Measurement of surface roughness of thin films by a hybrid interference microscope with different phase algorithms Chuen-Lin Tien,1,* Kuo-Chang Yu,1 Tsung-Yo Tsai,1 Chern-Sheng Lin,2 and Chi-Yuan Li1 1 2
Department of Electrical Engineering, Feng Chia University, Taichung 40724, Taiwan
Department of Automatic Control Engineering, Feng Chia University, Taichung 40724, Taiwan *Corresponding author: [email protected] Received 5 May 2014; revised 13 July 2014; accepted 23 July 2014; posted 21 August 2014 (Doc. ID 211290); published 19 September 2014
We propose a hybrid and flexible interference microscope combined with different phase algorithms to measure the surface roughness of thin films. Two phase measurement algorithms of the fast Fourier transform method and the five-step phase-shifting interferometry are used to evaluate the surface contour of aluminum-doped zinc oxide thin films coated using varying radio-frequency sputtering powers. The experimental results show that the proposed approach is feasible in determining the 3D deformation and surface roughness of thin films. © 2014 Optical Society of America OCIS codes: (310.0310) Thin films; (120.3180) Interferometry; (120.5050) Phase measurement; (120.6660) Surface measurements, roughness. http://dx.doi.org/10.1364/AO.53.00H213
1. Introduction
The surface roughness of optical thin films is an important parameter in determining the performance of optical devices. The detailed knowledge of the roughness characteristics of optical thin films contributes to the optimization of the process parameters of the optical coatings. A variety of suitable methods for inspecting the surface characteristics are available to measure the surface roughness, such as stylus profilometry [1], atomic force microscopy [1,2], scanning electron microscopy [3], scatterometer [4], and interferometry methods [5]. Stylus profilometry is widely used for surface roughness, but it lacks lateral resolution due to the tip geometry. It also can cause surface damage due to the high forces exerted on the surface. The atomic-force microscope possesses a lateral resolution to atomic dimensions, 1559-128X/14/29H213-07$15.00/0 © 2014 Optical Society of America
but its operation is somewhat elaborate. The above instruments are fairly expensive, and the analysis of thin films is highly complex and time-consuming. Interferometric measurements of surface roughness are commonly used for evaluating surface-finish quality. Wyant [6] suggested three different methods, which combine computers, electronics and software, to make possible improvements in the measurement of surface shape and surface roughness. To determine the root-mean-square (rms) roughness of super-smooth surfaces accurately, the effects of the reference surface roughness need to be removed. Creath and Wyant [7] proposed two techniques to yield accurate absolute measurements of the rms surface roughness. One technique involved averaging a number of the uncorrelated measurements of a mirror to generate a reference surface profile, which could then be subtracted from subsequent measurements, so that they would not contain errors due to the reference surface. The other technique provided an accurate rms roughness of the surface 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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by taking two uncorrelated measurements of the surface. It should be noted that these techniques are not meant to be used to determine the surface shape. In 2006, Quan et al. [8] reported a flexible optical interferometer incorporating the fast Fourier transform (FFT) and four-step phase-shifting methods for the 3D testing of microcomponents. Although the integration methods enabled the system to apply two alternatives to suit the deformation characterization of micro-optoelectromechanical system components with different surface features, they were not designed for the surface roughness measurement of thin films. Hence, there were obvious benefits to developing a system with sufficient flexibility to make surface roughness measurements on optical thin-film devices. To further improve the accuracy and to minimize the detuning error, a five‐step phase-retrieval algorithm, introduced by Hariharan in 1987, was adopted [9]. In this work, we present a hybrid approach for the measurement of the surface roughness of thin films based on microscopic interferometry combined with the FFT [10] and five-step phase-shifting methods. The surface roughness of aluminum-doped zinc oxide (AZO) thin films was measured by a hybrid interference microscope using the FFT method and a five-step phase-shifting technique to obtain a correct phase; the surface profile of the sample was then reconstructed. The surface profile of the thin films was filtered with a Gaussian filter after the phase change was converted to a surface height distribution [11]. The measurement of the surface roughness of AZO thin films by the FFT and the five-step phase-shifting interferometry (PSI) algorithms has been demonstrated and compared. 2. Method
This paper presents a hybrid and flexible microscopic interferometry for surface roughness measurement using FFT and five-step phase-shifting algorithms. This proposed method has an advantage over the traditional method in that the surface geometry is not touched and point-wise scanning is not required. The hybrid interference microscope mixed two different working modes: one mode used the tilt-plate method associated with the FFT algorithm to reconstruct the 3D contour and then to determine the surface roughness of thin films; the other mode for surface roughness measurements was continuously taking five frames by a piezoelectric transducer (PZT) controller, which was combined with a PSI algorithm. The hybrid interference microscope combined FFT and phase-shifting algorithms to evaluate the surface roughness of thin films, as shown in Fig. 1. This system comprised a modified Michelson-type interference microscope equipped with a 50× microscope objective, a two-axis translation stage, a computer-controlled PZT translation device, a CCD camera to capture images of the specimen surface to be characterized, and a specially developed MATLAB program based on FFT and five-step H214
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Fig. 1. Hybrid interference microscope for surface roughness measurement.
phase-shifting algorithms to analyze the captured interference images. An He–Ne laser with a wavelength of 632.8 nm was used as the light source. The light beam falls on a cube beam splitter, which splits the beam into a reference and a test beam that emerges in perpendicular directions. One beam is directed onto the test surface through a cube beam splitter and a microscope objective (50×); the other beam is reflected by a reference mirror (flatness λ∕20) and a cube beam splitter. The test surface within the field of view of the objectives is, thus, uniformly illuminated. The beams are reflected off the reference and the test surface onto a CCD sensor through a lens. The resulting interference fringe pattern is recorded by a digital CCD camera. Two different types of fringe patterns were used in our proposed system. One is a single-fringe pattern using a two-axis translation stage to introduce a spatial carrier frequency f 0. The intensity distribution of the two-beam interference can be written in the form of ix; y ax; y bx; y cos2πf 0 x ϕx; y;
(1)
where ax; y is the background intensity, bx; y is related to the local contrast of the fringe pattern, f 0 is the introduced spatial carrier frequency, and ϕx; y is the interference phase at pixel (x; y to be determined from ix; y. By using the definition cx; y 1 2 bx; y expiϕx; y and the Euler formula, the intensity distribution in Eq. (1) can be rewritten as ix; y ax; y cx; y exp2πif 0 x c x; y exp−2πif 0 x;
(2)
where the asterisk indicates the complex conjugate, and cx; y is a complex fringe pattern. Because of the high carrier frequency, the Fourier spectrum of the fringe signal splits into three spectrum components separated from each other. By
means of a suitable frequency filter, the remaining spectrum is no longer symmetric and yields a nonzero imaginary part after inverse transformation. Then, using inverse FFT for phase distribution, ϕx; y can be calculated by Imcx; y ; ϕx; y tan Recx; y −1
(3)
where Recx; y and Imcx; y are the real and imaginary parts of cx; y, respectively. With Eq. (3) based on FFT using only one image, a phase unwrapping process [12] is applied to retrieve phase ϕx; y. The other case, which captures five-frame fringe patterns, as the phase difference is varied through PZT scanning, introduces a subsequent phase change of 90°. The computer controls the programmable DC power supply to provide the voltage to drive the PZT. The PZT stage generates a 79.1 nm displacement and shifts the fringes to quarter fringes. Five interferograms with a constant phase difference (π∕2) between the frames are obtained. The phase of the fringe is calculated from the digitized intensities at each point in the interferograms using the Hariharan algorithm [9]: ϕx; y
tan−1
2I 2 − I 4 ; 2I 3 − I 5 − I 1
(4)
where ϕx; y is a phase function, and I 1 to I 5 represent the digitized intensity at particular points on the five interferograms. The above equation is evaluated at each measurement point to obtain a phase map of the measured wavefront. This wavefront is related to the surface height of the test plate or the optical path difference. A local surface height distribution, hx; y, on the test surface is given by scaling: hx; y
λ ϕx; y; 4π
Fig. 2. Flow chart for an FFT algorithm.
conveys to the user an impression of the surface quality under study and presents a suitable tool for roughness description. We developed a MATLAB program to reconstruct a 3D surface profile of the thin films and to calculate the surface roughness. Figure 2 shows the flow chart
(5)
where x and y are the spatial coordinates, and λ is the wavelength of the laser beam. The process of image acquisition is carried out with support of the 2D CCD array. Only the central 240 × 240 pixels, representing an actual dimension of 100 μm × 100 μm, were chosen for analysis in order to prevent edge effects. The mean phase is then subtracted from the surface height profile to obtain the roughness profile. Finally, the rms value of the surface roughness is determined by the following formula: (
Rrms
M X N 1 X zi; j − hzi; ji2 MN j1 i1
)1∕2 ;
(6)
where zi; j is the height of the surface profile, and hzi; ji is the mean value. The parameter commonly used for describing the roughness characteristics of a coating surface is the rms roughness, which rapidly
Fig. 3. Flow chart for a five-step phase-shifting algorithm. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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Fig. 4. FFT algorithm used for surface roughness measurements of AZO thin films coated using different sputtering powers: (a) 60 W; (b) 70 W; (c) 80 W; (d) 90 W; (e) 100 W.
of the FFT algorithm to measure the surface roughness of thin films. Interference occurs between the two beams producing interferograms. As height variations are proportional to the phase variations, ϕx; y, the phase measurement leads to the direct determination of the surface relief map. In this paper, we present a hybrid interference microscope associated with the FFT method to reconstruct the surface topography of thin film. Once the value of ϕx; y is known, the surface profile of the sample can be reconstructed. After reconstructing the film’s surface, a Gaussian filter [13] is used to filter out the high-frequency signal and to obtain the roughness profile. H216
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
Figure 3 shows the flow chart of the five-step phase-shifting algorithm to measure the surface roughness of thin films. The five-step phase-shifting algorithm assumes that the interferogram sequence has a temporal frequency of π∕2 rad and tolerates a small detuning around π∕2 rad. The system architecture uses a PZT and controller to change the optical path difference between the sample and reference arms of the interference microscope. Phase-shifting interferometry is used for the rapid retrieval of the phase images in the interference microscope. We used a self-calibrating five-step algorithm. In order to reduce optical noise and influence of vibration, digital filtering was used. The proposed
system possesses the advantages of instant measurement and the ability to measure in different microstructure sizes. Furthermore, the measurement of the surface topography and the roughness evaluation for the thin film characteristics can be accomplished by the same measuring system. 3. Results and Discussion
Aluminum-doped ZnO (AZO) thin films were deposited on silicon wafers and NBK7 substrates using a radio-frequency (RF) sputtering technique with
varying RF powers (i.e., 60–100 W). The rms surface roughness of the AZO thin films was investigated. An experimental setup was used to study a hybrid interference microscope associated with the FFT and the five-step phase-shifting methods for measuring the surface roughness of thin films. In this study, a MATLAB program with two different phase algorithms was developed to evaluate the surface roughness of AZO thin films by using a hybrid interference microscope. For the film’s surface contour reconstruction, the film’s surface profile was obtained by fringe
Fig. 5. PSI algorithm used for surface roughness measurements of AZO thin films coated using different sputtering powers: (a) 60 W; (b) 70 W; (c) 80 W; (d) 90 W; (e) 100 W. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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pattern analysis. The roughness profile was filtered by a Gaussian filter with a cut-off wavelength of 3.5 μm, and the phase was translated to a height scale by multiplying λ∕4π. Often, it is necessary to fully characterize surface topography with the direct visualization of a film’s surface. Figure 4 represents the surface roughness of AZO thin films by means of the 3D surface topography of the FFT algorithm to obtain the quantitative surface texture information. Figure 5 shows the 3D surface topography of the surface roughness of AZO thin films deposited with different RF powers by using the PSI algorithm. For surface roughness measurements, surface roughness values of AZO thin films were determined by two different phase algorithms: the FFT and PSI methods. The interferograms of AZO thin films were captured by a hybrid interference microscope; then the FFT or the five-step phase-shifting method was used to determine the surface profile of the thin films and to calculate the surface roughness values. In the case of the FFT method, the surface roughness values increased with the RF power increasing from 60 to 100 W. The measured roughness values changed from 1.89 to 2.23 nm for AZO thin films. In the case of the five-step phase-shifting method, the surface roughness measurement had a similar tendency. The rms surface roughness values were 1.97 to 2.21 nm, as shown in Fig. 6. Figure 6 indicates the variations in the rms surface roughness with the different RF sputtering powers. Both FFT and PSI methods showed that the rms surface roughness increased as the RF sputtering power increased. The values of the surface roughness obtained from the PSI algorithm were slightly higher than those determined by the FFT algorithm, but the variation tendency of both algorithms was the same. A reason for this trend was thought to be the surface damage caused by bombarding the surface with high-energy sputtered ions. In the case of a higher energy deposition, film surface damage occurs, but it is rapidly
Fig. 6. Surface roughness measurements of AZO thin films determined by different phase algorithms. H218
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
repaired when the incident ion energy is low [14]. When the rate of surface damage is larger than the rate of repair, a slightly rough film is formed. This measurement result was consistent with the observation in [15]. 4. Conclusion
This study proposed a hybrid and flexible interference microscope combining two phase algorithms to determine the surface roughness of thin films. In the measuring experiment, AZO thin films were coated on NBK7 substrates by RF magnetron sputtering at different RF powers. Then the roughness was measured by two types of phase algorithms: the FFT method and the five-step phase-shifting method. The differences were compared as well as the trends in the change of the surface roughness. From the experimental results, the use of the FFT algorithm or the five-step phase-shifting algorithm to measure the roughness of AZO thin films resulted in the same trend of the surface roughness varying with the RF sputtering power. The results showed that the proposed approach was feasible in determining the surface roughness of thin films. Our proposed system has the advantage of a relatively fast and low-cost implementation of a high-precision method for thin-film surface analysis. The authors express their appreciation to the Ministry of Science and Technology (MOST) of the Republic of China for support of this project under contract numbers NSC101-2221-E-035-055 and NSC102-2622-E-035-024-CC3. References 1. T. G. Mathia, H. Zahouani, J. Rousseau, and J. C. Le Bosse, “Functional significance of different techniques for surface morphology measurements,” Int. J. Mach. Tools Manufact. 35, 195–202 (1995). 2. J. M. Bennett, J. Jahanmir, J. C. Podlesny, T. L. Balter, and D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 34, 213–230 (1995). 3. P. K. Rastogi, Optical Measurement Techniques and Applications (Artech House, 1997), pp. 352–355. 4. J. R. McNeil, L. J. Wei, G. A. Al-Jumaily, S. Shakirs, and J. K. Mclver, “Surface smoothing effects of thin film deposition?” Appl. Opt. 24, 480–485 (1985). 5. J. C. Wyant, “Computerized interferometric surface measurements,” Appl. Opt. 52, 1–8 (2013). 6. J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE 6024, 602401 (2006). 7. K. Creath and J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 3823–3827 (1990). 8. C. Quan, S. H. Wang, and C. J. Tay, “Nanoscale surface deformation inspection using FFT and phase-shifting combined interferometry,” Precis. Eng. 30, 23–31 (2006). 9. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phaseshifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). 10. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). 11. C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517, 5110–5115 (2009).
12. W. W. Macy, Jr., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22, 3898–3901 (1983). 13. J. Raja, B. Muralikrishnan, and S. Fu, “Recent advances in separation of roughness, waviness and form,” Precis. Eng. 26, 222–235 (2002). 14. M. H. Cho, K. Jeong, and C. N. Whang, “Properties of ZnO thin films grown at room temperature by using ionized
cluster beam deposition,” J. Korean Phys. Soc. 37, 456–460 (2000). 15. C. A. Tseng, J. C. Lin, Y. F. Chang, S. D. Chyou, and K. C. Peng, “Microstructure and characterization of Al-doped ZnO films prepared by RF power sputtering on Al and ZnO targets,” Appl. Surf. Sci. 258, 5996–6002 (2012).
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Department of Electrical Engineering, Feng Chia University, Taichung 40724, Taiwan
Department of Automatic Control Engineering, Feng Chia University, Taichung 40724, Taiwan *Corresponding author: [email protected] Received 5 May 2014; revised 13 July 2014; accepted 23 July 2014; posted 21 August 2014 (Doc. ID 211290); published 19 September 2014
We propose a hybrid and flexible interference microscope combined with different phase algorithms to measure the surface roughness of thin films. Two phase measurement algorithms of the fast Fourier transform method and the five-step phase-shifting interferometry are used to evaluate the surface contour of aluminum-doped zinc oxide thin films coated using varying radio-frequency sputtering powers. The experimental results show that the proposed approach is feasible in determining the 3D deformation and surface roughness of thin films. © 2014 Optical Society of America OCIS codes: (310.0310) Thin films; (120.3180) Interferometry; (120.5050) Phase measurement; (120.6660) Surface measurements, roughness. http://dx.doi.org/10.1364/AO.53.00H213
1. Introduction
The surface roughness of optical thin films is an important parameter in determining the performance of optical devices. The detailed knowledge of the roughness characteristics of optical thin films contributes to the optimization of the process parameters of the optical coatings. A variety of suitable methods for inspecting the surface characteristics are available to measure the surface roughness, such as stylus profilometry [1], atomic force microscopy [1,2], scanning electron microscopy [3], scatterometer [4], and interferometry methods [5]. Stylus profilometry is widely used for surface roughness, but it lacks lateral resolution due to the tip geometry. It also can cause surface damage due to the high forces exerted on the surface. The atomic-force microscope possesses a lateral resolution to atomic dimensions, 1559-128X/14/29H213-07$15.00/0 © 2014 Optical Society of America
but its operation is somewhat elaborate. The above instruments are fairly expensive, and the analysis of thin films is highly complex and time-consuming. Interferometric measurements of surface roughness are commonly used for evaluating surface-finish quality. Wyant [6] suggested three different methods, which combine computers, electronics and software, to make possible improvements in the measurement of surface shape and surface roughness. To determine the root-mean-square (rms) roughness of super-smooth surfaces accurately, the effects of the reference surface roughness need to be removed. Creath and Wyant [7] proposed two techniques to yield accurate absolute measurements of the rms surface roughness. One technique involved averaging a number of the uncorrelated measurements of a mirror to generate a reference surface profile, which could then be subtracted from subsequent measurements, so that they would not contain errors due to the reference surface. The other technique provided an accurate rms roughness of the surface 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
H213
by taking two uncorrelated measurements of the surface. It should be noted that these techniques are not meant to be used to determine the surface shape. In 2006, Quan et al. [8] reported a flexible optical interferometer incorporating the fast Fourier transform (FFT) and four-step phase-shifting methods for the 3D testing of microcomponents. Although the integration methods enabled the system to apply two alternatives to suit the deformation characterization of micro-optoelectromechanical system components with different surface features, they were not designed for the surface roughness measurement of thin films. Hence, there were obvious benefits to developing a system with sufficient flexibility to make surface roughness measurements on optical thin-film devices. To further improve the accuracy and to minimize the detuning error, a five‐step phase-retrieval algorithm, introduced by Hariharan in 1987, was adopted [9]. In this work, we present a hybrid approach for the measurement of the surface roughness of thin films based on microscopic interferometry combined with the FFT [10] and five-step phase-shifting methods. The surface roughness of aluminum-doped zinc oxide (AZO) thin films was measured by a hybrid interference microscope using the FFT method and a five-step phase-shifting technique to obtain a correct phase; the surface profile of the sample was then reconstructed. The surface profile of the thin films was filtered with a Gaussian filter after the phase change was converted to a surface height distribution [11]. The measurement of the surface roughness of AZO thin films by the FFT and the five-step phase-shifting interferometry (PSI) algorithms has been demonstrated and compared. 2. Method
This paper presents a hybrid and flexible microscopic interferometry for surface roughness measurement using FFT and five-step phase-shifting algorithms. This proposed method has an advantage over the traditional method in that the surface geometry is not touched and point-wise scanning is not required. The hybrid interference microscope mixed two different working modes: one mode used the tilt-plate method associated with the FFT algorithm to reconstruct the 3D contour and then to determine the surface roughness of thin films; the other mode for surface roughness measurements was continuously taking five frames by a piezoelectric transducer (PZT) controller, which was combined with a PSI algorithm. The hybrid interference microscope combined FFT and phase-shifting algorithms to evaluate the surface roughness of thin films, as shown in Fig. 1. This system comprised a modified Michelson-type interference microscope equipped with a 50× microscope objective, a two-axis translation stage, a computer-controlled PZT translation device, a CCD camera to capture images of the specimen surface to be characterized, and a specially developed MATLAB program based on FFT and five-step H214
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
Fig. 1. Hybrid interference microscope for surface roughness measurement.
phase-shifting algorithms to analyze the captured interference images. An He–Ne laser with a wavelength of 632.8 nm was used as the light source. The light beam falls on a cube beam splitter, which splits the beam into a reference and a test beam that emerges in perpendicular directions. One beam is directed onto the test surface through a cube beam splitter and a microscope objective (50×); the other beam is reflected by a reference mirror (flatness λ∕20) and a cube beam splitter. The test surface within the field of view of the objectives is, thus, uniformly illuminated. The beams are reflected off the reference and the test surface onto a CCD sensor through a lens. The resulting interference fringe pattern is recorded by a digital CCD camera. Two different types of fringe patterns were used in our proposed system. One is a single-fringe pattern using a two-axis translation stage to introduce a spatial carrier frequency f 0. The intensity distribution of the two-beam interference can be written in the form of ix; y ax; y bx; y cos2πf 0 x ϕx; y;
(1)
where ax; y is the background intensity, bx; y is related to the local contrast of the fringe pattern, f 0 is the introduced spatial carrier frequency, and ϕx; y is the interference phase at pixel (x; y to be determined from ix; y. By using the definition cx; y 1 2 bx; y expiϕx; y and the Euler formula, the intensity distribution in Eq. (1) can be rewritten as ix; y ax; y cx; y exp2πif 0 x c x; y exp−2πif 0 x;
(2)
where the asterisk indicates the complex conjugate, and cx; y is a complex fringe pattern. Because of the high carrier frequency, the Fourier spectrum of the fringe signal splits into three spectrum components separated from each other. By
means of a suitable frequency filter, the remaining spectrum is no longer symmetric and yields a nonzero imaginary part after inverse transformation. Then, using inverse FFT for phase distribution, ϕx; y can be calculated by Imcx; y ; ϕx; y tan Recx; y −1
(3)
where Recx; y and Imcx; y are the real and imaginary parts of cx; y, respectively. With Eq. (3) based on FFT using only one image, a phase unwrapping process [12] is applied to retrieve phase ϕx; y. The other case, which captures five-frame fringe patterns, as the phase difference is varied through PZT scanning, introduces a subsequent phase change of 90°. The computer controls the programmable DC power supply to provide the voltage to drive the PZT. The PZT stage generates a 79.1 nm displacement and shifts the fringes to quarter fringes. Five interferograms with a constant phase difference (π∕2) between the frames are obtained. The phase of the fringe is calculated from the digitized intensities at each point in the interferograms using the Hariharan algorithm [9]: ϕx; y
tan−1
2I 2 − I 4 ; 2I 3 − I 5 − I 1
(4)
where ϕx; y is a phase function, and I 1 to I 5 represent the digitized intensity at particular points on the five interferograms. The above equation is evaluated at each measurement point to obtain a phase map of the measured wavefront. This wavefront is related to the surface height of the test plate or the optical path difference. A local surface height distribution, hx; y, on the test surface is given by scaling: hx; y
λ ϕx; y; 4π
Fig. 2. Flow chart for an FFT algorithm.
conveys to the user an impression of the surface quality under study and presents a suitable tool for roughness description. We developed a MATLAB program to reconstruct a 3D surface profile of the thin films and to calculate the surface roughness. Figure 2 shows the flow chart
(5)
where x and y are the spatial coordinates, and λ is the wavelength of the laser beam. The process of image acquisition is carried out with support of the 2D CCD array. Only the central 240 × 240 pixels, representing an actual dimension of 100 μm × 100 μm, were chosen for analysis in order to prevent edge effects. The mean phase is then subtracted from the surface height profile to obtain the roughness profile. Finally, the rms value of the surface roughness is determined by the following formula: (
Rrms
M X N 1 X zi; j − hzi; ji2 MN j1 i1
)1∕2 ;
(6)
where zi; j is the height of the surface profile, and hzi; ji is the mean value. The parameter commonly used for describing the roughness characteristics of a coating surface is the rms roughness, which rapidly
Fig. 3. Flow chart for a five-step phase-shifting algorithm. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
H215
Fig. 4. FFT algorithm used for surface roughness measurements of AZO thin films coated using different sputtering powers: (a) 60 W; (b) 70 W; (c) 80 W; (d) 90 W; (e) 100 W.
of the FFT algorithm to measure the surface roughness of thin films. Interference occurs between the two beams producing interferograms. As height variations are proportional to the phase variations, ϕx; y, the phase measurement leads to the direct determination of the surface relief map. In this paper, we present a hybrid interference microscope associated with the FFT method to reconstruct the surface topography of thin film. Once the value of ϕx; y is known, the surface profile of the sample can be reconstructed. After reconstructing the film’s surface, a Gaussian filter [13] is used to filter out the high-frequency signal and to obtain the roughness profile. H216
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
Figure 3 shows the flow chart of the five-step phase-shifting algorithm to measure the surface roughness of thin films. The five-step phase-shifting algorithm assumes that the interferogram sequence has a temporal frequency of π∕2 rad and tolerates a small detuning around π∕2 rad. The system architecture uses a PZT and controller to change the optical path difference between the sample and reference arms of the interference microscope. Phase-shifting interferometry is used for the rapid retrieval of the phase images in the interference microscope. We used a self-calibrating five-step algorithm. In order to reduce optical noise and influence of vibration, digital filtering was used. The proposed
system possesses the advantages of instant measurement and the ability to measure in different microstructure sizes. Furthermore, the measurement of the surface topography and the roughness evaluation for the thin film characteristics can be accomplished by the same measuring system. 3. Results and Discussion
Aluminum-doped ZnO (AZO) thin films were deposited on silicon wafers and NBK7 substrates using a radio-frequency (RF) sputtering technique with
varying RF powers (i.e., 60–100 W). The rms surface roughness of the AZO thin films was investigated. An experimental setup was used to study a hybrid interference microscope associated with the FFT and the five-step phase-shifting methods for measuring the surface roughness of thin films. In this study, a MATLAB program with two different phase algorithms was developed to evaluate the surface roughness of AZO thin films by using a hybrid interference microscope. For the film’s surface contour reconstruction, the film’s surface profile was obtained by fringe
Fig. 5. PSI algorithm used for surface roughness measurements of AZO thin films coated using different sputtering powers: (a) 60 W; (b) 70 W; (c) 80 W; (d) 90 W; (e) 100 W. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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pattern analysis. The roughness profile was filtered by a Gaussian filter with a cut-off wavelength of 3.5 μm, and the phase was translated to a height scale by multiplying λ∕4π. Often, it is necessary to fully characterize surface topography with the direct visualization of a film’s surface. Figure 4 represents the surface roughness of AZO thin films by means of the 3D surface topography of the FFT algorithm to obtain the quantitative surface texture information. Figure 5 shows the 3D surface topography of the surface roughness of AZO thin films deposited with different RF powers by using the PSI algorithm. For surface roughness measurements, surface roughness values of AZO thin films were determined by two different phase algorithms: the FFT and PSI methods. The interferograms of AZO thin films were captured by a hybrid interference microscope; then the FFT or the five-step phase-shifting method was used to determine the surface profile of the thin films and to calculate the surface roughness values. In the case of the FFT method, the surface roughness values increased with the RF power increasing from 60 to 100 W. The measured roughness values changed from 1.89 to 2.23 nm for AZO thin films. In the case of the five-step phase-shifting method, the surface roughness measurement had a similar tendency. The rms surface roughness values were 1.97 to 2.21 nm, as shown in Fig. 6. Figure 6 indicates the variations in the rms surface roughness with the different RF sputtering powers. Both FFT and PSI methods showed that the rms surface roughness increased as the RF sputtering power increased. The values of the surface roughness obtained from the PSI algorithm were slightly higher than those determined by the FFT algorithm, but the variation tendency of both algorithms was the same. A reason for this trend was thought to be the surface damage caused by bombarding the surface with high-energy sputtered ions. In the case of a higher energy deposition, film surface damage occurs, but it is rapidly
Fig. 6. Surface roughness measurements of AZO thin films determined by different phase algorithms. H218
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
repaired when the incident ion energy is low [14]. When the rate of surface damage is larger than the rate of repair, a slightly rough film is formed. This measurement result was consistent with the observation in [15]. 4. Conclusion
This study proposed a hybrid and flexible interference microscope combining two phase algorithms to determine the surface roughness of thin films. In the measuring experiment, AZO thin films were coated on NBK7 substrates by RF magnetron sputtering at different RF powers. Then the roughness was measured by two types of phase algorithms: the FFT method and the five-step phase-shifting method. The differences were compared as well as the trends in the change of the surface roughness. From the experimental results, the use of the FFT algorithm or the five-step phase-shifting algorithm to measure the roughness of AZO thin films resulted in the same trend of the surface roughness varying with the RF sputtering power. The results showed that the proposed approach was feasible in determining the surface roughness of thin films. Our proposed system has the advantage of a relatively fast and low-cost implementation of a high-precision method for thin-film surface analysis. The authors express their appreciation to the Ministry of Science and Technology (MOST) of the Republic of China for support of this project under contract numbers NSC101-2221-E-035-055 and NSC102-2622-E-035-024-CC3. References 1. T. G. Mathia, H. Zahouani, J. Rousseau, and J. C. Le Bosse, “Functional significance of different techniques for surface morphology measurements,” Int. J. Mach. Tools Manufact. 35, 195–202 (1995). 2. J. M. Bennett, J. Jahanmir, J. C. Podlesny, T. L. Balter, and D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 34, 213–230 (1995). 3. P. K. Rastogi, Optical Measurement Techniques and Applications (Artech House, 1997), pp. 352–355. 4. J. R. McNeil, L. J. Wei, G. A. Al-Jumaily, S. Shakirs, and J. K. Mclver, “Surface smoothing effects of thin film deposition?” Appl. Opt. 24, 480–485 (1985). 5. J. C. Wyant, “Computerized interferometric surface measurements,” Appl. Opt. 52, 1–8 (2013). 6. J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE 6024, 602401 (2006). 7. K. Creath and J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 3823–3827 (1990). 8. C. Quan, S. H. Wang, and C. J. Tay, “Nanoscale surface deformation inspection using FFT and phase-shifting combined interferometry,” Precis. Eng. 30, 23–31 (2006). 9. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phaseshifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). 10. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). 11. C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517, 5110–5115 (2009).
12. W. W. Macy, Jr., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22, 3898–3901 (1983). 13. J. Raja, B. Muralikrishnan, and S. Fu, “Recent advances in separation of roughness, waviness and form,” Precis. Eng. 26, 222–235 (2002). 14. M. H. Cho, K. Jeong, and C. N. Whang, “Properties of ZnO thin films grown at room temperature by using ionized
cluster beam deposition,” J. Korean Phys. Soc. 37, 456–460 (2000). 15. C. A. Tseng, J. C. Lin, Y. F. Chang, S. D. Chyou, and K. C. Peng, “Microstructure and characterization of Al-doped ZnO films prepared by RF power sputtering on Al and ZnO targets,” Appl. Surf. Sci. 258, 5996–6002 (2012).
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