# Formation of magnetic nanocolumns during vapor phase deposition of a metal-polymer nanocomposite: experiments and kinetic Monte Carlo simulations

###### Abstract

Metal-polymer nanocomposites have been investigated extensively during the last years due to their interesting functional applications. They are often produced by vapor phase deposition which generally leads to the self-organized formation of spherical metallic nanoparticles in the organic matrix, while nanocolumns are only obtained under very specific conditions. ExperimentsGrev+06 () have shown that co-evaporation of the metallic and organic components in a simple single-step process can give rise to the formation of ultrahigh-density Fe-Ni-Co nanocolumnar structures embedded in a fluoropolymer matrix. Here we present a kinetic Monte Carlo approach which is based on an new model involving the depression of the melting point on the nanoscale and a critical nanoparticle size required for solidification. In addition we present new experimental results down to a deposition temperature of and also report the magnetic properties. The simulations provide a detailed understanding of the transition from spherical cluster growth to formation of elongated structures and are in quantitative agreement with the experiments.

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^{†}thanks: deceased

## I Introduction

Nanocomposites containing metallic nanoparticles in a dielectric polymer matrix have very interesting functional applications ranging from plasmonics caseri_nanocomposites_2000 (); elbahri_omnidirectional_2011 () and high-frequency magnetic materialsgreve_nanostructured_2006 () to antibacterial coatingzaporojtchenko_physico-chemical_2006 (); hahn_therapeutic_2010 () (for recent reviews seefaupel_metal-polymer_2010 (); carotenuto_metal-polymer_2005 (); hanemann_polymer-nanoparticle_2010 ()). Such metal-polymer nanocomposites are often produced by vapor-phase co-deposition of the metallic and organic componentsheilmann_xps_1997 (); biederman_rf_2000 (); schurmann_controlled_2005 (), since this allows tailoring of the nanoparticle filling factor and other parameters, and even allows incorporation of alloy nanoparticles with well-defined compositionbeyene_vapor_2012 (). During co-deposition, metallic nanoparticles form by self-organization due to the much higher cohesive energy of the metal compared to the organic component and the low metal organic interaction energy (except for very reactive metals). One can assume that the self-organization mechanism during the deposition of polymer-based nanocomposites is analogous to metal cluster formation on a polymer surfaceFaupel_conf_1999 (). When energetic metal atoms impinge on the polymer surface they undergo various processes including random walk on the surface, diffusion into the bulk, and desorptionZapo_conf_2000 (); zaporojtchenko_metal_polymer_2000 (). Within their diffusion distance, metal atoms may encounter each other or may be captured by a surface defect. This leads to aggregation and formation of stable metal clusters which are embedded into in the polymer matrix upon growth of the nanocomposite film. The metal filling factor depends on the condensation coefficient of metal atoms on a given polymer surfacethran_condensation_1999 () as well as on the metal-polymer deposition ratiotakele_plasmonic_2006 (). In these terms, the volume fractions of metallic nanoparticles in the composite films can be easily controlled through the ratio of the deposition rates of metal and polymer components.

Generally, the nanoparticles obtained upon vapor phase co-deposition have spherical shape (as long as the filling factor is small enough to prevent nanoparticle coalescence). This is expected form the minimization of the surface energy and the above mentioned formation process. However, under specific conditions, involving a very high deposition rate ratio of the metallic over the organic components and a very low metal condensation coefficient, formation of elongated Fe-Ni-CoGrev+06 () and Aubiswas_2006 () nanocolumns has been reported in a Teflon AF matrix. While the formation process of the spherical nanoparticles is well understood and has also been modeled by kinetic Monte Carlo simulationssilverman_1991 (); thran_1997 (); faupel_diffusion_1998 (); rosenthal_diffusion_2011 (); bonitz_towards_2012 () only a crude qualitative model was suggested for nanocolumn formationGrev+06 (). According to this model, a very low condensation coefficient is crucial. Thus the metal atoms arriving on the growing nanocomposite film from the gas phase will stick whenever they encounter a growing metallic nanoparticle but will have a very large surface diffusivity and a high thermal desorption probability if they impinge on the organic matrix, due to the very low metal-organic interaction energy. On the organic surface, there is a competition between thermal desorption and diffusion to and trapping at a nanoparticle. In these terms, it was proposed that at a critical metal vs organic deposition rate ratio, metal nanoparticles can grow faster perpendicular to the surface, due to direct impingement of newly arriving metal atoms from the gas phase, then they are embedded by the growing organic matrix. However, kinetic Monte Carlo simulations based on this notion failed to reproduce the experimental results even qualitatively.

Here we report new experimental results on the formation of Fe-Ni-Co nanocolumns in a Teflon AF matrix via co-evaporation, which extend the temperature range of the previous experiments down to and include the magnetic characterization of the highly anisotropic properties. In addition, we propose a new model for nanocolumn formation and we present new kinetic Monte Carlo simulations which are able to explain the experimental results even quantitatively. A key new aspect of the present model is solidification of the nanoparticles at a critical size, which drastically slows down the kinetics for the establishment of the spherical equilibrium shape.

## Ii Experiments

The nancomposite films of thicknesses 100 nm to 200 nm were produced by co-evaporation of the organic and metallic components on Si
wafers using a homemade high vacuum deposition chamberbiswas_2003 (); Grev+06 (). Teflon^{®}AF (granulates, Dupont) and Fe-Ni-Co (99.99% pure
1 nm diameter wires, Good Fellow Industries, U.K.) were used as starting materials. For preparation of samples for transmission electron
microscopy (TEM) and magnetic characterization, polymer foils (Upilex-S^{®}) were used as substrates. Polymers
generally do not lend themselves for evaporation because they decompose upon heating, however, for some polymers such as Teflon AF, the monomer
structure is preserved upon thermal breaking of the covalent bonds along the backbone chain of the polymer, and a Teflon AF film can deposited
which differs from the starting material mainly by its much lower molecular weight. The molecular weight reduction is not critical for functional
applications. Deposition rates of nm/min and nm/min were typically used for TeflonAF and Fe-Ni-Co, respectively.
The metallic volume filling factor of the nanocomposites was determined by energy dispersive X-ray spectroscopy (EDX) as described in
Refschurmann_controlled_2005 (). The experimental error is 20%. The magnetic measurements were carried out with a LakeShore 7300
vibrating sample magnetometer (VSM). For further experimental details seeGrev+06 (); biswas_2003 (); greve_diss ().
Fig. 1 shows the metal volume filling factor f as function of the deposition rate ration of the
metallic vs the polymer components for deposition at different substrate temperatures. At the highest temperatures, one notes a sharp increase
in the filling factor above a critical value. The increase shifts to lower values and is more smeared out for lower substrate
temperatures, which is most pronounced at . At this temperature the data were fitted to the function

(1) |

Here the fitting parameter is the metal condensation coefficient. Equation 1 follows immediately by expressing f in terms of the effective deposition rates which are multiplied by the condensation coefficients, taking into account metal desorption, and assuming complete condensation for the organic component.

The fit yields in good agreement with the expectation that the condensation coefficient approaches unity at low temperatureszaporojtchenko_determination_2000 (). It has to be pointed out, however, that the condensation coefficient depends on the metal coverage at the surface of the growing composite and hence on because metal atoms stick with a probability of unity if they directly impinge on a metal nanoparticle or if they reach a metal nanoparticle via surface diffusion. Therefore, Eq. 1 is not applicable at higher temperatures, where the condensation coefficient on Teflon AF is expected to be very lowzaporojtchenko_determination_2000 (); thran_condensation_1999 (). Even the value of obtained at probably overestimates the condensation coefficient for the pure polymer.

The microstructure was investigated by means of transmission electron microscopy. Representative TEM micrographs are displayed in Figs. 2 and 3 (see Ref.greve_diss () for further details). Fig. 2 shows cross-sectional images of a nanocomposite prepared at . (As described in Ref.greve_diss (), the nanocomposite film was grown on top of an evaporated Teflon AF film containing spherical Ag nanoparticles. In order to exclude any influence of the Ag particles on the growth of the magnetic nanocolumns, a Teflon AF separation layer of 20 nm was evaporated on top of the Ag-Teflon AF nanocomposite film before the of the Fe-Ni-Co-Teflon AF nanocomposite was deposited.)

It is obvious from Fig. 2 that the Fe-Ni-Co nanoparticles have grown as nanocolumns with a diameter of about nm and a length extending through the whole film, resulting in an aspect ratio well above 10. The deposition was performed under conditions of normal incidence, and the orientation of the nanocolumns is perpendicular to the substrate. Experiments were also carried out with normal incidence of the organic component and with an incident angle of with respect to the substrate for the metallic component. Under these conditions, the resulting nanocolumns were inclined with an angle of with respect to the substrate, indicating that the growth direction can be controlled via the angle of incidence. Fig. 3 shows a top-view TEM micrograph of a nanocomposite film deposited at . The film has a thickness of 30 nm to ensure electron transparency. Evidence for the nanocolumnar shape of the metallic particles is provided from the fact that no overlap of particles is seen. For spherical particles of about 5 nm diameter, the electron beam would have a high probability to penetrate through more than one particle, giving the impression of coalesced particles as always seen in top-view images under the present conditions for spherical particlesfaupel_metal-polymer_2010 (); takele_tuning_2008 ().

The highly isotropic nanocolumnar structure is also reflected in highly anisotropic magnetic properties. Hysteresis curves for a sample deposited at are shown in Fig. 4. One notes a completely different behavior for measurements parallel and perpendicular to the film plane. The very soft magnetic behavior parallel to the film is a clear signature of magnetization reversal by domain wall movement, whereas saturation in the perpendicular direction requires very high fields indicating that magnetization reversal is only possible without domain wall movementcullity_introduction_2008 (). Apparently, the magnetization of the nanocolumns is different from the case of a long isolated column (Fig. 5 (a)) where shape anisotropy always leads to an orientation of the easy axis parallel the column, and reveals the presence of domain walls perpendicular to the long column axis (Fig. 5 (b)).

The observed magnetization behavior can be explained in terms of a competition of demagnetizing fields and dipoleâdipole fields. It has been shown, e.g., for arrays of much larger Co nanowires electrodeposited in anodic alumina, that the magnetization can be tuned parallel or perpendicular to the nanowires by changing their lengthstrijkers_structure_1999 (). In the present case, the dipole-dipole interaction dominates the behavior due to the small nanocolumn separation of only a few nanometers.

## Iii Kinetic Monte Carlo Simulations

The Kinetic Monte Carlo simulations described below are based on previous simulations of diffusion and growth of metal clusters in a polymer substratesilverman_1991 (); thran_1997 (); faupel_diffusion_1998 (); rosenthal_diffusion_2011 (); bonitz_towards_2012 (). The main idea behind these simulations is to condense the complex processes of cluster growth and nanocolumn formation during polymer metallization into a simplified selfconsistent continous-space simulation scheme. To get a practical simulation algorithm we applied the following assumptions: The atomic and chemical structure of the polymer substrate is essentially neglected. Instead the influence of the substrate is reflected in averaged cluster mobilities (expressed in rate constants) and diffusion jump lengths of clusters. The polymer is assumed to be a continuum with periodic boundary conditions in the x- and y-direction (parallel to the surface).

Metal atoms and clusters are modeled within the framework of the liquid drop model. They are considered as non-decomposing spheres with constant
density regardless of size, where a single atom is assumed to have a radius nm. Atoms are deposited randomly on the surface and
start immediately to perform isotropically distributed surface diffusion jumps with a diffusion frequency and an averaged diffusion
jump length which is chosen to be , which is approximately the diameter of a polycarbonate chain.
Clusters^{1}^{1}1for simplicity atoms are also referred to as clusters from now on. obey two different growth mechanism: the first one for liquid clusters is the
fusion of two clusters to a larger one according to the reaction scheme , where the subscript labels the number of
atoms the cluster consists of. Merging of clusters occures when the distance of two clusters falls below half of the jump length (0.3 nm)
and is assumed to take place without any finite equilibration time, i.e. the spherical shape of the new cluster is reached immediately after
encountering of the two constituting clusters. The second growth mechanism clusters undergo leads to the formation of elongated nanocolumns growing
into the direction of the surface. It is initialized when the radius of one of two merging clusters is above the melting radius ,i.e.
when the number of atoms exceeds a critical value . It occures when a monomer impinges directly into the interaction region of a preexisting
cluster (which is a circle with radius of 0.3 nm) which is partially buried by the surface, or a cluster merges with a partially buried cluster
after surface diffusion. We assume that the new cluster does not reach a spherical shape after equilibration. Instead the incoming cluster coalesces
with the part of the buried cluster which projects beyond the surface. These growth mechanisms are subject to two boundary conditions: The first one
is volume conservation. Furthermore the points and in Fig. 6 (which stand for the circular intersection line of
the cluster with the surface) are assumed to stay constant. Hence the resulting initial column consists of two spherical caps separated by the
surface dividing the column into a buried part and a part projecting above the surface. We note that the intersection line of the clusters with the
surface moves upwards during the deposition process due to the arrival of new organic molecules. These two mechanisms of nanocolumn growth are depicted in
Fig. 6. These mechanisms can repeat the same way with a free cluster and a pre-existing column where only the upper part of
the column is involved into the growth process.

To incorporate the effect of very low condensation coefficients , which is known for metals on Teflonthran_condensation_1999 (); zaporojtchenko_determination_2000 (), monomers are allowed to evaporate from the surface with a certain rate constant which is given in units of the surface diffusion rate and is adjusted to the values of known from the experiments.

To model the deposition process of metal, atoms are randomly deposited on the surface of the substrate with a constant deposition rate . A metal thickness of the diameter of a single atom corresponds to the amount of one monolayer (ML) of atoms which is defined to have a number density of 10 atoms per . Simultaneously with the deposition of metal atoms a constant shift of the surface in -direction with a certain rate is applied to model the codeposition processbonitz_towards_2012 (). Both rates are given in units of nm/s.

Very little is known from experiments about the size-dependence of diffusion coefficients of metal clusters on polymer surfaces. We use a power law depending on the cluster size , , , which is known from Molecular Dynamics simulations of cluster diffusion on crystalline surfacesJen99 ().

In order to obtain the best accordance with the experiments we decided to treat the diffusion constant and the melting radius as free parameters.

## Iv Simulation results

To check the applicability of our simulation model we performed simulations over a broad range of parameters. For all results presented below, the composites have a thickness of 100 nm and a surface cross section of . The metal deposition rate was kept to a constant value of 1.5 nm/min. The ratio of deposition rates was regulated by tuning the deposition rate of the polymer substrate to the desired value. The melting radius of the clusters was treated as a free parameter. In order to obtain good statistics, the results presented below are averaged over 20 runs of our code with constant parameter set. The deviations were usually less than one percent so that they are not included into the figures. The focus of our investigations will lie on the influence of the atomic evaporation (desorption from the surface) and the surface diffusion rate, which depends on the metal-polymer interaction and hence on the condensation (or sticking) coefficient . A low value is accompanied with a large diffusion length.

The main effect which was observed during experiments is a dramatic increase of the volume filling factor with the ratio . In contrast to the experiments, the simulations provide additional data such as the size distribution of clusters and the geometrical measurements and the exact number of the nanocolumns, which allows for a more complete understanding of the self-organized process of nanocolumn growth.

In Fig. 7 simulation results of different quantities as a function of the ratio of deposition rates are shown for a system with a surface area of and a final thickness (after the termination of both deposition processes) of 100 nm.

The simulations clearly show a strong increase of the metal filling factor for values of which is related to the formation of nanocolumns (cf. Fig. 7 a) and c)). The upper panel of Fig. 7 which shows the number of nanocolumns indicates that there is a sharp transition from the pure spherical growth regime to a regime of column growth that coincides with the strong increase of the filling factor. Within our model the explanation of this phenomenon is as follows: When atoms impinge on the surface they may undergo various competing processes like surface diffusion, reemission and nucleation after ecountering each other. One crucial point for the observed transition is the low condensation coefficient of metal on Teflon, which is caused by the weak chemical interaction of the two components. Metal atoms (clusters) have to encounter each other and form nuclei that can be stabilized in the polymer matrix and initiate the column growth. The simultaneous deposition of the polymer matrix works against the growth of nuclei and isolates the clusters from each other. For low values of the reemission of atoms and the growth of the polymer matrix are the dominant processes and prevent the growth of clusters that are big enough to initiate the column growth.

When exceeds a critical value the deposition of metal atoms plays the dominant role and the reemission and isolation of clusters by the growing matrix is compensated by agglomeration of atoms with pre-existing clusters. As a consequence the growth of clusters is strongly accelerated and some clusters reach the critical cluster size to initiate column growth.

### iv.1 Effect of atomic desorption

In Fig. 7 the effect of the desorption with an evaporation rate is shown for different column geometries and the metallic filling factor. The whole range of investigated values of can be divided into four regions: The first region is characterized by pure spherical growth and a relatively linear increase of the metal filling factor, see Fig. 7 c). In the second region the column growth is initiated, see Fig. 7 a), and with an increasing desorption rate and the concomitant increase in the surface diffusivity, the filling factor starts to increase nonlinearly and the transition to the columnar growth regime is shifted to larger values of (cf. Fig. 7 a)). This effect can be easily understood in terms of the underlying column growth model: As explained in sec. III, clusters have to grow beyond the melting size to act as initial nuclei for column growth. When the desorption rate of atoms from the surface increases the growth of clusters is slowed down and, consequently, the probability of cluster growth can only be enhanced by slowing down the embedding of clusters into the matrix, respectively by increasing the mobility of clusters which is both the effect of increasing (note that is tuned via changing the polymer deposition rate ).

A further effect of increasing the atomic desorption is a reduction in the total number of columns which is a direct consequence of the enhanced probability of atomic reemission. This effect can also be seen in Fig. 8 which shows a top view on the composite after termination of deposition. Here one can also see how columns become thicker with higher desorption rates.

The second stage is characterized by a relatively small rise of the number of columns with increasing . During this stage the columns are steadily growing thicker and hold an aspect ratio in a relatively small range (see Fig. 7 b)) implicating that the mean column length is also increasing with a comparable rate. Here one can see that the diameter of the columns is larger the higher the desorption rate is.

The third stage can be identified by a very abrupt increase of the total number of columns. from Fig. 7 c) one can see that the accelerated growth of columns is accompanied by a steep rise of the filling factor, which is more pronounced the higher the desorption rate is. The simulations have shown that this stage comes along with a considerably larger number of columns extending over the whole height of the final composite resulting in a higher metal coverage of the surface. The mean column-diameter is decreasing during this stage due to the increase in the number of nuclei for column growth causing a clearly higher aspect ratio as the mean column length has already reached its final value. The simulations have shown that the average height of the nanocolumns is some nm more than the height of the surface of the substrate, see Fig. 10 what means that the majority of the columns now projects over the surface. Consequently the incoming atoms are distributed to a larger number of columns as in the previous stage.

During the fourth growth stage, whose beginning is located between (see the blue curve in Fig. 7 c)) and (see the brown curve in Fig. 7 c)), the number of columns and their averaged length stays constant. Only the filling factor and the diameter, respectively the aspact ratio increase due to the higher amount of metal atoms impinging on the surface.

### iv.2 Influence of surface diffusion

Fig. 9 shows the same quantities as Fig. 7 but for different surface diffusion coefficients and constant desorption rate . The main effect resulting from increasing the surface diffusion coefficient is a shift of the transition from spherical growth to columnar growth to smaller values of (see Fig. 9 a) and c)). The reason for this shift is obviously the accelerated growth of clusters caused by their higher mobility: Whilst for slow surface diffusion the cluster growth by direct impingement of atoms on preexisting clusters plays an important role, for fast surface diffusion the probability of clusters encountering each other during surface diffusion is considerably enhanced. As a consequence clusters reach the critical nucleus size to induce the columnar growth already for smaller values of . Interestingly, the filling factors for higher values of () lie very close together. Our simulations have not shown a tendency of the surface diffusion coefficient to influence the filling factor.

The diffusion constant has also no major effect on the other quantities after the transition to columnar growth. Fig. 9 a)
shows that for all simulations the number of columns lies between 200 and 300 what corresponds to a surface density of columns
between nm^{−2} nm^{−2}
where the density is higher the lower is the surface diffusion coefficient. As one can see in Fig. 9 d) the thickness of the
columns follows the opposite trend: A higher surface diffusivity leads to thicker columns, which is not surprisingly as clusters grow faster.
The aspect ratio shows a different behavior, cf. Fig. 9 b). This implies that, in the simulated range of , the
averaged length of the nanoclumns stays nearly constant.

Fig. 10 shows the distribution of column lengths after termination of both deposition processes for different surface diffusion coefficients. All columns project some nm beyond the surface (which lies at 100 nm) and that the distribution of lengths is very narrow with a maximum at about 108 nm for all values of .

## V Conclusion

In conclusion, we presented new experimental data on the formation of magnetic Fe-Co-Ni nanocolums in a Teflon AF matrix upon co-evaporation of the metallic and organic components, extending the temperature range of deposition to low temperatures and reporting also magnetic properties. The nanocolums contain domain walls perpendicular to the column axis which is also the easy axis of magnetization. The formation of the nanocolums was modeled in terms of Kinetic Monte Carlo simulations which provide an even quantitative agreement with the key experimental observations such as the behavior of filling factor and column diameter. Unlike earlier approaches, the present simulations are able to explain the transition from growth of spherical clusters to nanocolumn formation. It was shown that, in addition to a low metal condensation coefficient on the organic surface and a high deposition rate ratio of metallic vs organic components, the solidification of the spherical nanoparticles at a critical radius has to be taken into account.

With respect to applications, the results show how to tailor the nanocolumnar structure in the matrix and which parameter ranges are accessible. The implications are not restricted to organic matrices but should hold for designing functional metal-dielectric nanocomposites in general, particularly with respect to magnetic and plasmonic applications. The magnetization of the nanocolumns can be tuned, for instance, via their length and separation. Moreover, an electrical field can be applied during deposition to orient the easy axis of magnetization. In particular, composites containing oriented nanoparticles with a small aspect ratio are very interesting for high-frequency magnetic materials up to the GHz rangeramprasad_magnetic_2004 ().

###### Acknowledgements.

This work was supported by the German Research Foundation (DFG) within the framework of the Collaborative Research Center SFB Transregio 24, projects A5, A7 and B13. The authors would like to thank Stefan Rehders for setting up the evaporation chamber and his continuous technical support. The magnetization measurements were performed by Michael Frommberger in the group of Eckhard Quandt.## References

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