Surface Ripple Formation by Bombardment with Clusters: Influence of Mass

Abstract

Nanostructure formation on Co(110) surfaces was studied by using irradiation with cluster ion beams with oblique incidence and an energy of 250 eV/atom. In this work, the effect of the mass of the cluster projectiles on the process was analyzed. The launched clusters were formed by different types of charged atoms: He, Ne, Ar, Kr, and Xe. Due to the different collision processes, the formed surface patterns stand out more if the mass of the projectile atoms is greater, regardless of the angle of incidence of the clusters. Two processes control the morphological evolution of the surface during the bombardment phase: sputtering erosion and surface atomic redistribution. At grazing angles, the contribution of sputtering is greater during the process. In fact, heavier species give greater sputtering, and the redistribution factor becomes lower. The weight of redistribution is greater for intermediate angles above the critical angle (50° and 60°), since the displacement is greater for heavier species, and the redistribution factor takes substantially higher values. The experimental results point to a shift in the critical angle with the mass of the projectile atom. In the case of He, a very light ion, the results are marked by channeling and vertical displacements.

1. Introduction

The nanopatterning effect caused by ion irradiation consists of self-organized nanoscale ripples that appear on the surface of the sample during the bombardment [1]. In fact, ion beam sputtering (IBS) is a technique that uses a source of ions to bombard a target material and leads to the formation of nanostructures on the substrate. The first theoretical model [2] stated that the process was the result of two opposing regimes. On the one hand, it consists of surface erosion, and on the other, it involves thermally activated diffusion dependent on curvature. However, recent work on the subject has shown that atomic displacement during bombardment can be the cause of nanostructure formation [3]. These studies, along with the theory of moments, have led to the formulation of new theoretical models [4]. The most recent developments focus on the analysis of the surface equations of motion (EOM) by studying atomic currents [5]. These models are not exempt from a complicated mathematical formulation. In general, almost all the theoretical research and a good part of the applied research have been performed on monatomic projectiles. However, ion bombardment with clusters also produces surface patterns [6].

From a physical point of view, the oblique incidence bombardment process involves two phases: erosive and diffusive [2]. The latter is masked by the former under conditions of high fluence and/or low surface temperature [7]. It is under these conditions that our results take on a special meaning. Recently, under low-energy bombardment conditions, molecular dynamics has shown that atomic redistribution can also be the cause of this effect on Si surfaces [8]. In fact, some of these authors attribute the formation of nanostructures in amorphous materials to redistribution processes and the same formation, in metals, to sputtering for grazing angles of incidence [9]. From the experimental point of view, measurement of atomic displacement allows us to predict the critical angle of incidence (above which the effect is possible) in cluster irradiation at 30 keV [10].

In this work, the influence of the mass of the cluster atoms on the bombardment process of a metallic substrate is analyzed. Clusters are used as projectiles in order to accelerate surface effects. This study also attempts to shed light on the phenomena that determine the nanostructure formation process for any angle of incidence above the critical angle. Clusters of a few atoms, specifically six, formed by different chemical elements: He, Ne, Ar, Kr, and Xe are used. A Co(110) surface is bombarded under different angles of incidence with cluster ions with an energy of 250 eV/atom. In the first part, the resulting superficial atomic morphologies after bombardment are compared. Next, the angular dependence of the sputtering and atomic displacement curves is studied. Finally, the specific weight of sputtering and redistribution using primarily volume considerations is discussed.

2. Model

In this study, the bombardment is focused on a longitudinal strip parallel to the y axis, similar to a linearly focused ion beam (Figure 1). This axis is parallel to the crystallographic <001> direction. This approach reduces the time it takes for the surface response to occur. This model has been previously introduced to analyze this phenomenon in other works [8,9]. Its main advantage is that it is simple and allows us to obtain results and draw conclusions from the processes involved. Furthermore, certain quantities, such as volumes, can be measured with some ease. A bombardment with a nonlinear focus would be a combination of the processes analyzed here. In fact, it is to be expected that the bombardment situation described here will also experimentally lead to pattern formation, with which our results will be completely valid for any bombardment process. The bombarded surface is a face-centered cubic (FCC) Co surface oriented in the <110> direction. The surface has dimensions of 56 × 28 × 14 unit cells (14.0 × 9.9 × 3.4 nm). The solid is considered to be periodic in the x and y directions (Figure 1). The three lowest z-layers remained fixed, and the five layers above these thermally controlled the system like a thermal bath. Their atoms satisfy a generalized Langevin equation in which the Debye temperature of FCC Co (385 K) is introduced as a parameter [11]. In essence, the force acting on an atom is written as the sum of a viscous force proportional to its speed and a random term that represents the effect of collisions with surrounding atoms.

The interaction between cobalt atoms took place with a second-moment tight binding potential [12]. Experimentally, this potential fits the lattice constant, cohesive energy, and elastic constants for Co. In this model, the cohesive energy E_i of an atom i is:

$$E_i={\displaystyle \sum _{j(\ne i)}\frac{1}{2}}V(r_{ij})-(\underset{j(\ne i)}{{\displaystyle \sum \Phi }}{)}^{1/2,}$$

(1)

where r_ij is the distance between atoms i and j. The first term is repulsive in nature and is of the modified Born–Mayer type. The second term is of the attractive type and models the many-body interaction that constitutes the energy band. At short distances, this potential merged smoothly into a more repulsive one, such as the ZBL [13], which is used to describe high-energy interactions. This potential is basically a Coulomb potential multiplied by a screening function. It also modeled the interactions between cluster atoms and Co. The number of implanted atoms from the cluster is small, and, therefore, its influence is also small. All the clusters launched had six atoms and an octahedral (without an atom in the center) shape. The shape of the cluster does not determine the results, as the impacts on the surface were random, so they always occurred in a different way [14]. The potential used in the clusters is of the Lennard–Jones type ($V\left(r_{ij}\right)=4\epsilon \left[\right(\sigma /r_{ij}{)}^m-{\left(\sigma /r_{ij}\right)}^n]$) with n = 6 and m = 12, with suitable choices for the interatomic distance, σ, and the depth, ε (see the values in [15,16] for He). In the case of He, which is a very light ion, the contribution of electronic stopping has been taken into account by means of another viscous force proportional to speed [17].

The surface is free of stress. A periodic FCC network at 5 K is heated to 300 K, scaling the temperature in steps. With each increase in temperature, the lattice relaxes in the canonical ensemble using an inertial factor Q = 10⁻³⁶ g cm² [18]. The final stress is removed by relaxing the system to zero pressure in the canonical isobaric ensemble with an associated inertia factor W = 10¹⁹ g [19]. The equations of motion of the particle system are derived from the Lagrangian of the so-called extended system, where the two previous adjustable parameters can appear depending on the ensemble. The last step consists of eliminating the periodic conditions in the z direction and relaxing the surface into a microcanonical ensemble coupled to the thermal bath.

The process of launching a cluster lasted 25 ps. This time interval is similar to that used in other works [20]. At first, the time step was 0.5 fs and 0.1 fs in the case of He. After 15 ps from launch, this time step was doubled, since the collisions were less energetic. At 20 ps, the system was scaled to 300 K. It was then relaxed for 5 ps so that the temperature conditions were the same on the next launch. The evolution of the system took place at all times in the microcanonical ensemble coupled to the thermal bath.

For simplicity, in each launch, the reference frame was translated in the y direction so that the cluster always hit the center of the surface. Of course, the model used does not depend on the y coordinate. The surface was bombarded with 167 clusters, 1002 atoms in total with 250 eV each. The x coordinate of the geometric center of the cluster initially points to a point randomly located between −10 and 0 Å. In this way, the bombardment occurred on a strip parallel to the Oy axis. The number of incident atoms per unit area (fluence) is approximately 10¹⁶ atoms·cm⁻². Experimentally, atom bombardment on Co at higher energies and slightly higher fluences produces surface ripples [21]. In our results, the fluence is not as high; however, the effect is amplified by cluster bombardment.

There are two main effects that alter the surface morphology. One of them is the formation of craters. Craters occur as a result of the extraction of atoms from the solid. In our simulations, each atom in the cluster extracts a number of solid atoms. This number Y, or sputter yield, can be obtained. The other is the formation of surface structures. Solid atoms move and form vacancies and surface accumulations as a result of induced atomic collisions with the cluster atoms. In general, this process of redistribution of atoms is measured by two displacements [8]: the horizontal displacement d_x and the vertical displacement d_z. These quantities measure the net distance traveled by the atoms of the solid in the two directions of initial motion of the cluster, x and z.

$$d_x={\displaystyle \sum _{i=1}^{N_d}(x_i-x_{i0})},\hspace{1em}{d}_z={\displaystyle \sum _{i=1}^{N_d}(z_i-z_{i0})}.$$

(2)

The previous sum extends to the number of displaced atoms N_d. In turn, (x_i0, y_i0, z_i0) and (x_i, y_i, z_i) are the initial and generic positions of any atom i of the substrate, respectively. If d_x is positive, there is mass transport in the positive x direction. If d_z is positive, there is upward mass transport opposite to the initial movement of the cluster atoms. This work analyzes the influence of the angle of incidence on the previous parameters for clusters formed by atoms of different atomic masses. This angle of incidence varied between 20° and 70°.

3. Results and Discussion

3.1. Atomic Description

Firstly, the surface morphology resulting from bombardment is analyzed for angles of incidence for which surface ripples typically form. Surface irregularities are accentuated if a solid is bombarded with clusters instead of atoms. Figure 2a,b show the surface after bombardment with Ne clusters for the fluence of 10¹⁶ atoms·cm⁻² and two angles of incidence: 70° and 50°, respectively. The structure induced after the bombardment and without considering diffusion effects is slot shaped. The lack of dependence on the y coordinate causes the craters produced after impacts to evolve towards this structure. The groove is shallower for the grazing angles (~70°) as the penetration of the cluster is less in that situation. The displaced atoms accumulate on both sides of the groove, forming adlayers and giving rise to two ridges. The right ridge accumulates many more atoms than the left one due to the initial linear momentum of the cluster in the x direction, i.e., the cluster atoms collide with the solid atoms and transfer velocities to them, which are directed towards the right ridge. Since the distance traveled by the solid atoms in the cascade is of the order of the size of the groove, these atoms are most likely deposited on the right ridge. Nanopatterns are surface ripples: valleys and ridges whose origins are excitations caused by irradiation. Initially, cluster bombardment erodes the surface locally, whereas surface redistribution acts in the same way, creating adlayers. However, only one of the processes usually dominates and maintains this structure in a stationary manner.

These irregularities are only stable for angles of incidence greater than a certain value, normally close to 50°. Diffusion effects are responsible for damping surface morphologies [2] since, for angles close to the normal, the width of the groove becomes small enough to be reabsorbed. Diffusion takes place in longer time intervals than those considered here, which means that molecular dynamics is limited to describing collisional processes. However, let us remember that the result of these simulations becomes a very good approximation to the final result under conditions of high influence and/or low surface temperature [7]. In fact, the theoretical models themselves have encountered problems when predicting the existence of the critical angle. Classical pattern formation theory did not predict the existence of any critical angle [2]. Certain authors [22] solved this problem by introducing a flux of cascade atoms directed toward the surface.

The most interesting aspect is how the surface structure is modified when bombardment with a heavier species, such as Xe, occurs. In the case of 50°, the groove becomes deeper and the right ridge higher. However, the widths of both surface structures are smaller, i.e., a heavier atom excites a surface nanostructure in the form of a higher and shorter wave pulse. In turn, in the case of 70°, the pulse amplitude is also accentuated: the groove becomes deeper and the ridge higher. However, the pulse also widens horizontally. The Xe atoms do not penetrate as much into the solid and displace more surface atoms, thus avoiding the creation of the interior cavity. In short, in the case of 50°, it seems to be observed that the solid atoms travel less distance on average with a heavier projectile atom. However, since the number of solid atoms moving is greater, both horizontal and vertical displacements (Equation (2)) increase.

The most curious case is that of He, a very light ion. It produces surface ripples associated with the vertical rise of atoms caused by defects, not by the formation of a groove. It manages to raise a right ridge of at least two layers, except for the case of 70°, for which only one layer is observed.

3.2. Temperature

Temperature plays a key role in the process, as, if kept low, diffusion processes can be considered negligible compared to collisional processes [7]. In a bombardment event with an Xe cluster and an incidence angle of 50°, the system temperature does not exceed 600 K, but in half a ps, it drops to 400 K. Therefore, diffusive processes do not have time to modify the surface structure of the solid appreciably. However, the collisional transfer of kinetic energy from the cluster to the substrate is different if the ion is light or heavy. To observe this circumstance, Figure 3 shows the local temperature of the atoms at a time instant of a bombardment event for a Ne cluster (a) and another Xe cluster (b). Specifically, cluster number 168 is launched at an angle of incidence of 50°. Only a strip which is parallel to the xz plane and centered around the point of impact is represented. The conservation of linear momentum in a collision with a more massive atom results in the exchange of a greater amount of linear momentum and, therefore, greater kinetic energy. The number of Co atoms that locally reach the melting temperature at that instant is of the order of 75 for Ne and 155 for Xe. It is verified that the quotient of both quantities is approximately proportional to the quotient of their square roots. This rule also holds for the rest of the atomic species. The zone of hot atoms is located on the surface and below the groove and runs up the wall of the right ridge. The maintenance of the temperature below the melting point avoids its influence on the processes studied, especially in the sputtering of light cluster atoms [23]. In the case of He, the number of atoms that reach the melting temperature (in the order of 25) is lower than that of Ne. However, the essential difference between both species is that the channeling effect can occur in He, which could increase said number in some cases, since the projectile He atoms would not be sputtered and would be stopped in the substrate.

3.3. Sputter Yield

As mentioned above, there are two collisional processes that induce the formation of surface waves: sputtering and redistribution. Sputtering allows the surface to be undermined, further highlights its morphology, and deepens the groove. Next, the sputter yield Y and the surface distortion are related. Figure 4 represents the angular dependence of sputtering for bombardment with clusters of different types of atoms. The proportionality of the sputter yield with the function ${\left(cos\theta \right)}^{-5/3}$ in the bombardment with atoms where θ is the angle of incidence is verified only for an incidence that is not too oblique and M₂/M₁ < 3, where M₂ is the mass of Co and M₁ is the mass of the projectile atom [24]. For He, the proportionality is with the function ${(cos\theta )}^{-1}$. Furthermore, there is another proportionality factor that depends on the stopping power. This parameter, in turn, is an exponential function of the mass ratio M₂/M₁. That is, the greater the mass of the projectile atom, the lower stopping power and, therefore, the lower sputter yield. This trend is also observed in Figure 4 for angles below the maximum for cluster bombardment. The sputtering curves have a more or less pronounced maximum, depending on the mass of the cluster atom. It is very abrupt in the curves of Xe and Kr and very smooth in those of Ne and Ar. In fact, this maximum depends essentially on the surface structure, as indicated by experiments [25]. Likewise, it is also difficult to make an approximate analytical prediction of the values at grazing incidence.

In the case of He, inelastic collisions cannot be neglected for any value of the initial bombardment energy, so the previous results would not apply to this case [26]. It is not even possible to use an amorphous solid model, such as the one that allows the deduction of the previous results [24], since channeling effects are important for non-grazing incidences. For example, at an angle of 20°, 29% of the He atoms pass through the solid. Both of these factors radically reduce sputtering; however, the latter is especially important.

Regarding the surface morphology formation, atom extraction is greater for heavier cluster atoms in the case of grazing incidence (Figure 4). These types of atoms are the ones that form the most prominent surface patterns. Therefore, it is clear that sputtering would play a more decisive role only for grazing angles (~70°) and even for close angles (~60°), but not in all the other cases. In the case of heavy atoms, the cascade energy is deposited deeper for non-grazing incidence, making it difficult for atoms to leave the solid and, therefore, not contributing to the formation of patterns.

3.4. Atomic Redistribution

The formation of surface ripples in the collisional phase may be due to atomic redistribution. Horizontal and vertical displacements, d_x and d_z, respectively, are measures of the redistribution effect and are plotted in Figure 5a,b, respectively, as a function of the angle of incidence. The vertical displacement may explain the larger pulse amplitude in Figure 2 except for the grazing angles and light ions. In fact, Figure 5a shows how the vertical displacements for intermediate angles are ordered with the mass of the atom, except for light atoms, where the differences are quite small. The normal incidence and close angles do not interest us because they are situations in which the flat surface is experimentally stable [7]. Heavy atoms displace more atoms toward the surface at intermediate angles to the point of creating a well-defined maximum at 50°. In turn, the horizontal displacement curve has a fairly defined maximum at 50° for all atoms except Xe. For this atomic species, the maximum moves towards 60°. Some authors [10] multiply the displacement by the volume associated with a deposited atom and add it for all the displaced atoms. These authors consider that the maximum in this quantity allows for obtaining the critical angle, above which the formation of surface ripples occurs. In our case, we have verified that the horizontal displacement curves are completely similar to the displacement-volume curves calculated by these authors. That is, the volume deposited does not confer any special characteristics to the displacement curves, especially with regard to the position of the maximum. Accordingly, heavy atoms, such as Xe, would have a higher critical angle.

Horizontal displacements justify the enhancement of surface morphology for intermediate angles. That is, heavier atoms would be associated with greater horizontal displacements for these angles (Figure 5b), and, in turn, the surface patterns would be enhanced. In the case of He, the horizontal displacement becomes very small. Therefore, the formation of ridges is due to the rise of atoms from the solid, except for grazing angles, since it is not observed in that case.

3.5. Distribution of Volumes

The specific weight of sputtering and redistribution and the mass effect can be studied by analyzing the volume distribution during bombardment. In the following calculations, the volume occupied by the implanted cluster atoms is neglected because their number is small compared to the rest of the atoms of the solid involved in the process. To do this, a series of quantities related to the volumes of atoms during the bombardment process are defined. If N_sp is the number of sputtered atoms, the volume occupied by the extracted atoms will then be V_sp = N_sp·V_at, where V_at is the atomic volume of a Co atom in the FCC lattice. If the number of atoms placed above the surface or adatoms is N_ad, the volume of adatoms is then V_ad = N_ad·V_at. The sum of these two volumes would be the volume of the groove V_gr if the atoms of the rest of the solid did not intervene in the process. However, the atoms of the solid can fill part of the volume of the groove. In short, any atom that occupies a volume in the groove can end up being extracted, forming part of an additional layer, or displaced internally. In this way, it is verified: $V_{gr}=V_{sp}+V_{ad}+V_{rd},$ where V_gr is the volume of the groove (the volume located below the surface) and V_rd is the redistributed volume, which turns out to be negative since the solid fills the groove.

In the reference [9], another different groove volume is introduced as the sum of two volumes.

$$V_{groove}=V_{no-redist}+V_{redist}=V_{sp}-V_{ad}+V_{redist},$$

(3)

where V_redist is the volume associated with the redistribution processes, and V_no-redist is the volume associated with the extraction processes. The latter volume is related to both the volume associated with the sputtering and with the adatoms. The following redistribution factor would measure the weight of redistribution in the process:

$$f_{rd}=\frac{V_{redist}}{V_{groove}}=\frac{V_{rd}+V_{ad}}{V_{gr}-V_{ad}}.$$

(4)

In Figure 6, this factor is represented for bombardment with different atoms and angles of incidence. In general, the effect of redistribution decreases with the angle of incidence. Furthermore, for any angle of incidence, the weight of redistribution is greater for heavier atoms and smaller for lighter atoms. This factor becomes practically zero for the grazing angles. In this sense, it coincides with the results obtained on metallic substrates in reference [9], which highlighted the importance of extraction processes in the surface ripple formation process. In the case of light ions, this fact also occurs for 60°. Therefore, in these cases, the surface ripple formation process is also dominated by sputtering. The exact model establishes a value of f_rd = 0.5, below which the extraction effects would begin to predominate. However, in view of all the previous results (i.e., sputter yield and displacement), this value would be somewhat lower (around 0.2).

For He, the internal redistribution of the atoms would lead to the formation of the added layers so that both quantities, V_ad and V_rd (<0), would approximately compensate $(V_{redis}\sim 0)$. However, the same does not occur with the difference in volumes of extracted material (V_sp) and additional layers (V_ad), which would be negative (V_no-redist < 0). In any case, it is verified that V_groove < 0 and the main contribution to this volume is due to the non-redistributed volume of negative origin, that is, induced by the formation of the added layers. Therefore, it should not be considered as an extraction effect.

In summary, this graph confirms that the formation of nanopatterns on metallic substrates is explained as a function of the angle of incidence. Thus, for intermediate angles, the underlying effect is atomic redistribution, and for grazing angles, it is sputtering. For any angle of incidence, the weight of redistribution increases with mass. In fact, for light atoms, the sputtering could explain the formation of surface ripples for angles close to grazing angles (60°). In the case of He, channeling occurs. However, superficial adlayers are formed for non-grazing incidences induced by internal displacements fundamentally associated with the formation of defects.

4. Conclusions

In this work, a Co(110) metal surface is bombarded with clusters of small dimensions (six atoms) and different angles of incidence. This study focuses on analyzing the effect of the mass of the cluster atoms on the process of surface ripple formation. For this, five types of atoms were used: He, Ne, Ar, Kr, and Xe. In all cases, the bombardment energy was 0.25 eV/atom, and the same fluence was used. Furthermore, diffusive effects have been ruled out, which would require considerably longer simulation times, since the surface temperature was not excessively high.

The bombardment is concentrated on a surface in the form of a longitudinal strip to accelerate surface processes. Bombardment with heavy species accentuates the effects of surface ripple formation. For this type of species, it is verified that in collisional processes, the transfer of energy to the solid is greater; therefore, the surface energy deposited is also greater. However, it is also true that the energy is deposited deeper for intermediate angles, so the sputter yield is lower. Only for grazing angles does the sputter yield for heavy atoms become greater than that for light species because the energy deposited superficially is greater. Therefore, sputtering can be the cause of surface pattern formation only for these angles.

Displacements generally increase with the mass of the cluster species. The horizontal displacement has a clearly defined maximum at 50°, which shifts towards 60° for heavy atoms, such as Xe. This fact points to redistribution as a predominant effect for these angles. It also means that, according to certain experimental results, the critical angle is greater for heavy atoms. This displacement is very small for light ions and grazing incidence, a fact that would rule out the redistribution effect as a cause of the appearance of surface ripples. For its part, the vertical displacement only has a maximum for heavy atoms around 50°, while for light ions, it decreases monotonically.

Finally, the redistribution factor confirms the importance of sputtering in the ripple formation process for the grazing angles, and close to the grazing angles if the projectile atoms are light, and of redistribution for all the other cases. The weight of redistribution decreases linearly in an approximate fashion as the angle of incidence increases. The redistribution effect increases with the mass of the projectile. In the case of He, the vertical displacements due to the formation of defects would justify the formation of small ripples for intermediate angles. In fact, sputter yields are very small due to channeling phenomena. For grazing angles, no surface patterns are observed.