence of the interstitial along the cigar.