Relaxation of asymmetric crystallographic tilt: In situ x-ray diffraction studies of epitaxial electrodeposition of bismuth on GaAs (110)

Mechanisms to deal with the long-range stress fields generated by lattice mismatches between a film and substrate are critically important to heteroepitaxial growth and have been studied extensively.¹ One possible mechanism is simply to strain a pseudomorphic film. In this case, the film typically exhibits a critical thickness, beyond which the film relaxes via the creation of misfit-dislocations.² A second possible mechanism, to relieve the strain energy, is to create a low-energy tilt boundary (a coherent, periodic distribution of edge dislocations) at the substrate-film interface, reducing the lattice mismatch and, therefore, the long-range strain fields.^3–5 (The tilt boundary is called asymmetric if the two lattices have different tilts relative to the interface.) Significant efforts, both experimental and theoretical,^6–10 have been made to understand asymmetric tilt boundaries and to use them to grow strain-free films.¹¹ Despite these efforts, the detailed structure and strain relaxation mechanisms of asymmetric tilt boundaries at heteroepitaxial interfaces remains poorly understood.

Hexagonal lattice metals on cubic substrates were some of the first epitaxial systems in which lattice tilt was observed.^12–14 Tilted $011¯LHEX$ epitaxial films exhibit two common features. First, they have the same tilt axis $21¯1¯0$⁠. (In hexagonal close packing metal films, the equivalent plane (⁠$101¯L$⁠) and tilt axis $12¯10$ are usually used.¹⁴) Second, the tilt is caused by a slip of the (0001) basal plane at the interface. This $(011¯L)$ epitaxial growth has also been observed in electrodeposition. Bismuth films, for example, show a strong $(011¯8)$ oriented texture when grown on GaAs(110) (⁠$(011¯8)Bi//(110)GaAs$⁠, $044¯1¯Bi//[001]GaAs$⁠, $21¯1¯0Bi//[11¯0]GaAs$⁠, see Fig. 1(a) and supplementary material for details).^15,16 Moreover, because bismuth exhibits high magnetoresistance,¹⁷ has a long mean free path,^18,19 and the interface between bismuth and GaAs forms a Schottky barrier that prevents electrical leakage from the bismuth film into GaAs,^15,16,20 bismuth films on GaAs are attractive candidates for spintronic devices.^21,22 These properties and applications are closely related to the epitaxial structure of Bi on GaAs. Therefore, we chose bismuth electrodeposition on GaAs(110) as a model system with which to study asymmetric tilt and its relaxation mechanism in the electrodeposition.

An electrochemical characterization of the system Bi³⁺/GaAs(110) was carried out using cyclic voltammetry (CV), with Ag/AgCl as the reference electrode (RE). We measured several consecutive scans starting at the open circuit potential (OCP ∼ 100 mV vs. RE) and initially examining the reduction processes. The potential was then reversed at −200 mV vs. RE towards positive values up to 300 mV vs. RE to completely dissolve the electrodeposited bismuth. Finally, the potential was returned to the OCP. We varied the sweep rate to explore the changes in both cathodic and anodic profiles. The CVs [Fig. 1(b)] exhibit cathodic and anodic peaks that correspond, respectively, to the deposition and dissolution of bismuth. The charge accumulated during both processes only differs by 5% for the sweep rates studied. When increasing the sweep rate, the cathodic peak moves to more negative values, while the anodic peak position shifts in the positive direction. This is a signature of the irreversibility of the Bi/Bi³⁺ redox couple in this particular electrolyte, due to the sluggish electron exchange.^23,24 The onset potential for bismuth deposition, obtained from the slowest sweep rate (5 mV/s), is about −60 mV vs. RE. Since the equilibrium potential for Bi³⁺/Bi at this concentration and at room temperature is approximately 40 mV vs. RE, we can conclude that a minimum overpotential of η = 100 mV is needed to nucleate bismuth onto the surface of GaAs(110).

To monitor, in real-time, the structure of bismuth films during electrodeposition, we used in situ high-energy X-ray diffraction. Combining high energy X-rays (∼30 keV) and a large area detector, we simultaneously monitored several Bragg reflections during electrodeposition under various deposition conditions with sufficient angular resolution to resolve the peak widths normal to the Ewald sphere.²⁵ 

The crystal structure of the bismuth film electrodeposited under chronoamperometry at various overpotentials was characterized using in situ XRD with a custom electrochemical cell [Fig. 2(a)].²⁶ The measurements were performed in the A2 station of the Cornell High Energy Synchrotron Source (CHESS). The X-ray energy was 30 keV and the diffracted X-rays were collected by a 41 cm × 41 cm large area detector (DXR250RT, GE Inspection Technologies), which covered an area in reciprocal space as large as 34/Ų. The substrate was aligned so that the projection of the incoming X-ray wavevector on the sample surface was along [$1¯10$]_GaAs, which is parallel to the asymmetric tilt axis $21¯1¯0$_Bi in (⁠$0 1 1¯ 8$⁠) texture (see Fig. S1 and the supplementary material for experimental details). Figures 2(b)–2(d) are the background-subtracted XRD patterns of bismuth films deposited for 30 min at different overpotentials (see Fig. S2 for the raw XRD pattern and Movies S1 to S4 in the supplementary material for the background subtracted XRD patterns as a function of deposition time). Diffraction peaks were indexed calculating their corresponding interplanar distances and classified, taking into account their calculated relative orientation, into three distinct single crystal domains with different orientations: (⁠$0 1 1¯ 8$⁠), (⁠$4 1¯ 3¯ 14$⁠), and (⁠$3 1¯ 2¯ 7$⁠). The in-plane orientations of the (⁠$4 1¯ 3¯ 14$⁠) and (⁠$3 1¯ 2¯ 7$⁠) oriented domains are shown in Fig. S4. In Fig. 2(b), the diffraction peaks from every domain are marked with a distinctive color: green, yellow, and red, respectively. No other diffractions were visible in the performed experiments. Although the (⁠$4 1¯ 3¯ 14$⁠) and (⁠$3 1¯ 2¯ 7$⁠) oriented domains are present and coexist with the (⁠$0 1 1¯ 8$⁠) oriented domain throughout our potential window, the relative growth rate to that of the (⁠$0 1 1¯ 8$⁠) oriented domain can be significantly reduced with the overpotential. Figure 2(e) shows the abundance of each domain as a function of the overpotential. To estimate the growth rate between domains, we averaged the integrated intensity of all diffractions from each domain. The green, red, and yellow bars represent the abundance percentage of (⁠$0 1 1¯ 8$⁠), (⁠$4 1¯ 3¯ 14$⁠), and (⁠$3 1¯ 2¯ 7$⁠) oriented domains, respectively. From this figure, we infer that increasing the overpotential promotes the (⁠$0 1 1¯ 8$⁠) over the two other orientations. The abundance of this domain rapidly grows from 11% to 94%, while the (⁠$3 1¯ 2¯ 7$⁠) oriented domain decreases from over 73% down to 4% and the (⁠$4 1¯ 3¯ 14$⁠) oriented domain decreases from 16% at low overpotentials to just 2% at high overpotentials. Moreover, increasing the overpotential significantly reduces the mosaicity of the film. As shown in Figs. 2(b)–2(d), the diffraction from bismuth domains exhibits an angular distribution along the corresponding Debye-Scherrer ring trajectories, from which the full width at half maximum (FWHM) can be used to characterize the mosaicity of the film. The mosaicity, as a function of the overpotential, is shown in Fig. 2(f). Green triangles in the figure are the averaged FWHM of peaks from (⁠$0 1 1¯ 8$⁠) oriented domains [except (⁠$022¯4$⁠), probably due to anisotropic mosaicity, see supplementary material] as a function of overpotential. At low overpotentials, the averaged FWHM is about 4.71°, whereas at the highest overpotential, it decreases down to 0.62°, a 7× decrease in mosaicity by increasing the overpotential. When we analyzed the other two domains, we also obtained a similar decrease in the FWHM with increasing overpotential [red circles and yellow squares in Fig. 2(f)]. It is worth noting that this difference in the mosaicity between different overpotentials is not simply caused by the thickness of the film because the average value of the angular FWHM of Bi peaks does not depend on film thickness (see the red dashed line in Fig. S6).

As mentioned previously in the experimental setup, we used 30 keV X-rays and aligned the asymmetric tilt axis $21¯1¯0$_Bi of (⁠$0 1 1¯ 8$⁠) oriented domain with the incident X-ray wavevector. The purpose of this setup was to observe the asymmetric tilt and its evolution during the deposition. As shown in Fig. 2(b), multiple diffraction peaks from (⁠$0 1 1¯ 8$⁠) oriented domains were observed simultaneously [green indexes in Fig. 2(b)], and, more importantly, all the diffraction peaks lie in the (⁠$0KK¯L$⁠) reciprocal lattice plane. Because the (⁠$0KK¯L$⁠) plane is perpendicular to the asymmetric tilt axis, if the asymmetric tilt angle about $21¯1¯0$_Bi varies during the deposition, a unique phenomenon would appear: all the diffraction peaks from bismuth (⁠$0 1 1¯ 8$⁠) oriented domains will rotate in the same direction, by the same value, while the diffraction peaks from the substrate will remain unaltered. For simplicity, the analysis was performed only for η = 240 mV, where (⁠$0 1 1¯ 8$⁠) oriented domains dominate and the mosaicity is at a minimum. All the (⁠$0 1 1¯ 8$⁠) diffraction peaks exhibited a continuous rotation during the deposition. As a representative example, in Fig. 3(a), we show the reciprocal space maps (RSMs) in the proximity of the (⁠$022¯7$⁠)_Bi diffraction peak as a function of deposition time. Plotting the contours of the (⁠$022¯7$⁠)_Bi diffraction peaks obtained at different deposition times, as shown in Fig. 3(b), it is clear that the radial position does not change (resolution $≈3×10−3 Å−1$⁠), indicating that neither the interplanar distances nor the lattice parameters evolve during the deposition. Instead, the angular position continuously changes with deposition. Figure 3(c) shows the intensity profile of the (⁠$022¯7$⁠) diffraction peak along the trajectory of the {$022¯7$} Debye-Scherrer ring during the deposition. The angular position of the (⁠$022¯7$⁠) diffraction peak varies, by up to several tenths of a degree, during electrodeposition. The same procedure was applied to other diffraction peaks from the (⁠$0 1 1¯ 8$⁠) oriented domains, as well as to diffraction peaks from GaAs, to obtain the change of their angular position with film thickness, as shown in Fig. 3(d). The film thickness was calculated from the integrated charge during electrodeposition. It is evident that the angular position of the substrate, for instance (331)_GaAs [the black dots in Fig. 3(d)], does not change. In contrast, the angular positions of all bismuth peaks show a monotonic dependence with film thickness. For thicknesses less than 100 nm, the angular position did not change. Beginning at a threshold thickness lying between 100 and 200 nm, the angular position of the bismuth peaks varied monotonically as a function of film thickness. When the film thickness reached 1.2 μm, the total shift of the Bi diffraction peaks was 0.23°. This suggests that the asymmetric tilt angle is constant only for thicknesses < 100 nm, and continuously relaxes beyond this range.

The absolute value of the asymmetric tilt angle of the bismuth film was calculated based on the difference of the crystallographic direction of (⁠$0 1 1¯ 8$⁠) and GaAs (110) (obtained from the position of (⁠$331¯$⁠)_GaAs and (331)_GaAs from the raw XRD pattern in Fig. S2). Based on the asymmetric tilt model, proposed by only considering the lattice mismatch at the interface,^14,27 the tilt angle between the (⁠$011¯8$⁠)_Bi and (110)_GaAs planes should be 0.70°. In our experiment, when the thickness of the film reaches 40 nm, the tilt angle is 0.45°, 64% of the theoretical prediction. The angle decreases to 0.22°, when the thickness reaches 1.2 μm. Our results suggest that the bismuth film relieves interface strain using tilt and, as the film grows, the tilt relaxes.

As shown in Fig. 3(b), the peak shape at late times contains the peaks shapes obtained at earlier times, which can also be clearly seen from the intensity profiles in Fig. 3(c). This suggests that the relaxation of the asymmetric tilt is not caused by a change in the orientation of the entire bismuth film that is already grown. Instead, the decrease in tilt angle arises by tuning the growth direction of bismuth from the initial asymmetric tilt back towards (⁠$011¯8$⁠). Microscopically, this tuning of the growth direction could be realized by forming a series of low angle grain boundaries during the film growth to compensate the initial tilt.²⁸ Using the Scherrer equation, the bismuth grain size was estimated to be about 120 nm along the surface normal. To test this hypothesis, a simplified model was proposed assuming the film is formed by equal-sized grains along the surface normal, and that each grain has the same relative tilt angle −Δθ with the neighbor. The first grain has an initial tilt angle of 0.45°. The diffraction pattern for this simple model was calculated and compared to the experimental results. Figures S7(a) and S7(b) present a comparison between the experimental data of the intensity profile of the (⁠$011¯8$⁠) diffraction, at different times, and the one calculated from the model, with Δθ equal to 0.05° and the grain size equal to 120 nm. Under these conditions, the model predicts the same threshold thickness and relaxation rate of the tilt angle as the experimental data, as shown in Figs. 4 and S7(c). Moreover, the calculations reveal that the formation of the low angle grain boundaries does not change the angular FWHM of the Bragg peak, consistent with the observed constancy of the angular FWHM of the diffraction peaks [see Fig. S7(d)]. The excellent agreement between experiment and calculation strongly supports the hypothesis that the relaxation of the asymmetric tilt originates from the generation of a series of small angle grain boundaries along the surface normal direction. A general microstructural mechanism developed for the deposition on stepped surfaces could be used to explain the formation of the low angle grain boundaries in the Bi film.¹¹ At the early stages of film growth, the film is tilted due to the lattice mismatch between the film and substrate. However, the tilt causes a change of the film surface plane from (⁠$0 1 1¯ 8$⁠) to (⁠$0 1 1¯ 8$+Δ), which can be considered to be a stepped surface of the (⁠$0 1 1¯ 8$⁠) plane. Thus, the steps on the surface plane generate an elastic strain through continuous deposition.¹¹ Once the newly deposited film reaches a critical thickness of 120 nm (based on calculations), misfit dislocations are created to relax the strain, causing the formation of grain boundaries. The value of Δ is 0.2 at the early stages of the tilt. After 30 min, the value of Δ, on the topmost layer, decreases and approaches almost 0, which, in turn, tunes the surface plane to (⁠$0 1 1¯ 8$⁠). As demonstrated by Read and Shockley, the energy to form the low angle grain boundary becomes smaller as the relative tilt angle between grains decreases.²⁹ Thus, when the strain accumulates with the film growth and reaches the energy to form this low angle grain boundary, this asymmetric tilt starts relaxing. Considering the previous attempts to use this asymmetric tilt to grow strain free films, our work suggests that there exists a threshold thickness beyond which the film starts relaxing the tilt by forming a series of low angle grain boundaries along the surface normal.

Using in situ synchrotron XRD, we have studied the asymmetric crystallographic tilt of epitaxial bismuth films during electrodeposition on GaAs(110) in real-time and found that the single crystallographic orientation $011¯8$ of the film can be selected by controlling the overpotential. From the angular position of the diffraction peaks from $0 1 1¯ 8$ oriented domains, we observed the asymmetric tilt of the film, which has previously only been observed in the UHV growth methods. We have measured the asymmetric tilt angle during deposition and found that there is a threshold thickness (around 120 nm) beyond which the tilt angle relaxes. Our work presents a new approach to unravel the complex processes happening in the epitaxial electrodeposition. To the best of our knowledge, the data in Fig. 3(d) represent the first observation of the dynamical response of asymmetric tilt during growth.

See supplementary material for Movies S1–S4, additional experimental details, raw XRD pattern, calculation of the tilt angle from the lattice mismatch, detailed comparison between measured Bragg peaks with the calculated model, etc.

This material is based upon work supported as part of the Energy Materials Center at Cornell (EMC2), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001086. This work is based upon research conducted in part at the Cornell High Energy Synchrotron Source (CHESS), which is supported by the National Science Foundation under Award No. DMR-1332208. This work made use of the Cornell Center for Materials Research Shared Facilities which are supported through the NSF MRSEC program (DMR-1719875). This work was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (Grant No. ECCS-1542081).