Abstract
The properties of artificially grown thin films are strongly affected by surface processes during growth. Coherent Xrays provide an approach to better understand such processes and fluctuations far from equilibrium. Here we report results for vacuum deposition of C_{60} on a graphenecoated surface investigated with Xray Photon Correlation Spectroscopy in surfacesensitive conditions. Stepflow is observed through measurement of the stepedge velocity in the late stages of growth after crystalline mounds have formed. We show that the stepedge velocity is coupled to the terrace length, and that there is a variation in the velocity from larger step spacing at the center of crystalline mounds to closelyspaced, more slowly propagating steps at their edges. The results extend theories of surface growth, since the behavior is consistent with surface evolution driven by processes that include surface diffusion, the motion of stepedges, and attachment at step edges with significant stepedge barriers.
Introduction
Studies of thin film growth seek to understand the dynamics of surface nanostructures that are simultaneously undergoing both stochastic particle deposition and random relaxation processes. These processes, which affect surface structure, morphology and composition^{1} as well as defect propagation^{2} play a central role in determining the properties of artificially grown thin films^{3,4,5}. However, traditional methods used to study growth in realtime such as electron diffraction^{6,7} and surface Xray scattering^{8,9} are unable to provide a complete understanding of surface dynamics since they suffer from the limitation that the surface must be an almost perfectly flat single crystal. For example, observations of layerbylayer oscillations yield kinetic information from which energy barriers to surface diffusion and interlayer transport can be deduced, but only during the early stages of growth before significant roughness develops. Although nucleation and coalescence continue locally, layerbylayer growth oscillations become unobservable in the presence of surface roughness since they are damped out by phase differences in the scattering from different regions of the surface.
Recent advances in coherent Xray methods that utilize Xray Photon Correlation Spectroscopy (XPCS)^{10} can yield crucial information on the dynamics where the structural fluctuations about an average configuration occur. This is possible since the scattering of coherent Xrays produces a speckle pattern, which depends sensitively on the detailed configuration within each coherence volume. The XPCS analysis characterizes the time correlations of fluctuations in equilibrium or outofequilibrium systems. Examples include stepedge fluctuations during annealing and evaporation^{11,12}, surface roughness fluctuations during deposition^{13}, fluctuations at polymer surfaces^{14}, and the dynamics of bulk phase transformations^{15,16}. These fluctuations are invisible to analysis with lowcoherence Xrays, since those methods average over local structures within the illuminated volume. Coherent Xrays can also be used to measure surface velocities where heterodyne mixing between scattering from different regions mix to produce oscillatory correlations. For example, defect velocity^{17}, has been studied during growth of amorphous thin films by sputter deposition.
Here, we show that it is possible to utilize coherent Xrays to study thin film growth without loss of information due to spatial averaging, even in the later stages where the growth surface is very rough, and the film is composed of many separate crystalline grains. Step flow processes are observable by correlation spectroscopy when there is no change of Xray intensity as the steps advance, and hence layerbylayer oscillations are not present. The effects are analogous to oscillations in homodyne correlations that have been observed under flow conditions or during elastic relaxation, which can be observed if there is a velocity gradient^{18,19,20,21}. The measurements show promise for making detailed comparisons with theories of crystal growth.
Figure 1a shows an overall schematic of the thin film deposition by thermal evaporation of solid C_{60} onto an amorphous substrate in a vacuum environment to form a polycrystalline thin film. We follow the surface evolution from the initial nucleation stage through to steadystate growth, focusing on the properties and dynamics of the steadystate regime. A coherent Xray beam is incident on the substrate surface during the growth, and scattered Xrays are detected by a fast area detector (see Methods for further details). Figure 1a also shows an example of surface topography obtained by postdeposition Atomic Force Microscopy, as well as a speckle pattern from the Grazing Incidence Small Angle Xray Scattering pattern acquired during the growth. The closeup inset in the speckle pattern corresponds to a small region of the scattering pattern near the Yoneda wing, which is visible as a horizontal streak in the main image. It is due to an enhancement of the surface diffuse scattering at exit angles α_{f} near the critical angle for total external reflection (α_{c} ≈ 0.16° for 9.65 keV Xrays incident on solid C_{60}). Figure 1b, c illustrates the principle of heterodyne mixing, where in this case strong scattering from the average configuration of surface mounds mixes coherently with the much weaker scattering from surface steps. As a result, oscillations are observed due to the motion of the steps across the surface, and the amplitude of the oscillation is much larger than the scattering from the steps separately. As we discuss in more detail below, valuable insight is obtained about the step motion in this experiment. Molecular steps do not move all in the same direction or at the same rate; instead, they slow down as they approach the edge of mounds where the terrace length becomes smaller.
Results
Correlations in high temperature growth
The nonstationary dynamics during surface growth is measured via twotime intensity autocorrelation functions, which are derived from experimental Xray intensities I(Q, t)^{15,22}:
The normalized intensity is obtained from \(I\prime ({\mathbf{Q}},t) = I({\mathbf{Q}},t) /\widetilde {I({\mathbf{Q}})}\), where \(\widetilde {I({\mathbf{Q}})}\) is averaged over time and over a few detector pixels to smoothen out the speckles. The average \(\langle \rangle\) is obtained by averaging over a range of Q having similar time correlations (Supplementary Note 1).
Figure 2 shows the twotime correlations G(Q, t_{1}, t_{2}) for deposition at T_{sub} = 144 °C. Figure 2a shows the complete deposition. Figure 2b shows twotime correlations from the start of deposition at t = 40 s and during the period of roughening where mounds initially form and stabilize. The most striking feature of the data is the transition to a pattern of parallel streaks that appear between 400 and 600 s (~9–13 monolayers). Layerbylayer oscillations have previously been observed for deposition of C_{60} on mica at 60 °C in the early stages of deposition^{23}. However, we note that the oscillations we observe have a different characteristic than the layerbylayer oscillations, which occur at the beginning of the growth process before the surface becomes rough. In contrast, the oscillations in the correlations observed in Fig. 2 emerge during 3D growth and persist for the remainder of the deposition without any discernable decay (Fig. 2c), indicating that they are part of the steadystate dynamics. These streaks cease when the growth shutter is closed at 3200 s (Fig. 2d). Correlations peak when t_{1} = t_{2}, and decay as a function of Δt = t_{1} − t_{2} over the entire time interval.
For steadystate dynamics, the onetime correlation function can be employed:
Figure 3a shows correlations for the same deposition shown in Fig. 2, averaged over the time interval from 650 s to the end of the deposition. The data exhibits pronounced oscillations as a function of Δt with a peak in amplitude at an inplane wavevector of Q_{max} = 0.0145 Å^{−1}, corresponding to a length scale of ≈43 nm. The period of the oscillations is T = 40 s, and it does not shift with Q_{}. The value calculated from the deposition rate (1.11 nm/min) and (111) layer spacing is T_{dep} = 43 s. Therefore, the period of oscillations is very close to the monolayer deposition time for C_{60} growth. Several additional features of the data can be seen more clearly in Fig. 3b, which is for a thin film deposited with a substrate temperature of T_{sub} = 216 °C. The maximum oscillation amplitude is at Q_{max} = 0.0050 Å^{−1}, which corresponds to a length scale of 126 nm. We observe a general trend that the maximum oscillations occur at a value of Q_{} that shifts lower, corresponding to a larger length scale for different samples, as the temperature is increased (Supplementary Note 2). The curve at Q_{} = 0.0085 Å^{−1} exhibits sharper maxima and broader minima, with weak maxima corresponding to correlations with a halfmonolayer period.
Figure 4 shows postgrowth characterization of one of the samples. Figure 4a shows an Atomic Force Microscope (AFM) scan of the film surface where the grain structure is visible. Molecular steps are also observed in the image. They are roughly circular, surrounding a high point near the center of each mound, and the mean step spacing on the tops of the mounds for growth at 216 °C is estimated to be ≈150 nm. This value can be compared to the length scale ≈126 nm derived from Q_{max} for the data in Fig. 3b and Supplementary Fig. 2e. The full amplitude mode and height mode images corresponding to the inset in Fig. 4a are shown in Supplementary Note 3. Figure 4b shows an Xray specular scan. Only (111) and (222) reflections are observed, indicating that the films are highly oriented.
The onetime correlation function (Eq. 2) can be decomposed into a simpler product of correlation functions of electric fields rather than intensities:
where \(F({\mathbf{Q}},{\it{\Delta }}t) = g^{(1)}({\mathbf{Q}},{\it{\Delta }}t)\)/\(g^{(1)}({\mathbf{Q}},0)\) is the normalized intermediate scattering function with \(g^{(1)}({\mathbf{Q}},{\it{\Delta }}t) \sim \langle E({\mathbf{Q}}, t\prime )E^ \ast ({\mathbf{Q}},t\prime + {\it{\Delta }}t)\rangle _{t^\prime }\), and β(Q) is the optical contrast factor^{24,25}. The intermediate scattering function is related to densitydensity variations in the sample, and in the case of Grazing Incidence Small Angle Xray Scattering (GISAXS) the surface scattering is related to variations in the height of the surface through \(g_s^{(1)}({\mathbf{Q}},{\it{\Delta }}t) \sim \langle h(Q_{\mathrm{r}},t\prime )h^ \ast (Q_{\mathrm{r}},t\prime + {\it{\Delta }}t)\rangle\). The experimental results suggest that the statistical properties of the growing surface can be described by an empiricallyderived intermediate scattering function of the form:
where \(\omega _1\) is the oscillation frequency, and \({\mathrm{\Gamma }}_j(Q_\parallel ) = 1/\tau _j(Q_\parallel )\) is the relaxation rate, or inverse of the relaxation time. This form matches closely to the heterodyne form describing capillary waves on liquid surfaces^{26}, with one notable difference: for capillary waves, the frequency is proportional to the inplane component of the wave vector transfer through the relation \(\omega = Q_\parallel v\) where v is the wave velocity, while in the present case the frequency is entirely independent of the wavevector transfer. Instead, it is related to the monolayer deposition time by \(\omega _1 = 2\pi\)/T_{dep} for all Q_{}. We also introduce a harmonic frequency \(2\omega _1\) in the last term in Eq. 4 to take into account the presence of the observed halfmonolayer correlations in the data. The stretching exponent n in the first term takes into account the deviation of the overall decay from a simple exponential shape. Figure 3b includes curves fitted to the correlation results using Eqs. 3 and 4, and good agreement is obtained. Additional fitting results for the correlations shown in Fig. 3a are shown in Supplementary Note 4.
These results present a puzzle for the interpretation of the observed oscillations, since they suggest that we are not simply measuring the mean velocity of a uniformly propagating array of steps. A propagating array of steps does not by itself produce oscillatory correlations, due to translational symmetry. Only the phase advances, which is not directly observable. A quasistatic reference signal can mix with the scattering from the moving steps, which would produce oscillations. In this case, a possible origin of such a quasistatic reference is the largescale mound features present on the surface. Alternately, a layerbylayer growth mode will produce oscillations with a frequency that is independent of Q. However, it is the surface roughness that oscillates in that case, so there will be a corresponding oscillation in the diffuse scattering intensity, which we do not observe (Supplementary Note 5). Moreover, layerbylayer growth with a significant EhrlichSchwoebel stepedge barrier leads to an unstable surface where the surface quickly becomes too rough for the topmost layer to reach completion before nucleation of the next layer^{27}. Layerbylayer oscillations are therefore incompatible with our observation of correlation oscillations that continue in the late stages of growth without significantly decreasing in amplitude.
We emphasize that it is possible to observe oscillatory correlations in a coherent scattering measurement without corresponding oscillations in the intensity. This occurs when individual speckles oscillate in time, but since there is no simple relationship in the temporal phases from one speckle to the next for scattering from a complex surface structure, averaging over a region of interest that contains hundreds of speckles leads to the intensity oscillations being averaged out. On the other hand, the correlation functions in Eqs. 1 and 2 correlate different times before the Qaveraging is performed. This preserves the temporal information so that peaks in the correlations are observed for time differences Δt where the surface reaches a selfsimilar state.
Step flow model
In order to improve on the models described above, we introduce the assumption that the steps are not uniformly spaced. Instead, the nth terrace has a variable length L_{n}, and the steps move at velocity v_{n} rather than at a single overall velocity (Fig. 5). The oscillation period is interpreted as the time for surface steps to advance by one terrace length. Within this model, the presence of oscillatory correlations is intuitive in the sense that the surface returns to a selfsimilar state each time the terraces advance by one terrace length, for time intervals that are integer multiples of the monolayer deposition time T_{dep}.
This model readily incorporates mounds, and we refer to it as the Local Step Flow (LSF) model since steps are confined to each crystalline mound. The terrace length L_{n} and step velocity v_{n} are proportional to each other as the mound configuration approaches a steady state^{28,29,30}. Hence, the period \(T_{\mathrm{LSF}} = L_n\)/v_{n} corresponds to the time for steps to advance by one terrace length as we require, but T_{LSF} is itself independent of n. As a result, there is only a single oscillation frequency \(\omega _{\mathrm{LSF}}\).
The LSF model fully embodies the properties needed to describe the results of Fig. 3. The first term in Eq. 4 is interpreted as arising from the timeaveraged mound structure, which reaches a nearly steadystate, or quasistatic configuration, as the film deposition proceeds. The second term is from a part of the nonuniform array of steps with an average spacing that matches 2π/Q_{} for a certain Q_{}. The frequency is set by the monolayer completion time T_{LSF}, as discussed above. The same segment of steps can also generate a (weak) doubled frequency at higher Q_{}, corresponding to a 2nd order reflection from the step array, which accounts for the third term on the rhs of Eq. 4. The combined signal is considered to be in a heterodyne mode since it consists of the very strong quasistatic term (average mounds) that mixes with a weaker scattering from the steps.
In order to study the LSF model, we employ a model for molecular beam epitaxy in 1 + 1 dimensions previously introduced by Politi and Villain, called the Zeno model^{31}. In the presence of an energy barrier that hinders interlayer diffusion, molecules landing on terraces cannot easily step down (the EhrlichSchwoebel effect)^{32,33}. Since grooves at the boundary between step arrays are not easily filled up, threedimensional islands or mounds are formed that have a wedding cake type structure. In the present case, mounds are practically guaranteed to form due to the polycrystalline nature of the C_{60} films. This is due to the fact that the islands forming the base layer of mounds nucleate without any preferred azimuthal orientation, so neighboring mounds are inhibited from merging as they impinge, ensuring that deep grooves develop at their boundaries. We note that a similar mechanism has previously been suggested to explain rapid roughening in diindenoperylene thin films with tilt domain boundaries^{34}. Given these considerations, a model that incorporates groove formation seems particularly apt. The model introduced by Politi and Villain is known as the Zeno model since the steps slow down as they approach the edges of the mound. Nucleation of new terraces occurs only at the top of the mounds^{35}, while steps propagate towards the mound edges. The model is entirely deterministic since nucleation always occurs at the exact center of the layer beneath it, at the moment when that step reaches the critical length for nucleation.
Figure 5 shows the terrace structure of a mound generated with the Zeno model. The model incorporates the EhrlichSchwoebel effect through a single parameter, L_{s}, the Schwoebel length, which characterizes the strength of stepedge barriers. The main equations of the model are shown in the inset of Fig. 5a. In our implementation of the model, the lattice unit a is set to unity and the flux F is set to 1/1000 so that the average height of the surface h(t) = aFt advances by one unit for every 1000 timesteps. The mound is generated starting from a fixed base layer with a radius of 200 lattice units, and the critical length for nucleation of a new top layer is set at 10 lattice units. The Schwoebel length L_{s} is defined as follows: if the width L of a terrace is smaller than L_{s}, most of the atoms landing on this terrace go to its upper edge, while if L > L_{s}, about onehalf of the atoms go to each edge because they are too far from the other one. The velocity of each step is calculated from the lengths of the lower (nth) and upper (n + 1th) terraces. The step spacing becomes very small as the steps slow down near the edge of the mound. However, the overall shape of the island approaches a nearly stationary state. Figure 5b shows the surface configuration for the last 9 lattice units of deposition. The step configuration at different times is almost identical for times separated by an integer number of deposited layers (1000 timesteps). However, for curves separated by only 0.5 layers, it is seen that the steps advance halfway across their lower terrace, and this behavior is independent of the local terrace length. This is precisely the behavior that we require in order to explain the experimental data, where the step velocity is a variable proportional to the upper and lower terrace widths, but the period T_{LSF} to advance by one step spacing is essentially fixed.
Figure 6 shows autocorrelations calculated for the LSFZeno model. Figure 6a is calculated using Eq. 2 over a range of Q_{} that corresponds to a length scale slightly larger than the mean terrace width (~10 lattice units between 0 and 150 radius). The results exhibit parallel diagonal streaks that are separated by 1000 timesteps, corresponding to integer monolayer time differences. An important feature of the results is that there are no strong modulations along the direction of the main diagonal, which indicates that correlations persist throughout the monolayer growth cycle. This indicates that the moment when nucleation occurs is not special as far as the correlations are concerned; only the time differences matter. This is the characteristic of stationary dynamics, i.e., where local fluctuations occur but the average structure does not change at an appreciable rate. In this case, the fluctuations take the form of an expanding array of concentric molecular steps.
As a result of the stationary dynamics, we can average over the age [t_{age} = (t_{1} + t_{2})/2], to produce onetime correlations as a function of Δt = (t_{1} − t_{2}) for the LSFZeno model. An example is shown in Fig. 6c, which exhibits oscillations with a period of 1 layer (1000 timesteps). The frequency does not change for autocorrelations at different Q_{}, however weak harmonic beats are observed for Q_{} values that corresponds to a length scale of approximately half of the mean terrace width in the central part of the mound (Fig. 6d). This behavior closely resembles the experimental data in Fig. 3b. In the Zeno model, the nucleation always occurs in the exact center of the top terrace. We note that random nucleation has been previously investigated in 1 + 1 dimensions, and is found to produce more disordered step arrays^{31}, which would have the effect of increasing the relaxation rates in Eq. 4.
Several key features of the experimental results are reproduced by the LSFZeno model of molecular beam epitaxy described above. First, the oscillations in the correlation results are independent of the phase of the growth cycle. Second, the unexpected observation of a single oscillation period T_{dep}, independent of Q_{} is found to be fundamental to local step flow with the specific step velocity distribution produced by the Zeno model. Third, the presence of mounds itself implies that nucleation occurs predominantly on the top terrace due to the fact that the mounds are a consequence of stepedge barriers leading to threedimensional growth. The layerbylayer process continues at the top of the mound, while the steps bounding lower terraces propagate by step flow. It is striking that all of these features of the LSFZeno model closely reproduce the experimental results.
Scaling behavior
Scaling relations can be useful for capturing the time and wavelengthdependence of surface evolution during thin film deposition. Powerlaw behavior is frequently encountered, both for stable surfaces that exhibit kinetic roughening, as well as for unstable surfaces that exhibit mound or pattern formation^{36,37}. We observe that C_{60} thin film growth is of the second type, i.e., it is unstable to the formation of mounds. The unstable case includes examples of both growth by molecular beam epitaxy of elemental metals such as Pt on singlecrystal Pt(111) substrates^{29}, as well as during sputter deposition of amorphous thin films of Zr_{65}Al_{7.5}Cu_{27.5} alloys^{38}. C_{60} growth on randomly oriented graphene domains falls into a third category of oriented polycrystalline thin films, which is a common mode for organic semiconductor materials when they are deposited on noncrystalline substrates.
In the early part of the growth of C_{60} on a graphenecoated substrate, we observe that the mound structure evolves quickly. After an induction period, it gradually approaches a nearly static configuration that we refer to as the steadystate. In order to confirm the convergence to a static structure, we use the same Xray scattering data used for the XPCS analysis by averaging over speckles to obtain the average intensity \(\bar I(Q_\parallel ,t)\). Figure 7a shows the intensity plotted as a function of Q_{}. In the early time, the scattering profile takes the form of a broad peak that is consistent with a longwavelength surface instability^{39}. It subsequently converges to a powerlaw form \(\bar I(Q_\parallel ) \propto Q_\parallel ^{  \gamma }\) for \(t \gtrsim 427\,s\), which corresponds to the time interval when the stepflow correlations appear in Fig. 2.
While the intensity profiles characterize the timeaveraged mound structure, the correlations characterize fluctuations about the timeaveraged structure. Step flow itself can be considered to be a fluctuation that produces periodic oscillations in the correlations. In addition, there can be significant fluctuations in the spacing and jaggedness of step edges because admolecules diffusing on the terraces attach at random positions^{40}, and because nucleation on the topmost terrace of the mounds is a stochastic process that does not occur precisely at the center^{31,35}. These effects cause the correlations to decay monotonically as a function of time difference. In order to characterize the dynamics from coherent X–ray scattering data, we assume a scaling form for the steadystate dynamics:
where h(q_{}, t) is the Fourier component of the surface amplitude at wave vector Q_{} and time t^{41}. This expression is valid for t_{1}, \(t_2 \to \infty\) and Δ\(t = t_1  t_2\) finite, i.e., the steadystate regime. Also, \({\mathrm{lim}}_{x \to \infty }{\kern 1pt} g_{SS}(x) = 0\), so Eq. 5 is consistent with an intermediate scattering function that decays as \(g^{(1)}(Q_\parallel ,{\it{\Delta }}t) = I_0{\kern 1pt} {\mathrm{exp}}\{  ({\it{\Delta }}t/\tau _0)^n\}\) with \(\tau _0(Q_\parallel ) \sim Q_\parallel ^{  z}\). We focus on the Q_{} dependence of 1/τ_{0} rather than the other time constants in Eq. 4 since it can be measured in both the high and lowtemperature growth regimes.
We have established in the previous section that the growth in the high temperature range is consistent with a stepflow model. This raises several interesting questions: do the dynamics obey the scaling relations in Eq. 5? Can a transition in the dynamics be observed from low deposition temperatures where local relaxation dominates, to higher temperatures where longerrange diffusion of molecules on terraces play a role? In order to investigate these questions, we have deposited C_{60} thin films with the substrate held at temperatures below 100 °C, which results in very small grain size polycrystalline thin films. Figure 7b shows the relaxation rates extracted by XPCS analysis for substrate temperatures of 27° and 73 °C. The dynamic exponent extracted from fitting to this data is in the range z = 2.2–2.5. These exponents can be compared to those measured for amorphous sputterdeposited Si and WSi_{2} thin films, z = 1.2 to 2.0^{13,17}. The difference may be related to the fact that sputterdeposited Si and WSi_{2} thin film surfaces exhibit characteristics of kinetic roughening, where roughening is driven by noise in the deposition flux. On the other hand, for C_{60} the surface is unstable to mound formation due to deterministic processes, which may dramatically shift the exponents. For example, Krug predicts a dynamic scaling exponent 1/z = 1/4 for unstable mound growth^{37}. Xray intensity profiles suggest that coarsening of crystalline domains also plays a role in determining the exponent for C_{60} films (Supplementary Note 6).
Figure 7b also shows a comparison with relaxation rates for C_{60} films deposited at temperatures above 140 °C where larger mounds with welldefined step arrays are formed. In this range, the XPCS results during steadystate growth exhibit clear oscillations, as illustrated in Figs. 2 and 3. At higher temperatures, the relaxation is characterized by the overall time constant \(\tau _0(Q_\parallel )\). The observed relaxation rates in Fig. 7b are significantly higher at temperatures >140 °C compared to low temperature deposition, and the dynamic exponent changes significantly, from z = 2.2 − 2.5 at lower temperatures to z = 0.53 − 0.65 at higher temperatures. These results clearly indicate a transition to a new regime.
This analysis reveals an important finding, that z characterizes the nonequilibrium dynamics of stepflow in the steadystate regime. The unusually low value of z ≈ 0.6 may be related to the fact that as Q_{} increases, the correlations are most sensitive to steps with smaller terrace spacing, which propagate more slowly according to the stepflow model presented in the previous section. This is opposite to many typical situations, such as Brownian motion or kinetic roughening, where relaxation rates increase at shorter length scales. We also find that the oscillations in the correlations are not observable for growth at 73 °C and below, which indicates that correlated stepflow does not occur at lower temperatures. Thus, the large change in the dynamic exponent is linked to a fundamental change in the dynamics of the surface during growth.
Discussion
In conclusion, coherent Xray scattering is used to investigate stepedge motion on surfaces. A transition of the surface dynamics has been observed on growing C_{60} surfaces that is related to a change from roughening dominated by admolecule diffusion at higher temperatures to a process at low temperatures where correlated step motion is absent. In the hightemperature regime, oscillations in correlations due to stepflow are observed as the surface returns to a selfsimilar state each time the steps advance by one terrace length. This information would be difficult to obtain by any other experimental technique, and it is completely invisible to methods based on lowcoherence Xrays. The results illustrate a broadly applicable and powerful method with great promise for characterizing surface dynamics, and for a direct comparison with theoretical models of surface growth and fluctuations.
Methods
Insitu coherent Xray experiments
The experiments were performed at the National Synchrotron Light Source II, Coherent Hard Xray beamline in a custom deposition chamber. C_{60} is deposited from a thermal source onto thermally oxidized silicon substrates coated with singlelayer graphene. The purpose of the graphene is to promote alignment of the thin films. The substrate temperatures are controlled between room temperature and 80 °C with a recirculating chiller/heater, while higher temperatures are achieved using a resistive heater embedded in the sample mount. The Xray energy was 9.65 keV, with a coherent flux at the sample of ~10^{11} ph/sec, and a focused beam size of 10 × 10 μm^{2}. The angle of incidence of Xrays on the sample was 0.4°. This low angle of incidence leads to an illuminated area of the surface that is elongated by a factor of 140 along the beam direction, so that the footprint of the Xray beam on the surface is 1400 × 10 μm^{2}. Xray diffuse scattering was monitored at a grazing exit angle of ~0.1°, significantly below the critical angle for total reflection in order to achieve good surface sensitivity. Xrays were detected with an Eiger 4M area detector at a rate of 2.5 fps. The detector has a pixel size of 75 μm, and it was placed at a distance of 10.2 m from the sample for these measurements. Xray Photon Correlation Spectroscopy data analysis was performed by standard methods (Supplementary Note 1).
Exsitu characterization of thin film surfaces
Postdeposition atomic force microscopy (Asylum MFP3D) and Xray diffraction (Bruker D8 Discover) was used to confirm that the films are polycrystalline with (111) orientation in all cases.
Simulated mound scattering intensities and correlations
Xray structure factors and scattering intensities were calculated for a simulated mound growing according to the Zeno growth model. The base layer radius is fixed at R = 200, and all higher layers are constrained from exceeding that size. The total height M of the mound increases as new layers nucleate at the mound’s apex, and the radii R_{j}(t) increase with time, representing the lateral propagation of steps. In this study, the growth was first propagated to M = 400 in order to establish a nearly stationary mound shape, and then an additional 10 layers were propagated with 1000 timesteps per layer in order to generate scattering intensities and correlations. See Supplementary Note 7 for details of the scattering intensity calculation for the simulated mound.
Data availability
Data supporting the findings of this study are available within the article and its Supplementary Information file and from the corresponding author on reasonable request.
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Acknowledgements
We are grateful for the contributions of Darren Sullivan for assistance in developing the sample heating and thermal evaporator control software; to Jeff Bacon of the Boston University MSE Core Research Facility for assistance with the exsitu Xray diffraction analysis; to Rick Greene for technical support at the CHX beamline; and to Nicole Bouffard of the Microscopy Imaging Center at the University of Vermont for technical assistance with the AFM imaging. This material is based upon work supported by the U.S. Department of Energy (DOE) Office of Science under Grant No. DE‐SC0017802. K.F.L. and P.M. were supported by the National Science Foundation (NSF) under Grant No. DMR1709380. The Bruker Xray diffractometer was acquired under NSF grant No. 1337471. This research used the 11ID beamline of the National Synchrotron Light Source II, a U.S. DOE Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DESC0012704.
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R.L.H., K.F.L., and J.G.U. conceived and designed the experiments. R.L.H., Y.L., K.F.L., P.M., J.G.U., and J.W. participated in the coherent Xray data collection. A.F., L.W., and Y.Z. developed the GISAXS instrumentation and the XPCS data reduction and correlation software. R.L.H. and J.G.U. constructed the growth chamber and analyzed the coherent Xray data. K.F.L. and P.M. performed postgrowth Xray diffraction analysis. Y.L. performed postgrowth AFM analysis. R.L.H. wrote the first draft of the manuscript. All authors discussed the results and reviewed the manuscript. R.L.H. supervised the project.
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Headrick, R.L., Ulbrandt, J.G., Myint, P. et al. Coherent Xray measurement of stepflow propagation during growth on polycrystalline thin film surfaces. Nat Commun 10, 2638 (2019). https://doi.org/10.1038/s41467019106298
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