Enhanced birefringence in vacuum evaporated silicon thin films Gisia Beydaghyan, Kate Kaminska, Tim Brown, and Kevin Robbie
We report an experimental study of enhanced optical birefringence in silicon thin films on glass substrates. Form anisotropy is introduced as an atomic-scale morphological structure through dynamic control of growth geometry. The resulting birefringence is large compared with naturally anisotropic crystals and is comparable to two-dimensional photonic crystals. The films are fabricated with serial bideposition onto a substrate held at a fixed tilt angle relative to the impinging vapor. Films were analyzed by spectroscopic ellipsometry and scanning electron microscopy, the latter clearly revealing form anisotropy in a morphology of bunched columns perpendicular to the deposition plane with dimensions of hundreds of nanometers and smaller. The observed linear birefringence varies with wavelength and tilt angle, with a maximum of 0.4 at a 630-nm wavelength and 0.25 at 1500 nm. © 2004 Optical Society of America OCIS codes: 160.1190, 260.1440, 260.2130, 310.1860, 310.6860.
1. Introduction
Optical materials with an anisotropic electromagnetic response are essential elements in optical systems, typically constructed from precisely cut naturally occurring uniaxial and biaxial crystals to create phase retardance plates, prisms, and polarizers.1 Vapor-deposited thin-film anisotropic coatings2,3 are promising candidates for inclusion as elements in integrated photonic systems employing photonic band engineering for communications,4 computation,5 and other applications. The atomicscale morphology of glancing-angle-deposited thinfilm materials provides an opportunity to tailor the anisotropic photonic response in new and predictable ways.6 Naturally occurring anisotropic materials are generally incompatible with integrated photonic technologies and often cannot be fabricated as thin films. The natural optical axes of these materials require at least one precise oblique cut of a crystal; otherwise the magnitude of birefringence available to light
The authors are with the Department of Physics, Queen’s University, Kingston, Ontario K7L 3N6, Canada. The e-mail address for G. Beydaghyan is
[email protected]. The e-mail address for K. Robbie is
[email protected]. Received 11 November 2003; revised manuscript received 22 June 2004; accepted 22 June 2004. 0003-6935兾04兾285343-07$15.00兾0 © 2004 Optical Society of America
propagating normal to the plane is limited. The small number of naturally occurring birefringent materials also strongly limits device possibilities. Onesided obliquely deposited thin films of many optically isotropic materials exhibit birefringence larger than that of natural uniaxial crystals7–10 and can be fabricated from a large selection of source materials; yet these films are optically biaxial with the birefringence available for light propagating normal to the substrate considerably smaller than the maximum birefringence. Serial bideposition11,12 significantly increases the normal-incidence birefringence, enabling new optical devices and systems. The serial bideposition technique produces large birefringence in metal oxide films for visible light propagating normal to the substrate2,3,11 and highly anisotropic electrical conductivity in metal films.12 A flat substrate is tilted relative to the arriving vapor flux and rotated about its normal with periodic film subdeposits made at azimuthal angles of 0, 180, 360, . . . deg by means of pausing the substrate rotation and depositing a small fixed amount of vapor. Large subdeposits produce a zigzag or chevron microstructure.9,12 For subdeposit thicknesses approaching a single atomic layer, the resulting films develop a porous nanostructure extending perpendicular to the substrate with large in-plane anisotropy, producing large optical birefringence. Hodgkinson and Wu measured birefringence at a light wavelength of 633 nm of ZrO2, Ta2O5, and TiO2 films bideposited at substrate tilt angles of 55, 60, 65, and 70 deg.3 In1 October 2004 兾 Vol. 43, No. 28 兾 APPLIED OPTICS
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plane birefringence, defined as the difference between the two in-plane refractive indices, as large as 0.15 was observed. Also, chiral films with large circular birefringence were fabricated by precessing the azimuthal location of the deposition with deposited film thickness.11 The films have three distinct, mutually perpendicular optical axes 共one perpendicular to the substrate plane and two in plane兲 and have a large birefringence of light propagating through the film in a direction normal to the substrate. The birefringence varies with film material and tilt angle and does not require that the film material be birefringent in bulk form. Consequently, this technique enables a tremendous range of design possibilities. The method is compatible with other thin-film technologies and can likely be used in integrated optical systems. Varying the optical response of the films, for example, with infiltration of liquid crystals, allows for tunable birefringence.13 Anisotropy in an optical,9 electrical,12,14 and magnetic15,16 response in thin films of many materials can be induced when the vapor is impinged onto the substrate at an off-perpendicular incidence. The anisotropic properties of one-sided obliquely deposited films vary with substrate tilt, growth temperature, vapor composition, and background gas; and bideposited films are expected to exhibit similar dependence. In this paper silicon thin films 共bideposited at ten substrate tilt angles from normal to perpendicular to the vapor flux兲 are analyzed with spectroscopic ellipsometry and scanning electron microscopy 共SEM兲. Spectroscopic ellipsometry combines precise measurement of the polarization state of light transmitted or reflected by the film and substrate, with effective-medium modeling and numerical regression, to quantify an optical response. The complex refractive index is determinable, quantifying light refraction and absorption. Birefringence, a measure of anisotropic refraction, is defined as the difference in refractive index between two orthogonal directions of light propagation 共or equivalently two orthogonal polarizations兲, ␦n ⬅ ny ⫺ nx. Dichroism, a measure of anisotropic absorption, is defined as the difference in absorption between orthogonal polarizations, ␦␣ ⬅ ␣y ⫺ ␣x. With an appropriate effective-medium model, ellisometry is capable of yielding measured complex indices of refraction in three mutually orthogonal directions. For bideposited films, deposition symmetry dictates that the three optical axes will be perpendicular to the substrate plane, in the substrate plane, and perpendicular to the vapor arrival vector in both the substrate plane and the deposition plane 共containing the vapor arrival vector and the substrate normal兲. Defining the planar birefringence as the difference in refractive index observed between orthogonal polarizations of light incident normal to the substrate surface plane, we show that the planar birefringence is a monotonically decreasing function of light wavelength for the range of our spectrometer, from 500 to 1500 nm, with the largest birefringence observed in films deposited with a substrate tilt angle of approximately 60 deg. SEM pro5344
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Fig. 1. Physical schematic of the evaporator used in this study. The vapor source is approximately 25 mm in diameter and 500 mm directly below the substrate.
vides accurate thickness measurements 共used to verify the accuracy of the effective-medium regression兲 and a morphological description of the films. Nanometer-scale form anisotropy, producing anisotropic polarizability, is seen to be the origin of optical birefringence, with Fourier-transform techniques providing a quasi-quantitative measure of the structural anisotropy observed with SEM. Serial bideposition is one variation of thin-film growth onto substrates tilted at a large angle with respect to the incoming vapor.3 When substrate tilt is sufficiently large, and there is limited adatom mobility on the surface, the resulting film structure is porous, with a fibrous, columnar, or fractal microstructure.12,17 Combining the dynamic variation of both substrate tilt and aximuthal angle 共rotation兲 generates a vast range of thin-film design possibilities6 with physical properties significantly different from those of the material in bulk form. As the nanostructure and the porosity of the resulting film can be controlled independently, to some extent, optical properties can be designed.18 2. Experimental Results A.
Method
Our evaporator equipment includes an ultra-highvacuum electron-beam evaporator, a stepper-motorcontrolled substrate holder and manipulator, and a quartz-crystal rate monitor, all housed in an ionpumped, copper-gasketted vacuum chamber 共see Fig. 1兲. The electron-beam evaporator, with four 7-cm3 crucible pockets, is located 50 cm directly beneath the substrate. The crucibles are on a linear translation stage, and each of the four crucibles can be alternately centered below the substrate. An annular reservoir inside the chamber between the evaporator and substrate, filled with liquid nitrogen, shields the substrate manipulator and the upper portions of the chamber from radiant heating and extraneous vapor deposition. The manipulator is equipped with two linear translation stages for the substrate transfer
and two stepper motors to provide tilt and azimuthal rotation of the substrate. Substrates are introduced through a turbomolecular-pumped load-lock chamber, which is pumped to approximately 10⫺4 Pa 共10⫺6 Torr兲 before the gate valve to the ultra-high-vacuum chambers is opened. Substrates are transferred from the load-lock chamber to the sample manipulator in the evaporator chamber in two steps, with an extendable transfer arm in a central distribution chamber. Fabrication of the films is monitored and controlled with a deposition program written in the LabVIEW instrumentation development environment. The deposition program controls the tilt and azimuthal angles of the substrate, controls the emission power of the electron beam, and can maintain the deposition rate at a constant desired value. Two pneumatic shutters are also controlled, shielding the quartzcrystal rate monitor or the substrate from the vapor. Substrate temperature 共measured with a thermocouple within the manipulator兲 and pressure 共measured with two ion gauges and two thermocouple gauges兲 are monitored throughout each deposition and logged for validation. The instrumentation software has many present film structures with tailorable parameters and can produce almost arbitrary motion profiles of desired substrate tilt and rotation as a function of measured accumulated film thickness. Substrate temperature is not yet dynamically variable and will be the subject of future development and study. We deposited thin films of silicon on glass substrates with serial bideposition at tilt angles of 0, 20, 40, 50, 60, 70, 75, 80, 85, and 90 deg. Films were deposited onto Corning 7059 glass substrates to a nominal thickness of 200 nm, as measured with the quartz-crystal microbalance thickness monitor situated near the substrate. The subdeposit thickness was kept constant at 5 nm for all films. The deposition rate was approximately 0.5 nm兾s, and the time taken by the stepper motor to rotate the substrate through each 180-deg rotation was approximately 1–2 s. The base pressure of the chamber was less than 10⫺7 Pa 共10⫺9 Torr兲 for all films, and the pressure during deposition was always below 10⫺5 Pa 共10⫺7 Torr兲. To maintain an accurate record of the orientation of the deposition plane, a small hole was made in the outside edge of each sample platen. Prior to each deposition, the holder was positioned with the hole oriented toward the evaporator, therefore locating the deposition plane. Immediately upon removal from the vacuum chamber, the orientation was marked with a scratch on the substrate with a diamond scribe. We performed ellipsometry measurements at varying orientations relative to this indication of the deposition plane on the substrate. As the precision of this alignment is limited to a few degrees, the true deposition plane was taken as the orientation that produced the largest measured birefringence. Observed deposition plane orientation and alignment marks were always in agreement within the precision of the alignment mark.
For comparison, two other sets of silicon films on glass were fabricated. We made films of pillar structures by keeping the substrate tilt constant and continuously rotating the substrate about its normal. These films were made at tilt angles of 40, 50, 60, 70, 75, 80, 85, and 87 deg. We fabricated another set of films, called six-sided, by pausing the substrate rotation every 60 deg and making subdeposits of 5 nm. These were made at tilt angles of 50, 60, 70, and 80 deg. The remaining deposition parameters for these two sets were identical to the bideposited films. B.
Ellipsometry of Bideposited Films
Ellipsometry measures the change in the polarization ellipse of light reflected 共or transmitted兲 from a sample material. The measurement is usually expressed in terms of the parameters ⌿ and ⌬ defined by tan共⌿兲exp共i⌬兲 ⫽ ⫽ R p兾R s, where Rp and Rs are the complex Fresnel reflection coefficients of the material for p- 共in the plane of incidence兲 and s- 共perpendicular to the plane of incidence兲 polarized light.19 Optical parameters of the material can be determined with regression analysis to fit the physically meaningful model of the system to the experimental data. Ellipsometric analysis of bideposited films was performed with a Woollam M-2000 rotating compensator ellipsometer20 covering a light vacuum wavelength range of 370 –1670 nm. The software used for data acquisition and regression fitting was WVASE32, which was provided with the instrument. For each film, reflection ellipsometry, transmittance, and depolarization spectra were measured with the incident polarization parallel to the deposition and perpendicular to it. Each film was modeled as a biaxial medium, with three mutually perpendicular optical axes defined as follows: The z axis was taken to be normal to the substrate, the y axis normal to the deposition plane and in the substrate plane, and the x axis in the substrate and deposition planes. We calculated the refractive indices as an effective-medium approximation mixture of amorphous silicon and void using a Bruggeman formalism.21,22 Measurements were performed in air at room temperature, with no response observed with a moderate humidity variation. Lack of optical absorption in silica 共SiO2兲 within the bandwidth of our spectrometer prevents distinction of the expected oxidized silicon surface from a void in the effective-medium model, precluding calculation of absolute porosity or oxygen content. Accurate calculated effective index and absorption measurements do not require this distinction. In situ ellipsometry can determine the absolute porosity of as-deposited silicon films, as little silica is formed in vacuum. In situ measurements are in progress. Depolarization factors in the x and y directions 共Lx and Ly兲 were treated as fit parameters, whereas Lz was kept fixed at zero, as expected from the columnar morphology of the films.22 Indeed, when taken as a 1 October 2004 兾 Vol. 43, No. 28 兾 APPLIED OPTICS
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Fig. 2. Ellipsometry of experimental and model fitted data for a bideposited film of silicon on glass at a tilt angle of 60 deg.
fitted parameter, Lz always converged to a small value. The fittings were done simultaneously for both sets of ellipsometry data 共parallel and perpendicular to the deposition plane兲, with the same model applied to both except for the Euler angle that was fixed at 0 or 90 deg. This analysis was used to quantitatively account for incoherent scattering from the back of the substrate. Other fitted parameters were the relative composition of amorphous silicon and void and the thickness of the film. The measured ellipsometry parameters for a film bideposited at a substrate tilt angle of 60 deg are shown in Fig. 2, together with the data fitted to the biaxial effectivemedium model of silicon on glass. The difference between experimental and generated data is quantified by the mean square error. The mean square error is usually normalized by experimental standard deviations so that noisy data are weighed less heavily. An effective-medium approximation model was used to fit the ellipsometric data to yield thicknesses and optical constants of the film. The thicknesses were further confirmed with SEM and were in good agreement with those produced with effectivemedium modeling. The thickness of the film decreases as a function of tilt angle, as illustrated in Fig. 3, consistent with other studies of glancingangle-deposited films.23 This decrease is primarily due to the magnitude of the vapor flux arriving on a unit area of the substrate decreasing as a cosine of the tilt angle. Atomic shadowing, on the other hand, increases with substrate tilt and creates increasing porosity in the film, increasing thickness above that predicted by the cosine trend, and lowering all three effective indices of refraction. The nanostructure of the film cross section exhibits an atomic-scale corrugated structure when SEM is imaged perpendicular to the deposition plane. The film in Fig. 4 was cleaved along the deposition plane and imaged perpendicular to the cleave. From the perspective of the scanning electron microscope image of the cleaved edge, the vapor arrived alternately from the left and the right, clearly producing the layered structure. Scanning electron microscope images perpendicular to Fig. 4 have a similar appearance, but with a less pronounced corrugation. 5346
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Fig. 3. Thickness of bideposited and rapid-rotation films as a function of tilt angle for a constant deposited thickness measured on the quartz thickness monitor. The theoretical vapor flux arriving at the substrate is proportional to the cosine of the tilt angle 共dotted curve兲. The difference between the predicted cosine dependence and the observed thicknesses is a result of nanometerscale porosity.
In-plane indices 共nx and ny兲 have a similar magnitude, decreasing with substrate tilt; the out-of-plane index nz is consistently larger, but shows a similar decrease with substrate tilt 共see Fig. 5兲. The variance of in-plane index ny with wavelength and substrate tilt is shown in Fig. 6. Furthermore, the results show that nx 共the index for light polarized parallel to the deposition plane兲 is consistently lower than ny 共the index for light polarized perpendicular to the deposition plane兲 for all tilt angles for the spectral range studied. We plotted the in-plane birefringence, ␦n ⫽ ny ⫺ nx, for three different wavelengths in the visible and infrared regions 共see Fig. 7兲. The
Fig. 4. Cross-sectional SEM image of a silicon film bideposited at a 60-deg tilt. The substrate and film were cleaved along the deposition plane and imaged perpendicular to it. 共The vapor arrives alternately from the left and the right.兲
Fig. 5. Optical indices and extinction coefficients for a bideposited film of silicon on glass at a tilt angle of 60 deg.
variations are similar, with maxima at a substrate tilt of approximately 60 deg, and fit reasonably well by third-degree polynomials. The shape of these response curves is consistent with previous studies of anisotropic properties of oblique films, notably resistivity and magnetic uniaxial anisotropy.14 Previous studies have shown that anisotropic properties of obliquely deposited films reach a maximum value at a substrate tilt of near 60 deg, then decrease and sometimes even change sign with a crossover tilt angle between 60 and 80 deg.14,16 Figure 8 also illustrates the large magnitude of the in-plane birefringence. For comparison, three common optical materials that are birefringent in bulk form are calcite 共␦n ⫽ 0.17兲, quartz 共␦n ⫽ 0.009兲, and magnesium fluoride 共␦n ⫽ 0.012兲, all measured at a 633-nm wavelength. For comparison, two sets of films were deposited with rapid substrate rotation and six-sided deposition. These films were analyzed with spectroscopic ellipsometry with the same initial model as the bideposited films. In all cases, the resulting birefrin-
Fig. 6. Measured index of refraction variation with wavelength 共dispersion兲 for eight different substrate tilt angles. Polarization direction x is parallel to both the deposition plane and the substrate surface plane. The perpendicular index, direction y, follows the same trend, but with an index that is always larger.
Fig. 7. Measured birefringence of bideposited films at selected wavelengths. The curves are the third-degree polynomial fits to each set. Birefringence of six-sided deposited films 共60 rotations兲 are also shown.
gence values were small compared with the bideposited films, supporting the conclusion that the source of the large birefringence is form anisotropy due to atomic shadowing.15 SEM of an 80-deg tilt bideposited film clearly shows bunched columns perpendicular to the deposition plane 共Fig. 9兲. The form anisotropy is further illustrated in a fast Fourier transform 共FFT兲 inset in the top right corner of Fig. 9. The two-lobe appearance is a spectral representation of the anisotropy of the morphological structure. A FFT of a structure lacking in-plane anisotropy yields a circularly symmetric image, as can be seen when we perform an identical analysis on a thin film deposited onto a rapidly rotating substrate, shown in Fig. 10. The distance of the lobes 共or the ring in the case of rapid rotation兲 from the origin represents the dominant or characteristic frequency 共or period兲 of the structure. In this case the two lobes reveal that the
Fig. 8. Maximum measured birefringence of bideposited films at varying substrate tilt angles. 1 October 2004 兾 Vol. 43, No. 28 兾 APPLIED OPTICS
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Fig. 9. Plan view scanning electron microscope image of a bideposited silicon film 共80-deg substrate tilt兲; inset is a twodimensional FFT of this image, clearly indicating the structural anisotropy of the thin-film nanostructure.
structure is anisotropic, as is visually obvious in the scanning electron microscope image. We have yet to determine to what extent this technique can be used to quantitatively compare anisotropy between different morphological structures, but it does appear capable of revealing anisotropic structure in micrographs that are not obviously anisotropic by human perception. Astigmatism in the electron lenses of scanning electron microscopes make it difficult to obtain reliable analysis of anisotropy in structure—it is difficult to effectively eliminate measurement contributions from high-magnification images.24 In the SEM analysis performed here, we took great care to repeatedly correct astigmatism by imaging sharp edges, corners, and defects. The image in Fig. 11 is a good representation of the success of this methodology. The central bright feature is presumed to be a dust particle existent on the substrate before deposition. Deposition has coated it with silicon and created
Fig. 11. Plan view scanning electron microscope image of a bideposited silicon film 共80-deg substrate tilt兲. The central particle is presumed to be a dust particle, now silicon coated, that created a geometric shadow during deposition. Film deposition occurred alternately from the right and left sides.
shadows extending left and right approximately 500 nm from the center. The features surrounding the particle, in particular inside the shadowed region and on the top of the particle itself, contain morphological features that do not exhibit the anisotropy of the film structure and therefore allow for effective elimination of astigmatism in the scanning electron microscope imaging. Away from the particle the film structure appears to become unperturbed by the defect within a short distance. Full-frame scanning electron microscope images 共including Fig. 9兲 were obtained in regions directly adjacent to the defects used for focusing and astigmatism correction and are believed to accurately represent the anisotropic morphological structure of the bideposited silicon thin films. Incidentally, defects like this one are common in high-angle oblique deposited films, with the size and number varying greatly with laboratory air cleanliness and substrate cleaning and handling procedures.
3. Summary and Discussion
Fig. 10. Plan view SEM scanning electron microscope image of a silicon film 共80-deg substrate tilt兲 deposited onto a rapidly rotating substrate; inset is a two-dimensional FFT of this image, where the rotational symmetry indicates the absence of in-plane anisotropy in the structure. 5348
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We have deposited films of silicon on glass substrates with serial bideposition and have shown that the resulting films exhibit high optical birefringence at visible and infrared wavelengths. The birefringence varies as a function of the substrate tilt, with a maximum at approximately 60 deg. These results, contrasted with insignificant birefringence observed in films deposited onto tilted, rotating substrates, indicate that the birefringence is a result of form anisotropy. SEM analysis and Fourier-transform analysis strongly support this conclusion and provide evidence that column bunching is the morphology of the form anisotropy. This type of structured thin-film photonic crystals seems particularly malleable to create designed optical devices and, when combined with their relative ease of manufacture and integration with other thin-film systems, appears likely to find broad application in integrated photonic systems.
The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Council of Canada and the Canadian Institute for Photonic Innovations.
13.
References
14.
1. I. Hodgkinson and Q. Wu, Birefringent Thin Films and Polarizing Elements 共World Scientific, Singapore, 1998兲. 2. I. Hodgkinson and Q. H. Wu, “Vacuum deposited biaxial thin films with all principal axes inclined to the substrate,” J. Vac. Sci. Technol. A 17, 2928 –2932 共1999兲. 3. I. Hodgkinson and Q. H. Wu, “Serial bideposition of anisotropic thin films with enhanced linear birefringence,” Appl. Opt. 38, 3621–3625 共1999兲. 4. S. Leonard, H. van Driel, A. Birner, U. Gosele, and P. Villeneuve, “Single-mode transmission in two-dimensional macroporous silicon photonic crystal waveguides,” Opt. Lett. 25, 1550 –1552 共2000兲. 5. S. John and M. Florescu, “Photonic bandgap materials: towards an all optical micro-transistor,” J. Opt. 3, S103–S120 共2001兲. 6. K. Robbie and M. Brett, “Sculptured thin films and glancing angle deposition: growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460 –1465 共1997兲. 7. I. Hodgkinson, Q. H. Wu, and J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 共1998兲. 8. T. Motohiro and Y. Taga, “Thin film retardation plate by oblique deposition,” Appl. Opt. 28, 2466 –2482 共1989兲. 9. M. Suzuki and Y. Taga, “Anisotropy in the optical absorption of Ag-SiO2 thin films with oblique columnar structures,” J. Appl. Phys. 71, 2448 –2454 共1992兲. 10. A. Zuber, H. Ja¨ nchen, and N. Kaiser, “Perpendicular-incidence photometric ellipsometry of biaxial anisotropic thin films,” Appl. Opt. 35, 5553–5556 共1996兲. 11. I. Hodgkinson, Q. Wu, B. Knight, A. Lakhtakia, and K. Robbie, “Vacuum deposition of chiral sculptured thin films with high optical activity,” Appl. Opt. 39, 642– 649 共2000兲. 12. K. Robbie, L. Friedrich, S. Dew, T. Smy, and M. Brett, “Fab-
15.
16. 17.
18.
19. 20.
21.
22.
23.
24.
rication of thin films with highly porous microstructures,” J. Vac. Sci. Technol. A 13, 1032–1035 共1995兲. K. Robbie, M. Brett, and D. Broer, “Chiral thin film兾liquid crystal hybrid materials,” Nature 共London兲 399, 764 –766 共1999兲. K. Kuwahara and J. Hirota, “Resistivity anisotropy in oblique incidence evaporated films,” Jpn. J. Appl. Phys. 13, 1093–1095 共1974兲. H. van Kranenburg and C. Lodder, “Tailoring growth and local composition by oblique-incidence deposition: a review and some new experimental data,” Mater. Sci. Eng. R 11, 295–354 共1994兲. M. Cohen, “Anisotropy in permalloy films evaporated at grazing incidence,” J. Appl. Phys. 32, 875– 885 共1961兲. R. Messier, A. Giri, and R. Roy, “Revised structure zone models for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500 –503 共1984兲. K. Robbie, J. Sit, and M. Brett, “Advanced techniques for glancing angle deposition 共GLAD兲,” J. Vac. Sci. Technol. B 16, 1115–1122 共1998兲. H. Tompkins and W. McGahan, Spectroscopic Ellipsometry and Reflectometry 共Wiley, New York, 1999兲. B. Johs, J. Hale, N. Ianno, G. Herzinger, T. Tiwald, and J. Woollam, “Recent developments in spectroscopic ellipsometry for in-situ applications,” in Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, A. Duparre and B. Singh, eds., Proc. SPIE 4449, 41–57 共2001兲. D. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen,” Ann. Phys. 共Leipzig兲 24, 635– 679 共1935兲. G. Smith, “Effective medium theory and angular dispersion of optical constants in films with oblique columnar structure,” Opt. Commun. 71, 279 –284 共1989兲. R. Tait, T. Smy, and M. Brett, “Modelling and characterization of columnar growth in evaporated films,” Thin Solid Films 226, 196 –201 共1993兲. J. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, A. D. Romig, Jr., C. E. Lyman, C. Fiori, and E. Lifshin, Scanning Electron Microscopy and X-Ray Microanalysis 共Plenum, New York, 1992兲.
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