Controlling hydrocarbon transport and electron beam induced deposition on single layer graphene: toward atomic scale synthesis in the scanning transmission electron microscope

Focused electron beam induced deposition (FEBID) is a direct write technique for depositing materials on a support substrate akin to 3D printing with an electron beam (e-beam). Opportunities exist for merging this existing technique with aberration-corrected scanning transmission electron microscopy to achieve molecular- or atomic-level spatial precision. Several demonstrations have been performed using graphene as the support substrate. A common challenge that arises during this process is e-beam-induced hydrocarbon deposition, suggesting greater control over the sample environment is needed. Various strategies exist for cleaning graphene in situ. One of the most effective methods is to rapidly heat to high temperatures, e.g., 600 C or higher. While this can produce large areas of what appears to be atomically clean graphene, mobile hydrocarbons can still be present on the surfaces. Here, we show that these hydrocarbons are primarily limited to surface migration and demonstrate an effective method for interrupting the flow using e-beam deposition to form corralled hydrocarbon regions. This strategy is effective for maintaining atomically clean graphene at high temperatures where hydrocarbon mobility can lead to substantial accumulation of unwanted e-beam deposition.


Introduction
Focused electron beam induced deposition (FEBID) has been used to fabricate numerous 3D objects on the nanoscale. [1][2][3][4][5][6][7][8] Coupling FEBID capabilities with modeling of the physical processes involved provides a deeper understanding of the process and enables highly controllable 2D and 3D nanomanufacturing. 9-14 FEBID is typically performed in a scanning electron microscope (SEM) where an organometallic precursor gas (containing e.g., Pt, Au, or W) is injected across a substrate and dissociates with the focused electron-beam (e-beam). The dissociated molecular fragments bind to the substrate and to each other to form e-beam directed deposits that can be built up in a process akin to 3D printing on the nanoscale.
A question to ask is if such a technology can be ported to scanning transmission electron microscopes (STEMs) and exploit the increase in resolution due to the aberration-corrected probes often employed in STEMs. Whereas SEMs are used for visualizing the surfaces of bulk materials, aberration-corrected STEMs routinely resolve atomic columns in thinned materials and every atom in 2D materials. 15 Recent investigations have ventured into this territory, leveraging the finely focused STEM probe to induce atomic-scale adjustments to materials. [16][17][18][19][20][21][22][23][24][25][26] Although aberration-corrected probes can be focused to sub-Ångstrom dimensions, interactions with the substrate are a significant contributing factor to the resolution of direct-write FEBID techniques due to the emission of secondary electrons (SEs). 27 Efforts to examine the role of substrate SE emission on FEBID in a STEM revealed substrate thickness-dependent growth rates, particularly in the early stages of nucleation where the majority of the material under the e-beam is the substrate. 28,29 By taking the idea of a reduced substrate thickness to the logical monolayer limit, one can envision working with graphene as the substrate 30 which is only one atom thick and is known to have a very low SE yield. [31][32][33] Working in this regime, van Dorp et al. deposited nanodots from a W(CO)6 precursor moleculeby-molecule to achieve deposits having dimensions less than 1 nm. 34 It becomes increasingly apparent, however, that extraneous material in the form of volatile hydrocarbons becomes a concern especially as the physical dimensions of the deposition site are edging toward the fundamental limit of single atoms. van 41,42,44,46 What is important for our discussion here is the model of gas adsorption onto a surface which presumes a gas phase, an adsorption layer, and the surface onto which the gas adsorbs. 45 In this work we employ a rapid heat treatment to remove the fixed contamination from graphene surfaces and then explore the nature of the volatile form of hydrocarbons that deposit under the ebeam. We show that surface deposition can be used to arrest the ingress of additional hydrocarbons, suggesting that surface diffusion, rather than adsorption from vacuum, is the primary mode of hydrocarbon transport at high temperatures. We further present a reaction-diffusion modeling framework for describing the surface diffusion and deposition and discuss the interplay between precursor density and diffusion rate.

Sample overview and initial conditions
To investigate the behavior of hydrocarbons on a graphene surface, a suspended graphene sample was prepared on a Protochips Fusion TM heater chip using a wet transfer method (described in the methods section). Figure 1(a) shows a medium angle annular dark field (MAADF)-STEM image of the suspended graphene sample at room temperature (RT) and a depiction of the amorphous web of surface contaminants adhered to the graphene surface. The contaminants are stable in high vacuum (~10 -9 Torr) and presumably have reasonably long hydrocarbon chain lengths. Initially, no hydrocarbon deposition was observed at RT. The heater chip was then ramped to 900 ℃ at a rate of 1000 ℃/s to remove the surface contaminants. 30,36 Figure 1(b) shows a MAADF-STEM image of the sample after heating to 900 °C and a schematic drawing illustrating the observed changes. Large areas of graphene became clean as shown in the higher resolution MAADF-STEM image inset. Overview images of the sample before and after heating are shown in Figure S1. Residual contamination remains in some areas due to excessive e-beam exposure prior to heating as discussed elsewhere, 30,36 also shown in supplementary Figure   S1. Upon decreasing the field of view to 64 nm (i.e., increasing the electron dose per unit area) rapid carbon deposition under the scanned area was observed. This is depicted in Figure 1(c), where a square area of carbon deposition appears in the center of the image as indicated by the outline/box. The schematic depicts deposition directed by the e-beam. This kind of deposition is quite pernicious as it grows under the e-beam and interferes with the imaging/processing of the region being investigated. This phenomenon, however, has been exploited as a direct-write nanoscale synthesis technique, as discussed in the introduction. Detailed Monte Carlo simulations of FEBID 9,48-50 shows that growth/etching proceeds via an interplay between the primary, secondary, and backscattered electrons with the precursor adsorbed in the ebeam interaction region. The supply of precursor to the e-beam interaction (raster) region is dictated by adsorption from the vapor phase as well as surface diffusion and is limited by the residence time of the adsorbed species. These transport mechanisms are all impacted by temperature, as recently studied in detail. 44 While growth was not observed at RT, the e-beam clearly affects the region, dissociating or crosslinking the carbonaceous layer, since it remains intact after high temperature heating (center of Figure S1(b)). Large areas of the carbonaceous layer are removed during the fast heating in unexposed regions, as observed in Figure 1(b) and (c). Thermal dissociation of longer hydrocarbon chain, CxHy molecules into smaller molecules is envisioned here. Subsequent carbon deposition at high temperature (Figure 1 (c)) suggests that transport of carbonaceous material occurs either by vapor phase adsorption or mobile and high-binding energy carbonaceous species that still reside on the surface.

Examination of e-beam deposition
To further illustrate high-temperature e-beam-induced deposition, a second example is shown in  Figure 2(b) just prior to initiating the capture of the data stack and a fourth nucleation site appears during acquisition). The areas of clean graphene from Figure 2(b) were artificially tinted orange with an opacity of 50% and overlaid on (c) to clearly highlight the locations where deposit growth occurred. Figure 2(d) shows a scatter plot of the linear growth rate as a function of electron dose obtained by analyzing the image stack, as described in the supplemental materials. On the right-hand side of the plot, a kernel density estimate (KDE) of the growth rate distribution is provided to illustrate the spread in measured growth rates within the observed data (see SI for additional details).
In contrast to the behavior observed in the region i "open area" shown in Figure 2(b-d), the second 20-frame image stack was acquired across an amorphous contaminant bridge that divides an "open area" forming an "enclosed area;" region ii is an area where the amorphous materials on the graphene surface completely surround a clean graphene area. Here, we note that growth only occurs on the open side and no growth occurs on the enclosed side of the bridge. The decrease in deposition rate was due to a global decrease in precursor availability over time as shown in supplementary Figure S3. The two datasets shown here were acquired 21 minutes apart. orange for an open region and blue for an enclosed region, set to 50% opacity, and overlaid on (f) to highlight regions of growth. We observe no hydrocarbon growth in the enclosed region. (g) Extracted growth rate for each area.
No hydrocarbon growth was observed in the enclosed area, which suggests that migration of the hydrocarbons responsible for deposition is effectively blocked/trapped by the carbonaceous barriers observed on the surface. To confirm this, we used the e-beam to deposit a bridge of material on the graphene surface, cutting off a previously open region and making an enclosed region. Figure 3    To test whether this strategy can work on a larger scale, we identified a region that was almost enclosed but exhibited heavy deposition. We used the deposition to form a barrier of material and generate a relatively large, enclosed region. Figure

Discussion
Regarding the transport mechanism responsible for the growth, adsorption from the vapor phase can be ruled out as the enclosed regions would also experience growth. The 10 -9 Torr base pressure is also prohibitively low to be the dominant precursor supply. Thus, surface diffusion must be the primary mechanism, which is evidently "blocked" by the deposited carbon. Interestingly, this suggests that the diffusing species has a high adsorption energy, otherwise it would quickly desorb at 900 o C. Regarding the blocking mechanism, questions regarding the diffusing species are 1) do they get trapped at/in the carbon barriers, 2) do they arrive at the carbon barriers and desorb, or 3) do they arrive and effectively reflect from the carbon barrier? If the diffusing species arrive and become trapped in the carbon deposits, then one would expect a coarsening of the carbon contamination regions everywhere at high temperature, which would be independent of e-beam exposure. If the diffusing species arrive and desorb, then one would expect the carbon growth rate to decay rapidly as the high mobility of the species would eventually exhaust the surface concentration. The deposition rate decays with time but deposition did continue for over an hour (see Figure S3), which suggests that if some desorption occurs at the edges it is not the primary interaction mode. Thus, the carbon barriers primarily reflect the mobile hydrocarbon species on the surface. Finally, regarding growth in the open regions, two scenarios are possible as high temperature growth appears to occur preferentially at the barriers, primarily through periodic nucleation, likely at vacancy sites created by knock-on damage (see Figure 2(b-c)). First, the ebeam could activate the diffusing species that can subsequently diffuse and stick to the sidewall of the barrier. Second, the e-beam-induced growth could be enhanced at the barrier sidewall due to enhanced e-beam interactions with the thicker carbon layer leading to more SE emission. It is likely that there is a combination of these two effects.

Modeling
A numerical simulation was developed to ascertain whether a reaction-diffusion mechanism could be responsible for determining the lateral film deposition rates observed for high-temperature STEM e-beam-induced deposition experiments conducted on graphene. The fact that the chemical composition of the carbon-based precursor is unknown presents a significant challenge to constructing a detailed model since many critical parameters that can influence deposition are unknown: the unknown parameters include the precursor surface diffusion coefficient, the equilibrium precursor surface concentration, and the electron impact dissociation cross-section of the precursor molecule. For this reason, a simple model was constructed to determine if the proposed mechanism is at least plausible, i.e., by using physically realistic ranges for unknown parameters, could the experimental deposition rate be accounted for?

Overview
To test the validity of the reaction-diffusion model, a set of physical parameters was sought that would predict the lateral film growth rate for a set of real experiments. Specifically, two parameters were varied over a multi-decade range of values to find a solution, namely the precursor surface diffusion coefficient (D) and the equilibrium precursor surface concentration (Co). Note that () will be used in place of (Co) when reporting simulation results where the parameter () represents the equilibrium precursor surface coverage for the beam-off condition; it is the fraction of the monolayer coverage of 60 sites/nm 2 , which is roughly the surface density of graphene atoms.
(D) and (Co) were selected to vary because they appear to have significant roles in determining experimental outcomes as rationalized by comparing experiments; reasonable guesses were made for additional unknowns as described below. Simulations revealed a range of (D and Co) combinations for each experiment that reproduced the observed experimental growth rates.
However, the proposed mechanism may only be deemed as a potential candidatea unique set of parameters was not identified that described all of the experiments. Nonetheless, if one considers the possibility of a decreasing vapor pressure during the experiments then a range of solution sets tend to align for multiple experiments.

Reaction-Diffusion Model for STEM EBID
A 2D numerical simulation of time-dependent precursor surface diffusion and e-beam-induced dissociation/deposition (EBID) was constructed using the fully implicit finite difference method to emulate actual STEM experiments. The Dirichlet boundary condition is applied at three of the four scanning frame boundaries (--) while a mass conservation balance is applied at the film/substrate interface. The former boundary condition was defined by the observation that EBID conducted in open regions yields a nearly continuous linear growth rate during STEM experiments suggesting a stable reservoir of precursor exists on the graphene surface while the latter boundary condition reflects the experimental observation that deposition is initiated at a preexisting interface and seems to depend strongly on the precursor surface diffusion. Thus, e-beam-induced dissociation/deposition only takes place at regions of contact with the film interface. Importantly, interface transport is emulated in the simulation by displacing the origin of the e-beam (in response to deposition), which makes it possible to keep the simulation domain effectively stationary, as summarized in Figure 5(a-b). The mathematical aspects of the simulation are described briefly while a more comprehensive description is provided in the supplemental information.
The 2D surface diffusion equation is solved for a rectangular domain represented schematically in where the first three terms on the right-hand side describe precursor surface diffusion and the last term accounts for the dissociation of precursor at the interface. The parameters () and () are constants for all experiments. () represents the number of deposited film molecules produced per precursor molecule dissociated. () was set to 1 because the precursor molecule chemistry is unknown while () was set nominally to 10 -2 nm 2 , a common order of magnitude for EBID. The SE surface density, or (iSE''), was simply set equal to the primary e-beam current density without knowledge of the SE yield on the film. Note that iSE'' is a function of (x), (y), and (t) as the beam is scanned through the frame but deposition is possible only at the current film interface position.
The lateral film deposition velocity (vf) is described by

Reaction-Diffusion Simulation for STEM EBID
The STEM square scan frame, shown from the point-of-view of the incident e-beam (see gray box), is shown in Figure 5(a) as a reference frame to explain the equivalent simulation frame-ofreference as well as to indicate key simulation aspects.
The primary e-beam executes a raster motion beginning with a linear scan in the x-direction, from left-to-right. Upon completion of a single line scan, the beam is displaced by one pixel in the positive y-direction and the process repeats. A frame is completed when the entire square is scanned. The frame edge dimension is defined as (yROI).
The simulation emulates real frame scanning using a modified reference frame, i.e., a frame that is fixed to the interface position per pixel row. This choice of reference frame ultimately leads to a moving and distorted simulation frame over time (see hatched, black frame). This frame of reference makes it possible to fix the simulation pixels in space: stationary simulation spatial nodes (see colored nodes) simplify simulation scripting and minimize the number of calculations required.
Also note, as a further means to improve time efficiency, the node spacing increases in the scanning directionat relatively large distances from the interface, surface gradients in C(x) are smaller, allowing for a larger step size and thus fewer computational nodes. The initial (xo) and final (xf) step sizes are reported in the SI 2. The step size in the y-dimension is a constant parameter (y).
Lastly, computation time is also minimized by advancing the primary e-beam to the starting position of the next scanning row when the precursor surface coverage in the entire frame domain returns to the equilibrium value (Co). The primary e-beam is modeled as a Gaussian probe (FWHM = 2 nm) so; in the limit of a small electron probe size relative to the frame size, negligible deposition occurs when the beam moves several nanometers beyond the interface allowing for the replenishment in the frame by precursor surface diffusion from the frame boundaries. This fact explains why the simulation frame width (xROI(v)) is smaller than the actual experimental frame size in the schematic in Figure 5(a).
The moving reference frame requires the definition of two beam shifts per row; (1) an initial shift xb,o(y) that equals the distance between the left edge of the frame and the initial contamination/graphene interface position and (2) the evolution of lateral film growth in the xdimension with time xf(y,t). Figure 5(b) shows this shift pair for a particular row in a real STEM image as a visual example of the mathematical shift. The left-most STEM image shows the experimental reference frame while the rightmost image shows the simulation frame. The shift variables for a single row are shown superimposed over the simulation frame for clarity in Figure   5(a).

Supporting Information 1
Graphene Sample Overview Figure S1 shows an overview of the sample used in these experiments. As described in the methods section of the main text, graphene was transferred from its Cu foil growth substrate onto a Protochips TM Fusion heater chip and examined in a Nion UltraSTEM 200 using an accelerating voltage of 100 kV. Figure S1(a) shows an overview medium angle annular dark field (MAADF) STEM image of the sample at room temperature prior to any heating. The graphene is observed suspended over a circular aperture in the heater chip substrate (the substrate appears bright around the edges of the image). Substantial surface contamination was observed on the suspended graphene and a magnified image of this contamination is shown as an inset. The overlaid text and arrows indicate a few example regions (the uniform darker gray areas) which correspond to the contamination morphology shown in the magnified view. The sample temperature was then ramped to 900 ℃ at a rate of 1000 ℃/s and held at that temperature. Figure S1(b) shows an overview image after this process (at 900 ℃). The surface contaminants indicated in (a) have desorbed, particularly along the edges of the aperture. Initial imaging of the sample was performed at the center of the suspended region and exposure of the contaminants to the electron beam (ebeam) has caused them to adhere more strongly to the graphene surface. This is the reason that less "cleaning" action is observed toward the center of the image. The darker areas indicated by the text and arrow overlay correspond to atomically clean areas of graphene. The inset shows an image obtained in one of these areas where we can clearly see the hexagonal single layer graphene lattice. The image in Figure S1(c) was acquired in the region indicated by the box in (b). At the center of this image appears a square of carbon deposited by the e-beam scanning over the boxed region as indicated by the overlaid text and arrow. This illustrates that while these areas appear to be atomically clean, mobile hydrocarbons diffuse under the e-beam and adhere to the surface. Thus, there exists some concentration of surface molecules that are not visible in the images.

Deposition Rate Analysis
In Figures 2-4 of the main text we show growth rates extracted from the accompanying STEM videos. The procedure used for extracting these growth rates is described here.
To calculate growth rates from sequential STEM images (videos) the trainable Weka segmentation plugin 1 for ImageJ/Fiji 2 was first used to create a segmentation mask to distinguish between areas of clean graphene and contamination. Figure S2(a) shows a typical image frame and Figure S2(b) shows the same frame with the segmentation mask color coded and overlaid. The number of pixels belonging to the contaminated regions were then counted and converted to area. This procedure allowed a reliable measure of areal growth (i.e. square nanometers covered per unit time or dose), shown in Figure S2(c). To extract a linear growth rate perpendicular to the growth front, the following procedure was used: edges were first detected in the segmentation mask video using Canny edge detection, 3 contours were then found using an algorithm developed for topological structural analysis. 4 These tools were used as implemented in the python OpenCV package. 5 Edge contours were rank ordered according to the level of nesting detected (e.g. contours contained within contours) and their pixel length logged. Contours which were not at the top level or had lengths less than 40 pixels were rejected to prevent inflation of the measured edge length from the addition of short, spurious edges (i.e. noise). Figure S2(c) shows the areal coverage as a function of time and dose. The increase in areal coverage, ∆ , between consecutive frames, and +1 , was then divided by the total edge length, , detected in frame , providing a measure of linear growth rate through time, shown in Figure S2(d). A kernel density estimate was calculated based on the observed linear growth to provide a visual representation of the estimated distribution of values. This is plotted vertically to the right of the scatterplot. A gaussian kernel was used for smoothing and Scott's Rule was used for bandwidth selection. 6 Circles represent experimental measurements and the line is a linear fit to the measurements. The slope of the linear fit is overlaid giving a measure of areal growth rate. Linear growth rate was calculated by taking the change in covered area, ∆ , between two sequential frames, and +1 , and dividing by the edge length measured in the i th frame, . These values are plotted in (d) as a function of dose. A kernel density estimate of the growth rate distribution is plotted on the vertical axis to the right to provide a qualitative visual for the spread of the underlying distribution.
To capture the deposition rate as a function of time several STEM data sets were acquired spanning over an hour. The average growth rate observed within each data set is shown in Figure  S3. An exponential fit was performed and is shown as a line. Fit parameters and equation are overlaid. Figure S3: Average deposition rate observed over time. Dots represent the average rate observed in a given STEM data set. Line represents an exponential decay fit to the data points shown. Equation and parameters of fit are overlaid. Table S1 summarizes the parameters used to acquire each STEM video presented in this manuscript. The STEM videos also accompany the manuscript as supplemental materials.

Diffusion and E-beam Deposition Model
Simulation and Model Details Figure S4: A schematic of the relationship between the computation pixel array (•), the real electron beam scanning frame (-) and the simulated beam scanning frame (--). The relationship between these features is described below.

Fourier Number
The Fourier Number (Fox) is User defined input. The diffusion coefficient (D) and initial x-grid spacing is provided (xo) are also User specified. This leaves one unknown in the time step (t). Figure S5: The experimentally defined electron beam scanning frame. The frame is defined by the dimensions (xROI) and (yROI). Fox = 1 thus represents the characteristic time required for surface bound precursor to traverse a single pixel by diffusion. Fox should be kept (< 1) to ensure that the contribution of precursor surface diffusion is not underestimated. The time step calculated from the User defined (Fox) is tested to make sure that the resolution is adequate to sample the various time-dependent processes that are relevant to the physical chemistry associated with the problem. This process is summarized below in the section 'Simulation time step conditioning'. The (Fox) is then updated to reflect the changes and reported to the User.

Node spacing in the {x}-coordinate
A variable node spacing in the {x}-coordinate makes it possible to force a relatively small node spacing at the film-substrate interface, on the order of the primary electron beam size, while expanding to significantly larger values at large {x}-coordinate, where the surface precursor concentration gradients expected are small. The number of pixels in the {x}-coordinate is thus minimized reducing the total simulation time. The node spacing in the {x}-coordinate is determined by The {y}-coordinate spacing is constant in the simulation.

Simulation time step conditioning
Multiple processes potentially limit the simulation time step to a maximum value. The smallest of these characteristic times determines the actual time step applied during the simulation. Integration of the PDE governing precursor surface transport during the pixel dwell time (td) must be sampled multiple times to accurately capture time-dependent changes in the precursor surface concentration inside the pixel -in principle (Fox) ensures proper time sampling. However, the steep concentration gradients that may be induced by the small STEM probe can generate relatively large gradients in both (dC/dx) and (dC/dy). The time sampling increment is set equal to ∆ ≤ 8 [ ] [3] where (td) is the dwell time per pixel. The pixel dwell time (d) is a User defined parameter. The simulation time step is next tested against a Scribe time (Sc). The scribe time is defined as the time required for the film/substrate interface to traverse the pixel width (xo). As will be described below, the film/beam interaction will always occur at the left most x-coordinate pixel, with spacing (xo). The scribe time is derived from the steady-state balance between the precursor dissociation rate and the film growth rate. The precursor dissociation rate (dnp/dt) at the half pixel located at the film/substrate interface [molecules/s] is [4] where ( . Please note that (iSE'') appears in the dissociation term which is the secondary electron flux at the film edge which has a standard deviation of (a = 2 nm), as opposed to the actual STEM probe size of (a ~ 0.1nm), because the model assumes that the SEs generated just inside the edge of the film drive dissociation. The value of 2 nm is on the order of the mean free path of an SE in carbon. 7 Also, since the secondary electron yield for the carbon-based film is unknown, the SE current density is taken simply as proportional to the beam current while the SE range is explicitly taken account of through (a).
As stated previously, the dissociation rate is in equilibrium with the film growth rate (dnf/dt) and the film deposition rate can be expressed in term of the lateral film velocity, or [5] where (Cf) is the film concentration, i.e., density, (dx/dt) is the lateral film growth velocity and (zo) is the film thickness which is taken as the molecular size ~0.3 nm. The scribe time is derived by combining equations 4 & 5, substituting tSc for (dt) and xo for (dx), and solving for tSc [ ] [6] The simulation time step (t) must be less than the scribe time. The following condition is used in the simulation ∆ ≤ 8 [ ] [7] Otherwise, the film/substrate interface will advance at rate that may be changing significantly during the time step (t) leading to a poor sampling of the electron beam edge intensity. A final conditioning step is applied to make sure that the time step is an integer number of the pixel dwell time, or

Scanning frame {x} length (virtual)
The equilibrium precursor surface concentration, i.e., the surface concentration under the beam off condition, is described by where () represents the fraction (0-1) of the maximum possible precursor surface concentration as dictated by the binding site density (sd). Often, exposure of the film interface with the electron beam leads to a depletion of (C) such that

≪ [10]
A relatively large diffusion coefficient (D) can lead to the nearly full recovery of C(x,y), or before the electron beam reaches the line scan boundary position of x = xROI. Simulation time is thus wasted if the electron beam continues to the x-frame boundary for this 'full precursor refresh' condition. The program is set to detect this situation by comparison of the minimum concentration inside the scanning frame against a User specified parameter that represents full precursor refresh, e.g., If the precursor refresh condition is met, the electron beam advances to the next line scan origin to begin growth. Also, as part of this special precursor refresh condition, the simulation time is advanced forward by the remaining line scan time to preserve the experiment and simulation time comparison. This technique is possible because film deposition only occurs as the beam passes over the film/substrate interface such that the total length of the scan is irrelevant, at least when the precursor refresh time is less than the total line scan time.
The primary electron beam moves at the velocity defined by the User defined pixel point pitch () and the primary electron beam dwell time per pixel (d) The real, primary electron linear beam scanning time is used to calculate the real growth rate, even when the simulation implements the full precursor refresh condition described in the previous section. The real frame scanning time is and the total simulation time where (P) is the number of frame loops. Figure S7: The simulation beam scan path (red lines) may not exactly match the experimental path if the simulation detects that the precursor surface concentration has reached steady-state in C(x,y). If this condition is met, the simulation automatically advances to the initial position for the next line scan thereby optimizing the simulation by minimizing the total simulation time.

Primary electron beam scanning
Film/interface growth is modeled by shifting the origin of the primary electron beam in the negative x-coordinate per simulation time step (t). This model is, at least in part, validated by the fact that the interface advances with a near constant x-coordinate, independent of the ycoordinate. This fact is derived from experimental results. Conversely, the case of a propagating curved interface would invalidate such a model because the PDE describing C(x,y) would be 'blind' to the curvature. In the framework of this linear interface propagation model, the electron beam flux equation require several terms to implement the displacement.
The variable (xb,o) represents the starting position of the beam, at t = 0, relative to the preexisting contamination on the surface. By default, the initial x beam position is shifted sufficiently in the negative direction to ensure at least a complete interaction of the primary electron beam profile with the initial contamination interface occurs during the initial irradiation frame.
and FWHM is related to the standard deviation of the beam profile, or (a), by way of a ~ FWHM/2.355. The variable xf(y,t), updated per Dt, tracks the interface growth at the m = 1 column of pixels. The hatched blue line (figure S10) shows the origin in the current example for each line in the frame due to the transformation. Ultimately, the outcome of the spatial reference frame transformation is (1) a fixed computational coordinate system with (2) a dynamically distorted ROI (black hatched line, figure S11) that exactly replicates the square frame experimental scan, at least in the limit of a nearly linear film interface ≈ 0[22] Figure S10: The primary electron beam origin is dynamically displaced in the negative x coordinate to establish a fixed film interface position @ xf(y,t) = 0.

Gradient Descent
A gradient descent was executed, in the two variables (D) and (), to attempt to identify a unique solution for each STEM experiment. The gradient descent is performed on an error function relative to real experiments Derivatives will be required to determine the gradient in each variable. The gradient is estimated using a finite difference approach and the range over which the gradient is calculated is based on the initial guess  Density on the order of a porous amorphous/glassy carbon.

Surface binding site density
Estimated from the clean graphene image presented as figure 1(b) in the manuscript.

Unknown Variables
Initial & boundary precursor surface concentration = We assume a relatively low concentration of precursor commiserate with predicted deposition rates observed experimentally = 1 10 −6 − 1 10 −3

Electron impact dissociation cross-section
The relatively large estimate reflects the higher probability of dissociation associated with a relatively large hydrocarbon species that can remain on the surface at elevated temperatures.
Precursor surface diffusion coefficient This range of value of (D) gave experimental results on the order of experiments as shown in the results below.

Evidence of Total Precursor Pressure Decrease
The simulation space maps below show that the path of solutions is consistent across all four experiments, if, a shift of (-) is applied to the solution curve. The magnitude of the shift is proportional to the total time the sample has been evacuated in the STEM chamber.