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An anisotropy microellipsometry (AME) study of anodic film formation on Ti and Zr single grains
Thin Solid Films 313]314 Ž1998. 756]763
An anisotropy microellipsometry Ž AME. study of anodic film formation on Ti and Zr single grains A. Michaelis, M. SchweinsbergU Institut fur 40225 Dusseldorf, Germany ¨ Physikalische Chemie und Elektrochemie, Heinrich-Heine-Uni¨ersitat ¨ Dusseldorf, ¨ ¨
Abstract Anisotropy microellipsometry ŽAME. and photoresist microelectrochemistry were applied simultaneously to study the anodic film formation on the optically anisotropic valve metals zirconium and titanium. All measurements were performed in situ Ž0.5 M H 2 SO4 . on single-substrate grains of technically relevant polycrystalline material. In addition to standard parameters, such as the film thickness and the optical constants of substrate and layer, AME yields the angle w between the optical axes of the samples and the surface normals. This allows a quantitative correlation of the microelectrochemically measured film properties with the crystallographic orientation of substrate grains. It was found that the properties of both TiO 2 and ZrO 2 films vary with the grain orientation in a systematic manner. For Ti, a significant increase of the thickness along with a decrease of the defect state density of the n-type semiconducting TiO 2 films with increasing substrate angle w was observed. The TiO 2 films were amorphous on all grains. In contrast, the ZrO 2 films were crystalline on all grain surfaces but the Ž0001. orientation which is the closest-packed one Ž w s 08.. Q 1998 Published by Elsevier Science S.A. Keywords: Anisotropy; Titanium; Zirconium; Passive films; Epitaxy
1. Overview 1.1. Introduction The reactivity of solids is often dominated by the properties of ultrathin passive films which cover and protect the surfaces. For instance, the valve metals Ti and Zr which are widely used in mechanical engineering and chemical apparatus construction owe their exceptional corrosion resistance against aggressive environments to their thin oxide films. However, local reactions, such as pitting can be critical for these passive materials. In order to elucidate the underlying local mechanisms, in situ micromethods must be applied which feature both high vertical and lateral resolution. This is of particular importance for technically relevant polycrystalline substrates since the passive film properties vary from grain to grain. This is
U
Corresponding author. Fax: q49 211 811803.
illustrated in Fig. 1, showing a micrograph of a Tisurface covered by an oxide film with an average thickness of 40 nm. The interference colors due to the oxide films exhibit a strong grain dependence. Consequently, all experiments presented in this study were performed on single grains. For this, microellipsometry, especially AME, was applied along with a recently developed photoresist microelectrode method which allows one to perform all kinds of electrochemical measurements at high lateral resolution. The latter method is described in full detail by Kudelka et al. w1,2x and is shown schematically in Fig. 2a. In this article the AME is emphasized. Fig. 2 illustrates that AME and photoresist microelectrochemistry can be applied on identical grains. 1.2. The AME method The fundamentals of AME and its application for the determination of crystal orientations of optically anisotropic systems are described in a recent publica-
0040-6090r98r$19.00 Q 1998 Published by Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00992-9
A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
757
Fig. 3. Illustration of an AME measurement on the ZrrZrO 2 system. Analysis of the DŽ a . and C Ž a . curves allows the determination of the angles w between the sample surface normal and the optical axes c.
Fig. 1. Micrograph of a polycrystalline TirTiO2 surface Žaverage Ti grain diameter: 50 m m, average TiO 2 film thickness: 40 nm.. The interference colors are due to the TiO 2 passive film and vary from grain to grain indicating that each substrate grain behaves independently.
tion w3x and will therefore be reviewed here only briefly. AME yields the angle w between the optical axis Ž c-axis. and the surface normal of any anisotropic system. For this, the ellipsometric parameters D and C are measured as a function of the angle a which describes rotation of the sample around the surface normal. The amplitudes of the resulting sinusoidal
Fig. 2. Electrochemical and optical micromethods under microscopic control. Ža. Schematic of the photoresist microelectrode set-up which allows us to perform electrochemical measurements in the standard three electrode configuration on single substrate grains ŽCE, counter electrode; RE, reference electrode; grain a is the working electrode, WE; lateral resolution ) 2 m m. w1,2x. Žb. Microellipsometry can be carried out on the same grains.
DŽ a . and C Ž a . curves are a direct measure for the orientation angle w . For the case of an additional optically anisotropic film on top of the substrate, characteristic changes in amplitude and phase of these curves occur depending on film thickness d f and crystallographic orientation of the substrate wsub and the film w f which can therefore be determined separately. Fig. 3 illustrates the AME method with the ZrrZrO 2 system as an example. Both Zr and Ti crystallize in the hcp lattice and are therefore uniaxially birefringent. Measurements on the particular grain surfaces Ž0001., Ž0111. and Žxxx0., which denotes any surface parallel to the c-axis, are presented here. The Ž0001. surface is the closestpacked one ŽTi: as 0.2952 nm, c s 0.4679 nm; Zr: as 0.3232 nm, c s 0.5147 nm.. The corresponding oxide layers TiO 2 and ZrO 2 exist in three different low-temperature modifications. The ones for TiO 2 are anatase Žtetragonal, as 0.3785 nm, c s 0.9514 nm., rutile Žtetragonal, as 0.4593 nm, c s 0.2959 nm. and brookite Žorthorhombic, as 0.9184 nm, bs 0.5447 nm, c s 0.5145 nm.. The most important ZrO 2 modification is baddeleyeite, which has a monoclinic unit cell Ž as 0.5169 nm, bs 0.5232 nm, c s 0.5341 nm, b s 998150 .. Additionally, tetragonal and hexagonal ZrO 2-structures are discussed in the literature w4,5x. All of these modifications are optically anisotropic and can therefore be detected and characterized by AME. Besides these crystalline modifications, amorphous films may be present on the metal surfaces w6x. 2. Experimental For all experiments Ti Ž99.98%. and Zr Ž99.98%. high-purity samples with a coarse grain texture were
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A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
used enabling us to carry out several independent measurements on each single grain Žaverage grain diameter ) 500 m m.. The samples were polished with emery paper up to grade 4000, yielding plane surfaces with closed grain boundaries. To obtain samples with open grain boundaries for investigations on single grains, the mechanically polished samples were subsequently electropolished as described by Arsov w7x. The anodic oxide films were formed potentiodynamically in aqueous 0.5 M H 2 SO4 solution using a high-voltage potentiostat. Electrochemical potentials are given with respect to the standard hydrogen electrode ŽSHE.. For spectroscopic ellipsometry a custom built rotating analyzer apparatus was used which was equipped with an optical multichannel analyzer ŽOMA. system and a 500-W Xe arc lamp as the light source. Additionally, single wavelength ellipsometry was performed by another automated rotating analyzer ellipsometer ŽSentech AFE 401. with a HeNe laser Ž l s 632.8 nm. as the light source. All measurements were carried out at an angle of incidence of 708. The polarizer azimuth was 458. In order to allow the AME sample rotation around the surface normal, a special in situ cell configuration was constructed. For this, the windows were mounted on the ellipsometer arms using an alignable connector and simply dipped into the electrolyte. Therefore rotation of the entire cell containing the sample in three electrode configuration was possible without affecting the window alignment. To obtain a lateral resolution of 50 m m, a singlet laser bestform lens with a focal length of f s 13 mm was employed in order to minimize focusing errors. For more details concerning the effect of focusing on the ellipsometric measurables, see Svitashev et al. w8x, Erman and Theeten w9x and Sushkov and Tischenko w10x. 3. Results 3.1. Spectroscopic anisotropy ellipsometry (SAME) In Fig. 4, ellipsometric spectra taken on Ti ŽFig. 4a. and Zr ŽFig. 4b. single grains are shown for different sample rotation angles a . For these measurements, freshly electropolished samples, i.e. almost layer-free surfaces were used. In both cases the AME effect, i.e. the dependence of the measurables D and C on a is obvious over the entire spectral range. Additionally, the DŽ a . and C Ž a . variation amplitudes are a function of the wavelength. This spectral dependence of the amplitudes is particularly pronounced for the Ti sample showing a maximum variation around 600 nm. Therefore in order to find the range of maximum AME sensitivity, spectroscopic ellipsometry is neces-
Fig. 4. Ellipsometric spectra for different sample rotation angles a Ž1 s 08, 2 s 308, 3 s 608, 4 s 908, 5 s 1208, 6 s 1508.. Ža. Electropolished Ti-crystal Žxxx0. orientation w1x, Žb. electropolished Zrcrystal.
sary. In case of Ti and Zr, single wavelength measurements at the HeNe-laser wavelength of 632.8 nm are sufficient for AME analysis. Consequently, the subsequent measurements were performed at this wavelength only. It must be emphasized that the anisotropy causes a very strong variation of the D and C measurables even exceeding 208 in the case of the D values on the Ti substrate. Consequently, the effect of anisotropy must never be neglected and each system has to be checked carefully before ellipsometry in isotropic approximation is applied. This is of particular importance for thin film analysis since internal film stresses due to lattice mismatches at the substraterfilm interface can cause a significant anisotropy even for isotropic crystal structures Žstress-birefringence. w11,12x. The quantitative interpretation of AME measurements on such isotropicrisotropic systems will be the subject of a forthcoming article.
A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
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3.2. Determination of the optical constants of the substrate In order to determine the ordinary Ž n o . and extraordinary Ž n ao . complex refractive indexes of the bare Ti and Zr substrates, AME measurements on four different oriented, freshly electropolished grains were carried out. These experimental curves were fitted simultaneously for each substrate by a leastsquare fit procedure as explained by Michaelis and Schultze w3x. The resulting DŽ a . and C Ž a . simulation curves are shown as a function of the orientation angle w in Fig. 5 for the case of Zr. The four experimental curves taken on the four different grains are indicated, allowing one to determine the corresponding grain orientation angles w . The resulting substrate parameters for the wavelength of 632.8 nm are n o ŽZr. s 2.18 y i3.41 and n ao s 2.225 y i2.54. These parameters can be checked independently by their comparison with macroscopically determined ones on mechanically polished samples. Mechanical polishing yields an amorphous and therefore isotropic Beilby layer resulting in an average isotropic complex refractive index n iso . The correlation between n iso and the anisotropic parameters is given by the equation: n iso s 2r3n ao q 1r3n o .
Ž1.
A value of n iso ŽZr. s 2.21 y i2.83 was measured showing excellent agreement with the calculated one according to Eq. Ž1., therefore confirming the determined anisotropic parameters. Analogous evaluations for Ti yielded n o ŽTi. s 2.91y i3.8 and n ao s 2.62y i3.38 w3x. 3.3. AME study of passi¨e film formation 3.3.1. The Ti r TiO2 system The TiO 2 films were formed potentiodynamically in 0.5 M H 2 SO4 at a sweep rate of 50 mVrs. AME measurements were performed on various deliberately chosen grains of a polycrystalline sample. In order to determine the optical film parameters, the crystallographic orientation angles w of substrate and layer and the film thickness d f simultaneously, the procedure of film thickness variation was applied assuming the optical film parameters to be independent of d f . The d f variation can simply be realized by measuring films formed at different potentials. According to the high field mechanism, the films are formed at a constant factor. As shown below this factor is approx. 2 nmrV varying with the grain orientation. As an example Fig. 6 shows AME measurements on Ž0001. and Ž0111. oriented grains for two different formation potentials Ž8 V and 16 V.,
Fig. 5. Calculated AME curves as a function of the orientation angle a for Zr using the optical parameters given in the text. The experimental curves obtained on four different oriented, freshly electropolished Zr grains are indicated.
yielding two different film thicknesses. The symbols refer to the experimental data, the solid lines to the fit. Interestingly, isotropic optical constants of n s 2.2 y i0 on top of the Ž0111. grain and n s 2 y i0 on top of the Ž0001. grain were found. The isotropic behaviour of the TiO 2 layers was observed on all grains, i.e. the films did not contribute to the AME effect at all. Consequently, no dependence of the amplitudes and phases of the DŽ a . and C Ž a . curves on the film thickness occurred. From these experimental findings it can be concluded that the TiO 2 films are amorphous or at least nanocrystalline without any preferential orientation. This is in agreement with photocurrent spectroscopic studies where a pronounced sub-band tailing ŽUrbach-tail . of the n-type semiconducting TiO 2 films is observed w13x. Therefore the TirTiO2 system can be considered as an anisotropicr isotropic system. Despite the amorphous character of the TiO 2 films, a significant texture dependence exists. This fact is obvious in the corresponding layer formation cyclic
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Fig. 7. Film formation cyclovoltammograms on different Ti grains measured by means of the photoresist electrode technique Žsweep rate 50 mVrs. w1x.
Fig. 6. AME curves on two differently oriented Ti grains and two different TiO 2 film thicknesses Žformation potentials: 8 V and 16 V.. The symbols refer to the measured data, the solid lines to the fit.
voltammograms taken on the different oriented Ti grains by means of the photoresist method. These measurements are shown in Fig. 7. Apparently, the grain orientation has a significant influence on the anodic current density. The total anodic current density i is composed of four contributions: i s i Ox q i O2 q i corr q i C with i Ox , oxide formation; i O2 , oxygen evolution; i corr , corrosion current; and i C , current due to capacitive charging of the Helmholtz layer. The latter two contributions are of minor importance Ž m Arcm2 range. and can therefore be neglected. Since no oxygen evolution takes place below potentials of 3 V, the corresponding current can be attributed exclusively to oxide formation i Ox . The coulometrical evaluation of the charges in this potential region yields oxide formation factors of approx. 2 nmrV which significantly depend on the grain orientation. Even more pronounced are the differences in the potential region above 3 V. Here, oxygen evolution occurs showing a strong dependence on the grain orientation.
The texture dependence of the film properties was confirmed by microelectrochemical capacity measurements which are discussed by Kudelka et al. w1,2x. From the Schottky]Mott analysis of these capacity measurements, electronic film properties, such as the defect state concentration ND can be determined. In Fig. 8 the film formation charges determined in the coulometrically evaluable region as well as the defect state concentration ND of the films are correlated with the orientation angle w of the substrate grains. The important result is that the film properties vary with the substrate crystallographic orientation in a systematic manner. The formation charge increases and the defect state concentration decreases with increasing orientation. This leads to the model shown in Fig. 9 illustrating the consistency of the experimental findings. On closely packed surfaces, such as the Ž0001. surface, thin layers with a high defect state concentration N are formed. This is explained by the corresponding band scheme shown in Fig. 9b for the case of an applied anodic potential of 2 V. Due to the high defect state concentration, the necessary potential drop for oxide growth according to the high field mechanism can not be maintained at the metalroxide interface leading to an inhibition of oxide growth. In contrast, the lower defect state concentration on loosely packed surfaces, such as Žxxx0. leads to a larger extension of the space charge layer resulting in the observed higher film thickness. The influence of the crystal substrate orientation on the film properties points towards a dominating effect of the metalroxide interface on the film formation reaction according to the Cabrera]Mott model w14x.
A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
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Fig. 8. Charge measured during the anodic oxide formation in the coulometrically evaluable region and TiO 2 defect state concentration ND from capacity measurements as a function of the substrate grain orientation angle w . Each data point refers to one measurement on a certain Ti grain w2x.
3.3.2. The Zr r ZrO2 system Measurements analogous to the above ones were carried out on the ZrrZrO 2 system. Fig. 10 shows AME measurements taken on a Ž0111. oriented Zr grain for four different formation potentials between 10 and 40 V. In contrast to the Ti measurements in Fig. 6, now a strong dependence of the amplitudes and phase relation between the DŽ a . and C Ž a . curves on the formation potential is observed. These amplitude and phase shifts are clearly due to the ZrO 2
Fig. 9. Model for the texture dependent oxide growth on Ti. The band structures were calculated for an 2 V anodic potential w2x.
films which contribute to the anisotropy of the system. The additional anisotropy effect of the anodic oxide constitutes clear evidence for the formation of an ordered crystalline passive film with a well defined epitaxial relation to the substrate grain. The mea-
Fig. 10. AME curves on a Ž0111. oriented Zr single grain for four different formation potentials; the corresponding film thicknesses are indicated. The symbols refer to the measured data, the lines to the fit. Significant amplitude and phase variations are observed.
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Fig. 12. Model for texture-dependent anodic oxide growth on Zr derived from the AME results.
for this system class. However, on Ž0001. oriented grains Žclosest-packed surfaces . no anisotropy contribution of the films were observed indicating an amorphous character of the layers formed on this particular orientation. The found epitaxial relations between substrate and films are summarized schematically in Fig. 12. Additionally, the ellipsometrically determined film formation factors are given in this figure. These measurements confirm that AME is well suited for investigation of epitaxial film formation. 4. Summary and conclusions Fig. 11. Calculated DŽ a . and C Ž a . curves as a function of the ZrO 2 film thickness for the Zr Ž0111. surface.
sured curves can be fitted excellently assuming a film orientation angle w f of 22.58 and the following optical constants: n o ŽZrO 2 . s 2.13y i0, n ao ŽZrO 2 . s 2.20y i0. These values are consistent with literature data for monoclinic crystalline ZrO 2 w15x. In spite of the biaxial nature of this material, a uniaxial approximation can be used because the two extraordinary indices are almost equal and can therefore be treated as identical. Fig. 11 shows the calculated DŽ a . and C Ž a . curves as a function of the film thickness using the determined parameters. Similar results were obtained on grains with orientation angles wsub between 108 and 608. No grains with higher orientation angles could be found on the investigated polycrystalline sample. The ZrO 2 films exhibited two major film axis orientations, namely w f s 22.58 for wsub ) 308 and w f s 458 for wsub - 308. Apparently, in all these cases an anisotropicranisotropic system exists and AME reveals its full power for the study of epitaxy relations
Anodic film formation was studied by AME on single titanium and zirconium grains. For both systems the crystallographic orientation angles w of the substrate grains were determined prior to oxide formation. Subsequently, AME measurements were performed on films grown at different formation potentials, different thicknesses, respectively. This allowed us to determine the film thickness as well as the optical and crystallographic parameters of the films simultaneously. It was shown that the properties of both the TiO 2 and ZrO 2 films vary with the grain orientation in a systematic manner. In case of Ti a significant increase of the thickness and decrease of the defect state density of the n-type semiconducting TiO 2 films with increasing substrate angle w was found. The oxide films were amorphous on all grains showing that TirTiO2 is an anisotropicrisotropic system. This can be explained by the large lattice mismatch between Ti and the crystalline TiO 2 modifications. In comparison, the lattice mismatch between Zr and the monoclinic ZrO 2 is smaller than for the TirTiO2 system leading to crystalline films on all grain surfaces Žanisotropicranisotropic system. but
A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
the Ž0001. orientation which is the closest-packed one. This study shows that AME provides a powerful tool for the study of film formation at high lateral resolution and points to the fact that the anisotropy of any system must not be neglected but has to be carefully checked before spectroscopic ellipsometry is applied. Moreover, it can be concluded, that measurements of passive films on macroscopic surfaces can in principle not be quantitatively understood in terms of classical models without taking texture effects into account, as macroscopic measurements can deliver only averaged data. Acknowledgements The financial support of the Deutsche Forschungsgemeinschaft DFG for one of us ŽAM. is gratefully acknowledged. References w1x S. Kudelka, A. Michaelis, J.W. Schultze, Ber. Bunsenges. Phys. Chem. 99 Ž1995. 1020.
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w2x S. Kudelka, A. Michaelis, J.W. Schultze, Electrochim. Acta 41 Ž1996. 863. w3x A. Michaelis, J.W. Schultze, Thin Solid Films 274 Ž1996. 82. w4x J.D. McCullough, K.N. Trueblood, Acta Cryst. 12 Ž1959. 507. w5x J. Fitzwilliam, A. Kaufmann, C. Squire, J. Chem. Phys. 9 Ž1941. 678. w6x M.M. Lohrengel, Mater. Sci. Eng. R11 Ž1993. 243. w7x Lj.D. Arsov, Electrochim. Acta 30 Ž1985. 1645. w8x K.K. Svitashev, A.I. Semenenko, L.V. Sevenenko, V.K. Sokolov, Opt. Spectrosc. 34 Ž1973. 542. w9x M. Erman, J.B. Theeten, J. Appl. Phys. 60 Ž1986. 859. w10x A.B. Sushkov, E.A. Tischenko, Opt. Spectrosc. ŽUSSR. 72 Ž1992. 265. w11x P.G. Etchegoin, J. Kircher, M. Cardona, Phys. Rev. B 47 Ž1993. 10292. w12x P.G. Etchegoin, M. Cardona, Solid State Commun. 82 Ž1992. 655. w13x A. Michaelis, J.W. Schultze, Appl. Surf. Sci. 106 Ž1996. 483. w14x N. Cabrera, N.F. Mott, Rep. Prog. Phys. 12 Ž1948. 163. w15x Landolt-Bornstein, 6th ed., vol. IIr8. ¨
An anisotropy microellipsometry Ž AME. study of anodic film formation on Ti and Zr single grains A. Michaelis, M. SchweinsbergU Institut fur 40225 Dusseldorf, Germany ¨ Physikalische Chemie und Elektrochemie, Heinrich-Heine-Uni¨ersitat ¨ Dusseldorf, ¨ ¨
Abstract Anisotropy microellipsometry ŽAME. and photoresist microelectrochemistry were applied simultaneously to study the anodic film formation on the optically anisotropic valve metals zirconium and titanium. All measurements were performed in situ Ž0.5 M H 2 SO4 . on single-substrate grains of technically relevant polycrystalline material. In addition to standard parameters, such as the film thickness and the optical constants of substrate and layer, AME yields the angle w between the optical axes of the samples and the surface normals. This allows a quantitative correlation of the microelectrochemically measured film properties with the crystallographic orientation of substrate grains. It was found that the properties of both TiO 2 and ZrO 2 films vary with the grain orientation in a systematic manner. For Ti, a significant increase of the thickness along with a decrease of the defect state density of the n-type semiconducting TiO 2 films with increasing substrate angle w was observed. The TiO 2 films were amorphous on all grains. In contrast, the ZrO 2 films were crystalline on all grain surfaces but the Ž0001. orientation which is the closest-packed one Ž w s 08.. Q 1998 Published by Elsevier Science S.A. Keywords: Anisotropy; Titanium; Zirconium; Passive films; Epitaxy
1. Overview 1.1. Introduction The reactivity of solids is often dominated by the properties of ultrathin passive films which cover and protect the surfaces. For instance, the valve metals Ti and Zr which are widely used in mechanical engineering and chemical apparatus construction owe their exceptional corrosion resistance against aggressive environments to their thin oxide films. However, local reactions, such as pitting can be critical for these passive materials. In order to elucidate the underlying local mechanisms, in situ micromethods must be applied which feature both high vertical and lateral resolution. This is of particular importance for technically relevant polycrystalline substrates since the passive film properties vary from grain to grain. This is
U
Corresponding author. Fax: q49 211 811803.
illustrated in Fig. 1, showing a micrograph of a Tisurface covered by an oxide film with an average thickness of 40 nm. The interference colors due to the oxide films exhibit a strong grain dependence. Consequently, all experiments presented in this study were performed on single grains. For this, microellipsometry, especially AME, was applied along with a recently developed photoresist microelectrode method which allows one to perform all kinds of electrochemical measurements at high lateral resolution. The latter method is described in full detail by Kudelka et al. w1,2x and is shown schematically in Fig. 2a. In this article the AME is emphasized. Fig. 2 illustrates that AME and photoresist microelectrochemistry can be applied on identical grains. 1.2. The AME method The fundamentals of AME and its application for the determination of crystal orientations of optically anisotropic systems are described in a recent publica-
0040-6090r98r$19.00 Q 1998 Published by Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00992-9
A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
757
Fig. 3. Illustration of an AME measurement on the ZrrZrO 2 system. Analysis of the DŽ a . and C Ž a . curves allows the determination of the angles w between the sample surface normal and the optical axes c.
Fig. 1. Micrograph of a polycrystalline TirTiO2 surface Žaverage Ti grain diameter: 50 m m, average TiO 2 film thickness: 40 nm.. The interference colors are due to the TiO 2 passive film and vary from grain to grain indicating that each substrate grain behaves independently.
tion w3x and will therefore be reviewed here only briefly. AME yields the angle w between the optical axis Ž c-axis. and the surface normal of any anisotropic system. For this, the ellipsometric parameters D and C are measured as a function of the angle a which describes rotation of the sample around the surface normal. The amplitudes of the resulting sinusoidal
Fig. 2. Electrochemical and optical micromethods under microscopic control. Ža. Schematic of the photoresist microelectrode set-up which allows us to perform electrochemical measurements in the standard three electrode configuration on single substrate grains ŽCE, counter electrode; RE, reference electrode; grain a is the working electrode, WE; lateral resolution ) 2 m m. w1,2x. Žb. Microellipsometry can be carried out on the same grains.
DŽ a . and C Ž a . curves are a direct measure for the orientation angle w . For the case of an additional optically anisotropic film on top of the substrate, characteristic changes in amplitude and phase of these curves occur depending on film thickness d f and crystallographic orientation of the substrate wsub and the film w f which can therefore be determined separately. Fig. 3 illustrates the AME method with the ZrrZrO 2 system as an example. Both Zr and Ti crystallize in the hcp lattice and are therefore uniaxially birefringent. Measurements on the particular grain surfaces Ž0001., Ž0111. and Žxxx0., which denotes any surface parallel to the c-axis, are presented here. The Ž0001. surface is the closestpacked one ŽTi: as 0.2952 nm, c s 0.4679 nm; Zr: as 0.3232 nm, c s 0.5147 nm.. The corresponding oxide layers TiO 2 and ZrO 2 exist in three different low-temperature modifications. The ones for TiO 2 are anatase Žtetragonal, as 0.3785 nm, c s 0.9514 nm., rutile Žtetragonal, as 0.4593 nm, c s 0.2959 nm. and brookite Žorthorhombic, as 0.9184 nm, bs 0.5447 nm, c s 0.5145 nm.. The most important ZrO 2 modification is baddeleyeite, which has a monoclinic unit cell Ž as 0.5169 nm, bs 0.5232 nm, c s 0.5341 nm, b s 998150 .. Additionally, tetragonal and hexagonal ZrO 2-structures are discussed in the literature w4,5x. All of these modifications are optically anisotropic and can therefore be detected and characterized by AME. Besides these crystalline modifications, amorphous films may be present on the metal surfaces w6x. 2. Experimental For all experiments Ti Ž99.98%. and Zr Ž99.98%. high-purity samples with a coarse grain texture were
758
A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
used enabling us to carry out several independent measurements on each single grain Žaverage grain diameter ) 500 m m.. The samples were polished with emery paper up to grade 4000, yielding plane surfaces with closed grain boundaries. To obtain samples with open grain boundaries for investigations on single grains, the mechanically polished samples were subsequently electropolished as described by Arsov w7x. The anodic oxide films were formed potentiodynamically in aqueous 0.5 M H 2 SO4 solution using a high-voltage potentiostat. Electrochemical potentials are given with respect to the standard hydrogen electrode ŽSHE.. For spectroscopic ellipsometry a custom built rotating analyzer apparatus was used which was equipped with an optical multichannel analyzer ŽOMA. system and a 500-W Xe arc lamp as the light source. Additionally, single wavelength ellipsometry was performed by another automated rotating analyzer ellipsometer ŽSentech AFE 401. with a HeNe laser Ž l s 632.8 nm. as the light source. All measurements were carried out at an angle of incidence of 708. The polarizer azimuth was 458. In order to allow the AME sample rotation around the surface normal, a special in situ cell configuration was constructed. For this, the windows were mounted on the ellipsometer arms using an alignable connector and simply dipped into the electrolyte. Therefore rotation of the entire cell containing the sample in three electrode configuration was possible without affecting the window alignment. To obtain a lateral resolution of 50 m m, a singlet laser bestform lens with a focal length of f s 13 mm was employed in order to minimize focusing errors. For more details concerning the effect of focusing on the ellipsometric measurables, see Svitashev et al. w8x, Erman and Theeten w9x and Sushkov and Tischenko w10x. 3. Results 3.1. Spectroscopic anisotropy ellipsometry (SAME) In Fig. 4, ellipsometric spectra taken on Ti ŽFig. 4a. and Zr ŽFig. 4b. single grains are shown for different sample rotation angles a . For these measurements, freshly electropolished samples, i.e. almost layer-free surfaces were used. In both cases the AME effect, i.e. the dependence of the measurables D and C on a is obvious over the entire spectral range. Additionally, the DŽ a . and C Ž a . variation amplitudes are a function of the wavelength. This spectral dependence of the amplitudes is particularly pronounced for the Ti sample showing a maximum variation around 600 nm. Therefore in order to find the range of maximum AME sensitivity, spectroscopic ellipsometry is neces-
Fig. 4. Ellipsometric spectra for different sample rotation angles a Ž1 s 08, 2 s 308, 3 s 608, 4 s 908, 5 s 1208, 6 s 1508.. Ža. Electropolished Ti-crystal Žxxx0. orientation w1x, Žb. electropolished Zrcrystal.
sary. In case of Ti and Zr, single wavelength measurements at the HeNe-laser wavelength of 632.8 nm are sufficient for AME analysis. Consequently, the subsequent measurements were performed at this wavelength only. It must be emphasized that the anisotropy causes a very strong variation of the D and C measurables even exceeding 208 in the case of the D values on the Ti substrate. Consequently, the effect of anisotropy must never be neglected and each system has to be checked carefully before ellipsometry in isotropic approximation is applied. This is of particular importance for thin film analysis since internal film stresses due to lattice mismatches at the substraterfilm interface can cause a significant anisotropy even for isotropic crystal structures Žstress-birefringence. w11,12x. The quantitative interpretation of AME measurements on such isotropicrisotropic systems will be the subject of a forthcoming article.
A. Michaelis, M. Schweinsberg r Thin Solid Films 313]314 (1998) 756]763
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3.2. Determination of the optical constants of the substrate In order to determine the ordinary Ž n o . and extraordinary Ž n ao . complex refractive indexes of the bare Ti and Zr substrates, AME measurements on four different oriented, freshly electropolished grains were carried out. These experimental curves were fitted simultaneously for each substrate by a leastsquare fit procedure as explained by Michaelis and Schultze w3x. The resulting DŽ a . and C Ž a . simulation curves are shown as a function of the orientation angle w in Fig. 5 for the case of Zr. The four experimental curves taken on the four different grains are indicated, allowing one to determine the corresponding grain orientation angles w . The resulting substrate parameters for the wavelength of 632.8 nm are n o ŽZr. s 2.18 y i3.41 and n ao s 2.225 y i2.54. These parameters can be checked independently by their comparison with macroscopically determined ones on mechanically polished samples. Mechanical polishing yields an amorphous and therefore isotropic Beilby layer resulting in an average isotropic complex refractive index n iso . The correlation between n iso and the anisotropic parameters is given by the equation: n iso s 2r3n ao q 1r3n o .
Ž1.
A value of n iso ŽZr. s 2.21 y i2.83 was measured showing excellent agreement with the calculated one according to Eq. Ž1., therefore confirming the determined anisotropic parameters. Analogous evaluations for Ti yielded n o ŽTi. s 2.91y i3.8 and n ao s 2.62y i3.38 w3x. 3.3. AME study of passi¨e film formation 3.3.1. The Ti r TiO2 system The TiO 2 films were formed potentiodynamically in 0.5 M H 2 SO4 at a sweep rate of 50 mVrs. AME measurements were performed on various deliberately chosen grains of a polycrystalline sample. In order to determine the optical film parameters, the crystallographic orientation angles w of substrate and layer and the film thickness d f simultaneously, the procedure of film thickness variation was applied assuming the optical film parameters to be independent of d f . The d f variation can simply be realized by measuring films formed at different potentials. According to the high field mechanism, the films are formed at a constant factor. As shown below this factor is approx. 2 nmrV varying with the grain orientation. As an example Fig. 6 shows AME measurements on Ž0001. and Ž0111. oriented grains for two different formation potentials Ž8 V and 16 V.,
Fig. 5. Calculated AME curves as a function of the orientation angle a for Zr using the optical parameters given in the text. The experimental curves obtained on four different oriented, freshly electropolished Zr grains are indicated.
yielding two different film thicknesses. The symbols refer to the experimental data, the solid lines to the fit. Interestingly, isotropic optical constants of n s 2.2 y i0 on top of the Ž0111. grain and n s 2 y i0 on top of the Ž0001. grain were found. The isotropic behaviour of the TiO 2 layers was observed on all grains, i.e. the films did not contribute to the AME effect at all. Consequently, no dependence of the amplitudes and phases of the DŽ a . and C Ž a . curves on the film thickness occurred. From these experimental findings it can be concluded that the TiO 2 films are amorphous or at least nanocrystalline without any preferential orientation. This is in agreement with photocurrent spectroscopic studies where a pronounced sub-band tailing ŽUrbach-tail . of the n-type semiconducting TiO 2 films is observed w13x. Therefore the TirTiO2 system can be considered as an anisotropicr isotropic system. Despite the amorphous character of the TiO 2 films, a significant texture dependence exists. This fact is obvious in the corresponding layer formation cyclic
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Fig. 7. Film formation cyclovoltammograms on different Ti grains measured by means of the photoresist electrode technique Žsweep rate 50 mVrs. w1x.
Fig. 6. AME curves on two differently oriented Ti grains and two different TiO 2 film thicknesses Žformation potentials: 8 V and 16 V.. The symbols refer to the measured data, the solid lines to the fit.
voltammograms taken on the different oriented Ti grains by means of the photoresist method. These measurements are shown in Fig. 7. Apparently, the grain orientation has a significant influence on the anodic current density. The total anodic current density i is composed of four contributions: i s i Ox q i O2 q i corr q i C with i Ox , oxide formation; i O2 , oxygen evolution; i corr , corrosion current; and i C , current due to capacitive charging of the Helmholtz layer. The latter two contributions are of minor importance Ž m Arcm2 range. and can therefore be neglected. Since no oxygen evolution takes place below potentials of 3 V, the corresponding current can be attributed exclusively to oxide formation i Ox . The coulometrical evaluation of the charges in this potential region yields oxide formation factors of approx. 2 nmrV which significantly depend on the grain orientation. Even more pronounced are the differences in the potential region above 3 V. Here, oxygen evolution occurs showing a strong dependence on the grain orientation.
The texture dependence of the film properties was confirmed by microelectrochemical capacity measurements which are discussed by Kudelka et al. w1,2x. From the Schottky]Mott analysis of these capacity measurements, electronic film properties, such as the defect state concentration ND can be determined. In Fig. 8 the film formation charges determined in the coulometrically evaluable region as well as the defect state concentration ND of the films are correlated with the orientation angle w of the substrate grains. The important result is that the film properties vary with the substrate crystallographic orientation in a systematic manner. The formation charge increases and the defect state concentration decreases with increasing orientation. This leads to the model shown in Fig. 9 illustrating the consistency of the experimental findings. On closely packed surfaces, such as the Ž0001. surface, thin layers with a high defect state concentration N are formed. This is explained by the corresponding band scheme shown in Fig. 9b for the case of an applied anodic potential of 2 V. Due to the high defect state concentration, the necessary potential drop for oxide growth according to the high field mechanism can not be maintained at the metalroxide interface leading to an inhibition of oxide growth. In contrast, the lower defect state concentration on loosely packed surfaces, such as Žxxx0. leads to a larger extension of the space charge layer resulting in the observed higher film thickness. The influence of the crystal substrate orientation on the film properties points towards a dominating effect of the metalroxide interface on the film formation reaction according to the Cabrera]Mott model w14x.
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Fig. 8. Charge measured during the anodic oxide formation in the coulometrically evaluable region and TiO 2 defect state concentration ND from capacity measurements as a function of the substrate grain orientation angle w . Each data point refers to one measurement on a certain Ti grain w2x.
3.3.2. The Zr r ZrO2 system Measurements analogous to the above ones were carried out on the ZrrZrO 2 system. Fig. 10 shows AME measurements taken on a Ž0111. oriented Zr grain for four different formation potentials between 10 and 40 V. In contrast to the Ti measurements in Fig. 6, now a strong dependence of the amplitudes and phase relation between the DŽ a . and C Ž a . curves on the formation potential is observed. These amplitude and phase shifts are clearly due to the ZrO 2
Fig. 9. Model for the texture dependent oxide growth on Ti. The band structures were calculated for an 2 V anodic potential w2x.
films which contribute to the anisotropy of the system. The additional anisotropy effect of the anodic oxide constitutes clear evidence for the formation of an ordered crystalline passive film with a well defined epitaxial relation to the substrate grain. The mea-
Fig. 10. AME curves on a Ž0111. oriented Zr single grain for four different formation potentials; the corresponding film thicknesses are indicated. The symbols refer to the measured data, the lines to the fit. Significant amplitude and phase variations are observed.
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Fig. 12. Model for texture-dependent anodic oxide growth on Zr derived from the AME results.
for this system class. However, on Ž0001. oriented grains Žclosest-packed surfaces . no anisotropy contribution of the films were observed indicating an amorphous character of the layers formed on this particular orientation. The found epitaxial relations between substrate and films are summarized schematically in Fig. 12. Additionally, the ellipsometrically determined film formation factors are given in this figure. These measurements confirm that AME is well suited for investigation of epitaxial film formation. 4. Summary and conclusions Fig. 11. Calculated DŽ a . and C Ž a . curves as a function of the ZrO 2 film thickness for the Zr Ž0111. surface.
sured curves can be fitted excellently assuming a film orientation angle w f of 22.58 and the following optical constants: n o ŽZrO 2 . s 2.13y i0, n ao ŽZrO 2 . s 2.20y i0. These values are consistent with literature data for monoclinic crystalline ZrO 2 w15x. In spite of the biaxial nature of this material, a uniaxial approximation can be used because the two extraordinary indices are almost equal and can therefore be treated as identical. Fig. 11 shows the calculated DŽ a . and C Ž a . curves as a function of the film thickness using the determined parameters. Similar results were obtained on grains with orientation angles wsub between 108 and 608. No grains with higher orientation angles could be found on the investigated polycrystalline sample. The ZrO 2 films exhibited two major film axis orientations, namely w f s 22.58 for wsub ) 308 and w f s 458 for wsub - 308. Apparently, in all these cases an anisotropicranisotropic system exists and AME reveals its full power for the study of epitaxy relations
Anodic film formation was studied by AME on single titanium and zirconium grains. For both systems the crystallographic orientation angles w of the substrate grains were determined prior to oxide formation. Subsequently, AME measurements were performed on films grown at different formation potentials, different thicknesses, respectively. This allowed us to determine the film thickness as well as the optical and crystallographic parameters of the films simultaneously. It was shown that the properties of both the TiO 2 and ZrO 2 films vary with the grain orientation in a systematic manner. In case of Ti a significant increase of the thickness and decrease of the defect state density of the n-type semiconducting TiO 2 films with increasing substrate angle w was found. The oxide films were amorphous on all grains showing that TirTiO2 is an anisotropicrisotropic system. This can be explained by the large lattice mismatch between Ti and the crystalline TiO 2 modifications. In comparison, the lattice mismatch between Zr and the monoclinic ZrO 2 is smaller than for the TirTiO2 system leading to crystalline films on all grain surfaces Žanisotropicranisotropic system. but
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the Ž0001. orientation which is the closest-packed one. This study shows that AME provides a powerful tool for the study of film formation at high lateral resolution and points to the fact that the anisotropy of any system must not be neglected but has to be carefully checked before spectroscopic ellipsometry is applied. Moreover, it can be concluded, that measurements of passive films on macroscopic surfaces can in principle not be quantitatively understood in terms of classical models without taking texture effects into account, as macroscopic measurements can deliver only averaged data. Acknowledgements The financial support of the Deutsche Forschungsgemeinschaft DFG for one of us ŽAM. is gratefully acknowledged. References w1x S. Kudelka, A. Michaelis, J.W. Schultze, Ber. Bunsenges. Phys. Chem. 99 Ž1995. 1020.
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w2x S. Kudelka, A. Michaelis, J.W. Schultze, Electrochim. Acta 41 Ž1996. 863. w3x A. Michaelis, J.W. Schultze, Thin Solid Films 274 Ž1996. 82. w4x J.D. McCullough, K.N. Trueblood, Acta Cryst. 12 Ž1959. 507. w5x J. Fitzwilliam, A. Kaufmann, C. Squire, J. Chem. Phys. 9 Ž1941. 678. w6x M.M. Lohrengel, Mater. Sci. Eng. R11 Ž1993. 243. w7x Lj.D. Arsov, Electrochim. Acta 30 Ž1985. 1645. w8x K.K. Svitashev, A.I. Semenenko, L.V. Sevenenko, V.K. Sokolov, Opt. Spectrosc. 34 Ž1973. 542. w9x M. Erman, J.B. Theeten, J. Appl. Phys. 60 Ž1986. 859. w10x A.B. Sushkov, E.A. Tischenko, Opt. Spectrosc. ŽUSSR. 72 Ž1992. 265. w11x P.G. Etchegoin, J. Kircher, M. Cardona, Phys. Rev. B 47 Ž1993. 10292. w12x P.G. Etchegoin, M. Cardona, Solid State Commun. 82 Ž1992. 655. w13x A. Michaelis, J.W. Schultze, Appl. Surf. Sci. 106 Ž1996. 483. w14x N. Cabrera, N.F. Mott, Rep. Prog. Phys. 12 Ž1948. 163. w15x Landolt-Bornstein, 6th ed., vol. IIr8. ¨