Complex oxide growth using simultaneous in situ reflection high-energy electron diffraction and x-ray reflectivity: When is one layer complete?

Thin-film growth changed dramatically more than three decades ago with the discovery of reflection high-energy electron diffraction (RHEED) intensity oscillations.^1,2 During RHEED, a high-energy (≈10–30 keV) electron beam is fired at grazing incidence onto a growth surface and the intensity of the reflected beam is recorded. During 2D monolayer-by-monolayer growth, electrons interacting with the topmost layer create oscillations in the intensity of the reflected RHEED beam, and the period of the oscillation corresponds to the addition of exactly one monolayer to the film. This discovery led to rapid implementation of RHEED systems for thin-film growth,^3–5 and it has become nearly ubiquitous in thin-film growth systems.⁶ 

Researchers have worked to understand RHEED intensity oscillations via a variety of different methods. In principle, the complete picture can only be understood using dynamical diffraction theories.^7,8 Before resorting to a full model, it often suffices to describe the RHEED intensity oscillations as the interference between two layers via a kinematic scattering approximation^9,10 or via the step density model^3,11 (or a combination of the two¹²).

In the step density model, as the areal step density increases the likelihood of diffuse scattering increases, thus the specular intensity decreases. As the layer reaches completion, the number of steps decreases, and thus the specular intensity recovers—ideally returning to its original value.⁶ The prediction is the same for the kinematic approximation: We expect the RHEED intensity to oscillate exactly out of phase with the surface roughness.

In practice, RHEED oscillations are often more complex. For nominally identical growths, the RHEED intensity can increase at the start of the growth¹³ or decrease and then recover to an intensity greater than the intensity before growth,¹⁴ or the RHEED intensity can (of course) oscillate exactly out of phase with the roughness.¹⁵ Even nominally identical RHEED and growth conditions can yield RHEED oscillations that are surprisingly 180° out-of-phase with each other.¹³ Thus, a major drawback when using RHEED is the fact that it is not obvious when a layer is complete.

RHEED oscillations during pulsed laser deposition (PLD) are more complex due to the movement of adatoms between laser pulses. During PLD, randomly deposited material creates a sharp decrease in RHEED intensity after each laser pulse. Between laser pulses, as the adatoms diffuse on the surface, fall into pits, and attach to step edges and islands, the surface “heals” and becomes smoother. As the surface heals, the RHEED intensity increases. This behavior agrees with the simple RHEED oscillation models—despite the fact that the overall growth oscillation is not necessarily exactly out of phase with the roughness.¹⁴ 

The period T of the RHEED intensity oscillations is easy to determine based on the maxima or minima of the intensity oscillations. We can define the phase of the RHEED oscillations by assuming that the growth begins at t = 0, and then finding the minimum of the RHEED intensity that occurs between t = T and t = 2 T. We label this time as t_3∕2,¹⁶ and define the phase of the RHEED oscillations as⁸ 

The simple models predict that RHEED intensity is a minimum when the surface is roughest, i.e., when t_3∕2 = 1.5 T. This in turn means $ϕ=0$⁠, so the RHEED intensity oscillation is exactly out of phase with the roughness.

RHEED is not the only in situ growth diagnostic tool. X-ray reflectivity (XRR) is highly surface sensitive and can also yield information about growth dynamics at incident angles smaller than that of the first Bragg peak.^17,18 Typically, the XRR intensity will oscillate not only due to roughness but also due to thin-film interference.¹⁹ In the case of homoepitaxy, because there is no thin-film interference, the XRR intensity oscillates due to roughness only. In addition, weakly interacting x-rays are well described with the kinematic scattering approximation,²⁰ and as a result, we can use Eq. (1) to find $ϕ=0$ always for XRR intensity oscillations.

XRR has advantages over RHEED in that, unlike RHEED, the intensity lost from the XRR specular reflections can be seen directly in the XRR diffuse scattering.²¹ In fact, the diffuse scattering is additional data that can be used to determine information about surface growth kinetics.²¹ Unfortunately, very bright synchrotron x-ray sources are required to be able to see XRR intensity oscillations due to changes in roughness, which is why XRR continues to be less common than RHEED.

In this article, we discuss direct, simultaneous comparison of RHEED and XRR during homoepitaxial growth of SrTiO₃ (STO) via pulsed laser deposition onto STO $〈001〉$ substrates. These measurements were performed on atomically smooth substrates²² using a custom PLD/x-ray diffraction system installed in the G3 hutch at the Cornell High Energy Synchrotron Source. Experimental details are described in the supplementary material.²³ Our conclusions can be applied to heteroepitaxial growth as well as any layer-by-layer growth regardless of crystallinity, however, the choice of homoepitaxy simplifies the analysis of XRR intensity oscillations.

Two typical growths of STO on STO $〈001〉$ via pulsed laser deposition are presented in Fig. 1. Each individual laser pulse is obvious, marked by the sharp decrease in intensity in both RHEED and XRR, followed by the exponential recovery between pulses. The number of pulses per layer is ≈11.3 and ≈10.2 for Figs. 1(a) and 1(b), respectively. In these figures, from the shape of the XRR intensity oscillations, we know that the growth was layer-by-layer, that the density of the film matches that of the substrate, and that there is no interface layer between the film and the substrate;^17,19 indicators that the epitaxial film has the same crystal quality as the substrate. Additional growths are presented in the supplementary material.²³ 

The growth conditions of these two films were nearly the same (deposition temperatures of 915 °C and 890 °C for Figs. 1(a) and 1(b), respectively). For both growths, the XRR intensity oscillation remains out of phase with the roughness, so $ϕ≈0.1π$⁠. However, in the RHEED intensity oscillation, the phase changes by 137°: $ϕ≈0.05π$ in Fig. 1(a) and $ϕ≈0.81π$ in Fig. 1(b). In our experiments, we can repeatedly adjust the phase not via growth conditions but rather via substrate annealing conditions. If the substrate is annealed just before growth in high vacuum, the RHEED and XRR oscillations are very nearly in phase; if the substrate is annealed in high O₂ pressure, the oscillations are very nearly out of phase. The substrate in Fig. 1(a) was annealed for 1 h in $2.7×10−6$ mbar, the substrate in Fig. 1(b) was annealed for 20 min in $1.7×10−3$ mbar.

RHEED oscillations have not been well studied in the oxides (in contrast to semiconductors⁸), and the mechanism that controls the phase of the RHEED oscillation is not well understood. In this report, we demonstrate the ability to reliably and repeatedly control the RHEED phase.

As a compelling visual confirmation that RHEED maxima do not necessarily correspond to complete layers, we characterized our substrates using an atomic force microscope (AFM) pre- and post-growth. These data are presented in Fig. 2 (one additional growth is presented in the supplementary material²³). We annealed the substrates in vacuum and achieved nearly out-of-phase RHEED and XRR intensity oscillations.²⁴ We interrupted the growth of (a) at t ≈ 2.5 T, or at 2.5 monolayers according to XRR intensity oscillations, which means the RHEED intensity oscillation was close to its maximum. We can see in the inset of Fig. 2(b) that the substrate was atomically smooth prior to growth, and after growth the sample has uniformly rough, featureless surface, where the height distribution on each terrace follows a Gaussian distribution with a FWHM of 3.8 ± 0.2 Å (very close to the 3.9 Å step height).²⁵ This maximum roughness, according to the morphology of the surface as measured by AFM, occurs at the minimum of the XRR oscillations, as expected. However, it occurs near the maximum of the RHEED oscillation—providing the clear proof that RHEED oscillation intensity cannot be used to determine layer completion.

Fig. 2(c) shows a similar growth interrupted at t ≈ 2 T, or 2 monolayers according to the XRR intensity oscillations. After two monolayers, the atomically smooth substrate before growth (inset of Fig. 2(d)) has pinholes covering 15% ± 2% of its surface.²⁶ These pinholes are expected for layer-by-layer growth and are why the XRR intensity does not recover to its initial maximum.^20,27 Here, the RHEED intensity is close to its minimum, yet the surface is very smooth.

Most growth systems do not have the capability to measure both RHEED and XRR simultaneously, so the question is: Using only RHEED, is there any way to know when a layer is complete? The answer is simple: Yes. As discussed above, determining the growth period T is straightforward. In the ideal case of true 2D growth when the starting surface is smooth, then each new monolayer is complete at times $t=T,2T,3T,…$ This is true independent of RHEED oscillation phase. However, in practice, surfaces are not perfect and growth is not ideal. In these cases, can RHEED be used to determine layer completion?

For 2D growth, it is still possible to determine when a layer is complete using RHEED—even if the starting surface is not smooth. Returning our attention to the measured intensity between pulses: Following each laser pulse, the deposition of randomly distributed atoms causes a sharp decrease in intensity followed by an exponential recovery as the adatoms move on the surface and the surface heals. The step density model predicts a recovery of the form $I≈Io(1−e(t−tpulse)/τ)$⁠, where τ is the relaxation time.²⁸ When the surface is rough, the relaxation time τ is short, as it takes very little time for the adatoms to diffuse the short distance required to find a hole, step edge, or island. By the same logic, when the sample is very smooth, this relaxation time is long.

An increase in the relaxation time between laser pulses indicating the completion of a layer has been seen explicitly in XRR^21,29 and RHEED when the phase $ϕRHEED=0$⁠.²⁸ The recovery between pulses will follow the step density model even when the overall RHEED oscillation is more complex than this simple model.³⁰ Thus, we can use the relaxation time after each laser pulse to characterize the layer coverage, as the relaxation times per pulse will still reach a maximum when the layer is complete, independent of the RHEED oscillation phase.

We fit the recovery after each laser pulse for the growth shown in Fig. 1(b), where $ϕ≈0.81π$⁠. In Fig. 3, the blue dashed curve represents the relaxation times per pulse as measured by XRR and the green solid line represents the relaxation times as measured by RHEED. As expected, the XRR relaxation times are a maxima when the layer is complete, roughly every 11 laser pulses. Since the XRR intensity is at its maximum when the layer is complete, the oscillations of the XRR relaxation times are roughly in phase with the XRR intensity oscillations. Remarkably, the maxima in the relaxation times in the RHEED data occur at the same laser pulse as the XRR relaxation times. Thus, the relaxation times measured by both techniques are a maxima at $t=T,2T,3T,…$ This means the RHEED relaxation times are a maximum when the layer is complete—despite the fact that the RHEED intensity oscillation phase is nearly 180°.

Similar behavior has been seen at other RHEED intensity oscillation phases. Khodan et al. grew STO on STO $〈001〉$ via PLD³¹ and used substrates etched using a similar HF etch. Assuming a smooth starting surface, their data present an oscillation phase of $ϕ≈−0.62π$ (69°),³¹ with RHEED relaxation times that are a maxima at $t=T,2T,3T…$⁠, again as expected.

In conclusion, we have studied the homoepitaxial growth of STO on STO $〈001〉$ via simultaneous in situ RHEED and XRR. We have shown that the RHEED intensity oscillation phase $ϕ$ can change even for identical growth conditions. In contrast, the XRR intensity oscillations are always at a maximum when the layer is complete (⁠$ϕ=0$ for XRR). From post-growth AFM images, we have shown that the substrate surface can be rough even when the RHEED intensity oscillation is near a maximum and smooth when the RHEED oscillation is near a minimum.

Finally, the main point of this article is to provide a tool to the thin film growth community to determine when a layer is complete, a tool that does not depend on the magnitude of the RHEED intensity oscillation. For PLD, the RHEED and XRR intensities increase after each laser pulse as the adatoms diffuse and the surface heals. The characteristic relaxation time between each laser pulse is a maximum when the surface is least rough, and can be used to determine when a layer is complete. We have shown in our own results that this relaxation time is a maximum at layer completion for various phases of RHEED growth.

The authors acknowledge Hanjong Paik, Charles Brooks, and Darrell Schlom for helpful discussions and assistance in etching substrates. Most of our substrates were etched at the Cornell NanoScale Facility, supported by the National Science Foundation (Grant No. ECCS-0335765).

M. C. Sullivan was supported in part by the Energy Materials Center at Cornell (EMC2), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award No. DE-SC0001086.

This work was based upon experiments conducted at the Cornell High Energy Synchrotron Source (CHESS), which was supported by the National Science Foundation and the National Institutes of Health/National Institute of General Medical Sciences under NSF Award Nos. DMR-1332208 and DMR-0936384. This work also made use of the Cornell Center for Materials Research Shared Facilities which are supported through the NSF MRSEC program (No. DMR-1120296).