Column-by-column observation of dislocation motion in CdTe: Dynamic scanning transmission electron microscopy Free

Motion of dislocations controls the mechanical properties of both bulk and nano materials, including their strength, deformability, and ductility.¹ Furthermore, dislocations introduce localized states, which undergo changes as the dislocations move, affecting the electronic properties of the materials.^2–4 Theoretical calculations including molecular dynamics,^5–7 ab initio,^3,8 and Kinetic Monte Carlo simulations^9,10 have been employed to explore the mechanisms by which dislocations move.^5,6,8–10 Such simulations show that bond switching between atoms controls the motion of dislocations.^5,8,10 In experiments, stress and heat treatments have been applied to study dislocation motion in the optical and electron microscopes.^5,11–13 However, the atomic-scale mechanics of partial-dislocation motion has not previously been resolved experimentally. Such observations would provide a critical test for theoretical models of dislocation motion.

Aberration-corrected transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) have recently been applied to study dynamics in-situ and at the atomic scale.^14–27 By providing atomic resolution at considerably lower beam energies, aberration correction enables one to study materials at atomic resolution across a wide range of energies, from as low as 20 kV to upwards of 300 kV. This often enables one to select a beam energy that is below the threshold for knock-on damage but high enough to drive and observe dynamic processes with atomic resolution. Aberration correction also increases the signal-to-noise ratio of atomic resolution Z-contrast annular dark field images in STEM, allowing one to decrease the beam current and increase the scan speed, both reducing sample damage^28–30 and increasing the attainable time resolution while retaining atomic number sensitivity. In the past few years, this technique has been used to investigate the dynamic motion of many low-dimensional defects, such as point defects in 2-dimensional graphene,^{16,19,21,27,31} atomic vacancies or impurities in nanostructures,^{15,17,18,22,25,32} and the fluctuations of ultra small nanoparticles.²³ STEM has recently also been used to study the atomic dynamics of a phase change in bulk materials.³³ Here, we extend the technique to study the motion of partial dislocations in semiconductors that are used in solar cells.

In this research, a 5th-order aberration-corrected STEM with sub-Å resolution has been used to manipulate and directly observe the glide of partial dislocations in II–VI semiconductor CdTe column-by-column, demonstrating that dynamic STEM not only can be used to study the defects in nanomaterials but can also be used to understand the atomistic motions that underlie classical dislocation motion. High-angle-annular-dark-field (HAADF) Z-contrast movies have been taken of the dynamics of different partial dislocations in CdTe. It was directly observed that the Cd-core 30° Shockley partial dislocation is more mobile than the Te-core dislocation. The dislocation configurations with unpaired columns are found to be more mobile than those without. Atomic models have been constructed based on STEM images to explain how the bonding configurations change after the glide in 3-dimensions. In addition, the dissociation of a screw dislocation along two different directions has been recorded. These results illustrate the insights dynamic-STEM can bring to the understanding of defect migration at the atomic scale, which could prove vital to engineering solutions to dislocation mediated mechanics and electronics problems.

Fig. 1 shows 3 sequential STEM Z-contrast images from a movie of a pair of 30° Shockley partial dislocations at the ends of a one-layer stacking fault (red frame) acquired at 200 kV (Multimedia view). In the [110] viewing direction, Cd and Te columns usually form close pairs that look like “dumbbells,” marked by the blue-yellow solid circle pairs in Fig. 1. As Te (Z_Te = 52) is slightly heavier than Cd (Z_Cd = 48), the Te (large yellow circles) and Cd (small blue circles) columns can be directly distinguished from the STEM Z-contrast images. The dumbbells in the stacking faults can be seen to have different orientations compared with the surrounding dumbbells. In the Shockley partial dislocation cores, instead of dumbbells, there exist an unpaired Cd column (dashed blue circle) and an unpaired Te column (dashed yellow circle), respectively. We refer to the dislocation cores with unpaired Cd and Te columns as Cd-core (or α dislocation as Cd is the cation) and Te-core dislocations (or β-dislocation as Te is the anion³⁴), respectively. The stoichiometry of the unpaired columns is identified not directly based on their image intensity, which is likely to be affected by the strain. Instead, it is identified by the bonding configuration with the surrounding columns for which we can directly identify the polarity.^35,36 The unpaired column connecting the CdTe and TeCd dumbbells is always Cd (and vice versa), as it is energetically favorable. These atomic configurations have been confirmed by density functional theory (DFT) calculations.^4,35,36

From Figs. 1(a) to 1(b), the position of the Cd-core dislocation shifted along the stacking fault by one dumbbell distance towards the right side. The position of the Te-core dislocation did not change. From Figs. 1(b) to 1(c), the position of the Cd-core dislocation remained constant, but the position of the Te-core dislocation shifted towards the right for one dumbbell distance. Cd-core and Te-core dislocations can both shift towards either the left or right directions along the stacking fault.

Both Cd-core and Te-core dislocations are very mobile under the 200 kV electron-beam (e-beam), but the rate for Cd-core dislocations to shift is almost twice that of Te-core dislocations in Multimedia view 01 (34 frames, 1.6 s per frame) in which the Cd-core shifted 14 times, Te-core 8 times. Furthermore, on three occasions, the Cd-dislocation was seen to move two dumbbell's distance, whereas no such motion was observed for the Te-dislocation. A similar movie has been taken under a 60 kV e-beam (100 frames, 1.05 s per frame), as shown in the supplementary material, Movie I. Under these conditions, the Te-core dislocation remained stable during the entire movie, but the Cd-core dislocation moved back and forth along the stacking fault eight times, as shown also in our previous paper.⁴ 

To evaluate how the e-beam affects the dislocation motion, we first consider the energy transfer from the e-beam to the sample. The displacement rate of an atomic column, p, is given by the product of the beam current density, j, and the scattering cross section σ. For a given set of microscope conditions, j remains constant. The cross section σ is an integrated value starting from the threshold scattering angle θ_min³⁷ 

When the e-beam energy E_beam is constant, the two effective factors for θ_min are the atomic mass number A and E_barrier, the activation energy for dislocation motion. The E_barrier is determined by the dislocation configuration. The extra factor that could make dislocation motion behave differently under the e-beam from normal stress or thermally induced motion is the dependence on atomic mass number A. A larger atomic mass leads to a larger θ_min and therefore a smaller σ and lower p, resulting in lower mobility. In other words, because of conservation of momentum in an elastic collision, the electron beam transfers more energy to light elements. In our case, the atomic mass of Cd (112.4) is very close to that of Te (127.6). Moreover, density functional theory (DFT) simulations (results shown below) have demonstrated that both Cd and Te atoms need to move during the motion of either Cd-core or Te-core dislocations. Therefore, in this research, the motion of the dislocations is unlikely to be significantly affected by the difference in mass of Cd and Te during the in-situ microscopy observations. The energy barriers have been extracted from the rates observed at the different cores and beam energies, but the values from different voltages are not consistent; hence, a more detailed study at intermediate voltages is necessary to understand the displacement rates quantitatively. However, the qualitative comparison on dislocation mobilities is feasible.

DFT simulations have been employed to identify which atoms govern the dislocation motion. The initial structure (IS) and the final structure (FS) have been chosen according to two sequential HAADF-STEM images, which show the glide of a Cd-core 30° Shockley partial dislocation (Figs. 2(a) and 2(b)). The configurations have been relaxed by DFT calculations, and views of the models from different crystalline directions are shown in Figs. 2(c)–2(f). The results show that the Te atoms in the Te₁ column shift along the diagonal direction between -X and -Z directions. The Cd atoms in Cd₀ and Cd₁ columns move slightly along the Z direction. For the motion of Te-core dislocation, it is also found that both Cd and Te atoms need to move. This indicates that the bias due to the e-beam effect between Cd-core and Te-core dislocations is negligible; therefore, the in-situ observation of the dislocation mobility is mostly determined by the energy barrier of the dislocation motion. Since the Cd-core dislocation is more mobile than the Te-core dislocation, the E_barrier for the Cd-core dislocation to glide is considerably lower than that of the Te-core. Note that due to the time resolution of STEM, there might exist intermediate steps in the migration process that we are unable to resolve. For instance, between the “initial” and “final” structures in Fig. 2, it is likely that kinks have formed and vanished during the movement of the entire dislocation.^8–10 How such intermediate steps play out is likely a reason why thicker regions migrate more slowly. However, the STEM observations still provide the relative mobilities of the dislocations from regions of similar thickness. These observed mobilities should be applicable to thermal or strain mediated dislocation motion for CdTe, when the zinc-blende CdTe phase keeps stable below 996 °C under pressure as high as 1.92 GPa.³⁸ 

This result is consistent with the results of molecular dynamics simulations by Zhou et al.,³⁹ although the atomic motion was not resolved in that paper. Thus, dynamic STEM observations are an effective means of directly comparing the mobilities of different dislocations in materials composed of elements with similar atomic masses, and especially for mono-elemental materials such as silicon, diamond, etc. However, for structures composed of elements with large atomic mass differences, further consideration of the detailed atomic configuration change and the effect of atomic mass would be necessary. Note the direct mobility comparison should be performed with dislocations of similar thickness (and even better from the same area, as the Cd- and Te-core dislocations in Fig. 1), so that the different thicknesses will not affect the mobility comparison.

Dynamic-STEM has also been used to study the mobility of dislocations with different configurations. The three successive frames from a movie (Multimedia view, 60 kV, 100 frames, 0.5 s per frame) displayed in Fig. 3 show the glide of a 90° Shockley partial dislocation associated with a 2-layer stacking fault. Two unpaired Cd columns were found to shift back and forth along the stacking fault simultaneously without a preferred direction. It is worth pointing out that this dislocation was exposed under the 60 kV e-beam for more than 1 h, but no sample damage was observed (no atoms knocked out as the image contrast did not change).

We have also investigated the dislocation glide process for four other types of partial dislocations in CdTe (as shown in our previous paper^35,36). The 2-layer 30° Shockley partial dislocation with the unpaired column is also mobile under the e-beam (supplementary material, Movie II). We were also able to capture the dislocation moving within one image during scanning (supplementary material, Fig. 1). The one-layer 90° Shockley partial dislocation without unpaired columns in the dislocation cores, nevertheless, has not been found to move around under the e-beam from 60 kV to 200 kV. The two Frank partial dislocations are sessile under the beam as expected, as their motion requires a climb process.

These results show a rule: for Shockley partial dislocations in CdTe, those with unpaired columns in the dislocation core can glide much more easily than those without. The mechanism can be explained by the bonding configuration change during the dislocation motion. The normal Cd and Te atoms in CdTe have four Cd-Te bonds. In contrast, each atom in the unpaired columns has only three Cd-Te bonds (shown by the three dashed white lines in Fig. 2). Therefore, each atom in the unpaired column (for example, Cd₀ in Fig. 2(a)) maintains a dangling bond, which attracts the adjacent atom (column Te₁ in Fig. 2(a)) to move closer and form a new bond. After this, the Cd atom in column Cd₁ is left with a dangling bond, thereby moving the Cd-core dislocation by one dumbbell. The same mechanism applies for the Te-core dislocation but with the roles of the two elements reversed.

For the “sessile” one-layer 90° Shockley partial dislocation without unpaired columns in the dislocation cores, instead of dangling bonds, the columns in the dislocation cores have three normal Cd-Te bonds plus a Cd-Cd or a Te-Te “wrong” bond. Therefore, extra energy is required to break the extra bond. This result shows that the “unpaired” columns in dislocation cores assist dislocation motion in CdTe. It is worth mentioning that the mobility comparison for group-IV materials diamond⁸ and silicon¹⁰ is the opposite of what we observe here, with the one-layer 90° Shockley partial dislocation more mobile than the 30° one. This might be due to their different atomic dislocation configurations and stereochemistry. The side view models in Figs. 2(e) and 2(f) also demonstrate that there is no “dimer” along the dislocation in the mobile 30° Shockley partial dislocation in CdTe. However, the immobile 30° Shockley partial dislocation in group-IV materials¹⁰ does have dimers along the dislocation line, which might increase the bond-breaking energy. Since there is no beam effect on atomic mass in either diamond or silicon (only one type of atoms), this dynamic-STEM method should be ideal to directly compare the dislocation mobility of different dislocations.

We have further observed the motion of a full screw dislocation as shown in Multimedia view (200 kV, 45 frames, 1.6 s per frame). Three different configurations from the movie have been presented in Fig. 4. Fig. 4(a) shows a 30° Shockley partial dislocation pair associating with a one-layer staking fault along the [$11¯2¯$] direction. From Figs. 4(a) to 4(b), the pair of dislocations annihilate, leaving some strain contrast in the center of the image. The Burgers vector of the full screw dislocation is parallel to the [110] viewing direction; therefore, no defect structure but only strain contrast can be observed. In Fig. 4(c), it is observed that the screw dislocation has again disassociated into a stacking fault and a pair of dislocations, but this time along the [$1¯12¯$] direction. Via this disassociation process, the full dislocation can move along two equivalent ⟨112⟩ directions and therefore everywhere in the sample.

In conclusion, aberration-corrected STEM has been used to resolve the atomic scale dynamics of dislocations in the II–IV semiconductor CdTe. The beam effect on dislocation mobility is negligible because the atomic masses of Cd and Te atoms are very similar; therefore, the in-situ dislocation mobilities are mainly dominated by the intrinsic energy barriers of the different dislocation configurations. For one-layer 30° Shockley partial dislocations, the Cd-core Shockley partial dislocations are more mobile than the Te-core partials. The mobility comparison of different dislocation structures indicates that the unpaired columns in dislocation cores mediate the dislocation glide in CdTe, because their dangling bonds assist the bond switching processes with the surrounding atoms. Under the e-beam, screw dislocations can easily dissociate into Shockley partial dislocation pairs and stacking faults along two different but crystallographically equivalent directions, and the dislocation pairs can associate again. It has been shown that this in-situ dynamic STEM method is effective and beneficial for understanding the atomic process of the motion of low-dimensional defects, especially for materials containing only one type of atoms such as silicon and diamond or containing atoms with similar atomic masses such as CdTe and GaAs.

See supplementary material for in-situ STEM Movie I and II as well as one supplementary image. Together with the Multimedia view, they show the motion of different dislocations. There is also a discussion of the details of the experiments and calculations, including the equations for calculating the energy transfer between the electron beam and the sample.

This research was sponsored by the U.S. DOE, Office of Energy Efficiency and Renewable Energy, Foundational Program to Advance Cell Efficiency (F-PACE, DE-FOA-0000492), (CL, YLW, NP, YFY, SJP), the Office of DOE-BES, Materials Science and Engineering Division (ARL), DOE Grant No. DE-FG02-09ER46554 (YYZ, STP), and a user project supported by ORNL's Center for Nanophase Materials Sciences (CNMS), which is also sponsored by DOE-BES. Supercomputer time was provided by the National Center for Supercomputing Applications which is supported by the DOE Office of Science under Contract No. DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. Chen Li [No. 656378] and Timothy Pennycook [No.655760] are currently funded by the European Union's Marie Skłodowska-Curie Grants.