Random Sequential Adsorption Simulations Research Articles

Blocking mechanisms in area-selective ALD by small molecule inhibitors of different sizes: Steric shielding versus chemical passivation

Small molecule inhibitors (SMIs) hold great promise for area-selective deposition due to their vapor-phase application being compatible with industrial processing. However, to date only a handful of SMIs have been studied, and the mechanisms of precursor blocking require further understanding. In this study, we explore the inhibition of SiO2 ALD on Al2O3 surfaces comparing three SMIs of different sizes: acetic acid (HAc), acetylacetone (Hacac), and 2,2,6,6-tetramethyl-3,5-heptanedione (Hthd). The goal is to unravel the contributions of two important factors to their blocking performance: steric shielding, i.e. physically covering reactive surface sites, and chemical passivation, i.e. chemically consuming surface reactive sites. Experimentally, it is found that HAc and Hthd outperform the previously studied Hacac, as revealed by longer nucleation delays on Al2O3 from in-situ spectroscopic ellipsometry, and by enhanced Si precursor blocking inferred from in-situ infrared spectroscopy. Through density functional theory and random sequential adsorption simulations, we illustrate that varying the size of SMIs brings benefits from either higher steric shielding or better chemical passivation. As compared to Hacac, HAc performs better due to its smaller size, yielding denser packing and thus higher chemical passivation. Hthd on the other hand, benefits from its bulkiness with a higher contribution from steric shielding.

Computational Investigation of Precursor Blocking during Area-Selective Atomic Layer Deposition Using Aniline as a Small-Molecule Inhibitor

Area-selective atomic layer deposition using small-molecule inhibitors (SMIs) involves vapor-phase dosing of inhibitor molecules, resulting in an industry-compatible approach. However, the identification of suitable SMIs that yield a high selectivity remains a challenging task. Recently, aniline (C6H5NH2) was shown to be an effective SMI during the area-selective deposition (ASD) of TiN, giving 6 nm of selective growth on SiO2 in the presence of Ru and Co non-growth areas. In this work, using density functional theory (DFT) and random sequential adsorption (RSA) simulations, we investigated how aniline can effectively block precursor adsorption on specific areas. Our DFT calculations confirmed that aniline selectively adsorbs on Ru and Co non-growth areas, whereas its adsorption on the SiO2 growth area is limited to physisorption. DFT reveals two stable adsorption configurations of aniline on the metal surfaces. Further calculations on the aniline-functionalized surfaces show that the aniline inhibitor significantly reduces the interaction of Ti precursor, tetrakis(dimethylamino)titanium, with the non-growth area. In addition, RSA simulations showed that the co-presence of two stable adsorption configurations allows for a high surface inhibitor coverage on both Co and Ru surfaces. As the surface saturates, there is a transition from the thermodynamically most favorable adsorption configuration to the sterically most favorable adsorption configuration, which results in a sufficiently dense inhibition layer, such that an incoming precursor molecule cannot fit in between the adsorbed precursor molecules. We also found that, as a result of the catalytic activity of the metallic non-growth area, further reactions of inhibitor molecules, such as hydrogenolysis, can play a role in precursor blocking.

Packing of inhibitor molecules during area-selective atomic layer deposition studied using random sequential adsorption simulations

Area-selective atomic layer deposition (ALD) is of interest for applications in self-aligned processing of nanoelectronics. Selective deposition is generally enabled by functionalization of the area where no growth is desired with inhibitor molecules. The packing of these inhibitor molecules, in terms of molecule arrangement and surface density, plays a vital role in deactivating the surface by blocking the precursor adsorption. In this work, we performed random sequential adsorption (RSA) simulations to investigate the packing of small molecule inhibitors (SMIs) on a surface in order to predict how effective the SMI blocks precursor adsorption. These simulations provide insight into how the packing of inhibitor molecules depends on the molecule size, molecule shape, and their ability to diffuse over the surface. Based on the RSA simulations, a statistical method was developed for analyzing the sizes of the gaps in between the adsorbed inhibitor molecules, serving as a quantitative parameter on the effectiveness of precursor blocking. This method was validated by experimental studies using several alcohol molecules as SMIs in an area-selective deposition process for SiO2. It is demonstrated that RSA simulations provide an insightful and straightforward method for screening SMIs in terms of their potential for area-selective ALD.

Extracting the equation of state of lattice gases from random sequential adsorption simulations by means of the Gibbs adsorption isotherm.

An alternative approach for deriving the equation of state for a two-dimensional lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. The relationship between surface coverage and excluded area is first extracted from random sequential adsorption simulations incorporating surface diffusion (RSAD). The adsorption isotherm is then obtained using kinetic arguments, and the Gibbs equation gives the relation between surface pressure and coverage. Provided surface diffusion is fast enough to ensure internal equilibrium within the monolayer during the RSAD simulations, the resulting equations of state are very close to the most accurate equivalents obtained by cumbersome thermodynamic methods. An internal test of the accuracy of the method is obtained by noting that adsorption RSAD simulations starting from an empty lattice and desorption simulations starting from a full lattice provide convergent upper and lower bounds on the surface pressure.

Understanding How Charged Nanoparticles Electrostatically Assemble and Distribute in 1-D.

The effects of increasing the driving forces for a 1-D assembly of nanoparticles onto a surface are investigated with experimental results and models. Modifications, which take into account not only the particle-particle interactions but also particle-surface interactions, to previously established extended random sequential adsorption simulations are tested and verified. Both data and model are compared against the heterogeneous random sequential adsorption simulations, and finally, a connection between the two models is suggested. The experiments and models show that increasing the particle-surface interaction leads to narrower particle distribution; this narrowing is attributed to the surface interactions compensating against the particle-particle interactions. The long-term advantage of this work is that the assembly of nanoparticles in solution is now understood as controlled not only by particle-particle interactions but also by particle-surface interactions. Both particle-particle and particle-surface interactions can be used to tune how nanoparticles distribute themselves on a surface.

Scaling Properties of the Number of Random Sequential Adsorption Iterations Needed to Generate Saturated Random Packing

The properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied. Numerical results obtained for one, two, and three dimensional packings were supported by analytical calculations valid for any dimension d. It has been shown that the number of iterations needed to generate finite saturated packing is subject to Pareto distribution with exponent -1-1/d and the median of this distribution scales with packing size according to the power-law characterized by exponent d. Obtained results can be used in designing effective random sequential adsorption simulations.

Managing numerical errors in random sequential adsorption

Aim of this study is to examine the influence of a finite surface size and a finite simulation time on a packing fraction estimated using random sequential adsorption simulations. The goal of particular interest is providing hints on simulation setup to achieve desired level of accuracy. The analysis is based on properties of saturated random packing of disks on continuous and flat surfaces of different sizes.

Structural properties of particle deposits at heterogeneous surfaces

The random sequential adsorption (RSA) approach is used to analyze adsorption of spherical particles of a fixed radius on nonuniform flat surfaces covered by rectangular cells. The configuration of the cells (heterogeneities) was produced by performing RSA simulations to a prescribed coverage fraction . Adsorption was assumed to occur if the particle (projected) center lies within a rectangular cell area, i.e. if sphere touches the cells. The jammed-state properties of the model were studied for different values of cell size α (comparable with the adsorbing particle size) and density . Numerical simulations were carried out to investigate adsorption kinetics, jamming coverage, and structure of coverings. Structural properties of the jammed-state coverings were analyzed in terms of the radial distribution function g(r) and distribution of the Delaunay ‘free’ volumes P(v). It was demonstrated that adsorption kinetics and the jamming coverage decreased significantly, at a fixed density , when the cell size α increased. The predictions following from our calculation suggest that the porosity (pore volumes) of deposited monolayer can be controlled by the size and shape of landing cells, and by anisotropy of the cell deposition procedure.

Kinetics of random sequential adsorption of nearly spherically symmetric particles.

Kinetics of random sequential adsorption (RSA) of disks on flat, two-dimensional surfaces is governed by a power law with exponent -1/2. The study has shown that for RSA of nearly spherically symmetric particles this exponent is -1/3, whereas other characteristics typically measured in RSA simulations approach values known for disks with the increase of symmetry of the particles.

A continuum hard-sphere model of protein adsorption

Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices.

Diffusional deposition of colloidal particles: electrostatic interaction and size polydispersity effects

In the deposition process of charged nanosized particles onto oppositely charged planar substrates two effects are being discussed: (1) The maximum surface coverage sensitively depends on the repulsive electrostatic particle–particle interactions. The ionic strength of the particle suspension defines the magnitude of the electrostatic repulsion between the particles, which in turn modifies the maximum surface coverage. The maximum surface coverage decreases with decreasing ionic strength, a trend that can be well described by an effective hard-sphere model based on random sequential adsorption (RSA), where the effective radius is estimated from the repulsive screened Coulomb potential. Measured radial pair-distribution functions also reveal ideal hard-sphere behavior as compared to RSA simulations for monodisperse disks. The magnitude of the interaction, however, is overestimated with the simple electrostatic model. (2) Particle size polydispersity does also influence strongly the deposition process. Small particles may fill voids left by larger particles such that the maximum surface coverage increases significantly. The size distribution of the deposited particles on the surface changes with time, whereby the small particles are adsorbed preferentially. These trends are observed experimentally and confirmed by computer simulation.

Random sequential adsorption on partially covered surfaces

The random sequential adsorption (RSA) approach was used to analyze adsorption of hard spheres at surfaces precovered with smaller sized particles. Numerical simulations were performed to determine the available surface function φl of larger particles for various particle size ratios λ=al/as and surface concentration of smaller particles θs. It was found that the numerical results were in a reasonable agreement with the formula stemming from the scaled particle theory with the modification for the sphere/sphere geometry. Particle adsorption kinetics was also determined in terms of the RSA simulations. By extrapolating the θl vs τ−1/2 dependencies, the jamming concentrations of larger spheres θl∞ were determined as a function of the initial smaller sphere concentration. It was found that θl∞ were considerably reduced by the presence of smaller sized particles, especially for λ≫1. The pair correlation function g of larger particles in the jamming state was also determined, showing more short range ordering (at the same θl) in comparison with monodisperse systems. The theoretical predictions stemming from our calculations suggest that the presence of trace amounts of very small particles may exert a decisive influence on adsorption of larger particles.