The Consequences of Random Sequential Adsorption for the Precursor Packing and Growth-Per-Cycle of Atomic Layer Deposition Processes

Atomic layer deposition (ALD) processes are known to deposit submonolayers of material per cycle, primarily attributed to steric hindrance and a limited number of surface sites. However, an often-overlooked factor is the random sequential adsorption (RSA) mechanism, where precursor molecules arrive one-by-one and adsorb at random surface sites. Consequently, the saturation coverage of precursors significantly deviates from ideal closed packing. In this study, we investigated the influence of RSA on precursor adsorption saturation and, consequently, on the growth per cycle (GPC) of the ALD processes. Our simulations revealed that the RSA model leads to a 22% to 40% lower surface density compared to the reference case of ordered packing. Furthermore, based on the precursor shape and size, we estimated GPC values with an average accuracy of 0.05 Å relative to experimental literature data. This work shows the critical role of RSA in ALD, emphasizing the need to consider this mechanism for a more accurate process design and optimization.


S2
The metal atoms in the bottom two layers of the surface slab were kept frozen at their bulk positions during adsorption studies.The periodicity of the slab in the direction perpendicular to the metal surface was avoided by adding a vacuum spacing of 17 Å.The thermodynamically most favorable adsorption geometries of CoCp on fcc and hcp hollow sites of the Co(0001) surface are reported in Figure S1.a-b.
Optimized lattice parameters of the Cu bulk with Fm3m space group (space group number= 225) was found as 3.56 Å, which is also in a good agreement with the literature (3.61 Å). 11 The methodologies used for the Co(0001) slab model and adsorption study are also followed for the modelling of Cu( 111

Random Sequential Adsorption Simulations:
A lattice RSA algorithm (see Figure S2) developed based on our earlier work has been adopted in this study for the adsorption of the molecules on the hollow sites on the substrate (Please see J. Vac.Sci. Technol.A 2022, 40 (6), 062409 for more information on the RSA methodology.). 12This RSA algorithm simulates one-by-one adsorption of precursor molecules on randomly selected sites on a substrate during the ALD process.The model substrates for all cases were prepared to include 5000 adsorption sites.The top-down 2D projections, i.e., 2D-footprints, of the precursor molecules were modelled based on the DFToptimized adsorption configurations of molecules on the substrate (see Figure 1).In this algorithm, every surface site can be chosen only once in a random order.A molecule can only adsorb if there is no physical overlap with other molecules on the surface.After adsorption, molecules were frozen in that position until the end of the simulation.If an overlap with another molecule was detected, the molecule was rotated and attempted to be placed again.Due to the geometric properties, there is no rotation needed for the precursors represented with circular footprint.For the discorectangular shapes, a rotation step of 9° is applied.If none of the possible random rotations result in adsorption, the surface site was flagged, and a new site was chosen.The simulations were terminated after all adsorption sites on the surface were tested.Cooperative effects, diffusion, or desorption of the adsorbates were not S4 considered in the RSA model development.For the ordered adsorption simulations, the same algorithm is used except for the selection of the surface sites.During the ordered adsorption iterations, the next adsorption site is selected as the next site on y-direction by keeping the x component constant.When all sites are tested on the y-direction, new attempts are started from the beginning of the neighboring x component.All RSA results reported in this study were averaged over 10 simulations for the same process.

EXPERIMENTAL DATA AND ESTIMATION OF GPC
Experimental literature data and our RSA results used for the comparison in Figure 5 in the manuscript are reported in Table S1.Experimental references used in Table S1 sometimes report a GPC range as a function of different experimental conditions (e.g.temperature, dose time, etc.) .In these cases, the maximum GPC reported is adopted in the last column of Table S1 assuming better precursor adsorption kinetics without CVD component.
Table S1: Curated data used (columns 1-5) and obtained (columns 6-9) for the preparation of Figure 5.All precursor molecules reported in the table are represented with the formula M(ligand)2 where the metal atoms and attached ligands are reported in columns 1 and 2. All surfaces reported in column 3 are modelled as hexagonal lattice in RSA simulations using the M-M distances reported in column 4. M-M distances and monolayer thickness values are obtained from DFT optimized perfect crystal structures.GPC is calculated as: GPC RSA = MLThickness DFT ) surface slab and the Cu(acac) adsorbate.The thermodynamically most favorable adsorption geometries of Cu(acac) on fcc and hcp hollow sites of the Cu(111) surface are reported in Figure S1.c-d.

Figure S1 .
Figure S1.DFT optimized geometries of a-b) CoCp on a Co(0001) surface, and c-d) Cu(acac) on a Cu(111) surface.Top layer metal atoms of the Co (0001) and Cu (111) surfaces were colored differently to enhance visibility.Yellow: C, white: H, red: O, light/dark blue: Co, light/dark brown: Cu.Total energies of the optimized systems are reported below each configuration.Since the adsorption mechanism is not studied in detail, adsorption energies were not calculated.

Figure S2 .
Figure S2.Algorithm followed in random sequential adsorption simulations.