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Behaviour of discontinuous gold films on SrTiO3 substrates under annealing
Applied Surface Science 253 (2006) 1160–1164 www.elsevier.com/locate/apsusc
Behaviour of discontinuous gold films on SrTiO3 substrates under annealing Imre Beszeda a,*, Tama´s Kocsis a, Gergely Imreh a, Frank Weigl b, Hans-Gerd Boyen b, Paul Ziemann b, Dezso˝ L. Beke a a
Department of Solid State Physics, University of Debrecen, H-4032 Debrecen, Egyetem te´r 1, Hungary Department of Solid State Physics, University of Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany
b
Received 8 November 2005; received in revised form 24 January 2006; accepted 24 January 2006 Available online 13 March 2006
Abstract Morphological changes of thin, discontinuous gold films on SrTiO3 substrates, resulting from evaporation in the temperature range of 1143– 1278 K, have been investigated by means of scanning electron microscopy (SEM) and atomic force microscopy (AFM). If the gold covered fraction of the surface is small, the evaporation kinetics can be related to the desorption of adatoms. Measuring the density of the gold beads and the time dependence of the effective thickness of the film as calculated from the diameter of the beads, the following parameters have been determined: the þ26:7 surface diffusion length of the gold adatoms, ls ðmÞ ¼ ð2:22:0 Þ 103 exp½ð77 26ÞkJ=mol=RT, the mass transfer surface diffusion þ433 0 2 10 35 coefficient, Ds ðm =sÞ ¼ ð3:253:23 Þ 10 exp½ð560 49ÞkJ=mol=RT and the evaporation flux, J ðm2 s1 Þð2:79þ267 2:76 Þ 10 exp½ ð426 46ÞkJ=mol=RT. # 2006 Elsevier B.V. All rights reserved. PACS: 68.08.Bc; 68.37.Hk; 68.37.Ps; 68.43.Jk; 68.43.Mn; 68.47.Jn; 68.55.-a Keywords: SrTiO3; Gold; Surface diffusion; Discontinuous film; Evaporation
1. Introduction Due to its excellent lattice matching, single crystalline SrTiO3 substrates play an important role in growing epitaxial YBa2Cu3O7d (Y–Ba–Cu–O) high temperature superconductor (HTSC) films. In this context, the idea of locally manipulating and controlling superconducting properties arises. One popular approach in this respect is to try and inhibit the epitaxial growth on a micro- or even nano-scale by depositing correspondingly patterned metallic layers on top of the substrate prior to the HTSC growth. A possible choice for such inhibit materials is gold due to its oxidation resistance in presence of the standard reactive atmospheres during the HTSC deposition. On the other hand, it has been reported that Au particles with diameters of the order of 50 nm, which were prepared on (0 0 1)-oriented SrTiO3 substrates by dewetting of
* Corresponding author. Fax: +36 52 316 073. E-mail address: [email protected] (I. Beszeda). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.01.053
previously evaporated thin Au films at 700 8C, are unstable during the subsequent HTSC growth. Rather, it could be revealed by transmission electron microscopy (TEM) that the Au particles were relocated from the substrate surface to the top of the deposited YBaCuO film [1]. This quite surprising behavior of Au particles on SrTiO3 substrates at elevated temperatures was the motivation to study morphological changes and the related surface diffusion of such particles in more detail. For this purpose, thin, discontinuous gold films on SrTiO3 substrates were investigated by means of scanning electron microscopy (SEM) and atomic force microscopy (AFM). In detail, from the study of morphological changes of thin, beaded gold films on SrTiO3 substrates, caused by evaporation, the diffusion parameters controlling these changes can be determined, i.e. the surface diffusion length of Au adatoms on this substrate, ls, the mass transfer surface diffusion coefficient of Au on SrTiO3, D0s , and the desorption flux of Au adatoms from the surface, J. A preliminary account of this work has been given in [2].
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is the mean residence time of adatoms on the surface. When the following four conditions fulfill [6]: (i) the evaporation of adatoms is responsible for the diminution of the effective thickness; (ii) the surface diffusion fields around the beads overlap (i.e. the average distance between the beads, ‘ < 2ls); (iii) the fraction of the surface, covered by beads, is small (i.e. evaporation from the adatom layer has to be considered only); and (iv) the surface diffusion process is slower than the detachment rate of the atoms from the periphery of the beads (surface diffusion control (SDC) regime), then the normalized effective thickness, Heff(t)/H(0) decreases linearly with time from its initial H(0) value as [6]: Heff ðtÞ dcs Jv dD0s ¼1 t ¼1 t ¼1 t: Hð0Þ Hð0Þ Hð0Þt Hð0Þl2s Fig. 1. Au beaded film on SrTiO3 substrate after a short anneal at 1223 K.
2. Theoretical Thin continuous, non-wetting metallic films on ceramic substrates become discontinuous during annealing in relatively short times [3–5], i.e. holes appear and grow in the film. After these voids have been coalesced and there are separate islands of gold with random shapes and sizes on the surface, a beaded film will be formed by means of transformation of the island shape to the equilibrium [5]. Fig. 1 illustrates Au beads on the SrTiO3 substrate after a short anneal at 1223 K, where flat particles with large diameter can be recognized, that have not reached the almost spherical equilibrium shape, yet. Morphological changes of such beaded films, caused by evaporation, can be described by the model of Beke and Kaganovskii [6], illustrated in Fig. 2. The beaded films are characterized by their effective thickness [6], Heff, as
Heff ¼
2p’ðQÞNs hR3 i ; 3
(1)
where Q and Ns are the contact angle and density of beads, w(Q) is a geometrical parameter (w(Q) = 1 3/2 cos Q + 1/ 2 cos3 Q) describing the shape of the beads, and hR3i the average cubic radius. The surface is considered as a twodimensional layer of width d = nv, where n is the surface density of sites and v the atomic volume. Motion of adatoms is characterized by the intrinsic surface diffusion coefficient, Dsi, and by the surface diffusion length, ls = (Dsi t)1/2, where t
(2)
Here cs is the fraction of adatoms in equilibrium with a plane film, J the evaporation flux given by J = ncs/t and D0s is the mass transfer surface diffusion coefficient defined by D0s ¼ Dsi cs. According to Eq. (2), the time dependence of the effective thickness of the film yields dcs/t, or Jv, or dD0s =l2s. Since the density of the beads, Ns, decreases during the annealing, the second of the above four conditions (i.e. the overlapping of the diffusion fields) will no longer be fulfilled after a certain time. A breakpoint can be observed here on the Heff(t) curves, and the effective thickness depends on time as Heff ðtÞ 2pdNs D0s ¼1 t: Hð0Þ Hð0Þ lnðls =R1 Þ
(3)
where R1 = R sin Q. Eq. (3) gives also a linear dependence for longer times, with different slope from that of Eq. (2). ls can be determined independently (see, e.g. Imre et al. [7]) from the break point on the Heff(t)/H(0) curve if the density of the beads, Ns, belonging to this time, is determined for example from scanning pffiffiffiffiffi electron microscopic images. In this case ls 1=2 Ns . The mass transfer surface diffusion coefficient can be determined from both of Eqs. (2) or (3). Additionally, if the atomic volume is known, the evaporation flux, J, can also be calculated from Eq. (2). Presently, along this route morphological changes of thin gold beaded films, caused by evaporation, were investigated on SrTiO3 substrates, allowing to extract the parameters of the corresponding surface mass transport. 3. Experimental
Fig. 2. Model of the beaded film [6].
Continuous Au layers of 20–30 nm thicknesses were evaporated onto single crystalline (0 0 1)-oriented SrTiO3 substrates (5 mm 10 mm 1 mm). Bead formation was achieved with 30–40 min annealings at 1223 K in vacuum at 2 106 mbar. Experimental measurements were carried out in the temperature range of 1143–1278 K for different times, in vacuum. The samples were investigated by SEM and three images were taken from different parts of the beaded film after
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each annealing. The photos were evaluated by the Vision Assistant software of the National Instruments and the average density and the diameters of the beads were determined. Then, samples were further annealed until very low effective thickness was achieved. The contact angle was determined by AFM. 4. Results and discussion The kinetics of evaporation was measured at temperatures of 1143, 1153, 1173, 1183, 1193, 1208, 1213, 1223, 1243 and 1278 K. Fig. 3 demonstrates the time dependence of the morphology of the Au beaded film for 0, 70, 100 and 170 min at 1213 K. Measuring the height and the diameter of the beads by AFM, the shape of the beads was determined as half spheres, i.e. formally the contact angle is about 908 and so w(Q) 1 in Eq. (1). The density and the diameters of the beads were determined by means of SEM and Heff(t) could be calculated from Eq. (1). Fig. 4 illustrates typical Heff(t)/H0 curves at 1153, 1183, 1213, 1243 and 1278 K. Fig. 4b presents Heff(t)/H0
separately at the lowest temperature, because only the very beginning of this curve can be seen in Fig. 4a. The first parts of these curves correspond to the case when ‘ < 2ls and this part can be fitted with a straight line, according to Eq. (2). At longer times, when the beads dissolve individually, a lower dissolution rate can be observed. This second parts correspond to the Eq. (3). The dD0s =H0 l2s and 2pdNs D0s =lnðls =R1 Þ values can be determined from the slopes of the first and second parts. The corresponding evaporation fluxes, J, were calculated using vAu = 1.69 1029 m3, and reported in Table 1. Plotting the logarithm of these values versus the reciprocal temperature, a linear function could be obtained, which is presented by full symbols in Fig. 5. The evaporation flux is given by Jð1143 1278 KÞ 35 ¼ ð2:79þ267 2:76 Þ 10 exp
ð426 46Þ kJ=mol RT
ðm2 s1 Þ:
Fig. 3. Morphology of the Au beaded film at 1213 K: (a) 0 min; (b) 70 min; (c) 100 min; and (d) 170 min.
(4)
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Fig. 5. Temperature dependence of the evaporation fluxes. Filled symbols and the fitted solid line correspond to the present measurements, while the dashed line represents the sublimation currents from bulk gold.
The calculated values of the surface diffusion length of adatoms, ls, listed also in Table 1., are plotted versus the reciprocal temperature in Fig. 6 for each temperature and the Arrhenius-relation is determined as ls ð1143 1278 KÞ 3 ¼ ð2:2þ26:7 exp 2:0 Þ 10
Fig. 4. (a) Normalized effective thicknesses vs. time at 1153, 1183, 1213, 1243 and 1278 K; (b) full time scale.
By comparing this evaporation flux to that obtained in [8] for evaporation of gold beaded films on sapphire, we can see, that there is a difference between the activation energies of a factor of two, i.e. Qevap = 196 9 kJ/mol for evaporation from sapphire surface. Sublimation currents from bulk gold, calculated from tabulated values of the equilibrium vapour pressures of gold, is also presented in Fig. 5 (dashed line). We can see that the evaporation currents from the adatom layer are about one order of magnitude less than those from the bulk metal. Table 1 The evaporation fluxes, surface diffusion lengths and mass transfer diffusion coefficients determined at different temperatures T (K)
1143 1153 1173 1183 1193 1208 1213 1223 1243 1243 1278
J (m2s1)
1.2 10 16 1.1 10 16 2.2 10 16 4.9 10 16 3.8 10 16 1.4 10 17 1.4 10 17 2.4 10 17 1.4 10 17 7.8 10 17 9.3 10 17
ls (m)
5.2 107 6.7 107 – 7.9 107 1.2 106 – 8.7 107 1.2 106 1.9 106 1.2 106 1.0 106
ð77 26Þ kJ=mol ðmÞ: (5) RT
This means that ls increases with increasing temperature. It is worth noting that it was not the case in the system Au on sapphire [8], where negative activation energy ðQls ¼ 70 kJ=molÞ was obtained, indicating an opposite temperature dependence. Qls , as well as the ls values, are in the order of magnitude of other data obtained from other measurements in different systems (for Ni, Cu, Ag, Pd and Au on alumina (Qls ¼ 100 kJ=mol [9], 7 kJ/mol [10], 0 kJ/mol [11], 87 kJ/mol [12] and 70 kJ/mol [8], respectively), so Eq. (5) is reliable. The mass transfer surface diffusion coefficients, D0s , have been determined both from the Eqs. (2) and (3), and their values are presented in Fig. 7. and collected in Table 1., as well. We can see, that the points obtained from the two parts of the Heff(t) curves can be fitted with straight lines and are parallel within the error limits, i.e. the two activation energies are equal. For
D0s (m2 s1) determined from dD0s =H0 l2s
2pdNs D0s =lnðls =R1 Þ
5.5 1016 8.5 1016 6.0 1015 5.2 1015 9.8 1015 3.4 1014 1.8 1014 5.8 1014 8.1 1014 1.8 1013 1.7 1013
1.2 1016 2.1 1016 3.9 1016 8.6 1016 6.8 1016 2.2 1015 3.4 1015 4.2 1015 1.3 1014 5.8 1015 2.8 1014
Fig. 6. Temperature dependence of the surface diffusion lengths.
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from the diameter of the beads, the following parameters have been determined in the temperature range of 1143–1278 K: the surface diffusion length of the gold adatoms, ls ðmÞ 3 ¼ ð2:2þ26:7 exp½ð77 26ÞkJ=mol=RT, the eva2:0 Þ 10 35 poration flux, J ðm2 s1 Þ ¼ ð2:79þ267 2:76 Þ 10 exp½ð426 46ÞkJ=mol=RT and the mass transfer surface diffusion 10 coefficient, D0s ðm2 =sÞ ¼ ð3:25þ433 3:23 Þ 10 exp½ð560 49ÞkJ=mol=RT. The relatively high errors on the preexponential factors and the activation energies can be attributed to the uncertainties of the measurements of the parameters of Ns, ls and R1. Acknowledgments Fig. 7. Temperature dependence of the mass transfer surface diffusion coefficients, determined from the first parts (filled symbols) and second parts (open symbols) of the Heff(t) curves.
illustration, the temperature dependence of the diffusion coefficients, determined from the first parts, is described by the following expression: D0s
ð1143 1278 KÞ ¼
ð3:25þ430 3:23 Þ
ð560 49Þ kJ=mol 10 exp RT 10
ðm2 s1 Þ:
(6)
It is important to note that the difference between the values of the diffusion coefficients, and the preexponential factors as well, on Fig. 7, which is approximately one order of magnitude, can be resulted from the uncertainties of the measurements of the parameters of Ns, ls and R1. The preexponential factor of D0s obtained is surprisingly high. Nevertheless, it is worth mentioning that the Arrhenius function of the surface mass transfer coefficients on insulators has usually an upward curvature at high temperatures, where the high temperature part is characterized by high preexponential factors (see Table 2 in [13]). Since the evaporation is responsible for the diminution of the effective thickness, QJ corresponds to the left hand side of Eq. (2), while QD0s and Qls correspond to the nominator and denominator on the right hand side of Eq. (2), respectively, and the relation QJ ¼ QD0s 2Qls :
(7)
has to be fulfilled. Indeed, substituting the activation energy values obtained in Eqs. (4)–(6) we get the approximate equality 426 kJ=mol 560 kJ=mol 2 77 kJ=mol:
(8)
which confirms the reliability of our results. 5. Conclusions Measuring the density of the gold beads and the time dependence of the effective thickness of the film, calculated
This work has been supported by a bilateral Hungarian¨ B, 50/2001 and the German Exchange Project DAAD-MO Hungarian Grant FKFP 0188/2001. References [1] G. Lengl, P. Ziemann, F. Banhart, P. Walther, Anomalous behavior of gold nanoislands on top of SrTiO3(0 0 1) during their overgrowth by thin YBaCuO films, Phys. C 390 (2003) 175–184. [2] I. Beszeda, T. Kocsis, G. Imreh, F. Weigl, H.-G. Boyen, P. Ziemann, D.L. Beke, Behaviour of discontinuous gold films on SrTiO3 substrates under ¨ chsner, J. Gra´cio, F. Barlat (Eds.). Proceedings of the annealing, in: A. O 1st International Conference on Diffusion in Solids and Liquids, University of Aveiro, Portugal, DSL-2005, 2005, pp. 53–56. [3] I. Beszeda, I.A. Szabo´, E.G. Gontier-Moya, Morphological evolution of thin gold films studied by Auger electron spectroscopy in beading conditions, Appl. Phys. A 78 (2004) 1079–1084. [4] I. Beszeda, E.G. Gontier-Moya, D.L. Beke, Investigation of mass transfer surface self-diffusion on palladium, Surf. Sci. 547 (2003) 229–238. [5] I. Beszeda, D.L. Beke, E.G. Gontier-Moya, Yu.S. Kaganovskii, D. Ianetz, Calculation of surface self diffusion coefficients from AES data on decay of thin metal films, Def. Diff. Forum 237–240 (2005) 727– 732. [6] D.L. Beke, Yu.S. Kaganovskii, Determination of parameters of surface mass transport from morphological changes of beaded thin films, Mater. Sci. Eng. B 32 (1995) 185–199. [7] A. Imre, E. Gontier-Moya, D.L. Beke, B. Ealet, Auger electron spectroscopy of the kinetics of evaporation of palladium beaded films from sapphire substrate, Appl. Phys. A 67 (1998) 469–473. ´ .W. Imre, Surface ostwald-ripening and [8] I. Beszeda, E.G. Gontier-Moya, A evaporation of gold beaded films on sapphire, Appl. Phys. A 81 (2005) 673–678. [9] I. Beszeda, D.L. Beke, Zs. To˝kei, G. Erde´lyi, Determination of parameters of surface mass transport of Ni on sapphire from the kinetics of morphologycal change of beaded films caused by evaporation, Def. Diff. Forum 143–147 (1997) 1527–1532. [10] I. Beszeda, D.L. Beke, Determination of parameters of Cu surface mass transport on sapphire from morphologycal changes of beaded films caused by evaporation, Appl. Phys. A 64 (1997) 583–588. [11] G. Erde´lyi, M. Barko´czi, E. Moya, H. Giordano, I. Beszeda, B. Aufray, D.L. Beke, Kinetics of evaporation of beaded Ag film on sapphire and on alumina scale, J. Appl. Phys. 80 (1996) 1474–1479. ´ . Imre, D.L. Beke, Determination of surface diffusion parameters of Pd [12] A on sapphire from SEM measurements of morphological changes of beaded films, Appl. Phys. A 72 (2001) 357–360. [13] E.G. Seebauer, C.E. Allen, in: D.L. Beke (Ed.). Surface Diffusion on Non-Metallic Solids in Landolt-Bo¨rnstein, New Series III/33 B, Springer, 1999.
Behaviour of discontinuous gold films on SrTiO3 substrates under annealing Imre Beszeda a,*, Tama´s Kocsis a, Gergely Imreh a, Frank Weigl b, Hans-Gerd Boyen b, Paul Ziemann b, Dezso˝ L. Beke a a
Department of Solid State Physics, University of Debrecen, H-4032 Debrecen, Egyetem te´r 1, Hungary Department of Solid State Physics, University of Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany
b
Received 8 November 2005; received in revised form 24 January 2006; accepted 24 January 2006 Available online 13 March 2006
Abstract Morphological changes of thin, discontinuous gold films on SrTiO3 substrates, resulting from evaporation in the temperature range of 1143– 1278 K, have been investigated by means of scanning electron microscopy (SEM) and atomic force microscopy (AFM). If the gold covered fraction of the surface is small, the evaporation kinetics can be related to the desorption of adatoms. Measuring the density of the gold beads and the time dependence of the effective thickness of the film as calculated from the diameter of the beads, the following parameters have been determined: the þ26:7 surface diffusion length of the gold adatoms, ls ðmÞ ¼ ð2:22:0 Þ 103 exp½ð77 26ÞkJ=mol=RT, the mass transfer surface diffusion þ433 0 2 10 35 coefficient, Ds ðm =sÞ ¼ ð3:253:23 Þ 10 exp½ð560 49ÞkJ=mol=RT and the evaporation flux, J ðm2 s1 Þð2:79þ267 2:76 Þ 10 exp½ ð426 46ÞkJ=mol=RT. # 2006 Elsevier B.V. All rights reserved. PACS: 68.08.Bc; 68.37.Hk; 68.37.Ps; 68.43.Jk; 68.43.Mn; 68.47.Jn; 68.55.-a Keywords: SrTiO3; Gold; Surface diffusion; Discontinuous film; Evaporation
1. Introduction Due to its excellent lattice matching, single crystalline SrTiO3 substrates play an important role in growing epitaxial YBa2Cu3O7d (Y–Ba–Cu–O) high temperature superconductor (HTSC) films. In this context, the idea of locally manipulating and controlling superconducting properties arises. One popular approach in this respect is to try and inhibit the epitaxial growth on a micro- or even nano-scale by depositing correspondingly patterned metallic layers on top of the substrate prior to the HTSC growth. A possible choice for such inhibit materials is gold due to its oxidation resistance in presence of the standard reactive atmospheres during the HTSC deposition. On the other hand, it has been reported that Au particles with diameters of the order of 50 nm, which were prepared on (0 0 1)-oriented SrTiO3 substrates by dewetting of
* Corresponding author. Fax: +36 52 316 073. E-mail address: [email protected] (I. Beszeda). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.01.053
previously evaporated thin Au films at 700 8C, are unstable during the subsequent HTSC growth. Rather, it could be revealed by transmission electron microscopy (TEM) that the Au particles were relocated from the substrate surface to the top of the deposited YBaCuO film [1]. This quite surprising behavior of Au particles on SrTiO3 substrates at elevated temperatures was the motivation to study morphological changes and the related surface diffusion of such particles in more detail. For this purpose, thin, discontinuous gold films on SrTiO3 substrates were investigated by means of scanning electron microscopy (SEM) and atomic force microscopy (AFM). In detail, from the study of morphological changes of thin, beaded gold films on SrTiO3 substrates, caused by evaporation, the diffusion parameters controlling these changes can be determined, i.e. the surface diffusion length of Au adatoms on this substrate, ls, the mass transfer surface diffusion coefficient of Au on SrTiO3, D0s , and the desorption flux of Au adatoms from the surface, J. A preliminary account of this work has been given in [2].
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is the mean residence time of adatoms on the surface. When the following four conditions fulfill [6]: (i) the evaporation of adatoms is responsible for the diminution of the effective thickness; (ii) the surface diffusion fields around the beads overlap (i.e. the average distance between the beads, ‘ < 2ls); (iii) the fraction of the surface, covered by beads, is small (i.e. evaporation from the adatom layer has to be considered only); and (iv) the surface diffusion process is slower than the detachment rate of the atoms from the periphery of the beads (surface diffusion control (SDC) regime), then the normalized effective thickness, Heff(t)/H(0) decreases linearly with time from its initial H(0) value as [6]: Heff ðtÞ dcs Jv dD0s ¼1 t ¼1 t ¼1 t: Hð0Þ Hð0Þ Hð0Þt Hð0Þl2s Fig. 1. Au beaded film on SrTiO3 substrate after a short anneal at 1223 K.
2. Theoretical Thin continuous, non-wetting metallic films on ceramic substrates become discontinuous during annealing in relatively short times [3–5], i.e. holes appear and grow in the film. After these voids have been coalesced and there are separate islands of gold with random shapes and sizes on the surface, a beaded film will be formed by means of transformation of the island shape to the equilibrium [5]. Fig. 1 illustrates Au beads on the SrTiO3 substrate after a short anneal at 1223 K, where flat particles with large diameter can be recognized, that have not reached the almost spherical equilibrium shape, yet. Morphological changes of such beaded films, caused by evaporation, can be described by the model of Beke and Kaganovskii [6], illustrated in Fig. 2. The beaded films are characterized by their effective thickness [6], Heff, as
Heff ¼
2p’ðQÞNs hR3 i ; 3
(1)
where Q and Ns are the contact angle and density of beads, w(Q) is a geometrical parameter (w(Q) = 1 3/2 cos Q + 1/ 2 cos3 Q) describing the shape of the beads, and hR3i the average cubic radius. The surface is considered as a twodimensional layer of width d = nv, where n is the surface density of sites and v the atomic volume. Motion of adatoms is characterized by the intrinsic surface diffusion coefficient, Dsi, and by the surface diffusion length, ls = (Dsi t)1/2, where t
(2)
Here cs is the fraction of adatoms in equilibrium with a plane film, J the evaporation flux given by J = ncs/t and D0s is the mass transfer surface diffusion coefficient defined by D0s ¼ Dsi cs. According to Eq. (2), the time dependence of the effective thickness of the film yields dcs/t, or Jv, or dD0s =l2s. Since the density of the beads, Ns, decreases during the annealing, the second of the above four conditions (i.e. the overlapping of the diffusion fields) will no longer be fulfilled after a certain time. A breakpoint can be observed here on the Heff(t) curves, and the effective thickness depends on time as Heff ðtÞ 2pdNs D0s ¼1 t: Hð0Þ Hð0Þ lnðls =R1 Þ
(3)
where R1 = R sin Q. Eq. (3) gives also a linear dependence for longer times, with different slope from that of Eq. (2). ls can be determined independently (see, e.g. Imre et al. [7]) from the break point on the Heff(t)/H(0) curve if the density of the beads, Ns, belonging to this time, is determined for example from scanning pffiffiffiffiffi electron microscopic images. In this case ls 1=2 Ns . The mass transfer surface diffusion coefficient can be determined from both of Eqs. (2) or (3). Additionally, if the atomic volume is known, the evaporation flux, J, can also be calculated from Eq. (2). Presently, along this route morphological changes of thin gold beaded films, caused by evaporation, were investigated on SrTiO3 substrates, allowing to extract the parameters of the corresponding surface mass transport. 3. Experimental
Fig. 2. Model of the beaded film [6].
Continuous Au layers of 20–30 nm thicknesses were evaporated onto single crystalline (0 0 1)-oriented SrTiO3 substrates (5 mm 10 mm 1 mm). Bead formation was achieved with 30–40 min annealings at 1223 K in vacuum at 2 106 mbar. Experimental measurements were carried out in the temperature range of 1143–1278 K for different times, in vacuum. The samples were investigated by SEM and three images were taken from different parts of the beaded film after
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each annealing. The photos were evaluated by the Vision Assistant software of the National Instruments and the average density and the diameters of the beads were determined. Then, samples were further annealed until very low effective thickness was achieved. The contact angle was determined by AFM. 4. Results and discussion The kinetics of evaporation was measured at temperatures of 1143, 1153, 1173, 1183, 1193, 1208, 1213, 1223, 1243 and 1278 K. Fig. 3 demonstrates the time dependence of the morphology of the Au beaded film for 0, 70, 100 and 170 min at 1213 K. Measuring the height and the diameter of the beads by AFM, the shape of the beads was determined as half spheres, i.e. formally the contact angle is about 908 and so w(Q) 1 in Eq. (1). The density and the diameters of the beads were determined by means of SEM and Heff(t) could be calculated from Eq. (1). Fig. 4 illustrates typical Heff(t)/H0 curves at 1153, 1183, 1213, 1243 and 1278 K. Fig. 4b presents Heff(t)/H0
separately at the lowest temperature, because only the very beginning of this curve can be seen in Fig. 4a. The first parts of these curves correspond to the case when ‘ < 2ls and this part can be fitted with a straight line, according to Eq. (2). At longer times, when the beads dissolve individually, a lower dissolution rate can be observed. This second parts correspond to the Eq. (3). The dD0s =H0 l2s and 2pdNs D0s =lnðls =R1 Þ values can be determined from the slopes of the first and second parts. The corresponding evaporation fluxes, J, were calculated using vAu = 1.69 1029 m3, and reported in Table 1. Plotting the logarithm of these values versus the reciprocal temperature, a linear function could be obtained, which is presented by full symbols in Fig. 5. The evaporation flux is given by Jð1143 1278 KÞ 35 ¼ ð2:79þ267 2:76 Þ 10 exp
ð426 46Þ kJ=mol RT
ðm2 s1 Þ:
Fig. 3. Morphology of the Au beaded film at 1213 K: (a) 0 min; (b) 70 min; (c) 100 min; and (d) 170 min.
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Fig. 5. Temperature dependence of the evaporation fluxes. Filled symbols and the fitted solid line correspond to the present measurements, while the dashed line represents the sublimation currents from bulk gold.
The calculated values of the surface diffusion length of adatoms, ls, listed also in Table 1., are plotted versus the reciprocal temperature in Fig. 6 for each temperature and the Arrhenius-relation is determined as ls ð1143 1278 KÞ 3 ¼ ð2:2þ26:7 exp 2:0 Þ 10
Fig. 4. (a) Normalized effective thicknesses vs. time at 1153, 1183, 1213, 1243 and 1278 K; (b) full time scale.
By comparing this evaporation flux to that obtained in [8] for evaporation of gold beaded films on sapphire, we can see, that there is a difference between the activation energies of a factor of two, i.e. Qevap = 196 9 kJ/mol for evaporation from sapphire surface. Sublimation currents from bulk gold, calculated from tabulated values of the equilibrium vapour pressures of gold, is also presented in Fig. 5 (dashed line). We can see that the evaporation currents from the adatom layer are about one order of magnitude less than those from the bulk metal. Table 1 The evaporation fluxes, surface diffusion lengths and mass transfer diffusion coefficients determined at different temperatures T (K)
1143 1153 1173 1183 1193 1208 1213 1223 1243 1243 1278
J (m2s1)
1.2 10 16 1.1 10 16 2.2 10 16 4.9 10 16 3.8 10 16 1.4 10 17 1.4 10 17 2.4 10 17 1.4 10 17 7.8 10 17 9.3 10 17
ls (m)
5.2 107 6.7 107 – 7.9 107 1.2 106 – 8.7 107 1.2 106 1.9 106 1.2 106 1.0 106
ð77 26Þ kJ=mol ðmÞ: (5) RT
This means that ls increases with increasing temperature. It is worth noting that it was not the case in the system Au on sapphire [8], where negative activation energy ðQls ¼ 70 kJ=molÞ was obtained, indicating an opposite temperature dependence. Qls , as well as the ls values, are in the order of magnitude of other data obtained from other measurements in different systems (for Ni, Cu, Ag, Pd and Au on alumina (Qls ¼ 100 kJ=mol [9], 7 kJ/mol [10], 0 kJ/mol [11], 87 kJ/mol [12] and 70 kJ/mol [8], respectively), so Eq. (5) is reliable. The mass transfer surface diffusion coefficients, D0s , have been determined both from the Eqs. (2) and (3), and their values are presented in Fig. 7. and collected in Table 1., as well. We can see, that the points obtained from the two parts of the Heff(t) curves can be fitted with straight lines and are parallel within the error limits, i.e. the two activation energies are equal. For
D0s (m2 s1) determined from dD0s =H0 l2s
2pdNs D0s =lnðls =R1 Þ
5.5 1016 8.5 1016 6.0 1015 5.2 1015 9.8 1015 3.4 1014 1.8 1014 5.8 1014 8.1 1014 1.8 1013 1.7 1013
1.2 1016 2.1 1016 3.9 1016 8.6 1016 6.8 1016 2.2 1015 3.4 1015 4.2 1015 1.3 1014 5.8 1015 2.8 1014
Fig. 6. Temperature dependence of the surface diffusion lengths.
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I. Beszeda et al. / Applied Surface Science 253 (2006) 1160–1164
from the diameter of the beads, the following parameters have been determined in the temperature range of 1143–1278 K: the surface diffusion length of the gold adatoms, ls ðmÞ 3 ¼ ð2:2þ26:7 exp½ð77 26ÞkJ=mol=RT, the eva2:0 Þ 10 35 poration flux, J ðm2 s1 Þ ¼ ð2:79þ267 2:76 Þ 10 exp½ð426 46ÞkJ=mol=RT and the mass transfer surface diffusion 10 coefficient, D0s ðm2 =sÞ ¼ ð3:25þ433 3:23 Þ 10 exp½ð560 49ÞkJ=mol=RT. The relatively high errors on the preexponential factors and the activation energies can be attributed to the uncertainties of the measurements of the parameters of Ns, ls and R1. Acknowledgments Fig. 7. Temperature dependence of the mass transfer surface diffusion coefficients, determined from the first parts (filled symbols) and second parts (open symbols) of the Heff(t) curves.
illustration, the temperature dependence of the diffusion coefficients, determined from the first parts, is described by the following expression: D0s
ð1143 1278 KÞ ¼
ð3:25þ430 3:23 Þ
ð560 49Þ kJ=mol 10 exp RT 10
ðm2 s1 Þ:
(6)
It is important to note that the difference between the values of the diffusion coefficients, and the preexponential factors as well, on Fig. 7, which is approximately one order of magnitude, can be resulted from the uncertainties of the measurements of the parameters of Ns, ls and R1. The preexponential factor of D0s obtained is surprisingly high. Nevertheless, it is worth mentioning that the Arrhenius function of the surface mass transfer coefficients on insulators has usually an upward curvature at high temperatures, where the high temperature part is characterized by high preexponential factors (see Table 2 in [13]). Since the evaporation is responsible for the diminution of the effective thickness, QJ corresponds to the left hand side of Eq. (2), while QD0s and Qls correspond to the nominator and denominator on the right hand side of Eq. (2), respectively, and the relation QJ ¼ QD0s 2Qls :
(7)
has to be fulfilled. Indeed, substituting the activation energy values obtained in Eqs. (4)–(6) we get the approximate equality 426 kJ=mol 560 kJ=mol 2 77 kJ=mol:
(8)
which confirms the reliability of our results. 5. Conclusions Measuring the density of the gold beads and the time dependence of the effective thickness of the film, calculated
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