Understanding chemical and physical mechanisms in atomic layer deposition

The growth of highly conformal thin films or uniform nanoparticles (NPs) onto a solid support is important for many commercial applications such as microelectronic devices,^1,2 energy storage,³ solar energy conversion,^4,5 and catalysis.⁶ The morphology of the deposited material for these applications, while often critical, can be difficult to precisely control. Atomic layer deposition (ALD) is a process defined by the sequential addition of precursors which undergo a self-limiting reaction with the growth surface after each cycle of precursor exposure.^7–9 Because of its self-limiting nature, ALD has the potential to provide the highest level of control over thickness, conformality, and morphology of such materials. In order to maximize the potential of ALD, it is important to fully understand the mechanisms that take place in the ALD process since these mechanisms will govern the growth of the material.

Ideal depictions of ALD growth typically show a perfect monolayer of deposited material forming after each half cycle which grows into a perfect layer-by-layer (LBL) film [Figs. 1(a), 1(c), and 1(f)]. However, many ALD processes deviate from this ideal model in one or more ways. For instance, most ALD processes result in a sub-monolayer of growth after each cycle, an outcome which is typically considered to be due to steric effects from the precursor’s ligands blocking active sites, competing chemisorption pathways, or other effects [Fig. 1(d)].^10–12 Furthermore, various effects such as sparse nucleation sites or diffusion can result in the growth of islands or nanoparticles (NPs) instead of a conformal film [Fig. 1(g)].¹³ For these systems, pinhole-free films can be obtained by extending the process to higher numbers of ALD cycles in order to coalesce the NPs. However, these coalesced films are often rougher and require higher mass loadings to achieve continuous films than films which grow in an LBL fashion.^14,15 Other interesting behaviors can also influence the growth of these NPs. For instance, several ALD processes show that the average NP size does not increase linearly with the number of ALD cycles [Fig. 1(h)], as might be expected for a process that utilizes self-limiting monolayer adsorption.^16,17 In such cases, nonideal mechanisms for growth must be occurring, which in turn will influence how islands nucleate and evolve into films during the ALD process. Understanding these mechanisms would allow for control over the morphology of the deposited materials, from mono- to poly-dispersed NPs or thin films, which is currently one of the exciting challenges within ALD. Two fundamental processes, chemisorption and diffusion, underlie the majority of mechanisms which contribute to material growth during a given ALD process, and we focus here on these two processes.

In this Perspective, we will cover recent reports that have helped to broaden the field’s understanding of the mechanisms that drive chemisorption and diffusion in various ALD processes. We will first discuss mechanisms for the chemisorption of precursors onto a substrate. Understanding the various mechanisms for chemisorption is important for ALD as it can dictate the difference in island or layer-by-layer growth and can be useful for predicting phenomena such as nucleation delays. We will then follow this discussion with a section reviewing mechanisms of diffusion for the growing material during the ALD process with a focus on how to distinguish between different diffusion mechanisms and how control over these mechanisms can affect the growing material’s morphology. Through discussion of both chemisorption and nucleation mechanisms in this Perspective, we hope to better unify these two important components of ALD which are often considered separate from one another.

Many model systems of ALD can be described as growth through successive adsorption of precursors. For a true ALD process, precursor adsorption self-limits to no more than one monolayer of adsorbed precursor after each exposure. Adsorption can take place through one of two broadly defined mechanisms: physisorption or chemisorption. Chemisorption occurs when a formal chemical bond is created between the precursor and the growth substrate. Meanwhile, physisorption is the result of intermolecular forces, such as van der Waals attraction or hydrogen bonding, between the precursor and the growth substrate.

Chemisorption is often the result of a chemical reaction between a precursor and the substrate’s surface, resulting in a new bond between the two, often at the expense of another metal-ligand bond. At the temperature of a given ALD process, a precursor should react with the growth surface but not itself, which leads to the self-limiting characteristic of ALD. When chemisorption results in the production of volatile byproducts, those byproducts should readily desorb from the surface and be purged away, making the chemisorption in these cases essentially irreversible. In cases where byproducts are not produced or do not desorb, chemisorption can potentially be reversible.¹⁸ In these cases, it is important for the adsorption to be effectively irreversible during the time scale of the ALD cycle, i.e., during the purge time following the precursor pulse and throughout the pulse of the second reactant.

Physisorption is not typically considered to be a primary step toward growth in ALD for two reasons. First, intermolecular forces are generally weak (often <10 kcal/mol) between the growth substrate and the precursors, which should result in desorption from the surface during the purging step of ALD.¹⁹ Second, physisorption through van der Waals forces does not have an inherent mechanism for self-limitation since van der Waals forces arise not just between the surface and adsorbed precursors but also between different molecules of the precursor. Nevertheless, physisorption is considered to play a contributing role in many ALD processes. In most theoretical calculations of ALD, physisorption of the precursor to the surface is taken as the first step and may assist in the subsequent chemisorption step.^20,21 Physisorption through these weak intermolecular interactions can be considered similar to chemisorption through association (vide infra) and will not be discussed in further detail.

While there are thousands of reported ALD processes in the literature, many of these processes are assumed to follow one or more of several chemisorption mechanisms. These mechanisms are commonly referred to as ligand exchange, dissociation, association, and oxidation. We will discuss each of these separately, with an emphasis on the steps where chemical bonds are broken and formed during chemisorption to distinguish each mechanism. We will also establish subcategories within some of these mechanisms to highlight the more nuanced effects that one may need to consider when selecting appropriate precursor combinations. It is worth noting that while these mechanisms are portrayed as quite simple, the actual number of mechanistic steps and intermediates is often unknown and has been the topic of many theoretical calculations.^12,21–24 We will also discuss one other, unique, chemisorption mechanism as well as briefly describe chemical mechanisms which occur in ALD but do not result in chemisorption to highlight that the chemistry involved in ALD is more varied than previously thought.

As the name suggests, ligand exchange reactions involve the swapping of ligands between two species with a general reaction scheme of

where A/A′ can be considered as a metal center or proton and B/B′ are their ligands. For chemisorption, this exchange is between a ligand on the substrate’s surface and on the precursor, which results in a new surface-precursor bond,

where $∥$ denotes the surface. An archetype of this mechanism is in the chemisorption of trimethylaluminum [Al(CH₃)₃] onto a hydroxyl terminated surface which releases methane as the byproduct,¹⁰ 

Also, although only the first ligand-exchange is required for chemisorption, ligand exchange can continue to occur if there are nearby active sites, resulting in the formation of multiple precursor-surface bonds.²⁵ 

A significant majority of ligand exchange mechanisms observed in ALD can be considered as proton mediated ligand exchange reactions. These reactions occur through Brønsted-Lowry (BL) acid-base reactions, in which the ligand exchange occurs when a BL base accepts a proton from a BL acid. In these reactions, the ligand of a metalorganic species typically acts as a BL base and abstracts a proton from a more BL acidic species, such as a hydroxyl surface group. This acid-base reactivity is most favorable for metalorganic species of electropositive elements where the metal-ligand bond has significant ionic character. The ionic nature of the metal-ligand bond results in the ligand being similar to its free anionic form, which in turn results in more favorable abstraction of the acidic surface protons than precursors with more covalent metal-ligand bonding. This acid-base ligand exchange is perhaps best highlighted by comparing the energetics of ALD from a metalorganic precursor (with very basic ligands such as alkyls or amides) to its metal halide (very weak bases) counterpart. As an example, Oh et al. has investigated ALD of HfO₂ from Hf(N(CH₃)₂)₄ and HfCl₄ on silicon with native oxide.²⁴ They found that the ligand exchange products were 97 kJ/mol more favorable for the Hf(N(CH₃)₂)₄ precursor than for HfCl₄ and that the most stable state for HfCl₄ was actually the pre-ligand exchange coordination of the intact HfCl₄ to the surface.

We recently hypothesized a variation of this proton transfer mechanism to explain the precursor chemisorption during platinum ALD when the surface was pretreated with a small molecule organometallic precursor.²⁶ In this case, we noted that treatment of SiO₂ with Al(CH₃)₃ and Zn(C₂H₅)₂ made the surface significantly more basic in nature than the normal, slightly acidic, hydroxyl-terminated SiO₂ surface. This led us to hypothesize that the organometallic platinum precursor was acting as a BL acid rather than as a BL base, as normally proposed for chemisorption of the platinum precursor on nontreated oxide surfaces.^27,28

To our knowledge, there are two other subcategories of ligand exchange reactions found in ALD processes: halogen abstraction and transmetalation. Halogen abstraction mechanisms typically occur when a nonmetal halogen-phile, such as a silane, is used as a counter-reactant to a metal halide precursor. For instance, E(SiR₃)₂ (where E = Se or Te and R = methyl or ethyl) have been used with several different metal chlorides to grow the corresponding metal chalcogenide,^29,30

Several early transition metal films have also been deposited by halogen abstraction reactions using silane (SiH₄) or disilane (Si₂H₆) and a metal fluoride.^31–33 These reactions produce fluorosilanes, such as SiF₄ and SiHF₃, and H₂ gas as byproducts.³⁴ This H₂ gas likely comes from a short lived metal hydride intermediate from the ligand exchange reaction that undergoes a reductive elimination from the surface, a process which also results in the reduced metal film.

Another subcategory of ligand exchange is transmetalation in which two metalorganic species ligand exchange with one another to produce the desired film. This mechanism is best known from the deposition of copper from Cu(dmap)₂ (dmap = dimethylamino-2-propoxide) and diethylzinc. In this reaction, the dmap ligand from the copper is transferred to the zinc to form Zn(dmap)₂, which is volatile and purges away. This transmetalation leads to the deposition of metallic copper because the ethyl copper surface species are unstable and subsequently undergo reductive elimination which also produces butane gas,^35,36

Transmetalation reactions have also been used to deposit several metal fluoride films, such as CaF₂,³⁷ MgF₂,³⁸ YF₃,³⁹ and LaF₃.⁴⁰ For all of these examples, TiF₄ is used as the fluoride precursor with β-diketonate (typically 2,2,6,6-tetramethyl-3,5-heptanedionato) complexes of the desired deposited metal. The resulting transmetalation then produces the desire metal fluoride and a titanium β-diketonate complex which is volatile and readily desorbs. Additional subcategories of ligand exchange reactions will likely be discovered in the future and come with their own unique considerations.

In general, one deems ligand exchange to occur when at least two bonds are broken to facilitate the formation of an equal number of new bonds. In ALD, then, one could consider ligand exchange when bonds are broken within both the precursor (e.g., the Al–C bond) and the substrate (e.g., the O–H bond) in order to facilitate chemisorption. However, another stipulation to the ligand exchange reaction is often added as it applies to ALD, which is that one of the newly formed species must be volatile and capable of desorbing from the surface. Cases which result in both precursor fragments becoming chemisorbed to the surface are no longer considered ligand exchange, even if a surface bond is broken and are instead referred to as dissociation reactions.

Dissociation is simply defined as a splitting of a compound into two or more fragments, which is often triggered by a form of external energy such as heat or light,

Chemisorption via dissociation can occur through two primary pathways. Classical dissociative chemisorption occurs through a surface assisted pathway that results in all of the fragments from the precursor being chemisorbed to the surface,

Alternatively, one or more of the dissociated fragments may not readily chemisorb to the surface and instead desorb into the gas phase, leaving only one of the fragments chemisorbed,

Reactions as present in Eq. (8) are not formally considered dissociative chemisorption since not all fragments remain on the surface; instead, we would propose calling these reactions dissociative substitutions.

Dissociative chemisorption most often occurs on high surface energy substrates, such as metal substrates like platinum or ruthenium, for which adsorption can reduce surface energy. This mechanism occurs for metalorganic precursors by assisting in the dissociation of organic ligands, as illustrated for Ru(Cp)₂,^41–43 

Dissociative chemisorption can also occur with common counter-reactants, such as H₂ or O₂, by splitting them into their atomic counterparts,

which can be useful for increasing their reactivity toward the next precursor pulse.^44,45 In some cases, this involves breaking one intrasubstrate bond in order to generate a binding site for a precursor fragment. For instance, Al(CH₃)₃ has been shown to undergo dissociative chemisorption onto siloxane bridges,^46,47

In this mechanism, an intrasubstrate Si–O bond is broken and replaced with a new Si–C bond from one of the Al(CH₃)₃ precursor CH₃ ligands. While very similar to a ligand exchange mechanism, because both the CH₃ and Al(CH₃)₂ fragments remain bonded to the surface, this reaction is categorized as dissociative chemisorption.

Meanwhile, dissociative substitution reactions will commonly occur when a metal precursor containing one or more neutral ligands interacts with a Lewis basic surface. Since ligands are Lewis bases (electron donors) and neutral ligands can dissociate without resulting in a separation of charge or production of radicals, they can often be displaced by another Lewis base, such as the lone pairs of surface hydroxyls. Because the ligand and surface are both Lewis basic in this scenario, they do not strongly interact with one another and the neutral ligand can be purged away. Common neutral ligands found in ALD precursors which may participate in dissociative substitutions include carbon monoxide and alkenes. For instance, calculations have shown that chemisorption of Ru(DMBD)(CO)₃ occurred through the dissociative substitution of 2,3-dimethylbutadiene (DMBD),⁴⁸ 

Of the mechanisms for chemisorption, association is perhaps one of the rarest and is often only considered as a first step in other chemisorption mechanisms. Chemisorption via association occurs when a bond is made between a precursor and surface with no other bonds being broken,

The bond formed during an association mechanism is typically a coordination bond (sometimes called dative bond) between a lone pair of electrons on a Lewis base and an empty orbital of a Lewis acidic species. For this process to occur, either the precursor or surface must be electron deficient and capable of accepting electrons from a Lewis base. For instance, Al(CH₃)₃ is a neutral six electron species with an empty Al 3p orbital capable of accepting additional electrons. Calculations have shown that this 3p orbital strongly interacts with a lone pair of electrons from a Lewis basic surface hydroxyl or bridged oxygen group prior to the ligand exchange reaction, as illustrated for the case of surface hydroxyl in the following equation:^49,50

These calculations show that ligand exchange is not necessary for initial chemisorption of TMA onto a surface; chemisorption could occur instead through the association process shown in Eq. (14) and may be a possible mechanism for other electron deficient species as well.

Association is typically barrierless, without any transition state or intermediate that needs to be formed. Because of this, association can be reversible during the nonequilibrium ALD process as adsorbed species may desorb, as we will discuss in Sec. II C. In this regard, associated species are similar to physisorbed species and so association is often overlooked as a primary chemisorption pathway itself. However, it does differ from physisorption in that the coordination bond is dependent on orbital overlap and so can result in surface saturation of the precursor. Also, for some precursors, the strength of the association to a surface may be strong enough to resist desorption during purge times. For example, many metal halides have more favorable coordination to a surface than their metalorganic analogs due to the more electron withdrawing nature of the halide ligand.^23,24 In fact, theoretical calculations for these metal halide precursors often indicate that the most favorable chemisorption state is the associated state and we believe that it is possible that a portion of the adsorbed species are only associated, especially at lower growth temperatures.

Association mechanisms are considered when no bonds are broken, in either the precursor or substrate, and only a new substrate-precursor bond is formed. Occasionally, chemisorption via association will only occur after a gas-phase dissociation process which results in an electron deficient species. For instance, Al(CH₃)₃ actually exists as the dimer Al₂(CH₃)₆ at room temperature and must dissociate into monomeric Al(CH₃)₃ in order to make the 3p orbital accessible for association.⁵¹ In these cases, it can be challenging to distinguish between a surface-assisted dissociation mechanism and a gas-phase dissociation followed by an association mechanism. Also, as is the case in Al(CH₃)₃, association is often thought to precede ligand exchange reactions and is commonly included as the first step in many calculations.^21,49 This scenario raises the question of when should one consider chemisorption to have occurred? Should it be considered as the first step with a suitable stability enhancement (association) or in the final stable state after all ligand exchange reactions that will take place do? In general, the latter is used since it can be more readily determined experimentally.

Oxidation (i.e., combustion) is another mechanism for chemisorption observed in ALD. Oxidation is not uncommon in ALD, yet it is not often discussed in the context of chemisorption. Many ALD processes already use strong oxidizers such as O₂, O₃, and O₂ plasma to remove organic fragments from metalorganic precursors through combustion reactions. For non-noble metals, this oxidant typically results in the formation of the metal oxide as the oxygen is also incorporated into the film.^52–54 However, for many noble metal ALD processes during the steady growth regime (i.e., in which the surface is fully or mostly covered by the noble metal being deposited), such as the deposition of platinum with O₂, the oxygen results in a partially oxidized surface which helps to chemisorb the next cycle of metal precursor through oxidation of the ligands.^45,55 In these noble metal cases, chemisorption is often a mixture of both dissociation and oxidation mechanisms which can be hard to distinguish experimentally. A rather unique recent example of oxidation is in the chemisorption of RuO₄. In this case, RuO₄ was found to readily react with oxidizable surfaces such as H-terminated silicon or with silica alkylated with a Al(CH₃)₃ prepulse but suffered from a nucleation delay on already oxidized substrates such as SiO₂ [Fig. 2(a)].^56,57 This mechanism is unique in that the metal-containing precursor and not the counter-reactant is the oxidant, leading to oxidation of the surface species and reduction of the metal in the precursor.

The four mechanisms described above are the typical mechanisms observed or proposed for almost all ALD processes. However, several recent examples have shown that chemisorption can also follow some more unique mechanisms. For example, Kwon et al. have recently shown that ^tBu-AllylCo(CO)₃ inserts into the Si–H bond of H-terminated silicon [Fig. 2(b)].⁵⁸ For this mechanism, if one looks at only the starting precursor and final products, it could easily be mislabeled as a ligand exchange reaction. However, the prototypical BL acid-base ligand exchange reaction tends to be quite unfavorable with Si-H surfaces, whereas in this system, reaction on Si–H was facile while significant nucleation delays (typical of poor chemisorption) were observed for the more acidic Si–OH terminated surfaces. On the basis of these observations, calculations were performed and showed that the chemisorption step occurs via insertion of Co into the Si–H bond to form Si–Co–H. A second, postchemisorption, insertion then takes place between the hydride and the allyl ligand which results in the ligand exchangelike byproduct of 2,3,3,-trimethylbut-1-ene.

This unique mechanism hints at the existence of an even wider variety of possible chemisorption mechanisms in ALD and suggests that one should not become complacent with the general mechanisms. Furthermore, it is worth noting that the chemistry within ALD expands beyond chemisorption and important reactions can occur post chemisorption. Reduction, for instance, can occur post chemisorption if the resulting chemisorbed species are only sparingly stable, as we discussed in the case of the deposition of copper through transmetalation or tungsten through halogen abstraction reactions.^32,35 These processes are typically assumed to undergo what is known as reductive elimination reactions which, as the name might suggest, requires elimination of a species from the surface and so is often not compatible with chemisorption in which a bond needs to be formed.²⁰ Further investigations of precursor-surface reactions are needed to truly understand the scope of mechanisms present in ALD processes, and such studies will hopefully continue to shine light on other mechanistic pathways.

Self-limiting saturation of precursors is a hallmark of the ALD process. Saturation is typically considered dependent on either the steric effect of the adsorbed precursor fragments or the surface concentration of active sites. When active sites are sparse, the loading will likely be governed by the surface concentration (i.e., coverage) of the active sites.⁵⁹ However, when there is a high density of active sites, an adsorbed precursor fragment may block other nearby active sites due to steric hindrance.^10,60 In these cases, the loading per cycle may be limited by precursor steric hindrance alone. The temperature at which a given process self-saturates is called an ALD window.⁷ For many processes, the growth per cycle (GPC) over the ALD window’s temperatures is constant, although several processes deviate from this because higher temperatures can promote additional reactions or desorption of precursor without loss of the self-saturating behavior.¹⁰ 

Adsorption can be modeled through basic principles in chemical kinetics to provide a better quantitative understanding of the processes of saturation and film growth in ALD. The adsorption kinetics are especially important when using ALD to deposit onto topographically complex substrates with small feature sizes, where the kinetics, along with gas flow regime, can have a big impact on film conformality.⁶¹ Several studies have used kinetic modeling to analyze ALD growth.^10,19,61

The first step of any chemisorption mechanism is the physisorption or association of the gas-phase precursor molecule (A^gas) onto an accessible surface site (θ^*),

This step is typically assumed to be a reversible reaction since no byproducts are formed and purged away and is often referred to as a physiosorbed state, although as discussed above could also be considered as chemisorption through association. Once a precursor is adsorbed in this manner, it may further react once, or more than once, with the surface. This second reaction involves the breaking of a bond within the precursor through one of the previously described mechanisms and is often modeled as irreversible,

In this manner, one can postulate a reaction scheme composed of all the possible kinetic steps of a given process. Reaction rates are then modeled assuming all reactions are elementary. Finally, coverages are calculated by analytically or numerically solving all the rate equations or alternatively using other techniques such as Monte Carlo simulations. The analytical solution to the kinetic model can be fitted to experimental data and used to predict coverages, growth per cycle (GPC), temperature dependence, and conformality of various processes.

Based on this type of kinetic modeling, Muneshwar and Cadien showed that the saturation kinetics of separate kinetic regimes responds differently to changes in the substrate temperature.¹⁹ In a chemisorption-limited saturation (i.e., chemisorption is the rate limiting step), higher temperatures promote surface reactions and, as a result, lead to faster saturation. In the physisorption- or association-limited saturation regime, increasing the temperature leads to slower saturation. The slower saturation is a result of desorption kinetics as higher temperatures can accelerate desorption. This desorption kinetics has also shown to influence GPC within a given ALD temperature window. Several processes show a decrease in GPC as temperature is increased which may be due to desorption of adsorbed species.⁸ Figure 3 presents a back of the envelope calculation of the fraction of associatively chemisorbed precursors that remain chemisorbed throughout the purging step based on transition state theory and first order kinetics as a function of association energy,

where $CC0$ is the fraction of chemisorbed precursor, k is the Boltzmann constant, h is Planck’s constant, R is the gas constant, t is the purge time (30 s is used), and E_a is the association energy which is based on those reported in the literature.^23,24 From this figure, we see that strongly associated precursors (>30 kcal/mol) could play a role in growth at typical ALD temperature regimes. For ALD processes that show a decrease in GPC as temperature is increased, it may be possible that the lower GPCs are due to desorption of associated species, even though saturation is still achieved. The fraction of species that desorb will also be dependent on the purge time (t), although relatively few ALD investigations study this parameter. If the association bond is strong enough to withstand long purge times, to a first approximation, this process can be considered as time independent. It is therefore important to optimize deposition conditions, such as pulse and purge times, at both ends of the ALD window for processes which do not show a constant GPC across the window. The reversibility of association and the incorporation of a time component are reminiscent of traditional chemical vapor deposition, where the amount of material deposited is a function of time, rather than cycle number. However, since saturation is still achieved during the precursor pulse, we would consider this process to be a kinetically driven ALD process.

Nucleation delay is a general term used in ALD to describe the period of an ALD process prior to when a significant number of nuclei have formed or a steady GPC is achieved. In many of these cases, the nucleation delay can be explained primarily through a lack of chemisorption of the precursor onto the growth substrate. This occurs when the preferred mechanism of precursor chemisorption is incompatible with the growth surface and so chemisorption will only occur slowly, over tens or hundreds of ALD cycles, at a small number of defect sites or through a small amount of precursor pyrolysis. For instance, a precursor which normally undergoes an acid/base ligand exchange, as discussed above, will often have a nucleation delay on substrates free of acidic protons, such as on low surface energy metals or Si–H surfaces.^15,62,63 Likewise, precursors which resist ligand exchange, such as cyclopentadienyl (Cp) ligated precursors which need to break the aromaticity and resonance of the Cp anion to form HCp, often have very long nucleation delays on protic, low-energy surfaces but almost no nucleation delay on high-energy metallic surfaces which promote dissociation.^64,65 Of course, the above cases are broad generalizations, and more nuanced effects can also affect the chemisorption of precursor molecules. As an example, although bis(ethylcyclopentadienyl)manganese is a Cp ligated precursor, the bond between Mn(ii) and C of the Cp rings has unusually high ionic character, which results in facile ligand exchange and no nucleation delay when bis(ethylcyclopentadienyl)manganese is used for MnO deposition on Si-OH terminated substrates.^66,67

The nature of the substrate can also play a significant role in the chemisorption. For instance, not all protic surfaces are the same and the reactivity of –OH terminated surfaces can be significantly different than –NH_x terminated surfaces, which can further be influenced by the underlying substrate (i.e., Si vs Ti based substrates).^68,69 Even for the same material, different binding motifs can result in different reactivity, as observed for the isolated, vicinal, and germinal binding modes of surface hydroxyls in silicon.^70,71 For example, Lemaire et al. showed that tungsten chemisorption was more favored at vicinal hydroxyl sites and that removing these vicinal sites through high temperature annealing caused longer nucleation delays.⁷² High free energy substrates may also result in a favorable dissociation mechanism, where a ligand exchange reaction might normally be typical. This effect was shown by Lu et al. for TMA, where no chemisorption of TMA was noted on a copper surface while Pt and Pd surfaces showed significant dissociative chemisorption due to their higher surface energies.^22,73

When using a substrate that has two chemically different surfaces, a nucleation delay on one of the surfaces can be exploited to achieve area-selective ALD.^74–76 In these cases, chemisorption and growth occur on the reactive surface, while a lack of chemisorption on the other surface prevents growth. Two chemically dissimilar surfaces are often achieved using a dielectric substrate with a metal pattern since these surfaces promote chemisorption through distinct mechanisms, either ligand exchange or dissociation, respectively.^45,77 Precursors which preferentially chemisorb through a dissociation mechanism can then grow on the metal surface, while the dielectric surface remains unaffected or vice versa for precursors which favor ligand exchange [Fig. 4(a)]. Other types of patterns, such as Si–H/SiO₂, Si₃N₄/SiO₂, or others, can also be used as long as the chemisorption on the nongrowth surface is significantly inhibited compared to the growth surface.⁶⁸ 

Besides the inherent nucleation delay on a surface, other methods have also been used to further increase the delay on the nongrowth surface. Our group and others have had great success using self-assembled monolayers with long, unreactive alkyl chains that block active sites on the surface and prevent precursors from chemisorbing [Fig. 4(b)].^78,79 Alternatively, an etching step can be performed post processing or even incorporated into the ALD process which removes chemisorbed material from the nongrowth surface.⁸⁰ For a more detailed discussion on area-selective ALD and these processes, we recommend several review articles.^74–76,81

For most ALD processes, layer-by-layer (LBL) growth is generally considered the ideal case, with each cycle resulting in no more than one atomic layer of the deposited material. While this ideal growth mode is often used to illustrate the concepts of ALD, it is almost never achieved in practice. If we consider the first cycle of ALD onto a bare substrate, for cases in which precursor adsorption is highly favorable and active sites for chemisorption are in excess, precursor saturation is primarily controlled by the steric effects of the adsorbed precursor’s remaining ligands.^{10–12,18,60} This steric hindrance prevents the formation of a full layer of ALD-deposited material after a single ALD cycle. If the following ALD cycle results in deposition solely onto the unfilled substrate until a monolayer is formed, this is considered two-dimensional, or LBL, growth.¹⁰ Frequently, however, the following cycle will preferentially chemisorb onto the existing ALD-deposited material rather than on the bare substrate. This type of growth is known as island growth since the preferential deposition onto the ALD-deposited material will result in the formation and growth of islands that are separated by the bare substrate. While LBL and other possible growth mechanisms (such as random deposition, in which deposition occurs equally on the substrate and the ALD-deposited material) are important in ALD, we will focus our discussion in Secs. III A–III E primarily on island growth due to the distinct diffusion mechanisms that it entails.

Generally, island growth can occur in the presence or absence of surface diffusion. In the cases where surface diffusion does not occur, particle diameter exhibits linearity with respect to cycle number since each cycle results in a monolayer of adsorbed precursor on the surface of the island.¹⁷ Diffusion during ALD processes will cause the mean particle diameter to deviate from linearity (LBL and island growth mechanism with and without diffusion are illustrated in Fig. 5). While this deviation from linearity is indicative of a growth mechanism that involves diffusion, the observation of nonlinear particle size growth does not by itself provide enough additional insight into the diffusion mechanism. Yet, the role of diffusion in ALD is clearly an important consideration. We do note that nonidealities, such as nonlinearity and polydispersity (as illustrated in Fig. 5), could also appear in diffusion-free island growth for systems in which precursor chemisorption occurs very slowly. However, this scenario is rare in ALD as will be discussed later. Diffusion has been widely discussed in the literature for other thin-film deposition techniques, such as chemical solution deposition,^82–84 and has been well studied in catalysis literature, where diffusion and sintering during reaction conditions affect the catalytic activity and reactivity of the NP catalysts.^85–87 The literature investigating how these physical phenomena incorporate into growth mechanisms of ALD has flourished in the past few years following the work of Grillo, Soethoudt, Dendooven, Mackus, and others.^{16,17,88–92} There still remain many ALD processes for which the study of diffusion phenomena during ALD growth is unfortunately scarce.

In the context of diffusion, the noncontinuous nature of the ALD process and the cyclically changing chemical properties of its growth surface give rise to special considerations. While some reports mention the potential effect of diffusion and aggregation during metal ALD,^91,93–95 there have been only a few studies aimed at identifying and modeling the exact diffusion mechanism that governs ALD growth.^16,88–90 Grillo et al. simulated several different growth mechanisms in ALD that included various diffusion phenomena and found that modeling the island (or NP) size distribution is an efficient way of assessing the diffusion mechanisms that take part in the ALD growth.⁸⁸ In Secs. III A–III E, we will summarize the current understanding about the role of diffusion on island growth in ALD. We will first describe island growth without diffusion and then turn to the physical aspects of diffusion mechanisms that have been reported or postulated to occur during ALD. Next, we will discuss the effect that diffusion has on the particle size distribution (PSD) during ALD and survey selected literature examples to analyze the most prominent diffusion phenomena observed based on the reported PSDs in those studies. Finally, we will discuss how the ALD process can be tailored to meet specific requirements regarding the PSD. We will primarily focus our discussion on the ALD of metals onto nonmetallic, low surface-energy substrates since this is where most of the interesting diffusion phenomena occur.

In part II, we discussed the various chemical pathways by which precursors can chemisorb onto surfaces. In some cases, this chemisorption reaction is the main consideration that must be taken into account when modeling ALD growth, without the need to include diffusion.¹⁸ The modeling of growth through chemisorption-only reactions has been successfully implemented by Puurunen and Vandervorst for the island growth of ZrCl₄/H₂O and AlMe₃/H₂O ALD processes on hydrogen-terminated silicon.¹⁷ According to their model, which fits the experimental data well, all of the active sites on the substrate are consumed upon the first cycle of ALD and additional active sites are not generated upon additional cycles. Islands initiate from these active sites and grow in a linear fashion with ongoing ALD cycles. While this model is suitable for various dielectric ALD systems, it does not describe island growth as observed in ALD systems where chemisorption is very slow (i.e., not all active sites are consumed upon the first cycle), or diffusion is a key part of the growth mechanism.^{16,65,99,88–91,93,96–98} Many of the processes that entail slow precursor chemisorption (i.e., island growth with ongoing chemisorption on the support) are those of metal ALD on nonmetal supports and thus contain a diffusion component. However, we note that diffusion-free island growth could, under certain circumstances, lead to nonlinear island growth and polydispersity.

Let us consider the first metalorganic precursor pulse in a metal ALD process onto a low energy noncatalytic surface such as a metal oxide or carbon which results in a sub-monolayer of chemisorbed precursor fragments. The metalorganic complex is bonded to the surface through the metal atom, and the surface is partially covered by the complex’s ligands, as illustrated in Figs. 1(c) and 1(d).^12,27 From this point onwards, surface diffusivity must be considered. Diffusion of the chemisorbed species may lead to collisions between adsorbed precursors followed by cluster formation. The growth of NPs as a result of this diffusion adds a new mechanism for the growth of NPs that is not just a result of the cyclic, self-saturating deposition in ALD but also depends on diffusion of species into clusters which eventually become larger NPs. In turn, this diffusion can cause the mean NP size to deviate from linearity with respect to the number of ALD cycles. These collisions are generally considered to be nonreversible, except in the case of Ostwald ripening that will be discussed later. Surface diffusion of atoms and molecular species can be treated with a localized-hopping model.^100,101 The surface diffusivity is measured by a diffusion coefficient, which is the proportionality constant between the flux of atoms and the driving force for diffusion. Qualitatively, the diffusion coefficient is an estimate of the ability of a species to diffuse under a driving force. The general description for the diffusion coefficient according to the localized-hopping model is given by¹⁰⁰ 

where D₀ is a diffusion constant, H_m is the energy barrier for migration (m = migration), k is the Boltzmann constant, and T is temperature. The subscript 1 is given to emphasize that this is for a single atom or molecule. A nearest neighbor model gives H_m = −ε_mo, where ε_mo is the bond energy of the adsorbed metal atom to the surface. According to this expression, high temperatures and weak metal-surface bonds will lead to higher atomic diffusivities.

One example of how a change in the diffusivity of adsorbed species might translate into different particle behavior during ALD was presented by Grillo et al. Grillo et al. used transmission electron microscopy (TEM) to study the aggregation of Pt during Pt ALD from MeCpPtMe₃ and O₂ on graphene nanoplatelets.¹⁶ In their study, they found that during the first MeCpPtMe₃ half-cycle pulse at 100 °C, the chemisorbed Pt precursor does not aggregate into visible NPs. This implies that the precursor fragments do not easily diffuse under these conditions since aggregation is dependent on the ability of the chemisorbed species to diffuse and come together, ideally forming strong metal-metal bonds. This can be understood since, generally, adsorbed organic ligands on the surface suppress metal aggregation by lowering surface mobility.^102–104 In addition to the lower surface mobility, the steric effect of the Cp ligands could hinder the formation of Pt–Pt bonds.¹⁰⁰ However, Grillo et al. observed different behavior at the next step in the Pt ALD process, which was the introduction of the O₂ counter-reactant. This step serves to combust the organic ligands and activate the surface toward the next MeCpPtMe₃ pulse. In their study, Grillo et al. found that this oxidation step leads to formation of Pt aggregates on the surface of the graphene. They proposed that the removal of the organic ligands and the release of heat as a result of ligand combustion, along with release of combustion by-products,¹⁰⁵ can increase surface diffusivity and the ability to form Pt–Pt bonds. An additional explanation to the increase in atomic diffusivity is the formation and subsequent diffusion of metastable metal oxide species (PtO_x) upon O₂ exposure. These noble metal oxide species have been shown to promote molecular diffusion.^106–112 In principle, partial or full reduction of the metal center during the counter-reactant step could weaken the metal-surface bond and increase atomic/molecular diffusivity, which could promote aggregation. However, experimental determination of the Pt center’s oxidation state following combustion, but prior to aggregation, would be difficult since it would require the use of in situ techniques with extremely high special resolution on small time scales.

Island growth is observed for many noble metal ALD processes on dielectric substrates, as illustrated for the case of Pt ALD on SiO₂ shown in Figs. 6(a)–6(d).¹¹³ Noble metal island growth can also be influenced by the catalytic property of the metal itself. This catalytic activity assists in the initial chemisorption of precursors through dissociation, as discussed in Sec. II B 2, and can further catalyze the decomposition of organic ligands into a carbonaceous layer.¹¹⁴ Note that the small aggregates formed after the first few ALD cycles may not be catalytically active since the catalytic activity of NPs is known to be size dependent.^115–119 It may be that only after a NP of a certain size (large enough to enable catalytic activity) has formed will the metal-containing precursor from the subsequent pulses preferentially chemisorb onto the active NPs, in turn promoting further island growth. This catalytic mechanism for enhancing formation and growth of NPs has been shown to be present in some noble metal ALD systems, such as Pt and Ru.^89,91 Through modeling, Delabie and co-workers found that the critical size at which Ru NPs become active to further Ru growth due to ALD surface reactions is 0.85 nm.⁸⁹ In the example of Pt ALD from MeCpPtMe₃ and O₂, the work by Mackus et al. showed that a low O₂ pressure or short O₂ exposure time during the first few cycles of Pt ALD onto an inert substrate leads to incomplete ligand elimination due to the slow kinetics of noncatalytic combustion. Incomplete ligand elimination inhibits the diffusion of adsorbed platinum, as described above, and reduces the formation of Pt islands, which are able to catalyze ligand combustion. This, in turn, compromises further MeCpPtMe₃ chemisorption.⁹¹ The lack of active chemisorption sites results in a long nucleation delay that leads to inhibited growth of Pt, as seen in Fig. 6(e). The studies presented above emphasize the importance of island formation as a crucial component of noble-metal ALD chemistry. It is this diffusion process that leads to formation of NPs that in turn enables further precursor chemisorption through catalytic reactions and prevents longer nucleation delays.

Ostwald ripening is an interparticle transport phenomenon that describes the growth of large NPs at the expense of small NPs through atomic or molecular diffusion, which results in a minimization of the NP chemical potential.¹²⁰ Let us consider a single atom diffusing on a surface which attaches to a NP that consists of k number of atoms. The change in chemical potential (i.e., the work) per atom transferred from a flat substrate to the NP with isotropic surface energy is given by the Gibbs-Thompson effect,^100,120,121

where γ is the average surface energy of the NP; μ_k+1 and μ_k are the chemical potentials of the NPs with k + 1 and k atoms, respectively; μ₀ is the chemical potential of an atom on the flat substrate; Ω is the atomic volume; and r_k+1 and r_k are the radii of curvature of the NPs with k + 1 and k number of atoms, respectively. For a surface with a positive radius of curvature, such as a nanoparticle surface, the attachment of an atom to a nanoparticle will involve a decrease in the total chemical potential. It is clear from Eq. (19) that minimization of the chemical potential is the driving force for attachment of single atoms to NPs and for the growth of larger NPs (low curvature) at the expense of smaller NPs (high curvature). The attachment of a single atom to a NP is especially favorable if the adatom has a weak interaction with the support.^100,122,123 There are two main interparticle mass transport paths by which atoms can move: surface diffusion of single atoms and gas phase diffusion through volatile species.

Ostwald ripening in noble metal ALD systems has been postulated to occur through diffusion of metastable or volatile noble metal oxide species as the dominant growth mechanism.^{91,93,124–126} This mechanism may be especially relevant for noble metal ALD processes that use oxidizing agents as counter-reactants.^{106–109,111,127} Solano and Dendooven et al. showed through annealing experiments under various oxidizing and reducing environments that the formation of PtO_x species is crucial for Ostwald ripening at the temperature regime that is relevant for most ALD processes (<600 °C).¹¹² The rate of particle growth or shrinkage is determined by the net flux of PtO_x molecules impinging on the NP surface. Since smaller NPs have a higher surface-to-volume ratio, they will shrink, and large NPs will grow, as expected for Ostwald ripening and the Gibbs-Thomson relation. Overall, NP stability is an exponential function of the inverse of the NP size.¹²⁸ 

Figure 7 shows the illustration of gas-phase and surface-assisted Ostwald ripening. Although in the literature, Ostwald ripening has been proposed to cause PSD-broadening, and even bimodal PSDs,^129–131 Grillo et al. found from their modeling that under ALD conditions (i.e., ongoing deposition), Ostwald ripening leads to very narrow PSDs.⁸⁸ Compared to all other growth mechanisms that we will review in this perspective, Ostwald ripening leads to the narrowest PSD since small NPs that form with ongoing deposition are highly unstable in this growth regime. Interestingly, although some papers hypothesize the growth of NPs in ALD through Ostwald ripening,^{91,93,124–126} to our knowledge, there is currently no report of an ALD process that presents concrete experimental evidence for Ostwald ripening being the dominant diffusion mechanism. Most reports we have reviewed present either significantly broadened or multimodal PSDs. While Ostwald ripening cannot be ruled out as a participating diffusion mechanism, especially in the case of noble metal ALD when volatile or metastable metal oxides may form, other diffusion mechanisms appear to be more dominant during ALD. We will discuss the origin of the PSDs and present specific examples in Sec. III D and III E.

In Secs. III B and III C, we have considered atomistic or molecular diffusion during ALD. However, to complete the picture of diffusion processes during island growth, we must account for NP diffusion (Fig. 8) as a possible pathway for NP growth. Although NP diffusion has been extensively studied in other literature such as catalysis,^85,132–135 the noncontinuous and cyclical nature of ALD gives rise to special considerations for NP diffusion during ALD.

Similar to Ostwald ripening, NP diffusion and coalescence are also governed by minimization of the chemical potential. The relation between metal-support interactions and NP diffusion (and consequently sintering) has been widely discussed in the literature.^{105,122,123,136–138} Here, we outline some of the main concepts of surface free energies and adhesion energies and their role in NP diffusion. It has been well-established that when a NP has a high chemical potential, it experiences a higher thermodynamic driving force to diffuse and sinter.^{105,122,134,139} The chemical potential of a NP on a surface is influenced by the nature of the metal, the surface, the NP shape and size, and the interface between the NP and the surface. Campbell and Sellers have shown that the internal energy of a metal NP on a support is given by^122,123

where U is the total internal energy of the NP, U_bulk is the internal energy of the bulk metal, U_sup is the internal energy of the particle free support, n_M (M = metal) is the number of moles of metal that the NP consists of, γ_M is the surface energy of the metal NP, E_adh is the adhesion energy of the NP to the surface, A is the interfacial area between the NP and the surface, and A_M is the NP surface area. The adhesion energy is defined as the work needed to separate the metal/substrate interface under UHV conditions and is given by^140,141

where γ_M, γ_S, γ_MS are the surface energies of the metal NP, substrate, and metal/substrate interface, respectively. These energies dictate the degree of wetting of the metal (illustrated in Fig. 9), which can be measured by a contact angle, θ, according to the following equation:¹²¹ 

To obtain the chemical potential, we return to Eq. (21). Assuming molar entropy does not change with particle size, the chemical potential is given by the partial derivative of the internal energy with respect to n_M. It is therefore important to understand how each expression relates to n_M. The bulk energy, U_bulk, is a constant and can be set to 0 as the reference energy. The surface-NP interfacial area, A, and NP surface area, A_M, are proportional to $nM23$⁠. Assuming E_adh and γ_M are constant, we can see that the chemical potential increases with γ_M and decreases with E_adh,

where C₁ and C₂ are proportionality constants. Therefore, the choice of deposited metal and substrate material will largely affect the interactions between the metal NP and the low surface-energy substrate, consequently affecting the NP’s diffusion properties.

Campbell and co-workers have also demonstrated a linear correlation between the adhesion of a given metal to an oxide support and the strength of the bond which the metal makes to the oxygen atoms (i.e., the metal’s oxophilicity),^122,123,134

where ΔH_sub,M is the enthalpy of sublimation of the bulk metal and ΔH_f,MOx is the heat of formation of the metal’s most stable oxide. This linear correlation is demonstrated in Fig. 10.¹²³ The offsets on the y-axis of the linear trends in Fig. 10 are independent of the metal and are correlated with the heat of formation of the oxide support. Oxide supports with higher formation energies have lower stability, and their oxygen atoms have higher chemical potentials. As a result, the adhesion energy of the metal to these oxygen atoms will increase. For a given metal, the adhesion energy has also been shown to increase on supports with higher oxygen density.¹³⁸ Hence, metals with high surface free energy should exhibit high NP diffusivities when deposited on substrates with high heat of formations and low oxygen densities.

We now turn to additional challenges in applying the above analysis of NP diffusion to an ALD process. In ALD, chemical reactions can influence the local gaseous environment, affect local temperature, and introduce chemical impurities which can make quantitative analysis of the driving forces for NP diffusion and sintering less straightforward. Additional difficulties arise from the impact of the support’s chemical properties (such as Brønsted acidity/basicity) and the chemistry of the counter-reactant on precursor chemisorption, both of which will affect NP formation. Nevertheless, the analysis presented above can serve as a guide to how the choice of deposited metal and support can impact the driving force for NP diffusion during the ALD process. To complete this picture, in Sec. III E, we will discuss the effect of NP diffusion during ALD processes and the relevant ALD conditions that impact the diffusivity of NPs and resulting PSDs.

The various diffusion processes reviewed in the Secs. III B–III D can influence how islands nucleate and evolve into films during ALD. A recent study by Grillo et al. provides a valuable comparison of the growth behavior across some of the different possible diffusion regimes. In their work, they performed kinetic modeling of NP growth in ALD with the addition of NP diffusion processes based on Smoluchowski kinetics.^16,88 Figure 11 presents PSDs resulting from three different growth scenarios involving NP diffusion, rescaled with respect to the average diameter. In all three scenarios, every ALD cycle involves deposition on both the support and existing NPs, and all three scenarios involve adatom diffusion. Where the three scenarios differ is in the size-dependency of NP diffusion, which correlates, among other parameters, to the strength of the metal-substrate interactions. In the Smoluchowski kinetics formalism, the diffusion rate of a NP of k atoms is represented as the product of the diffusion rate of a single atom and a size-dependent power term, i.e., D_k = D₁k^−s, where D_k is the diffusion rate of a particle of size k atoms. The size-dependency, s, is usually regarded as a fitting parameter and is understood to be a function of the NP-support interaction, temperature, morphology, and more.^142–144 As we have discussed previously, NPs that exhibit a stronger metal-support interaction will have a lower driving force for diffusion (and thus lower surface mobility) than those which interact weakly with the substrate.^85,122 We would expect that NPs that have strong interactions with the support will have higher resistance to diffusion with increasing NP size (i.e., stronger size-dependent diffusivity that results in large values of s) due to the increasing number of strong bonds to the surface with increasing size. Similar considerations dictate that higher temperatures should also result in a weaker size-dependent diffusivity.¹⁴⁵ 

Given these basics, Grillo et al. considered three different values of s in the Smoluchowski model. For the scenario with s = 1/3, which is an example of weak size-dependent diffusion [Fig. 11(a)], the diffusivity and the probability of coalescence will not vary significantly with size. Therefore, with each ALD cycle, adatoms are deposited and aggregate into small NPs. Some of these small, newly formed NPs, along with previously existing large NPs, diffuse and coalesce into larger NPs. This broadens the PSD, which becomes heavily right-skewed, with a tail to longer particle sizes. The distribution’s mode, corresponding to the new NPs formed from aggregation of adatoms deposited on the surface during each cycle, remains approximately constant since these smaller NPs are generated in a cyclic manner. The scenario with stronger size-dependent diffusion (s = 4/3), on the other hand, has a bimodal PSD [Fig. 11(b)]. Because diffusion in this scenario is size-dependent, the larger immobile NPs will act as sinks for the smaller, more mobile NPs. As a result, large NPs will show fast growth at the expense of smaller NPs. Nonetheless, with every ALD cycle, new adatoms will deposit, diffuse, and aggregate, which accounts for the peak seen in the PSD at the lower particle sizes. In the scenario with the strongest size-dependency (s = ∞), only adatom (or molecular) diffusion is allowed. Therefore, the new small NPs that form as a result of adatom aggregation in each ALD cycle are not eliminated by diffusion. This adatom/molecular diffusion process results in a left-skewed multimodal PSD [Fig. 11(c)]. The multimodality might be difficult to resolve experimentally due to the high-frequency and low amplitude oscillations and appear only as a left-skewed distribution. Overall, these PSDs presented by Grillo et al. can serve as excellent guidelines to qualitatively identify and estimate the diffusion mechanisms that take place during ALD. In Secs. III E 1 and III E 3, we will demonstrate how these simulated diffusion mechanisms appear in experimental data found in the ALD literature.

Interestingly, while evidence of NP diffusion can be found in various studies involving metals such as Pt and Ru,^{16,89,146,147} annealing experiments of Pt in oxidizing environments and temperatures typical to ALD found that there is no evidence of particle migration under those conditions.¹¹² This observation is on par with the suggestion of Grillo et al. that heat released as a result of combustion reactions during ALD and the local gaseous environment under ALD processing help promote NP diffusion during ALD.¹⁶ Therefore, precursors that do not require oxidizing counter-reactants might be a good choice if the goal is to impede NP diffusion.

One of the great strengths of ALD is the many degrees of freedom that it provides which, if tuned wisely, can allow for precise control over NP size, size distribution, dispersion, and more. These degrees of freedom include, among others, the substrate’s temperature, choice of counter-reactant, and identity of the substrate. Temperature, counter-reactant, and substrate can all exert a strong influence on NP growth through ALD. The effect of each of these three process parameters will be described in Secs. III E 1–III E 3.

In Sec. II C, we discussed potential chemical mechanisms that affect growth within the ALD temperature window. Yet, modifying the temperature of a process can also impact the diffusion properties of the growing material. The effect of temperature on ALD has been illustrated in the work by Grillo et al. and Mackus et al. for Pt ALD.^16,93 Grillo et al. modeled particle size distributions of Pt ALD from MeCpPtMe₃ and O₂ on activated graphene at 100 °C and 200 °C. They found by fitting their model to experimental PSDs that at 100 °C, size-dependent dynamic coalescence was the dominant diffusion mechanism (⁠$Dk=D1k−23$⁠, where $k−23$ is proportional to the contact area of the NP), whereas at the more elevated temperature of 200 °C, the dominant diffusion mechanism was size-independent dynamic coalescence (D_k = D₁k⁰).

Mackus et al. experimentally compared particle size distributions of Pt ALD from MeCpPtMe₃ and O₂ (referred to as an “AB” process) at 300 °C to Pt ALD from MeCpPtMe₃ and O₂ plasma followed by H₂ plasma (referred to as an “ABC” process) at room temperature [Figs. 12(a) and 12(b)].⁹³ In the latter case, O₂ plasma was used to promote ligand combustion at room temperature and the H₂ plasma was used to reduce any PtO_x that might have been formed in the previous step. In their study, Mackus et al. attributed the broader PSD, shown in Fig. 12(a), resulting from the AB process to a lower atomistic diffusivity due to higher carbon impurities incorporated into the NPs in the absence of plasma (<5 at. % of carbon impurities from the AB process compared to <1% from the ABC process). Indeed, it has been shown that thermal Pt ALD under typical conditions on flat substrates does not remove all the organic ligands, leading to the carbon impurities reported by the authors.⁹² However, inhibition of atomistic diffusion alone should not result in the broadening of the PSD.⁸⁸ Here, we offer a possible alternative explanation for the difference between the AB and the ABC processes based on the work of Grillo et al. If we qualitatively compare the PSDs from the work of Mackus et al. to the PSDs from the simulation presented by Grillo et al., we postulate that two distinct diffusion mechanisms may be accountable for the different PSDs. The PSD of the AB process at 300 °C qualitatively matches a dynamic NP coalescence in which NP diffusion dominates. On the other hand, the multimodality of the ABC process at room temperature resembles the model in which deposition is accompanied by adatom aggregation and does not involve NP diffusion (D_k = D₁k^∞). This multimodality might be a consequence of insufficient thermal energy to activate NP diffusion.

The counter-reactant used in an ALD process can allow for fine tuning of adhesion energy and surface diffusivity. This in turn can exert an influence on island growth and film evolution during ALD. Dendooven et al. used scanning electron microscopy (SEM) and grazing incidence small angle scattering (GISAXS) to compare NP growth during O₂-based and N₂-plasma-based Pt ALD.⁹⁰ Interestingly, they found that diffusion strongly depended on the identity of the counter-reactant. When the N₂ plasma was used as a counter-reactant, NP density and center-to-center distance stayed constant as a function of ALD cycle number. On the other hand, when O₂ was used as a counter-reactant, center-to-center distance and NP density decreased with the ALD cycle number. The average particle width and degree of wetting (measured by the ratio of particle height to width) of the O₂-based process were consistently higher than those of the N₂-plasma based process. These results show that diffusion occurs primarily during the counter-reactant step, when O₂ is used as the counter-reactant. On the other hand, when N₂ plasma is used as a counter-reactant, diffusion is suppressed. The authors exploited this to implement a two-step ALD process that allowed for independent tuning of the particle size and coverage. The first step was O₂-based Pt ALD that was used to achieve a desired amount of particle coverage. Subsequently, the process was switched to the N₂-plasma-based process. This additional step enabled particle growth without an increase in coverage, as illustrated in Fig. 13. Interestingly, the effect of diffusion does not simply affect the mean values measured (such as particle width, center-to-center distance, and NP density). The standard deviations of these values are also consistently larger for the O₂-based Pt ALD. This observation is consistent with the broader PSD simulated when growth involves NP diffusion. It is interesting to note that the diffusion did not, however, have a large impact on total Pt loading.

Finally, as a highly surface-sensitive deposition method, ALD will be impacted by the choice of substrate because the identity of the substrate influences the amount of precursor that chemisorbs, the driving force for aggregation, and the surface diffusivity. Atomic and NP diffusion are tightly related to the bond strength, or adhesion energy, of the atom or NP to the surface. Delabie and co-workers studied the growth of Ru ALD from (ethylbenzyl) (1-ethyl-1,4-cyclohexadienyl) ruthenium (EBECHRu) and O₂ at 325 °C on various dielectric surfaces.⁸⁹ In general, the reactivity of EBECHRu was shown to be largest with the hydroxyl rich oxides. The authors compared PSDs and mean particle sizes on hydrophilic SiO₂ (surface -OH density of 2.5 nm⁻²), hydrophobic SiO₂ (surface -OH density of 0.42 nm⁻²), and organosilicate glass (OSG, surface -OH density of <0.1 nm⁻²). In all three cases, the average particle size was larger than what would have been predicted by the diffusion-free growth model from fixed defect sites on the surface that was discussed in the beginning of Sec. III.¹⁸ Along with the general shape of the PSDs of the Ru NPs on these substrates (extracted from the SEM images shown in Figs. 14(a)–14(c)), the disagreement between the particle sizes measured and predicted by the diffusion-free growth model implies that diffusion-mediated growth of NPs is occurring on all three surfaces. The authors compared the mean particle size [Fig. 14(d)] at a Ru atomic coverage of $4*1015atcm−2$⁠. The NP size was found to be the largest on the least reactive surface (i.e., OSG) and smallest on the most reactive surface (i.e., hydrophilic SiO₂). In addition, shapes of the PSDs on the three surfaces are distinct from each other. While the Ru PSD on the most reactive surface (hydrophilic SiO₂) and the least reactive surface (OSG) are both right skewed, the PSD on the OSG is significantly broader than the PSD on the hydrophilic SiO₂. On the other hand, the hydrophobic SiO₂ presents a bimodal PSD.

In the context of the discussion above, using the analysis of Fig. 11 as a guide, the authors hypothesize based on the PSDs that the highly hydrophobic OSG substrate experiences the most NP diffusion and the hydrophilic SiO₂ experiences the least. This simplistic picture is consistent with chemical intuition. Hydrophobic surfaces with low surface energy will provide a higher driving force to the high surface energy Ru atoms and NPs to diffuse. Therefore, the larger driving force for diffusion and sintering along with the lower reactivity to chemisorption exhibited by the most hydrophobic surface will result in a lower density of larger NPs with a broader PSD, as observed experimentally. Delabie et al. quantitatively modeled the Ru growth on the OSG surface to gain further insight into the growth mechanism. The best fit was achieved for a model that consisted of three components: cyclic deposition on NPs and support, adatom aggregation along with size-dependent NP diffusion (⁠$Dk=D1k−83$⁠), and size-dependent growth. The size-dependent catalytic activity that was discussed previously manifests itself in the size-dependent growth. In other words, growth on Ru NPs as a result of deposition begins only after reaching a critical size, in which the NPs become catalytically active. This example illustrates how the choice of substrate affects growth not only through variation in surface energy but also through chemical functionality. This example also demonstrates how an observation that can be intuitively attributed to differences in chemisorption alone entails complex diffusion mechanisms which, if overlooked, would result in only a partial understanding of the ALD process.

Atomic layer deposition is a powerful technique for the deposition of thin films as well as nanoparticles. The overall goal of ALD and other deposition techniques in general is full control over the deposited material’s morphology and loading. To accomplish this level of control, we need a strong understanding of the mechanisms which govern the growth of materials during the ALD process. However, the underlying mechanisms driving this growth are often oversimplified or not fully understood. In this perspective, we discussed several mechanisms pertaining to precursor chemisorption and diffusion during ALD to highlight and more clearly define these processes.

In Sec. II of this perspective, we covered mechanisms related to chemisorption of precursors onto a substrate. While these chemisorption mechanisms are typically generalized into one of four mechanisms, we proposed several subcategories to further distinguish the more nuanced effects that differentiate apparently similar mechanisms as well as highlighted several other mechanisms which do not fit into these broad classes. We also considered how an understanding of the chemisorption mechanism can be used to better predict nucleation delays that occur for certain precursor/substrate combinations. In Sec. III, we discussed island nucleation and growth of NPs, an important step in the evolution of film deposition that is found in many ALD systems, with a focus on the diffusion mechanisms that control NP size distributions. We discussed the driving forces behind different diffusion mechanisms, highlighted how one can distinguish the predominant diffusion mechanism through the resulting PSD of the growing NPs, and gave examples of how deposition conditions can be used to affect diffusion and hence control the resulting PSDs. Most of the studies cited in this section heavily rely on the modeling of particle size distribution to examine the diffusion properties of islands during ALD. In situ GISAXS has also proven to be a valuable tool to study the presence or lack of diffusion during ALD, but this technique is most effective in extracting average morphological properties of the nucleating islands. In addition, modeling GISAXS patterns can be quite challenging and introduce additional ambiguities. Direct, in situ measurements of diffusion rates, such as by means of TEM, although challenging, could resolve the ambiguities introduced by modeling and provide a more direct approach to study diffusion during ALD.

While we have discussed relevant studies throughout this perspective, such detailed studies are still relatively sparse in the ALD literature. More investigation is needed to fully understand the hundreds of different ALD processes that have been reported. We believe that these future studies should put specific emphasis on the parameters that are unique to the nonequilibrium and noncontinuous nature of ALD systems. Our goal throughout this perspective has been to encourage the reader to consider how each different choice, such as precursor selection, substrate material, or growth temperature, within an ALD process could potentially influence the final deposited material from the vantage point of mechanistic understanding. Ideally, ALD scientists will one day be able to fully control the morphology and distribution of their deposited materials by tailoring the precursor and counter-reactant selection to the desired substrate and deposition conditions used for a specific application.

This work was supported by the U.S. Department of Energy under Award No. DE-SC0004782. N.E.R. acknowledges support from Intel. We thank Dr. Fabio Grillo for fruitful discussions on nanoparticle growth mechanisms.