Growth of nanocone arrays on a metal catalyst: The effect of carbon flux ionization I. Levchenko, K. Ostrikov, J. Khachan, and S. V. Vladimirov

Citation: Physics of Plasmas (1994-present) 15, 103501 (2008); doi: 10.1063/1.2988781 View online: http://dx.doi.org/10.1063/1.2988781 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/15/10?ver=pdfcov Published by the AIP Publishing

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This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.181.251.131 On: Tue, 15 Jul 2014 04:34:25 PHYSICS OF PLASMAS 15, 103501 ͑2008͒

Growth of carbon nanocone arrays on a metal catalyst: The effect of carbon flux ionization ͒ I. Levchenko,1 K. Ostrikov,2,1,a J. Khachan,1 and S. V. Vladimirov1 1Plasma Nanoscience, School of Physics, The University of Sydney, Sydney NSW 2006, Australia 2CSIRO Materials Science and Engineering, P.O. Box 218, Lindfield NSW 2070, Australia ͑Received 8 August 2008; accepted 3 September 2008; published online 2 October 2008͒ The growth of carbon nanocone arrays on metal catalyst particles by deposition from a low-temperature plasma is studied by multiscale Monte Carlo/surface diffusion numerical simulation. It is demonstrated that the variation in the degree of ionization of the carbon flux provides an effective control of the growth kinetics of the carbon nanocones, and leads to the formation of more uniform arrays of nanostructures. In the case of zero degree of ionization ͑neutral gas process͒, a width of the distribution of nanocone heights reaches 360 nm with the nanocone mean height of 150 nm. When the carbon flux of 75% ionization is used, the width of the distribution of nanocone heights decreases to 100 nm, i.e., by a factor of 3.6. A higher degree of ionization leads to a better uniformity of the metal catalyst saturation and the nanocone growth, thus contributing to the formation of more height-uniform arrays of carbon nanostructures. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2988781͔

I. INTRODUCTION the most perspective techniques.14–17 It has been convinc- ingly demonstrated that the use of low-temperature plasma Arrays of vertically aligned high aspect ratio nanostruc- environments results in much more uniform and simulta- tures, such as nanorods, nanocones, and nanotubes1–3 dem- neous saturation of the metal catalyst used for onstrate outstanding characteristics that make them attractive 18 4–7 catalyzing the nanostructure growth, thus enabling a simul- for various applications, such as nanoelectronic devices, electron emitters,8 and gas sensors.9,10 In the fabrication of taneous nucleation and development of the carbon nanostruc- such arrays, the ultimate goal is to achieve the highest level tures at early growth stages. In this paper we analyze, using of the ordering and size uniformity of the individual nano- a complex numerical Monte Carlo/surface diffusion tech- structures within the entire pattern.11 In most cases, the ar- nique, the growth of nanocone arrays on the surface in neu- rays of vertically aligned nanostructures should be made of tral and plasma environments, and pay special attention to highly conductive materials and be placed on a conductive the stages 2 and 3, i.e., the growth of the nanocones on the substrate to sustain a high electron field emission current saturated metal nanoparticles. It is shown that the use of the from the sharp tips with a curvature radius of several low-temperature plasma provides a narrower distribution of nanometers.12,13 From this point of view, carbon nanostruc- the nanocone heights, i.e., results in the growth of a more tures on doped silicon substrates are often considered as one height-uniform array of the carbon nanocones. Besides, we of the most promising choices of a suitable material system. demonstrate that nanocone arrays with much smaller maxi- The process of the carbon nanostructure array growth on mum nanocone heights can be synthesized in a low- the surface may be conditionally divided into three main temperature plasma environment. Moreover, the use of stages. During the first stage ͑catalyst pattern formation highly ionized carbon fluxes provides the formation of the which is achieved by metal deposition on the substrate sur- nanocone arrays of higher quality, in terms of their size uni- face͒, carbon material is not supplied to the surface. During formity which determines the electron emitting and other the second and the third stages, i.e., the metal catalyst nano- size-dependent characteristics. Therefore, the variation of the particle saturation with carbon and the carbon nanostructure plasma parameters ͑specifically, the degree of ionization of growth, carbon species are supplied to the substrate surface the carbon flux͒ turns out to be a convenient tool for control- from the process environment. During these stages, carbon ling the nanostructure array characteristics. precursors are dissolved in the metal nanoparticles since car- In this article, we report on a complex numerical simu- bon ions and atoms are usually delivered to the metal nano- lation of the nanoarray growth by modeling the three main particles directly from the process environment, as well as physical phenomena that play a key role in the nanostructure from the substrate surface by adatom diffusion. The nano- formation: diffusion of adsorbed carbon atoms on the sub- structure nucleation process is triggered as soon as the cata- strate surface, saturation of metal catalyst with carbon, and lyst nanoparticles get saturated with carbon. sputtering of the growing nanocones with carbon ions im- In the synthesis of dense arrays of vertically aligned car- pinging from the plasma. The first two important effects, bon nanostructures, plasma based methods, such as plasma- namely the surface diffusion and the catalyst saturation, have enhanced chemical vapor deposition ͑PECVD͒ are among been studied in detail in our previous works which were mainly devoted to the initial stages of the nanostructure ͒ a Electronic mail: [email protected]. growth. At the further stages of growth, when the nanostruc-

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ture heights become large enough to play a role in the redis- tribution of the electric field near the surface, the third key phenomenon, namely, the sputtering of the nanostructures should be taken into account. In this article, this important effect is systematically taken into account. The article is structured as follows: In Sec. II, we present the details of the numerical model and simulation routines. In Sec. III, the main results of our numerical simulations are summarized. Section IV is devoted to the discussion and interpretation of the results of our numerical experiments. The main results of this work are summarized in Sec. V.

II. MODEL In this work, we have adopted the following scenario for the formation and growth of the nanocone array. First of all, we have assumed that the nucleation of the carbon nano- FIG. 1. ͑Color online͒ Scheme of the main plasma and surface processes structures is possible only on the carbon-saturated metal taken into account in the simulation of nanocone array formation. catalyst nanoparticles, and the nanostructures cannot nucle- ate and grow on the “free” surface of the substrate, as well as on nonsaturated nanoparticles. Thus, the growth of carbon strate with the metal ͑specifically, nickel͒ catalyst particles nanocones proceeds through several stages: formation of an and the growing nanocones, immersed in a low-temperature 21,22 initial pattern of ultrasmall metal catalyst nanoparticles; then, plasma environment. A low-temperature plasma of suit- the saturation of this pattern with carbon material; and fi- able characteristics can be produced by various methods, 23 24 nally, the growth of nanocones on the saturated nanopar- e.g., by inductive and capacitive radio frequency 16 25 26,27 ticles. In the model, we do not consider the formation of the discharges, cathodic and anodic vacuum arcs, and mi- 28 metal nanoparticles ͑which involves the different physical crowave discharges. mechanisms and hence different modes, like those described The effect of carbon sputtering on the growth and shap- in Ref. 19͒ and mainly concentrate on the saturation and ing of carbon nanocones was quantified in this work by tak- growth stages that are characterized by the supply of carbon ing into account the dependence of the sputtering yield on precursors to the surface ͑in contrast to the metal nanopar- the energy and angles of incidence of the impinging species. ticle formation stage when the carbon is not supplied but the A strong increase of carbon sputtering at angles of incidence metal is deposited͒. approaching 90° ͑measured with respect to the normal to the During the saturation and growth stages of our interest surface, i.e., at grazing angles͒ has previously been reported here, carbon species are deposited on the surface to effect the for Ar and metal ions.29–31 Quite similar effects also take saturation of the catalyst nanoparticles and the growth of the place in the sputtering of .32 A very important obser- nanocones on the nanoparticles that were saturated. In this vation is that the ion reflection at angles of incidence exceed- case, carbon precursors are predominantly deposited on the ing 85° ͑carbon on carbon͒ were not observed when the ion substrate surface between the catalyst nanoparticles ͑we con- energies were lower than 300 eV, i.e., in the practically im- sider the low surface coverage case which is typical for car- portant case. On the other hand, the sputtering yield does not bon nanocone arrays͒, then they diffuse on the surface to the exceed 0.6–0.7 for low energies.33 At energies lower than nanoparticles, dissolve in the catalyst, and the catalyst mate- 50 eV, the sputtering proceeds through the chemical route rial eventually reaches the saturation point. Upon the catalyst and the angular dependence is almost negligible.33 It was material saturation, a nanostructure nucleate on the top of the also demonstrated that under oblique ion incidence the ma- catalyst , presumably, due to the local oversatu- terials feature a low sticking coefficient and enhanced ration is caused by the additional carbon atoms deposited on self-sputtering.34 the nanoparticle. Upon the nanocone nucleation on the satu- The processes described in our model are shown in Fig. rated catalyst nanoparticles, the nanocone nuclei grow by 1. We consider the deposition of carbon ions onto the sub- simultaneously increasing their height and the base radius. strate, catalyst particles, and nanocones. The flux of carbon The main reason for setting the height nonuniformity is most atoms is distributed uniformly about the entire surface of the likely due to nonsimultaneous saturation of the metal nano- substrate. The ion motion between the plasma bulk and the particles. During the final stage, the nanocones continue catalyst nanoparticles with the growing nanocones on them growing until the moment of catalyst poisoning; this process is determined by the electric field. It is assumed that the ions ␷ ͱ / is outside the scope of this work. It is important to stress that enter the plasma sheath with the Bohm velocity B = Te m, during the growth the nanocone sputtering is one of the key where m is the carbon ion mass, and Te is the electron shape-determining processes.20 temperature. The case of a thin sheath ͑i.e., the case of the As it was said above, the process of formation of the substrate at floating potential or at low bias͒ is considered. ␭ ␭ ␭ catalyst pattern is not considered here. In our numerical ex- Thus, the sheath width S can be estimated as S =k␭ D ͱ␧ / ␭ periments, we consider a system consisting of a biased sub- =k␭ 0Te npe, where D is the Debye length, k␭ is a constant This article is copyrighted as indicated in the article. 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TABLE I. Main simulation parameters.

Parameter, dimension Notation Value

Mean radius of catalyst nanopartciles, nm Rm 5

Carbon nanocone height range, nm Hm 0–2500 Number of nanocones N 2000 ␭ Mean spacing between nanocones, nm n 45

Electron temperature in the plasma, eV Te 2 ␧ Ion energy at the sheath edge, eV i 2

Gas temperature, °C Tg 250

Gas pressure, Pa Pg 2.5

Substrate bias, V UB 50 ␮ 2 Substrate area, m SB 4 −1 Carbon flux to substrate, MLϫs ⌿⌺ 0.1 Ϫ 5 Number of carbon ions in Monte Carlo simulations, Ni 10

Surface temperature, °C Ts 600

Time of deposition, s td up to 2500 −1 ␯ ϫ 13 Frequency of lattice atom oscillations, s 0 3.5 10

35 ␧ ⌿ ␩␯ ͑ ␧ / ͒ ͑ ͒ of the order of 1, e is the electron charge, 0 is the dielec- E = 0 exp − a kTS , 2 tric constant, and np is the electron density in the plasma. The ion trajectories in the vicinity of the nanocones were ␧ calculated using the Monte Carlo ͑MC͒ technique. The de- where a is the energy of adatom evaporation from the sub- tails of the MC simulations are described elsewhere.36,37 The strate surface, k is Boltzmann’s constant, TS is the surface ␯ distribution of the ion flux on the substrate surface between temperature, 0 is the frequency of lattice atom oscillations. the nanocones was used to calculate the diffusion fluxes to The flux of carbon adatoms at the border of each catalyst the catalyst nanoparticles. For this purpose, we used the sur- nanoparticle can be calculated using the relation face diffusion equation38 ␲ / 2␩ di ␧ץ 2␩ץ ␩ץ ␸ = ␯ e− d kTS, ͑3͒ = D ͑x,y͒ͩ + ͪ + ⌿ − ⌿ − ⌿ , ͑1͒ i ␭ 0 y2 D E A Sץ x2ץ t Sץ

where D͑x,y͒ is the surface diffusion coefficient, ␩ is the where d is the diameter of the metal catalyst nanoparticle, ␧ surface density of carbon adatoms, ⌿ ͑x,y͒ is the deposition i d D is the surface diffusion activation energy, and ␭ is the lattice flux of atoms and ions to the substrate surface, ⌿ ͑x,y͒ is S E constant of the substrate material. the evaporation flux from the substrate surface, ⌿ ͑x,y͒ is A Finally, the surface diffusion coefficient used in Eq. ͑1͒ the flux of carbon adatoms to the catalyst nanoparticles on was taken in the form the surface, and ͑x,y͒ are the Cartesian coordinates. The ⌿ ͑ ͒ deposition flux to the substrate surface D x,y is calculated by the above described MC technique. In this model, we did ␭2␯ a 0 ␧ / − d kTS ͑ ͒ not consider the carbon ion collisions with the carbon ada- DS = e . 4 4 toms on the surface, since the probability of such collisions ⌿ ͑ ͒ is low. The evaporation flux E x,y is determined by the The growth of the carbon nanocones was modeled by the evaporation rate equation length equation

͑ ͒ FIG. 2. Distributions of nanocone lengths for the neutral gas process with the deposition time td as a parameter. Weakly ionized carbon flux ki =0.05 , ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ⌿ / td =100 s a , td =300 s b , td =500 s c , td =1000 s d , and td =2500 s e . Electron temperature Te =2 eV, carbon influx C =0.1 ML s. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.181.251.131 On: Tue, 15 Jul 2014 04:34:25 103501-4 Levchenko et al. Phys. Plasmas 15, 103501 ͑2008͒

FIG. 3. Same as in Fig. 2, for weakly ionized carbon flux with ki =0.25.

␭3 t the fluxes of carbon precursor to the borders of each catalyst l =3 C ͑␸ + ␸ + ␸ − ␸ ͒, ͑5͒ ͑ ͒ i·nc ␲r2 i i·p i·a i·S nanoparticle. As boundary conditions for Eq. 1 , we used, i first, the set of equations for the adatom re-evaporation ␸ ␸ where i is the flux of carbon adatoms to the border of the ith fluxes i·e from the boundaries of catalyst nanoparticles to nanoparticle calculated by numerically solving Eqs. ͑1͒–͑3͒; the two-dimensional adatom vapor on the surface ␸ i·p is the total flux of carbon ions to the ith catalyst nano- ␲ di ␧ / particle and the ith nanocone surface from the plasma, deter- ␸ = ␯ e− d·S kTS, ͑6͒ i·e ␭ 0 ␸ m mined by the above described MC technique; i·S is the sput- tered flux of carbon atoms from the nanocone surface; ␸ is ␧ i·a where d·S is the surface diffusion activation energy for the the total flux of carbon atoms to the ith catalyst nanoparticle desorption of carbon atoms from the boundary of the catalyst ␭ from the plasma; C is the lattice constant of the carbon nanoparticle to the two-dimensional adatom vapor on the nanocone. We have assumed that the carbon nanocones substrate surface. Second, we assumed that the carbon ada- nucleate at the center of the catalyst nanoparticle and then tom density at the boundary of the simulation domain is grow by increasing their base radius until the catalyst nano- equal to the mean carbon adatom density throughout the particle is fully covered. Then, the nanocone height in- whole surface. Then, we have calculated the kinetics of the creases, i.e., the apex angle decreases during the growth pro- catalyst nanoparticle saturation and carbon nanocone nucle- cess. This assumption is supported by a large number of ation using the technique described in detail elsewhere.40,41 39 systematic experimental observations. The surface simulation domain was 2000ϫ2000 nm, The Monte Carlo technique was used to simulate the ion with 2000 initial ͑nonsaturated͒ catalyst nanoparticles placed motion towards the surface system comprising approxi- randomly. We have used an experimental catalyst pattern as a mately 2000 nanocones. An initial position of each ion was model for constructing the catalyst pattern used in the simu- randomly chosen at the sheath boundary, with the ion veloc- lation. The list of the main simulation parameters is shown in ity equal to the Bohm velocity. During the simulation, the Table I. coordinates of the ion impact on the substrate surface were recorded, and thus the microscopic topography of the ion current over the surface was obtained. Besides, we have also III. RESULTS recorded the coordinates of ion impact on the nanocone sur- face, and thus the ion flux to the nanocone surface from the The main results of our numerical experiments are plasma was obtained. The flux of carbon atoms sputtered shown in Figs. 2–7. Specifically, Figs. 2–4 illustrate temporal ␸ from the nanocone surface i·S was calculated using the sput- dependencies of the distributions of nanocone lengths for the ter coefficient and the ion flux to the nanocone surface from neutral, weakly ionized, and highly ionized process environ- the plasma. ments, respectively, with the deposition time td as a param- Equation ͑1͒ was solved numerically to calculate the car- eter. The time evolution of the nanocone pattern is presented bon adatom balance on the surface and finally to calculate in the form of bar charts, with the total number of carbon

FIG. 4. Same as in Fig. 2, for highly ionized carbon flux with ki =0.75. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.181.251.131 On: Tue, 15 Jul 2014 04:34:25 103501-5 Growth of carbon nanocone arrays… Phys. Plasmas 15, 103501 ͑2008͒

␦ FIG. 5. Dependence of the width of nanocone length distribution W on deposition time with the carbon flux ionization degree as a parameter. The inset corresponds to the catalyst saturation stage and reveals a strongly nonlinear dependence of the width of the nanocone length distribution due to the different kinetics of the catalyst saturation in the plasma environments with different degrees of ionization of carbon precursor fluxes.

nanocones NCN=2000. Each bar represents a group of the nanocones with the length difference not exceeding 5 nm. From these figures one can see that the time evolution of the nanocone ensemble changes dramatically with the ioniza- ͑ ͒ tion degree. The distribution function of the carbon nano- FIG. 7. Color online 3D visualization of carbon nanocone patterns grown ͑ on Ni catalyst particles, after incubation time ti =2500 s, on substrate frag- cones grown from the neutral gas environment with the flux ment 500ϫ500 nm, total flux of carbon material ⌿⌺ =0.1 ml/s. The maxi- ͒ ionization coefficient ki =0 is wide and comprises nanocones mum length shown is 2000 nm, carbon flux with ionization degree ͑ ͒ ͑ ͒ with the lengths ranging from zero to 300 nm, as shown in ki =0.75 a and ki =0.0 b . ͑ ͒ Fig. 2. With the flux ionization coefficient ki =0.25 Fig. 3 , the distribution function becomes narrower; the nanocones shorter than 50 nm are absent, and the number of the nano- efficient k =0.75 ͑Fig. 4͒, the distribution becomes very nar- ͑ i cones with the length of around 100 nm corresponding to row, without the nanocones less than 150 nm and higher than ͒ the distribution peak increases. With the high ionization co- 250 nm. It can also be noted that the distribution function has a similar shape in all the three cases considered, namely the position of the distribution peak is located in the first third of the nanocone length range. Nevertheless, there is a clear dif- ference between the nanocone length distribution shown in Fig. 2 ͑neutral gas-based͒ and the distributions shown in Figs. 2 and 3. Indeed, in the array grown in the neutral gas process the nanocones of a very small ͑close to zero͒ length are still present even after a long ͑2500 s͒ time of deposition. On the contrary, in the plasma-based process, short nano- cones are absent. One can thus introduce an additional parameter—the minimum nanocone length Lmin which actually is zero for the neutral gas process ͑Fig. 2͒ and Lmin=50 nm for ki =0.25, and Lmin=125 nm for ki =0.75. The dependence of the width of the nanocone length ␦ distribution W on the deposition time with the carbon flux ionization degree as a parameter is shown in Fig. 5. The width of the distribution increases with time for all ki, FIG. 6. Dependence of the maximum nanocone height on time with the reaches 360 nm for the zero ionization, and only 100 nm for carbon flux ionization degree as a parameter. The inset corresponds to the the highest ionization coefficient k =0.75 considered here. At catalyst saturation stage. In the highly ionized flux case the maximum nano- i cone height decreases for 100 s of the start of deposition due to strong the initial moment of deposition, the rates of the distribution sputtering of the highest nanocones. widening are the same for all ionization degrees, as it is seen This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.181.251.131 On: Tue, 15 Jul 2014 04:34:25 103501-6 Levchenko et al. Phys. Plasmas 15, 103501 ͑2008͒

from the same angle of the curve inclination in the graph. different. It is quite clear that the reduction of the maximum Then, with the nanocones growing, the rates change. Be- nanocone height Lmax is mainly due to the sputtering of the sides, a close examination reveals an interesting point. In the longest nanocones with energetic ions deflected by the strong neutral gas-based process, the width of the distribution in- electric field in the vicinity of the long nanocones, as has creases almost linearly with time in the entire time range; in already been demonstrated by the numerical simulations.42 the highly ionized flux case, this dependence demonstrates a Besides, an effective use of the nanocone arrays as cold elec- clearly visible plateau, which means that the nanocone pat- tron emitters proves the results of the electric field tern develops without any widening of the distribution. An calculations.43 Thus we can conclude that the longest nano- inset in Fig. 5 illustrates the saturation which occurs at cones are effectively sputtered during the growth, and even- ␦ 500 nm; with the distribution width exceeding 1000 nm, W tually the distribution function of the nanocone lengths is for the highly ionized flux process starts increasing again but effectively restricted from the “long tail” side. On the other with the rate noticeable lower than the rates in other cases hand, an increase of the minimum nanocone length Lmin can- considered. not be explained by the direct influence of the energetic ions Figure 6 shows the results of calculations of the maxi- on the growing nanocones, since the smallest nanostructures mum nanocone height Lmax as a function of time, with the ͑with the length of several tens of nm͒ create a much weaker flux ionization degree as a parameter. The Lmax increases at electric field that is suppressed by the field of longer nano- all process parameters and shows the tendency similar to that cones. To explain the increase in the minimum nanocone illustrated in Fig. 5: the rate of the maximum nanocone length Lmin, let us first examine the reasons of the occurrence height increase is lower for the process of a higher ionization of very short nanocones in the pattern. degree. An inset in this figure also illustrates the process in We have already demonstrated in our previous works the time range of 0–500 s; in this case, one can notice that that the metal catalyst nanoparticles on the surface are satu- the curve corresponding to the higher ionization degree has a rated nonsimultaneously due to their different sizes; in the downward slope, i.e., the maximum nanocone height Lmax case of the plasma environment used, the redistribution of decreases during the carbon deposition during the first 150 s the electric field promotes more uniform ͑more simulta- into the process. In Fig. 7 we show the 3D visualization of neous͒ saturation, i.e., reduction of the incubation time dis- the two carbon nanocone patterns grown in the process en- persion for the catalyst nanoparticles of different sizes.18,41 ͑ ͒ vironments with ionization coefficients ki =0.75 a and Nevertheless, with the nonuniform catalyst nanoparticles on ͑ ͒ ki =0 b . the surface ͑note that the real technological processes of the metal nanopatterning usually result in the formation of metal IV. DISCUSSION island patterns with some size dispersion, see for example, Ref. 44͒, a completely simultaneous saturation cannot be Now we will discuss and interpret the results of the achieved and thus the nanocones are nucleated at different simulations of the carbon nanocone growth in the neutral time moments; as a result, some initial dispersion on the gas- and plasma-based processes. We recall that our main nanocone length is unavoidable. Then, the growth rates of aim here is to study the nanocone formation on Ni catalyst the nanocones on metal catalyst nanoparticles depend mainly nanoparticle patterns, with the main focus on the nanocone on the supply of carbon precursors from the surface to the height uniformity. The results will be discussed from the nanoparticles. Since smaller nanoparticles have shorter pe- point of view of the two main processes: first, growth of rimeters, they collect lower fluxes of carbon species and nanocones by carbon influx through the catalyst ͑surface dif- eventually lead to lower nanocone growth rates; this effect fusion model͒, and second, carbon nanocone sputtering by also contributes to the nonuniformity of the nanocone the carbon ions ͑ion motion model͒. lengths. One of the most important observations is that the dis- In the neutral gas and plasma-based processes, the nano- tribution of the nanocone lengths is much narrower when the cone pattern itself influences the growth of the shortest nano- deposition process is conducted with the use of a carbon flux cones in different ways. In the neutral gas process, due to the of a higher degree of ionization. Indeed, as is seen from Figs. random orientation of the velocities of neutral particles, most ⌬ 2–4, the width of the distribution w obtained for the carbon of the flux is collected by the long nanostructures and cannot 12 flux with degree of ionization ki =0.75 reaches 80 nm for the reach the substrate. As a result, the shortest nanostructures deposition time td =2500 s, but the deposition process with ͑the nanocones in our case, but this conclusion may be re- ki =0 leads to a much wider distribution. For the case of a lated to any long nanostructures on the surface͒ are subjected partially ionized carbon flux with ki =0.25, the width reaches to substantially lower carbon supply and eventually reach the ⌬ w =250 nm. Another important observation is the nonzero zero-supply situation which results in the zero growth rate. minimum nanocone length Lmin observed in the plasma- Besides, some catalyst nanoparticles may get into the “zero- based process. supply” conditions before they are fully saturated with car- Thus, a conclusion can be made that the width of the bon; as a result, these nanoparticles will be unable to nucle- nanocone distribution reduces strongly with an increase in ate nanocones and hence they will be “lost” for the array. the carbon flux ionization degree, and that this reduction is Finally, in the gas-based process the zero-length tail of the due to both the shortening of the nanocone maximum height nanocone length distribution is unavoidable. In the plasma Lmax and increasing the minimum nanocone length Lmin,as process, the electric field created by the longest nanocones illustrated in Figs. 2–6. The reasons for these two effects are changes the ion flux distribution on the substrate, and spe- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.181.251.131 On: Tue, 15 Jul 2014 04:34:25 103501-7 Growth of carbon nanocone arrays… Phys. Plasmas 15, 103501 ͑2008͒

cifically, provides deposition of the ions directly on the sub- ACKNOWLEDGMENTS strate surface between the nanostructures. Under such condi- This work was partially supported by the Australian Re- tions the catalyst nanoparticles with the shortest nanocones search Council, the University of Sydney, CSIRO, and the on them collect ͑through the surface diffusion mechanism͒ a International Research Network for Deterministic Plasma- carbon flux sufficient to sustain the nanocone growth. As a Aided Nanofabrication. result, the shortest nanocones grow and, most importantly, all the catalyst nanoparticles will be saturated and will not be 1M. Keidar, Y. Raitses, A. Knapp, and A. M. Waas, Carbon 44, 1022 lost for the array; thus, the array density will be the highest ͑2006͒. 2A. Okita, Y. Suda, A. Oda, J. Nakamura, A. Ozeki, K. Bhattacharyya, H. in this case. Sugawara, and Y. Sakaia, Carbon 45, 1518 ͑2007͒. Another effect that contributes to the increase in the 3I. Levchenko, K. Ostrikov, A. E. Rider, E. Tam, and S. V. Vladimirov, minimum nanocone length L is the redistribution of car- Phys. Plasmas 14, 063502 ͑2007͒. min 4 bon atoms sputtered from the side surfaces of the longest J. D. Long, S. Xu, S. Y. Huang, P. P. Rutkevych, M. Xu, and C. Diong, IEEE Trans. Plasma Sci. 33, 240 ͑2005͒. nanocones. It is quite logical to assume that the sputtered 5K. Ostrikov, J. D. Long, and S. Xu, Vacuum 80, 1126 ͑2006͒. carbon atoms will be directed mainly towards the substrate 6Z. L. Tsakadze, I. Levchenko, K. Ostrikov, and S. Xu, Carbon 45,2022 surface, due to the glancing angle of the ion impact on the ͑2007͒. 7 ͑ ͒ nanocone side surfaces. As a result, an effective mass trans- K. Ostrikov and A. B. Murphy, J. Phys. D 40, 2223 2007 . 8S. H. Jeong, H. Y. Hwang, and K. H. Lee, Appl. Phys. Lett. 78, 2052 fer from the longest nanocones to the substrate surface will ͑2001͒. contribute to the growth of the shortest nanocones and to the 9U. Cvelbar, K. Ostrikov, A. Drenik, and M. 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