The influence of the internal microstructure on the surface parameters of polycrystalline thin films C. Eisenmenger-Sittner and A. Bergauer Institut für Angewandte und Technische Physik, Technische Universität Wien, Wiedner Hauptstraße 8-10 A-1040 Vienna, Austria ABSTRACT Physical Vapor Deposition (PVD) processes commonly lead to the formation of polycrystalline thin films due to the effects of island nucleation and growth. Scanning probe Methods such as Atomic Force Microscopy (AFM) or Scanning Tunneling Microscopy (STM) are widely used for the characterization of the film surface. The topographic data obtained from these measurements can be converted to roughness values, Power Spectral Densities (PSD's) or correlation functions. It is the objective of this paper to evaluate the possibilities to characterize the polycrystalline template which generates the film surface solely by quantities derived from topographic data. For this purpose roughness values, PSD's and correlation functions of polycrystalline Al-Films deposited on glass substrates and from simulated surfaces are compared. The main factors which influence the shape of PSD's and correlation functions are determined and possible connections between the constitution of the polycrystalline template (e. g. shape and size-distribution of the crystalline domains) and the film roughness are discussed. INTRODUCTION Whenever an initially smooth surface is exposed to a beam of incoming particles the growing interface begins to build up random, uncorrelated height fluctuations. Provided the flux of incoming particles is uncorrelated in space and time and no particle movement is allowed on the surface the spatial and temporal behavior of the surface fluctuations can be described by the mechanisms of kinetic roughening and dynamic scaling[1,]. In case of a realistic growth process the roughness evolution is influenced by additional mechanisms of particle transfer along the growing surface which lead to the formation of laterally correlated features. The most prominent of these processes are island formation in the pre-coalescence phase, surface diffusion and surface energy minimization by the growth of grains bounded by low index crystallographic planes[3-6]. The activation of these surface relaxation events can depend on the deposition parameters (deposition temperature, deposition rate) and/or on film thickness. Each of the previously described processes has a characteristic influence on specific topographical properties of the film surface which can be assessed by Scanning probe techniques such as contact or non-contact Atomic Force Microscopy (AFM). It is the intention of this paper to compare several theoretical models for the different stages of film growth with experimentally assessed Power Spectral Densities (PSD s) and Correlation Functions (CF s) [7] obtained from 1
the surfaces of polycrystalline Aluminum-films deposited on amorphous glass substrates. The comparison with the experimental data shall give a general view how the surface geometry influences PSD s or CF s and shall provide a picture which of the previously discussed feature formation processes is actually operating during which stage of growth. EXPERIMENTAL DATA AND GENERAL DEFINITTIONS The Al films were prepared in a diffusion pumped sputter plant (Alcatel SCM 450, base pressure 10-5 Pa) equipped with a planar magnetron cathode of 100 mm diameter and a loadlock-system for fast sample transfer. Argon was used as working gas at a pressure of 0.4 Pa. The films were deposited at a rate of 1 nm/s onto amorphous glass substrates (RMS-roughness < nm) mounted in a distance of 110 mm from the magnetron source. The deposition temperature was 80 C (T/T M = 0.59) and was controlled by a Pt-100 temperature sensitive resistor. The temperature reading was found to be accurate within ± 5 C. The film thickness ranged from 10 5000 nm and was controlled by a carefully calibrated quartz microbalance. After deposition the samples were allowed to cool to room temperature in the vacuum chamber and were then investigated by AFM (TOPOMETRIX EXPLORER, 100 nm radius Si 3 N 4 tip, scan length 10 µm) under atmospheric conditions. From the AFM topographs the PSD's of the film surfaces were determined. The Power Spectral Density, P(F), depends on the spatial frequency of the different surface features, F, according to 1 πifr P(F) = hre ( ) dr L all Lines h [ 0, L] (1) where h is the local height of the surface at a given point r, L is the total lateral extension of the surface and... denotes the ensemble average over all line scans which form the d surface. P(F)is also the Fourier transform of the autocorrelation function G(R) of a surface [7], 1 GR ( ) hrhr ( ) ( + R) σ all Lines σ = RMS-Roughness (a) πifr P(F) = σ G( R) e dr with r and R indicating a given position on the surface. Because G(R) and P(F) can be Fourier transformed into each only PSD's were explicitly determined in this paper. Nonetheless, G(R) is very important for the understanding of the specific shape of the PSD. A thin film can be considered as discontinuous array of 3-dimensional islands located at specific positions on the substrate. Under some fairly general assumptions about the island shape and island density G(R) can be calculated following the work of Trofimov [8]: For parabolically shaped islands with an areal density of N islands per unit surface one obtains a Gaussian G(R) of the form R (b) GR ( )= σ Λ e (3a) Λ=( απn) 1 /, α= 06. 08.. (3b)
Λ is the so-called autocovariance-length related to the island density according to eqn (3b). The Power Spectral Density is the Fourier transform of eqn (3a), i. e. σ Λ P(F) = exp ( ) 4π [ πλ F ]. (4) Informations about the island, or, more generally, about the feature density N can directly be derived from the PSD by locating e. g. the half width of expression (4). Equations 1 4 allow the interpretation of PSD's which are obtained from the different phases of film growth PHASES OF FILM GROWTH Unsaturated Island Densities and Random Island Positions In the very beginning of film growth three dimensional stable islands form at random positions of the substrate. This situation is explicitly described by the theory presented above. Figure 1 shows the PSD's obtained from a 10 nm thick Al-film together with a PSD calculated from eqn (4) and a PSD derived from a surface consisting of randomly distributed spherical cap shaped islands. Figure 1. Power spectral densities and surface morphologies of a 10 nm thick Al-film: (a) Comparison of experimentally assessed and calculated PSD's (b) Experimentally determined Al-Surface (c) Simulated surface consisting of an array or randomly distributed islands on a smooth substrate The autocovariance length Λ extracted from the Gaussian PSD which was derived from eqn. (4) is Λ = 50 nm. This value corresponds well with the average distance of the surface features displayed in Fig. 1b. The wiggles in the high frequency part of the PSD determined from the simulated surface are due to the mathematical definition of the island shape as spherical caps of equal size. The introduction of an island size distribution would suppress this effect. 3
Saturated Island Densities and Regular Island Positions As growth proceeds the experimentally determined PSD of a 30 nm thick Al-film is no longer Gaussian shaped but exhibits pronounced power law behavior. The sharp edge which separates the part of constant PSD values and the part where the PSD decays cannot be fitted by a Gaussian shaped PSD reasonably as figure shows. Figure. Power spectral densities and surface morphologies of a 30 nm thick Al-film: (a) Comparison of experimentally assessed and calculated PSD's (b) Experimentally determined Al-Surface (c) Simulated surface consisting of an array or regularly distributed islands on a smooth substrate The power-law exponent is close to -5, a form that can only reasonably be approximated by a regular array of islands close to coalescence as the simulated PSD, which results form island arrays similar to the one displayed in Fig. c, shows. The regularity of the island arrangement results from the suppression of nucleation in the vicinity of stable islands. In the simulation this effect is represented by the introduction of an exclusion zone around each island where no other island may be positioned. The undulations of the simulated PSD should again vanish by the introduction of a island size distribution. The appearance of the definite power-law behavior of the PSD most probably reflects the fact that in the stage of beginning island coalescence the global properties of the aggregate of islands begin to gain importance. The island array can be considered as a d colloidal aggregate which yields power law type PSD's in analogy to three dimensional colloidal aggregates [9]. The Regime of Grain Growth The experimentally assessed PSD of a 5000 nm thick Al-film shows two distinctly different power-law slopes which are approx. - at intermediate and -4 at high frequencies. The quadratic decay of the PSD can be attributed the grain structure of the film surface. A polycrystalline surface can be generated by the multi-state the Potts model [10] which yields the polycrystalline template determining the surface morphology due to the fact that each single-crystalline domain is bounded by a crystal facet of low surface energy. These facets can be approximated by planes 4
of random tilt which are erected above the single crystalline domains [11]. This algorithm was used to construct the surface displayed in Fig. 3c. The PSD obtained from this surface also yields a power law slope of which is well comparable with the behavior of the experimentally obtained PSD at intermediate Frequencies (Fig. 3a). Figure 3. Power spectral densities and surface morphologies of a 5000 nm thick Al-film: (a) Comparison of experimentally assessed and calculated PSD's (b) Experimentally determined Al-Surface (c) Simulated surface derived from the 48 state Potts model [10,11] The power law slope of 4 present in the high frequency part is usually attributed to the process of feature decay by surface diffusion based on the mechanisms described by Mullins' seminal work [1,13]. On the other hand the high frequency part of the PSD can alternatively bed fitted by a Gaussian PSD (Fig. 3a, dashed line). This alternative approach to reproduce the functional form of the high frequency part of the PSD may be explained by the permanent formation of islands during growth. DISCUSSION AND CONCLUSION Experimental observations of the growth of polycrystalline Al-films growth at different length scales were interpreted by theoretical models of island distributions and in the framework of the theory of grain growth. In the pre-coalescence phase the shape of the PSD could well be described by a random arrangement of three dimensional islands as it was proposed by Trofimov [8]. Island coalescence has a distinct influence on the PSD, transforming the frequency dependent part from a Gaussian to a power-law behavior. In this stage the surface generated by the array of three dimensional islands can be considered as a -dimensional colloidal aggregate. Once the region of columnar grain growth is reached it was found that, apart from Mullins classical theory[1,13] of feature decay by surface diffusion, also the formation of three dimensional islands may exert significant influence on the high frequency part of the PSD which can be approximated by a Gaussian function. The intermediate frequency power-law decay of the PSD in this thickness range could well be approximated by spectra obtained from polycrystalline surfaces constructed by the 48 state Potts model. An interesting approach to a better description of polycrystalline film growth would therefore be the incorporation of constant re-nucleation and island formation processes into the Potts model. 5
ACKNOWLEDGEMENTS This work was supported by the Austrian "Fonds zur Förderung der Wissenschaftlichen Forschung" (FWF) under Grant No. P-1 81-PHY REFERENCES 1. A.-L. Barabási, H. E. Stanley, Fractal concepts in surface growth, (Cambridge University Press, 1995).. M. Kardar, G. Parisi, Y.-C. Zhang, Phys. Rev. Lett. 56(9) 889 (1986), 3. J. A. Venables, G. D. T. Spiller, M. Hanbücken, Rep. Prog. Phys. 47 399 (1984). 4. M. C. Bartelt, J. V. Evans, Phys. Rev. B 46 1675 (199). 5. D. E. Wolf, J. Villain, Europhys. Lett. 13(5) 389(1990). 6. D. J. Srolovitz, J. Vac. Sci. Technol. A4(6) 95 (1986). 7. J. A. Oglivy, Theory of Wave Scattering From Random Rough Surfaces, (IOP Publishing, Philadelphia, 1991). 8. V. I. Trofimov, Mat. Res. Soc. Proc. 440 401 (1997). 9. T. Vicsek, Fractal growth phenomena (World Scientific, Singapore 1989). 10. P. S. Sahni, D. J. Srolovitz, G. S. Grest, M. P. Anderson, S. A. Safran, Phys. Rev. B 8(5) 705 (1983). 11. C. Eisenmenger-Sittner, J. Appl. Phys. 89(11) (001), in print. 1. W. W. Mullins, J. Appl. Phys. 8(3) 333 (1957). 13. W. W. Mullins, J. Appl. Phys. 30(1) 77 (1959). 6