Anomalous scaling during glancing angle deposition - Rensselaer

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Oct 27, 2009 - ... p=0.5 is pre- dicted for GLAD with substrate rotation at Ts=0 K, i.e., no ... ture =Ts/Tm, where Tm is the melting point. The measured .... 9G. W. Mbise, D. Le Bellac, G. A. Niklasson, and C. G. Granqvist, J. Phys. D 30, 2103 (1997). 10S. Chhajed, M. F. Schubert, J. K. Kim, and E. F. Schubert, Appl. Phys. Lett.
APPLIED PHYSICS LETTERS 95, 173106 共2009兲

Anomalous scaling during glancing angle deposition S. Mukherjee and D. Galla兲 Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA

共Received 21 September 2009; accepted 8 October 2009; published online 27 October 2009兲 Metallic nanorods grown by glancing angle deposition at Ts = 300– 1123 K exhibit self-affine scaling, where the average rod width w increases with height h according to w ⬀ h p. The growth exponent p for the investigated metals 共Ta, Nb, and Cr兲 varies with temperature and material but collapses onto a single curve when plotted against the homologous temperature ␪ = Ts / Tm. It decreases from p = 0.5 at ␪ = 0 to 0.39 at ␪ = 0.22, consistent with reported theoretical predictions, but exhibits a transition to an anomalous value of p = 0.7 at ␪ = 0.26, followed by a decrease to 0.33 at ␪ = 0.41. The cause for the anomalous scaling at 0.24ⱕ ␪ ⱕ 0.34 is unknown but may be due to a gradual transition from two-dimensional to three-dimensional surface island growth. © 2009 American Institute of Physics. 关doi:10.1063/1.3257377兴 Glancing angle deposition 共GLAD兲1 is a physical vapor deposition technique that exploits atomic shadowing effects to nanoengineer porous layers consisting of uniquely shaped nanorods including straight and slanted pillars,1 springs,2 spirals,3 tubes,4 and branched5,6 or multicomponent nanorods,7 with a range of potential applications such as sensors,2,8 optical filters,9,10 antireflecting coatings,11 fuel-cells,12 and magnetic data storage.13 GLAD on flat substrates, which are rotated about their surface normal, results in vertical nanorods that broaden with increasing height h. The rods form a self-affine structure14 which is described by an average rod width w that follows a power law w ⬀ h p, where p is referred to as the growth exponent.15 Considerable progress has been made in experimentally controlling the rod morphology and the growth exponent by complex cyclic substrate rotation,16–18 variation of the deposition angle,19–21 choice of material22 and initial substrate patterning,1,3,17,23 but the development of a generic framework that relates deposition conditions to nanorod morphologies is still a challenge, primarily due to long-range shadowing interactions which cause chaotic growth instabilities.24–26 The substrate temperature Ts has been reported to modify the GLAD nanorod morphology27 by reducing the probability for branching,6 enhancing nanorod merging,28 and increasing w at a constant h.24 The effect of Ts on scaling relations has not yet been investigated experimentally, but is the subject of various theoretical models.22,29–34 In particular, p = 0.5 is predicted for GLAD with substrate rotation at Ts = 0 K, i.e., no surface diffusion.22 This value corresponds to the average between p = 1 / 3 and 2/3 for the two orthogonal in-plane directions during GLAD with a stationary substrate.29 Incorporating surface diffusion by adatom motion to neighboring sites with a higher coordination number reduces p to 0.3125,22 which is the average of the predicted 1/4 and 3/8 for stationary substrates.15,30 Different values, p = 0.25 and 0.33,31 are obtained in a 1 + 1 dimensional analysis when allowing adatom motion to a site with the lowest height32 or the largest curvature,33 respectively, and increasing Ts → ⬁ results in a planar surface and p = 0.34 a兲

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In this letter, we experimentally determine p as a function of Ts = 300– 1123 K for three metals, Ta, Nb, and Cr, deposited from an oblique deposition angle ␣ = 84° onto rotating Si共001兲 wafers in a ultrahigh vacuum magnetron sputter deposition system operated with 3 mTorr Ar.35 We find that the temperature dependence of p is identical for all three metals if plotted against the homologous deposition temperature ␪ = Ts / Tm, where Tm is the melting point. The measured growth exponent is in agreement with the theoretical predictions for ␪ ⱕ 0.22, but exhibits a transition at ␪ = 0.24⫾ 0.02 to an anomalous value of p = 0.7⫾ 0.1 at ␪ = 0.26, indicating a change in the nanorod growth front morphology. Figure 1 shows exemplary cross-sectional micrographs of Nb layers grown by GLAD onto Si共001兲 substrates at three different temperatures Ts = 523, 723, and 1123 K, obtained in a Carl Zeiss Supra field emission scanning electron microscope. The microstructure for the layer grown at 523 K in Fig. 1共a兲 shows a high density of 50–60 nm wide grains near the substrate that form during the initial nucleation stage of layer growth but are overgrown by well-separated vertical rods with a total height of 510⫾ 15 nm and an average width that increases with h and shows a maximum of 168⫾ 12 nm at h = 342⫾ 8 nm, as determined using a statistical analysis involving more than 100 rods from multiple micrographs of the same sample. The nanorod formation is attributed to atomic shadowing which is exacerbated by the high deposition angle ␣ = 84°, leading to preferential growth

FIG. 1. Cross-sectional scanning electron micrographs of Nb layers grown on Si共001兲 by glancing angle deposition at substrate temperatures of 共a兲 523, 共b兲 723, and 共c兲 1123 K. White lines show the minimum height used for the scaling analysis.

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© 2009 American Institute of Physics

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of the highest points of the rough layer surface. This leads to a competitive growth mode, where the tallest grains 共and developing rods兲 capture the largest fraction of the deposition flux and grow at the expense of their neighbors that die out.1 The rods grow vertical due to the cylindrically symmetric deposition flux achieved by continuous substrate rotation and exhibit broadening with increasing h, which is a consequence of the growth competition6 and is quantified below. The rod tops have a slight tendency for faceting. Figure 1共b兲 shows a Nb layer deposited under identical conditions as the one shown in Fig. 1共a兲, but with Ts = 723 K. The layer consists of small grains near the substrate that are overgrown by well separated columns that broaden considerably with increasing height to a maximum width of 261⫾ 7 nm at h = 368⫾ 8 nm. That is, the rods are 55% wider than for Ts = 523 K, which is attributed to an increase in the surface diffusion length which enhances the shadowing mediated growth competition between rods. The larger diffusion length at 723 K also results in stronger faceting. Increasing Ts to 1123 K, as shown in Fig. 1共c兲, leads to 110–150 nm wide grains near the substrate, and rods with a maximum width of 500⫾ 32 nm at h = 600⫾ 15 nm. The rods exhibit sharp pointed tops and facets that approach the size of the rods, indicating a large adatom diffusion length. The higher diffusion at 1123 K also enhances growth competition, which, in turn, decreases layer density. This is quantified by the maximum rod height that increases from 510 nm for Ts = 523 K to 1120 nm for Ts = 1123 K, indicating a 50% decrease in the layer density, since the deposition rate and time are identical for these samples. The observed substrate roughness increases with increasing temperature as Nb reacts with the substrate to form NbSi2 grains.36 This reaction may affect layer nucleation but has no effect on the rod morphologies some distance from the substrate, which are controlled by the growth front that remains completely metallic. The horizontal dashed lines in Figs. 1共a兲–1共c兲 indicate the minimum h = 100 nm that was used in the rod scaling analysis. Lower h-values are excluded since grain morphologies near the substrate are governed by the nucleation process which is not expected to follow the scaling relationship.37 Figure 2 is a log-log plot of the average rod width versus height for the same three exemplary Nb samples presented in Fig. 1. The data was obtained by analyzing 15 crosssectional micrographs for each growth temperature, measuring the width of more than 100 rods at each h = 100– 400 nm and for each Ts. The plotted error bars correspond to the standard deviation of the rod width variation at a given height and the solid lines are obtained from fitting the data with the expected power law w ⬀ h p. At large h, ⬎280, 320, and 400 nm for Ts = 523, 723, and 1123 K, respectively, the data is excluded from the fitting procedure since the finite rod height and the decreasing width near the top of individual rods causes the measured average w for a finite deposition time to be below the expected width for continued deposition, which is indicated by the dashed line in Fig. 2. The sample grown at Ts = 523 K, corresponding to a relatively low homologous temperature of ␪ = 0.19, exhibits a growth exponent p = 0.42⫾ 0.03, which is slightly below the analytically predicted value of 0.5 for GLAD without surface diffusion.22 Increasing Ts to 723 K 共␪ = 0.26兲, leads to a 20%–50% wider w and an anomalous growth exponent of 0.71⫾ 0.01 which is attributed to a morphological transition

Appl. Phys. Lett. 95, 173106 共2009兲

FIG. 2. 共Color online兲 Log-log plot of the average rod width w vs height h for the same Nb samples as in Fig. 1. The lines are obtained from fitting with a power law w ⬀ h p.

at ␪ = 0.24⫾ 0.02, as discussed below. The highest growth temperature Ts = 1123 K, corresponding to ␪ = 0.41, yields considerably 共⬃2⫻兲 wider rods and p = 0.34⫾ 0.01. The latter value is close to the expected p = 0.3125 for growth with significant surface diffusion.22 Figure 3 is a plot of the growth exponent as a function of the homologous temperature for the investigated metals Ta, Nb, and Cr. Each data point is obtained from a power-law fit using data from statistical rod-width analyses involving 28 samples that were characterized with more than 300 distinct micrographs showing ⬃3000 rods for which the width was determined as a function of h, corresponding to a total of ⬃30, 000 individual width measurements. The error bars in Fig. 3 correspond to the uncertainty in the growth exponents extracted from the power law fit. The three data sets have different ranges for ␪, 0.09–0.34, 0.11–0.41, and 0.14–0.52, corresponding to the experimentally accessible temperature range Ts = 300– 1123 K and melting points of 3290, 2750, and 2180 K for Ta, Nb, and Cr, respectively. The growth

FIG. 3. 共Color online兲 Growth exponent p for Ta, Nb, and Cr nanorods as a function of the homologous substrate temperature ␪ = Ts / Tm.

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exponents for the three metals show good agreement, forming a single p versus ␪ curve which decreases from p = 0.49⫾ 0.02 at ␪ = 0.10 to p = 0.39⫾ 0.02 at ␪ = 0.22, exhibits a steep increase to p = 0.7⫾ 0.1 at ␪ = 0.26, and then decreases again to reach p = 0.33⫾ 0.03 at ␪ = 0.41, with a possible slight increase for ␪ ⬎ 0.41. The overall curve shape is not fully understood, but the agreement of the three metals as well as the anomaly at ␪ = 0.24⫾ 0.02 is remarkable. The sample with the lowest ␪ 共=0.10兲, Ta nanorods deposited at room temperature, has a p of 0.49⫾ 0.02. This is in excellent agreement with the theoretical prediction that the growth exponent should be 0.5 in the absence of surface diffusion.22 The observed decrease of p with increasing ␪ is also consistent with established theoretical results for normal deposition,34 which predict a decrease in the exponent with increasing surface diffusion to 0.375, 0.33, or 0.25, depending on how surface diffusion is incorporated in the theoretical model.31 However, our measured p-values for 0.24ⱕ ␪ ⱕ 0.34 are all larger than 0.5 and are, therefore, outside the theoretically predicted range.22 Similar anomalous exponents 共⬎0.5兲 have been observed previously for polymers deposited by plasma enhanced chemical vapor deposition,38 etch fronts of reactively ion-etched Si,39 and sputter deposited SiO2 and Nb2O5.40 They have been attributed to surface desorption40 and low sticking coefficients,41 which, however, does not explain our observations since metal growth rates of ⬃0.2 nm-s−1 at ␪ ⬍ 0.55 yield sticking coefficients ⬃1 and negligible surface desorption. We have recently reported on a comparative analysis of GLAD nanorod morphologies for nine different metals deposited by various researchers, indicating a transition from two-dimensional 共2D兲 to threedimensional 共3D兲 islands on the growing nanorod surfaces at ␪ = 0.20⫾ 0.03.24 The 3D islands at higher homologous temperatures correspond to a larger local surface roughness which increases inter-rod shadowing interactions and, therefore, exacerbates the competitive growth mode, accelerates column extinction, and broadens the remaining rods, causing an increase in the average rod width.24 A similar process may also explain the anomalous growth exponent observed in Fig. 3, as follows: For a temperature just slightly above the transition temperature for 3D island formation, ␪ = 0.24⫾ 0.02, islands initially form 2D and only slowly transition to true 3D islands during nanorod growth. In that case, column competition is initially relatively weak as shadowing is dominated by smooth rod surfaces with 2D islands but becomes stronger as the rods gradually develop rough surfaces with 3D islands causing exacerbated rod broadening and anomalous growth exponents ⬎0.5. For growth well above the transition temperature, ␪ ⬎ 0.34, the rods exhibit rough surfaces with 3D islands throughout layer growth, yielding broad rods, as observed in Fig. 1共c兲, which follow conventional scaling with p decreasing from 0.5 to ⬃0.3 as the surface diffusion increases. In conclusion, we have shown that the growth exponents of Ta, Nb, and Cr GLAD nanorods exhibit the same temperature dependence if plotted against the homologous temperature. The exponent decreases with increasing temperature,

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