- Email: [email protected]
Expanded beam (macro-imaging) ellipsometry
Thin Solid Films 519 (2011) 2730–2736
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Expanded beam (macro-imaging) ellipsometry M. Fried a,⁎, G. Juhász a, C. Major a, P. Petrik a, O. Polgár a, Z. Horváth b, A. Nutsch c a b c
Res. Inst. for Technical Physics and Materials Science (MFA), H-1525 Budapest, POB 49, Hungary Res. Inst. for Solid State Physics and Optics (SZFKI), H-1525 Budapest, POB 49, Hungary Fraunhofer Institut für Integrierte Systeme und Bauelementetechnologie IISB, Schottkystr. 10, 91058 Erlangen, Germany
a r t i c l e
i n f o
Available online 21 December 2010 Keywords: Ellipsometry Mapping Thin film
a b s t r a c t Our aim was to make possible to use spectroscopic ellipsometry for mapping purposes during one measuring cycle (minimum one rotation period of polarizer or analyzer) on many sample points. Our new technique uses non-collimated (non-parallel, mostly diffuse) illumination with an angle of incidence sensitive pinhole camera detector system and it works as an unusual kind of imaging ellipsometry. Adding multicolour supplemets, it provides spectral (a few wavelengths on a 2D image or a full spectrum along a line) information from rapid measurements of many points on a large (several dm2) area. This technique can be expanded by upscaling the geometry (upscaling the dimensions of the instrument, and characteristic imaging parameters such as focal lengths, distances, etc.). The lateral resolution is limited by the minimum resolved-angle determined by the detector system, mainly by the diameter of the pinhole. (The diameter of the pinhole is a compromise between the light intensity and the lateral resolution.) Small-aperture (25 mm diameter) polarizers are incorporated into both the polarization state generator (PSG) and polarization state detection (PSD) components of the instrument. The detection is almost without background because the pinhole serves as a filter against the scattered light. One rapid measuring cycle (less than 10 s) is enough to determine the polarization state at all the points inside the illuminated area. The collected data can be processed very fast (seconds) providing nearly real-time thicknesses and/or refractive index maps over many points of the sample surface even in the case of multilayer samples. The speed of the measuring system makes it suitable for using even on production lines. The necessary (in each sample-point different) angle-of-incidence and the mirror-effect calibration are made via well-known and optimized structures such as silicon/silicon-dioxide samples. The precision is suitable for detecting sub-nanometer thickness and a refractive index change of 0.01. The method can be used for mapping and quality control in the case of large area solar cell table production lines even in a vacuum chamber with 5–10 mm lateral resolution. © 2010 Published by Elsevier B.V.
1. Introduction Ellipsometry determines angle of incidence dependent data of light reflection, so generally it works by parallel light beams with a well defined angle of incidence. Here we present a fundamentally different method from the usual ellipsometric techniques. The target is illuminated by non-parallel, almost diffuse, “expanded beam” light in our case, providing a lot of beams with diverse angles of incidence at every point of the sample. The precise “angle-selection” is made at the detector side, by a pinhole camera. (The pinhole works as an “angle-filter,” selecting only one single light beam from every direction. The angle resolution of a camera of this kind is depending on the diameter of the pinhole.) In the case of a single wavelength measurement, this solution is appropriate for measuring a sample of large area with a range of angles ⁎ Corresponding author. E-mail address: [email protected] (M. Fried). 0040-6090/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.tsf.2010.12.067
wide enough but different angles of incidence belong to each sample points. If the sample is moved along a line during the measurement (for example on a production line) each sample points will be measured at multiple angles of incidence successively. Repeating the measurement with light of various wavelengths we can get spectral (few wavelengths) ellipsometric data. Reducing the number of the measured sample points into a narrow range along a line only, we can provide full spectral data from one measurement, using white light illumination with a spectral selector (grating) after the pinhole. It produces geometrical information (sample points/angle of incidence) of the reflected light intensity on a CCDmatrix in one direction, and spectral information in the perpendicular direction at the same time. One of the key problems of the practical ellipsometry is the quality of the polarizers which can be very expensive as the size increases. To reduce this problem our aim was to minimize the sizes of the polarizers both in the light source and at the detector side. We solved this problem by constructing a special, angle-persistent optical system which allows
M. Fried et al. / Thin Solid Films 519 (2011) 2730–2736
reducing the diameters of the polarizers and lowers the light-losses in the same time. Mapping ellipsometry methods can be classified into two main groups: a) Scanning methods based on one narrow beam (collimated or focused microspot) are very accurate but make these methods relatively slow for mapping purposes. b) Imaging techniques based on a twodimensional detector array can speed up the measurement. In the latter case the measured surface is illuminated by a collimated light beam, and the reflected light is usually detected by a CCD camera. [1,2] In this way the entire surface is measured simultaneously, and the measured values of each point are evaluated to determine the lateral distribution as an image. If the magnification (ratio of the measured area and the image on the CCD camera) is greater than 1 we call it “microscopic imaging” [1]. If magnification is smaller than 1 we can call it “macroscopic imaging” [2]. One disadvantage of using collimated beam is that the greatest measurable size of the sample surface is strongly limited by the diameter of the used polarizer, so this method is used mainly for microscopic imaging. One can overcome these problems by building a device [3] which is capable of measuring the polarization state changes upon reflection from a large (theoretically any size) surface rapidly. The new technique (which can be considered as a “turned-around” microscope) uses noncollimated (divergent or focusing in different arrangements) illumination providing multi-wavelength (a few wavelengths on a 2D image or full spectral along a line) information from rapid measurements of a large area, which can be expanded by upscaling the geometry. The lateral resolution is limited by the minimum resolved-angle determined by the detector system, mainly by the diameter of the pinhole. The diameter of the pinhole is a compromise between the light intensity and the lateral resolution. Ray-tracking simulations show that 0.1–0.2 mm diameter pinhole is a good compromise and this diameter makes a 30 × 30 points mapping resolution possible on any size of the mapping area. Multiwavelength expanded beam ellipsometer was developed in the last few years [3–5]. To study the specific features of the new technique we have built some prototypes in the form of a wide-angle 3wavelength, PSA ellipsometers using film polarizers. In the first version the light source was the exit aperture of an optical fiber driven by three
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different wavelength laser sources (781 nm, 661 nm, 533 nm) [5]. The lasers can be used as very intensive, stabile wavelength, narrow bandwidth point-like sources; therefore, they are very suitable monochrome illuminator for our application but to avoid their disadvantageous effects we have had to take care of the speckle noise reduction and of the polarization state homogeneity. In this version the intensity detection system is a screen camera assembly (with an analyzer bigger than the illuminated sample area); therefore, we cannot eliminate the background of scattered light from the inner parts of the device [5]. The second version applied a pinhole camera detection technique, Fig. 1a. The light source here was a high intensity (Luxeon Lumiled) LED matrix with three different wavelengths of 637 nm, 523 nm, and 460 nm with a bandwidth of 15 nm, 30 nm, and 20 nm, respectively. A diffusor plate served as a homogenizer and the pinhole “selects” the convergent rays. In this version the polarizer is bigger than the illuminated sample area, but the main advantage is that the pinhole eliminates the background of scattered light from the inner parts of the device [5]. Because of the poor spectral information the capabilities of the method are limited to the cases where the measurements can be evaluated using three spectral points. The precision of the method is sufficient for detecting subnanometer thickness change of well-known structures such as silicon/silicon-dioxide samples or a refractive index change of 0.01. In case of more complex structures and/or unknown refractive indices a higher resolution spectral sampling is necessary for the precise evaluation of the measurements. For the elimination of the problem, we developed a modified version of expanded beam spectroscopic ellipsometry that uses whole spectra of a large number of sample points (along a line) in the near UV-VIS range (presently 350–630 nm) acquired in one measuring cycle (minimum two rotation periods of polarizer or analyzer). The spectral technique can speed up the mapping of physical properties (such as thickness, transparency, conductance) of transparent conductive oxides such as Al-doped ZnO layers [6]. Since characteristic spectral features of different layers can be far away from each other, the near UV-VIS range (presently 350–630 nm) is not satisfactory in all cases, but an extended spectral range is necessary
Fig. 1. a (1) Light source (LED-panel) (2) diffusor (3) film-polarizer (4) analyzer (6) sample (5) detector (pinhole + CCD-detector) (Installed version (right) in the Student Lab, Technical University, Budapest).b (1) “white” source (fiber-coupled RGB-laser in version 2, Xe-lamp in version 3), (2) film-polarizer, (3) spherical mirror, (4) convergent beam, (5) sample, (13) narrow, rectangular aperture (only in version 3) (6) cylindrical mirror, (7) corrected beam, (8) analyzer, (9) pinhole, (10) divergent beam, (11) correctiondispersion (with diffraction grating) optics (only in version 3) (12) detector-matrix (CCD).
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onto the near infrared region. Using a broadened spectral range multilayer structures become monitorable. Because of non-collimated beam, where different rays travel in different directions with different angles of incidence, expanded beam ellipsometers must be assembled with film polarizers, the only ones with symmetric and relatively high acceptance angle. Detection of the spectra from near UV to near IR using one polarizer–analyzer pair is impossible because of the characteristics of film polarizers. Therefore dual-spectral range application seems to be a convenient solution where the optical elements (polarizer–analyzer pairs, optical grating) are exchangeable; thus, the whole spectra (near UV to near IR) of many sample points is detectable in two steps using only one CCD camera. The newest version of the instrument (presently under development, see Fig. 8) has a switchable PSG + PSD configuration which allows the operation of the instrument at the NIR and VIS + UV regions (350–1000 nm).
2. Intrumentation To study the new technique we have built several PSA ellipsometer prototypes using film polarizers, including (version 1) a wide-angle 3wavelength, 2D-imaging prototype (see Fig. 1a) [5], (version 2) a special beam path controlled convergent mirror arrangement in a wide-angle 3-wavelength, 2D-imaging prototype [4], (version 3) a special mirror arrangement with spectroscopic option in a prototype that measures many points along a line (“1D-imaging”), see Fig. 1b. The special mirror arrangements make it possible to use small-aperture (25 mm diameter)
polarizers both in the light source and the detector side. The detection is almost without background. The pinhole “selects” the rays which are coming directly from the illuminated sample area, and the main advantage is that the pinhole eliminates the background of scattered light from the inner parts of the device. One rapid (less than 10 s) measurement cycle is sufficient to determine the polarization state at all points inside the illuminated area. The main advantage is the limitless sample area if a sufficiently strong light source is available. The collected data can be processed at high speed (faster than the acquisition time) even in the case of multilayer samples, providing nearly real-time thickness and/or refractive index maps over a large area of the sample surface (even~m2 with limited lateral resolution). The speed of the measurement system makes it suitable for use even on production lines. 2.1. Calibration The calibration of the angle-of-incidence (coupling of pixels to angles) and the mirror-effects is performed via well-known and optimized structures such as 3 different SiO2/Si samples. The precision and accuracy of the device is not higher than that of standard ellipsometers, but it is suitable for determining the thickness of a silicon-dioxide film with sub-nanometer precision and the angle-ofincidence with sub-tenth-degree precision. Mirror-(window-)effects are calculated using the following equation: ρopt = ρmeas ρmirror ðdifferent for each point and each wavelengthÞ
ð1Þ
Fig. 2. Calibration maps (angle of incidence, upper; real and imaginary part of ρmirror, middle; and oxide thicknesses, low). First note: real and imaginary part of ρmirror are nearly independent from the wavelength in the 400–630 nm range. Second note: the thickness maps in the right column are not smoothed alone, the “smoothing” is only the result of the recalculation with the smoothed values of the angle of incidence and ρmirror!
M. Fried et al. / Thin Solid Films 519 (2011) 2730–2736
Fig. 3. Possible arrangement for one-window vacuum chambers.
where ρopt is the measured value without mirrrors, ρmeas is the actually measured value and ρmirror is the effect of the mirrors and the windows of chamber, if any. (The actual values of ρmirror are different for each sample point and each wavelength; however, these values have only a small lateral position and wavelength dependence.) We measure three SiO2/Si samples with different thicknesses. We determine 3 N*2 Psi and Delta (where N is the number of different wavelengths) and we should calculate (fit) 2*N + 3 + 1 unknown
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calibration values for a full calibration: N*real(ρmirror) and N*im (ρmirror) + 3 thicknesses + 1 actual angle of incidence. The calibration can be made independently for each pixel but better if we summarize the intensities in pixel-groups (better dynamics) according to the lateral resolution of the system and after a first calibration we re-calculate the values using a small (second order polinomial) smoothing as we can see in Fig. 2. A flat change is presumable from either the angle of incidence and ρmirror value; thus, smoothing on the angle-map and on ρmirror reduces the error caused by calibration measurement. A feasibility study installation was performed in the Fraunhofer Institute, IISB, Erlangen, Germany, see Fig. 3. Additional advantage of this arrengement is that only one window is needed. The present installation had some geometrical limitations originated from the geometrical constrains of the given vacuum chamber construction. However, the device is suitable for making maps in a 30 × 80 mm area with a lateral resolution of at least 4 mm (see Fig. 3, upper right). SiO2/Si layers were measured by the expanded beam ellipsometer and the results were compared with the measurements by a Woollam M2000DI desktop device, see Fig. 4. 3. Applications In this section we demonstrate the capabilities of the device for 1) thickness and complex refractive index mapping for high-k layers (3-
Fig. 4. Oxide-thickness maps in different arrangements. Four pieces of 2-inch oxidized-wafers are put on a 200 mm oxidized-wafer (upper, measurement performed with the device in Fig. 3) or the same 4 wafers are in a line (lower, measurement performed with the device in Fig. 2b, version 2, 3-color 2D-maging). Note that the shape of the inhomogeneities is very similar in comparison with the M2000 desktop results but the mapping speed is very different!
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color mapping, used device in Fig. 3); 2) homogeneity check of ion implantation in silicon (full spectral, version 3); 3) mapping of physical properties (such as transparency, conductance, and thickness) of transparent conductive oxides (ZnO:Al, full spectral, version 3). High-k layer (3-color mapping, measurement performed with the device in Fig. 3). Barium strontium titanate (BST) films – prepared using metal organic chemical vapor deposition on 200 mm diameter silicon wafers – were investigated. The thickness of the high-k layer was about 400 nm in the middle of the sample, with an intentional nonuniformity towards the edge. The uniform part was within a diameter of about 150 mm (the central quarter circle in Fig. 5a). The thickness increases from 400 to 700 nm from the central area of the sample to the ring shape area at the edge of the sample. The optical properties of the deposited material depend strongly on the conditions of the sample preparation; therefore, the standard approach of using reference libraries for the material to determine the layer thickness cannot be applied. The optical properties have to be determined together with other material parameters (like layer thickness) directly (wavelength by wavelength) or by fitting whole spectra (using dispersion models). The direct determination can be used only with simple model structures, and with the multiple angle of incidence approach to increase the number of measured data and the precision using parameter fitting. With dispersion models the dielectric function of the layer is described using a limited number of parameters in a given spectral range. We used this latter approach,
describing the dispersion of the dielectric function (ε) of the high-k samples using the equation of Adachi [7,8]: εðEÞ =
A0 2−ð1 + X0 Þ0:5 −ð1−X0 Þ0:5 ; E01:5 X02
ð2Þ
with X0 = ðE + iΓÞ = E0 ;
ð3Þ
where A0, E0 and Γ are the amplitude, transition energy, and broadening, respectively. As the most important parameter, the thickness map on the SBT sample is shown in Fig. 5a. The homogeneous part near the middle of the sample is about 400 nm. The thickness increases to about 700 nm near the edge of the sample. Between the two regions, the layer quality is not good for the fit—our optical model is not suitable to evaluate the measured data. This is shown by the poor fit quality in the transition region, revealed at the lower part of Fig. 5b. The tendencies are the same in the case of desktop SE, see Fig. 5, circular diagrams. 3.1. Homogeneity check of ion implantation in silicon (full spectral, version 3) Arsenic (2 keV) (implanted by Applied Materials) ions were implanted at room temperature into single-crystalline silicon at doses of 1, 5, 10, 50*1014 As/cm2.
Fig. 5. Thickness (upper figures, a part) and fit quality (lower figures, b part) maps on the barium strontium titanate (BST, high-k layer) sample by the expanded beam ellipsometer (3D diagrams) and full (desktop) SE (circular diagrams). A quarter of a 200-mm BST sample was used for the experiment. The grid (top picture, a part) shows the measured area (points) by the mapping ellipsometer. One-layer dispersion model: limited number of parameters (thickness plus transition energy, amplitude and broadening) in a given spectral range [7,8].
M. Fried et al. / Thin Solid Films 519 (2011) 2730–2736
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Arsenic is a relatively high atomic mass ion, so even at the lower doses creates significant damage which can be described as a mixture of amorphous (a-Si) and crystalline (c-Si) silicon [9–12]. As a good approximation, we show (Fig. 6) the imaginary part of the complex pseudo-dielectric functions at different doses (middle diagram), and the upper 3D diagram shows b eps2 N (at 365 nm) map on a sample with 4 different ion-dose level (0, 1, 5, 10*1014 As/cm2). Fitting the measured beps2N (at 365 nm) values (involving the virgin sample corresponding to the point at the dose of zero) we obtain a good fit with a simple exponential function, see the bottom diagram. This curve can be used as a bε2N - N dose level conversion function. It is obvious that the steepest part is at the lower doses, so this method is more sensitive at the lower doses.
3.2. Mapping of transparent conductive ZnO:Al layers (full spectral, version 3) Al-doped ZnO (ZAO) thin films were deposited by reactive magnetron sputtering from an Al:Zn metallic alloy target for solar cell (transparent) contacts. Two pieces of 4-inch Si-wafers were placed to juxtapose in the sputtering chamber, see Fig. 7 upper picture. Specific resistance were measured (by standard 4-pin method) on the samples prior to expanded beam ellipsometric measurement. Since our layers are of dielectric character, i.e. of minor absorption in case of higher conductivity transparent layers, and the band gap equivalent wavelength lies outside of our spectral range, a good and robust choice for the fitting is the Cauchy dispersion relation: n(λ) = An + B n/λ2 + C n/λ4 , k(λ) = Ak*exp(B k*(1/λ-1/λ0 ) where λ0 = 375 nm is the wavelength corresponding to the bandgap value of the pure (undoped) ZnO. A three phase model (ambient, ZnO layer, and silicon substrate) was used to evaluate the measurements in this analysis. The results show that the samples at different positions (which have different
Fig. 7. Top picture shows the measured positions on the wafers. Lowers graphs show the Ak, Bk values at the different positions (in comparisons with the specific resistance) and the thickness distributions.
electrical and optical behaviors) have different model parameters (see Fig. 7, bottom part); thus, the samples can be measured by spectroscopic ellipsometry. Six parameters were fitted (five of the dispersion relation plus one layer thickness) using the least squares method, in order to minimize the difference between the measured and fitted ellipsometric curves. As reported in refs. [6,13,14], the amplitude (Ak) and the exponent (Bk) of the imaginary part of the complex refractive index function depend on the transparency and are well correlated with the specific resistance of the layers, so expanded beam spectral ellipsometry is a good method to check the homogeneity of such layers.
4. Future applications
Fig. 6. Homogenity check of ion implantation (2 keV As) in silicon layer. Top 3D diagram shows b eps2N (at wl = 365 nm) map on a sample with 4 different ion-dose level (0, 1, 5, 10*1014 As/cm2). Bottom diagram shows a simple exponential (b eps2N - N ion-dose level) conversion function.
Expanded beam macro-imaging ellipsometry can be used for in situ quality control in large width (150–900 mm) solar panel production lines (measurement in vacuum chamber) with limited (5–30 mm) lateral resolution. An extended spectral range (350– 1000 nm) is necesssary for multilayer structures. We are building (Fig. 8) a dual-spectral region (350–650 nm and 550–1000 nm) device for quality control of different photovoltaic materials. Expanded (non-collimated) beam ellipsometers should be assemblied with film polarizers, so 2 polarizer–analyzer pairs are needed to detect the spectra from near UV to near IR.
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Acknowledgment We are grateful for the support from EU FP6 ANNA project, Hungarian NKTH projects ICMET07, TFSOLAR2 and PVMET08, as well as for the DAAD-MÖB (P-MÖB/845) project.
References [1] D. Beaglehole, Rev. Sci. Instrum. 59 (1988) 2557. [2] G. Jin, R. Jansson, H. Arwin, Rev. Sci. Instrum. 67 (1996) 2930. [3] HORVÁTH, Zoltán György; JUHÁSZ, György; FRIED, Miklós; MAJOR, Csaba; PETRIK, Péter; Pub. No.: WO/2008/142468; International Application No.: PCT/ HU2008/000058; Publication Date: 27.11.2008; Priority Data: P 0700366 23.05.2007 HU. [4] C. Major, G. Juhasz, Z. Horvath, O. Polgar, M. Fried, Phys. Stat. Sol. C 5 (2008) 1077. [5] G. Juhász, Z. Horváth, C. Major, P. Petrik, O. Polgar, M. Fried, Phys. Stat. Sol. C 5 (2008) 1081. [6] C. Major, G. Juhasz, P. Petrik, Z. Horvath, O. Polgar, M. Fried, Vacuum 84 (2009) 119. [7] S. Adachi, Phys. Rev. B35 (1987) 7454. [8] P. Petrik, N.Q. Khánh, Z.E. Horváth, Z. Zolnai, I. Bársony, T. Lohner, M. Fried, J. Gyulai, C. Schmidt, C. Schneider, H. Ryssel, Mater. Sci. Semicond. Process. 5 (2003) 141. [9] M. Fried, T. Lohner, W.A.M. Aarnink, I.J. Hahnekamp, A. van Silfhout, J. Appl. Phys. 71 (1992) 2835. [10] T. Lohner, N.Q. Khanh, Z. Zolnai, Acta Phys. Slovaka 48 (1998) 441. [11] T. Lohner, C. Angelov, V. Mikli, Thin Solid Films 516 (2008) 8009. [12] P. Petrik, O. Polgár, M. Fried, T. Lohner, N.Q. Khánh, J. Gyulai, J. Appl. Phys. 93 (2003) 1987. [13] A. Nemeth, C. Major, M. Fried, Z. Labadi, I. Barsony, Thin Solid Films 516 (2008) 7016. [14] C. Major, A. Nemeth, G. Radnoczi, Zs. Czigany, M. Fried, Z. Labadi, I. Barsony, Appl. Surf. Sci. 255 (2009) 8907.
Fig. 8. The prototype is under work and will be installed on the experimental vacuum chamber of the PhotoVoltaic Innovation and Commercialization Center at University of Toledo (Ohio).
This device can be used for monitoring of solar cell purpose layers such as amorphous and crystalline silicon, CdTe, CIGS (CuIn1-xGaxSe2) layers or transparent conductive oxide layers.
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Expanded beam (macro-imaging) ellipsometry M. Fried a,⁎, G. Juhász a, C. Major a, P. Petrik a, O. Polgár a, Z. Horváth b, A. Nutsch c a b c
Res. Inst. for Technical Physics and Materials Science (MFA), H-1525 Budapest, POB 49, Hungary Res. Inst. for Solid State Physics and Optics (SZFKI), H-1525 Budapest, POB 49, Hungary Fraunhofer Institut für Integrierte Systeme und Bauelementetechnologie IISB, Schottkystr. 10, 91058 Erlangen, Germany
a r t i c l e
i n f o
Available online 21 December 2010 Keywords: Ellipsometry Mapping Thin film
a b s t r a c t Our aim was to make possible to use spectroscopic ellipsometry for mapping purposes during one measuring cycle (minimum one rotation period of polarizer or analyzer) on many sample points. Our new technique uses non-collimated (non-parallel, mostly diffuse) illumination with an angle of incidence sensitive pinhole camera detector system and it works as an unusual kind of imaging ellipsometry. Adding multicolour supplemets, it provides spectral (a few wavelengths on a 2D image or a full spectrum along a line) information from rapid measurements of many points on a large (several dm2) area. This technique can be expanded by upscaling the geometry (upscaling the dimensions of the instrument, and characteristic imaging parameters such as focal lengths, distances, etc.). The lateral resolution is limited by the minimum resolved-angle determined by the detector system, mainly by the diameter of the pinhole. (The diameter of the pinhole is a compromise between the light intensity and the lateral resolution.) Small-aperture (25 mm diameter) polarizers are incorporated into both the polarization state generator (PSG) and polarization state detection (PSD) components of the instrument. The detection is almost without background because the pinhole serves as a filter against the scattered light. One rapid measuring cycle (less than 10 s) is enough to determine the polarization state at all the points inside the illuminated area. The collected data can be processed very fast (seconds) providing nearly real-time thicknesses and/or refractive index maps over many points of the sample surface even in the case of multilayer samples. The speed of the measuring system makes it suitable for using even on production lines. The necessary (in each sample-point different) angle-of-incidence and the mirror-effect calibration are made via well-known and optimized structures such as silicon/silicon-dioxide samples. The precision is suitable for detecting sub-nanometer thickness and a refractive index change of 0.01. The method can be used for mapping and quality control in the case of large area solar cell table production lines even in a vacuum chamber with 5–10 mm lateral resolution. © 2010 Published by Elsevier B.V.
1. Introduction Ellipsometry determines angle of incidence dependent data of light reflection, so generally it works by parallel light beams with a well defined angle of incidence. Here we present a fundamentally different method from the usual ellipsometric techniques. The target is illuminated by non-parallel, almost diffuse, “expanded beam” light in our case, providing a lot of beams with diverse angles of incidence at every point of the sample. The precise “angle-selection” is made at the detector side, by a pinhole camera. (The pinhole works as an “angle-filter,” selecting only one single light beam from every direction. The angle resolution of a camera of this kind is depending on the diameter of the pinhole.) In the case of a single wavelength measurement, this solution is appropriate for measuring a sample of large area with a range of angles ⁎ Corresponding author. E-mail address: [email protected] (M. Fried). 0040-6090/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.tsf.2010.12.067
wide enough but different angles of incidence belong to each sample points. If the sample is moved along a line during the measurement (for example on a production line) each sample points will be measured at multiple angles of incidence successively. Repeating the measurement with light of various wavelengths we can get spectral (few wavelengths) ellipsometric data. Reducing the number of the measured sample points into a narrow range along a line only, we can provide full spectral data from one measurement, using white light illumination with a spectral selector (grating) after the pinhole. It produces geometrical information (sample points/angle of incidence) of the reflected light intensity on a CCDmatrix in one direction, and spectral information in the perpendicular direction at the same time. One of the key problems of the practical ellipsometry is the quality of the polarizers which can be very expensive as the size increases. To reduce this problem our aim was to minimize the sizes of the polarizers both in the light source and at the detector side. We solved this problem by constructing a special, angle-persistent optical system which allows
M. Fried et al. / Thin Solid Films 519 (2011) 2730–2736
reducing the diameters of the polarizers and lowers the light-losses in the same time. Mapping ellipsometry methods can be classified into two main groups: a) Scanning methods based on one narrow beam (collimated or focused microspot) are very accurate but make these methods relatively slow for mapping purposes. b) Imaging techniques based on a twodimensional detector array can speed up the measurement. In the latter case the measured surface is illuminated by a collimated light beam, and the reflected light is usually detected by a CCD camera. [1,2] In this way the entire surface is measured simultaneously, and the measured values of each point are evaluated to determine the lateral distribution as an image. If the magnification (ratio of the measured area and the image on the CCD camera) is greater than 1 we call it “microscopic imaging” [1]. If magnification is smaller than 1 we can call it “macroscopic imaging” [2]. One disadvantage of using collimated beam is that the greatest measurable size of the sample surface is strongly limited by the diameter of the used polarizer, so this method is used mainly for microscopic imaging. One can overcome these problems by building a device [3] which is capable of measuring the polarization state changes upon reflection from a large (theoretically any size) surface rapidly. The new technique (which can be considered as a “turned-around” microscope) uses noncollimated (divergent or focusing in different arrangements) illumination providing multi-wavelength (a few wavelengths on a 2D image or full spectral along a line) information from rapid measurements of a large area, which can be expanded by upscaling the geometry. The lateral resolution is limited by the minimum resolved-angle determined by the detector system, mainly by the diameter of the pinhole. The diameter of the pinhole is a compromise between the light intensity and the lateral resolution. Ray-tracking simulations show that 0.1–0.2 mm diameter pinhole is a good compromise and this diameter makes a 30 × 30 points mapping resolution possible on any size of the mapping area. Multiwavelength expanded beam ellipsometer was developed in the last few years [3–5]. To study the specific features of the new technique we have built some prototypes in the form of a wide-angle 3wavelength, PSA ellipsometers using film polarizers. In the first version the light source was the exit aperture of an optical fiber driven by three
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different wavelength laser sources (781 nm, 661 nm, 533 nm) [5]. The lasers can be used as very intensive, stabile wavelength, narrow bandwidth point-like sources; therefore, they are very suitable monochrome illuminator for our application but to avoid their disadvantageous effects we have had to take care of the speckle noise reduction and of the polarization state homogeneity. In this version the intensity detection system is a screen camera assembly (with an analyzer bigger than the illuminated sample area); therefore, we cannot eliminate the background of scattered light from the inner parts of the device [5]. The second version applied a pinhole camera detection technique, Fig. 1a. The light source here was a high intensity (Luxeon Lumiled) LED matrix with three different wavelengths of 637 nm, 523 nm, and 460 nm with a bandwidth of 15 nm, 30 nm, and 20 nm, respectively. A diffusor plate served as a homogenizer and the pinhole “selects” the convergent rays. In this version the polarizer is bigger than the illuminated sample area, but the main advantage is that the pinhole eliminates the background of scattered light from the inner parts of the device [5]. Because of the poor spectral information the capabilities of the method are limited to the cases where the measurements can be evaluated using three spectral points. The precision of the method is sufficient for detecting subnanometer thickness change of well-known structures such as silicon/silicon-dioxide samples or a refractive index change of 0.01. In case of more complex structures and/or unknown refractive indices a higher resolution spectral sampling is necessary for the precise evaluation of the measurements. For the elimination of the problem, we developed a modified version of expanded beam spectroscopic ellipsometry that uses whole spectra of a large number of sample points (along a line) in the near UV-VIS range (presently 350–630 nm) acquired in one measuring cycle (minimum two rotation periods of polarizer or analyzer). The spectral technique can speed up the mapping of physical properties (such as thickness, transparency, conductance) of transparent conductive oxides such as Al-doped ZnO layers [6]. Since characteristic spectral features of different layers can be far away from each other, the near UV-VIS range (presently 350–630 nm) is not satisfactory in all cases, but an extended spectral range is necessary
Fig. 1. a (1) Light source (LED-panel) (2) diffusor (3) film-polarizer (4) analyzer (6) sample (5) detector (pinhole + CCD-detector) (Installed version (right) in the Student Lab, Technical University, Budapest).b (1) “white” source (fiber-coupled RGB-laser in version 2, Xe-lamp in version 3), (2) film-polarizer, (3) spherical mirror, (4) convergent beam, (5) sample, (13) narrow, rectangular aperture (only in version 3) (6) cylindrical mirror, (7) corrected beam, (8) analyzer, (9) pinhole, (10) divergent beam, (11) correctiondispersion (with diffraction grating) optics (only in version 3) (12) detector-matrix (CCD).
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onto the near infrared region. Using a broadened spectral range multilayer structures become monitorable. Because of non-collimated beam, where different rays travel in different directions with different angles of incidence, expanded beam ellipsometers must be assembled with film polarizers, the only ones with symmetric and relatively high acceptance angle. Detection of the spectra from near UV to near IR using one polarizer–analyzer pair is impossible because of the characteristics of film polarizers. Therefore dual-spectral range application seems to be a convenient solution where the optical elements (polarizer–analyzer pairs, optical grating) are exchangeable; thus, the whole spectra (near UV to near IR) of many sample points is detectable in two steps using only one CCD camera. The newest version of the instrument (presently under development, see Fig. 8) has a switchable PSG + PSD configuration which allows the operation of the instrument at the NIR and VIS + UV regions (350–1000 nm).
2. Intrumentation To study the new technique we have built several PSA ellipsometer prototypes using film polarizers, including (version 1) a wide-angle 3wavelength, 2D-imaging prototype (see Fig. 1a) [5], (version 2) a special beam path controlled convergent mirror arrangement in a wide-angle 3-wavelength, 2D-imaging prototype [4], (version 3) a special mirror arrangement with spectroscopic option in a prototype that measures many points along a line (“1D-imaging”), see Fig. 1b. The special mirror arrangements make it possible to use small-aperture (25 mm diameter)
polarizers both in the light source and the detector side. The detection is almost without background. The pinhole “selects” the rays which are coming directly from the illuminated sample area, and the main advantage is that the pinhole eliminates the background of scattered light from the inner parts of the device. One rapid (less than 10 s) measurement cycle is sufficient to determine the polarization state at all points inside the illuminated area. The main advantage is the limitless sample area if a sufficiently strong light source is available. The collected data can be processed at high speed (faster than the acquisition time) even in the case of multilayer samples, providing nearly real-time thickness and/or refractive index maps over a large area of the sample surface (even~m2 with limited lateral resolution). The speed of the measurement system makes it suitable for use even on production lines. 2.1. Calibration The calibration of the angle-of-incidence (coupling of pixels to angles) and the mirror-effects is performed via well-known and optimized structures such as 3 different SiO2/Si samples. The precision and accuracy of the device is not higher than that of standard ellipsometers, but it is suitable for determining the thickness of a silicon-dioxide film with sub-nanometer precision and the angle-ofincidence with sub-tenth-degree precision. Mirror-(window-)effects are calculated using the following equation: ρopt = ρmeas ρmirror ðdifferent for each point and each wavelengthÞ
ð1Þ
Fig. 2. Calibration maps (angle of incidence, upper; real and imaginary part of ρmirror, middle; and oxide thicknesses, low). First note: real and imaginary part of ρmirror are nearly independent from the wavelength in the 400–630 nm range. Second note: the thickness maps in the right column are not smoothed alone, the “smoothing” is only the result of the recalculation with the smoothed values of the angle of incidence and ρmirror!
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Fig. 3. Possible arrangement for one-window vacuum chambers.
where ρopt is the measured value without mirrrors, ρmeas is the actually measured value and ρmirror is the effect of the mirrors and the windows of chamber, if any. (The actual values of ρmirror are different for each sample point and each wavelength; however, these values have only a small lateral position and wavelength dependence.) We measure three SiO2/Si samples with different thicknesses. We determine 3 N*2 Psi and Delta (where N is the number of different wavelengths) and we should calculate (fit) 2*N + 3 + 1 unknown
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calibration values for a full calibration: N*real(ρmirror) and N*im (ρmirror) + 3 thicknesses + 1 actual angle of incidence. The calibration can be made independently for each pixel but better if we summarize the intensities in pixel-groups (better dynamics) according to the lateral resolution of the system and after a first calibration we re-calculate the values using a small (second order polinomial) smoothing as we can see in Fig. 2. A flat change is presumable from either the angle of incidence and ρmirror value; thus, smoothing on the angle-map and on ρmirror reduces the error caused by calibration measurement. A feasibility study installation was performed in the Fraunhofer Institute, IISB, Erlangen, Germany, see Fig. 3. Additional advantage of this arrengement is that only one window is needed. The present installation had some geometrical limitations originated from the geometrical constrains of the given vacuum chamber construction. However, the device is suitable for making maps in a 30 × 80 mm area with a lateral resolution of at least 4 mm (see Fig. 3, upper right). SiO2/Si layers were measured by the expanded beam ellipsometer and the results were compared with the measurements by a Woollam M2000DI desktop device, see Fig. 4. 3. Applications In this section we demonstrate the capabilities of the device for 1) thickness and complex refractive index mapping for high-k layers (3-
Fig. 4. Oxide-thickness maps in different arrangements. Four pieces of 2-inch oxidized-wafers are put on a 200 mm oxidized-wafer (upper, measurement performed with the device in Fig. 3) or the same 4 wafers are in a line (lower, measurement performed with the device in Fig. 2b, version 2, 3-color 2D-maging). Note that the shape of the inhomogeneities is very similar in comparison with the M2000 desktop results but the mapping speed is very different!
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color mapping, used device in Fig. 3); 2) homogeneity check of ion implantation in silicon (full spectral, version 3); 3) mapping of physical properties (such as transparency, conductance, and thickness) of transparent conductive oxides (ZnO:Al, full spectral, version 3). High-k layer (3-color mapping, measurement performed with the device in Fig. 3). Barium strontium titanate (BST) films – prepared using metal organic chemical vapor deposition on 200 mm diameter silicon wafers – were investigated. The thickness of the high-k layer was about 400 nm in the middle of the sample, with an intentional nonuniformity towards the edge. The uniform part was within a diameter of about 150 mm (the central quarter circle in Fig. 5a). The thickness increases from 400 to 700 nm from the central area of the sample to the ring shape area at the edge of the sample. The optical properties of the deposited material depend strongly on the conditions of the sample preparation; therefore, the standard approach of using reference libraries for the material to determine the layer thickness cannot be applied. The optical properties have to be determined together with other material parameters (like layer thickness) directly (wavelength by wavelength) or by fitting whole spectra (using dispersion models). The direct determination can be used only with simple model structures, and with the multiple angle of incidence approach to increase the number of measured data and the precision using parameter fitting. With dispersion models the dielectric function of the layer is described using a limited number of parameters in a given spectral range. We used this latter approach,
describing the dispersion of the dielectric function (ε) of the high-k samples using the equation of Adachi [7,8]: εðEÞ =
A0 2−ð1 + X0 Þ0:5 −ð1−X0 Þ0:5 ; E01:5 X02
ð2Þ
with X0 = ðE + iΓÞ = E0 ;
ð3Þ
where A0, E0 and Γ are the amplitude, transition energy, and broadening, respectively. As the most important parameter, the thickness map on the SBT sample is shown in Fig. 5a. The homogeneous part near the middle of the sample is about 400 nm. The thickness increases to about 700 nm near the edge of the sample. Between the two regions, the layer quality is not good for the fit—our optical model is not suitable to evaluate the measured data. This is shown by the poor fit quality in the transition region, revealed at the lower part of Fig. 5b. The tendencies are the same in the case of desktop SE, see Fig. 5, circular diagrams. 3.1. Homogeneity check of ion implantation in silicon (full spectral, version 3) Arsenic (2 keV) (implanted by Applied Materials) ions were implanted at room temperature into single-crystalline silicon at doses of 1, 5, 10, 50*1014 As/cm2.
Fig. 5. Thickness (upper figures, a part) and fit quality (lower figures, b part) maps on the barium strontium titanate (BST, high-k layer) sample by the expanded beam ellipsometer (3D diagrams) and full (desktop) SE (circular diagrams). A quarter of a 200-mm BST sample was used for the experiment. The grid (top picture, a part) shows the measured area (points) by the mapping ellipsometer. One-layer dispersion model: limited number of parameters (thickness plus transition energy, amplitude and broadening) in a given spectral range [7,8].
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Arsenic is a relatively high atomic mass ion, so even at the lower doses creates significant damage which can be described as a mixture of amorphous (a-Si) and crystalline (c-Si) silicon [9–12]. As a good approximation, we show (Fig. 6) the imaginary part of the complex pseudo-dielectric functions at different doses (middle diagram), and the upper 3D diagram shows b eps2 N (at 365 nm) map on a sample with 4 different ion-dose level (0, 1, 5, 10*1014 As/cm2). Fitting the measured beps2N (at 365 nm) values (involving the virgin sample corresponding to the point at the dose of zero) we obtain a good fit with a simple exponential function, see the bottom diagram. This curve can be used as a bε2N - N dose level conversion function. It is obvious that the steepest part is at the lower doses, so this method is more sensitive at the lower doses.
3.2. Mapping of transparent conductive ZnO:Al layers (full spectral, version 3) Al-doped ZnO (ZAO) thin films were deposited by reactive magnetron sputtering from an Al:Zn metallic alloy target for solar cell (transparent) contacts. Two pieces of 4-inch Si-wafers were placed to juxtapose in the sputtering chamber, see Fig. 7 upper picture. Specific resistance were measured (by standard 4-pin method) on the samples prior to expanded beam ellipsometric measurement. Since our layers are of dielectric character, i.e. of minor absorption in case of higher conductivity transparent layers, and the band gap equivalent wavelength lies outside of our spectral range, a good and robust choice for the fitting is the Cauchy dispersion relation: n(λ) = An + B n/λ2 + C n/λ4 , k(λ) = Ak*exp(B k*(1/λ-1/λ0 ) where λ0 = 375 nm is the wavelength corresponding to the bandgap value of the pure (undoped) ZnO. A three phase model (ambient, ZnO layer, and silicon substrate) was used to evaluate the measurements in this analysis. The results show that the samples at different positions (which have different
Fig. 7. Top picture shows the measured positions on the wafers. Lowers graphs show the Ak, Bk values at the different positions (in comparisons with the specific resistance) and the thickness distributions.
electrical and optical behaviors) have different model parameters (see Fig. 7, bottom part); thus, the samples can be measured by spectroscopic ellipsometry. Six parameters were fitted (five of the dispersion relation plus one layer thickness) using the least squares method, in order to minimize the difference between the measured and fitted ellipsometric curves. As reported in refs. [6,13,14], the amplitude (Ak) and the exponent (Bk) of the imaginary part of the complex refractive index function depend on the transparency and are well correlated with the specific resistance of the layers, so expanded beam spectral ellipsometry is a good method to check the homogeneity of such layers.
4. Future applications
Fig. 6. Homogenity check of ion implantation (2 keV As) in silicon layer. Top 3D diagram shows b eps2N (at wl = 365 nm) map on a sample with 4 different ion-dose level (0, 1, 5, 10*1014 As/cm2). Bottom diagram shows a simple exponential (b eps2N - N ion-dose level) conversion function.
Expanded beam macro-imaging ellipsometry can be used for in situ quality control in large width (150–900 mm) solar panel production lines (measurement in vacuum chamber) with limited (5–30 mm) lateral resolution. An extended spectral range (350– 1000 nm) is necesssary for multilayer structures. We are building (Fig. 8) a dual-spectral region (350–650 nm and 550–1000 nm) device for quality control of different photovoltaic materials. Expanded (non-collimated) beam ellipsometers should be assemblied with film polarizers, so 2 polarizer–analyzer pairs are needed to detect the spectra from near UV to near IR.
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Acknowledgment We are grateful for the support from EU FP6 ANNA project, Hungarian NKTH projects ICMET07, TFSOLAR2 and PVMET08, as well as for the DAAD-MÖB (P-MÖB/845) project.
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Fig. 8. The prototype is under work and will be installed on the experimental vacuum chamber of the PhotoVoltaic Innovation and Commercialization Center at University of Toledo (Ohio).
This device can be used for monitoring of solar cell purpose layers such as amorphous and crystalline silicon, CdTe, CIGS (CuIn1-xGaxSe2) layers or transparent conductive oxide layers.