Enabling solution-based printing techniques for sub-100 nm thin semiconductors for the application in large-area organic electronics is a challenging task. In order to optimize the process parameters, the layers have to be characterized on a large lateral scale while determining the nanometer thickness at the same time. We present a lateral and vertical resolving measurement method for large-area, semi-transparent thin films based on optical interference effects. We analyzed the RGB color images of up to 150 mm square-sized thin film samples obtained by a modified commercial flatbed scanner. Utilizing and comparing theoretical and measured color contrast values, we determined most probable thickness values of the imaged sample area pixel by pixel. Within specific boundary conditions, we found very good agreement between the presented imaging color reflectometry and reference methods. Due to its simple setup, our method is suitable to be implemented as part of a color vision inspection system in in-line printing and coating processes.
© 2013 Optical Society of America
Recent progress in applying and processing printed layers for organic light emitting diodes (OLED), organic thin film transistors (OTFT) or organic photovoltaics (OPV) pave the way for industrial relevance of printed electronics [1–4]. On that way, there are still many issues to overcome. Obeying a stable printing process to produce for example the sub-100 nm thick emitting layer of an OLED lighting panel is very challenging. Layer formation is often afflicted by different kinds of thin film or process instabilities [2, 5]. These layer irregularities occur on rigid glass substrate sizes from 30 mm × 30 mm to 150 mm × 150 mm commonly used in sheet-fed processes as well as in roll-to-roll processing of flexible organic electronics. Specifying the layer topography on a large lateral scale and the thicknesses in the nm-range are difficult to determine simultaneously. The lack of affordable, fast and reliable measurement methods for this application hampers the development of high-throughput solution processing techniques in printed electronics.
According to this, X-ray based measurement methods are usually laterally limited to few millimeters and destroy the sample by sputtering , and electron microscopy requires a cross section, an edge or a layer step to determine the thickness . The latter holds also true for other profiling techniques which operate optically or mechanically. For example, accurate thickness determination in the middle of a 150 mm squared substrate which has been fully printed with a sub-100 nm layer is not possible with these methods without scratching or breaking the sample. There are basically two optical methods which are applicable for non-destructive large-area thin film metrology: ellipsometry  and spectroscopic reflectometry . Both methods require the films to be semi-transparent. This is often fulfilled for the materials used in organic electronic devices. Usually, for both methods measuring large areas, the sample has to be scanned step by step resulting in long measurement times. Imaging ellipsometry does not have this drawback and is apart from high procurement costs a fast and reliable measurement method [10–12].
The application of spectroscopic reflectometry additionally requires the prior knowledge of the refractive indices of the films and the substrate. The operating principle involves measuring the change in the spectrum which undergoes the light when being reflected from the sample. For thin, semi-transparent films, the reflected light from the air-film, film-film and the film-substrate interface interfere at the photo-detector dependent on the film thicknesses and the refractive indices. The characteristic change in the spectrum is analyzed using a spectrometer and results in an estimate for the film thickness.
An interesting alternative to spectroscopic reflectometry is to use a camera instead of a spectrometer. Several authors show that this approach can lead to reliable results for the determination of thin films. Oxide layers on metal  or silicon wafers [14–16] and the number of atomic mono-layers of graphene coatings [17–19] were successfully analyzed using color vision. The setups were usually limited to small areas.
The substrate sizes which are commonly used in laboratory and advance development for sheet-to-sheet printed OLED and OTFT are still below DINA4. Therefore, we utilized a modified commercial flatbed scanner instead of a spectrometer to apply the concept of interference-based imaging reflectometry. It has been shown that beyond scanning documents, flatbed scanners can be successfully applied to different kind of measurements [20–25]. They are fast and posses a high lateral resolution at the same time. We mainly adapted a beam-splitter to obtain a common optical path for illumination and light detection within the scanner. Additionally, we placed a diffusor in front of the light source to homogenize the illumination and we characterized all optical elements according to their spectral optical response. For data analysis, we developed an algorithm which compared contrast values of the red, green and blue channels of the images to theoretical ones. Thereby, we determined the most probable film thickness at each pixel. Using the contrast values we converted the RGB images of the captured thin films to thickness maps independent of variations of the light source’s intensity. Applying the proposed method to a silicon dioxide coated wafer and an organic semiconductor printed on an indium tin oxide (ITO) coated glass substrate proved that it is an affordable, reliable and fast measurement technique for large-area thin films. The fact that only images or videos were required predestines the method for in-line thickness measurements in printing and coating processes.
The paper is organized as follows. We describe the measurement principle which includes the optical model and the algorithm for the image analysis in the second section. In the third section, we introduce the underlaying measurement hardware and show how we characterized all optical components to predict the system behavior. In the fourth section, we compare the results of the different samples to reference methods and discuss the estimated thickness maps as well as the drawbacks of our method. We close the topic with the conclusion in the fifth section.
2. Measurement principle
Figure 1 shows the basic optical setup of the measurement method. A light source illuminates the sample, the corresponding spectral power distribution (or spectrum) is denoted with I(λ) where λ is the wavelength. The thin films on the substrate reflect a spectrum modified by optical interference according to the thicknesses dl and the refractive indices Nl(λ) of the layers, its spectral reflectance is labeled with Rf(λ, dl, Nl). The latter is summed with incoherent reflections from the backside of a transparent substrate Rbs(λ, dl, Nl) (indicated as dashed arrows in Fig. 1) to yield the total spectral reflectance Rtotal(λ, dl, Nl). The summarized spectral transmittance of optical elements such as lenses and mirrors which might be used in a real system to inspect the sample are labeled with P(λ). We modeled the CCD (Charged Coupled Device) color sensor with the spectral transmittance of the red (k = 1), green (k = 2) and blue (k = 3) RGB-filter Fk(λ) and a linear optoelectronic transfer function S(λ). The function S(λ) depends mainly on the exposure time or so to say on the number of photons reaching the photo-detector pixels within a given time. The assumption of the linearity of the sensor is justified for considerable brightness and for avoiding to saturate the sensor with photons. We neglected noise and errors of the optoelectronic system which are definitively present and which could be treated according to Hardeberg  or Burns .
In contrast to our sketch in Fig. 1, we always assumed normal orientation of the illumination and the inspection to the sample surface in our optical setup and in our physical model (section 2.1). In this context, we also neglected the opening angles of our optical inspection system. In the following, we treat lateral varying quantities such as the thickness of the layers or a non-homogeneous illumination in terms of the sample area which is imaged by the digital optical system onto a 2D sensor of imax × jmax pixels (with i ∈ [1, imax] and j ∈ [1, jmax]). Therefore, the layer thicknesses and the total reflectance of the sample now reads and according to the pixel position ij. The spectral radiance of the light source is described by the normalized spectral power distribution I(λ) multiplied by a lateral varying intensity constant which is dependent on the surface area projected onto the pixel position ij as followsFig. 1, the optoelectronic response from a pixel at position ij is given by Eqs. (1) and (2), we result in Eq. (4),S(λ), P(λ), Fk(λ), I(λ) are accessible via separate measurements, i.e. by spectral characterization (see section 3.1). The remaining unknown quantities are the constant Cij which we leave unknown because of using contrast values (see section 2.2) and the spectral reflectance of the thin film sample. The latter is mainly defined by the refractive indices which we assumed to be fixed for a given stack and the thicknesses of the thin films. The following subsection gives a detailed description of the optical model for the spectral reflectance of thin films on a thick, and possibly transparent substrate.
2.1. Thin film interference
In order to model the spectral reflectance Rf of the multilayer stack (omitting the lateral dimensions ij here), we used the Abeles matrix notation for thin film interference  as described in common optical textbooks, see for example Mcleod . To apply this formalism we had to ensure that the light is coherent within the vertical dimensions of the multilayer. This is valid for our samples because the thin films possessed thicknesses far below 1 μm which is below the coherent length of the light used for illumination. For normal incidence, the lth layer is described by a 2 × 2 transfer matrix of the form 
The matrix Ml (Eq. 5) describes the complete evolution of the corresponding electromagnetic fields within layer l.
The representative matrix describing the thin film stack with its interfaces and thicknesses of q layers is Eq. (7) are multiplied from the left. Therewith, the reflectance and the transmittance coefficients for the amplitudes of the multilayer yield Equations (8) and (9) result in the total reflectance and transmittance Fig. 1. We had to treat backside reflections differently because we could not assume that the light is coherent anymore when traveling through the mm-thick substrate. If we sum up multiple reflections inside the substrate, the spectral reflectance originating from the backside will be given by  Eq. (6),Rs-air is the spectral reflectance inside the substrate from the backside and T′f and R′f are the spectral reflectance (Eq. (10)) and transmittance (Eq. (11)) but in reverse order of the layers. Then, the total spectral reflectance becomes
2.2. Data acquisition and thickness estimation
The images captured by the scanner device had to be available in raw format, specially without a gamma correction. Three measured RGB values were assigned to each pixel of the picture denoted with providing the basis for the film thickness determination. We implemented an algorithm in MATLAB which was able to estimate the thickness of the top, qth layer of a thin film stack. We found that contrast values ∈ [−1, 1] defined byEq. (14), we had to measure or find reference values of a completely defined sample or a sample region with known film thicknesses . Usually, we took an image of the sample before printing the qth layer so that we could assume zero thickness of this one. The actual thickness estimation algorithm compared the contrast values from the images (Eq. (14)) to a list of theoretically determined ones. For the latter, we used theoretical RGB values defined in Eq. (4) with a characterized optical setup, i.e. known S(λ), P(λ), Fk(λ) and I(λ). The total reflection (see Eq. (13)) was calculated with known thicknesses of up to the (q − 1)th layer and within a defined thickness interval dq,r, r ∈ [1, p] of the top, qth layer. The interval was made of p values between dq,1 and dq,p, usually in 1 nm steps, in order to create the list of theoretical contrast values ∈ [−1, 1] as follows Eq. (4) and where the labeling “ref” denotes the values of the reference sample. For the thickness range dq,r, r ∈ [1, p], we had to set limits which we usually guessed from printing or coating process parameters. Additionally, we determined the reference values by prior knowledge of the values of the reference thickness dq,refij, the thicknesses of up to the (q − 1)th layer and all refractive indices Nl, l ∈ [1, q] in advance. The theoretical contrast values take advantage of being independent of the constant Cij of Eq. (4) because under the assumption that (image and reference image were acquired under the same conditions) the constants cancel. This also meant that and would be independent of intensity variations of the illumination across the sample and also independent of exposure time because of the linearity of the sensor. Therewith, we found the thickness within the list of theoretical contrast values (Eq. (15)) which obeyed the smallest Euclidean distance to the measured contrast values (Eq. (14)) pixel by pixel according to
3. Experimental setup
The flatbed scanner used in the present study was an Epson Perfection 3170. The bright field illumination was originally set by two fluorescent bulbs positioned around ±40° off the normal to the sample surface. We reduced the illumination to one bulb only and implemented a beam-splitter to provide normal orientation and a diffuser for homogeneous illumination. The basic optical setup of the modified commercial flatbed scanner is shown in Fig. 2. Additionally, we adapted a substrate holder on top of the scanner to ensure reproducible and adjustable sample position, depicted in Fig. 3(a). The original scan head was modified and equipped with an adjustable holder for a plate beam-splitter of variable length in the optical path, as illustrated in the drawing in Fig. 3(b). After several attempts with thin glass beam-splitters (0.7 mm thickness), we installed a 50R/50T plate beam-splitter of 10 mm × 178 mm mm from Edmund Optics, Germany. Its thickness of 3 mm ensured minimal bending over the width of 178 mm.
The scanner exhibits an optical resolution of 3200 DPI in scan direction and 6400 DPI over the scan width. This would correspond to a minimal surface area of 4 μm × 8 μm resolved by a single image pixel of the system. We did not perform an analysis of the lateral resolution of the system, but we observed that the minimal lateral resolution was about a factor of five above the theoretical value without the modifications. Removing one bulb and including the beam-splitter, the diffusor and the substrate holder, we lost a further factor of about two of the lateral resolution possibly due to scattering effects and multiple reflections within the system.
3.1. Optical characterization
As mentioned before, the optical setup of the flatbed scanner had to be known according to its spectral characteristics. This meant that the normalized spectral radiance of the scanner illumination I(λ), the spectral transmittance of the optical path (beam-splitter, mirrors and lenses) P(λ), the spectral transmittances of the filters of the CCD chip Fk(λ) and the optoelectronic transfer function S(λ) had to be determined, see Figs. 1 and 2 for labeling. We used the spectrophotometer CS1000A from Konica Minolta with 1 nm resolution for spectral characterization. The normalized spectral radiance of the scanner’s light source I(λ) when it illuminates the sample according to Fig. 2, i.e. has passed the beam-splitter and the diffuser, is depicted in Fig. 4.
We combined the three remaining quantities S(λ), Fk(λ) and P(λ) toFig. 4.
We inspected a single and a double-layer on a non-transparent and a transparent substrate with the proposed method. The first one was a 100 mm silicon (Si) wafer with six different fields of silicon dioxide (SiO2) ranging from 0 to 500 nm thickness in steps of 100 nm from Ocean Optics, Germany. The layer thicknesses were determined by the manufacturer using spectroscopic ellipsometry with a Plasmos ellipsometer (SD2300), at a single central millimeter spot of the wafer, listed in Table 1.
The second sample, a 150 mm × 150 mm glass substrate, was fully vacuum coated with indium tin oxide (ITO) of 160 nm thickness which we determined with the spectroscopic reflectometry tool NanoCalc from Mikropack, Germany. Using the gravure printing method we printed the organic semiconductor Spiro-MeO-TAD (C81H68N4O8) dissolved in toluene to produce several 30 mm × 30 mm squares on top of the ITO layer of thicknesses below 60 nm. The layer thicknesses of the printed squares were determined with a second method, namely by phase shifting interferometry (PSI) with a Sensofar Plu Neox, Spain, at generated edges (or swiped lines) at different small sized (254 μm × 190 μm) positions ranging from 18 to 25 nm, listed in Table 2.
The refractive indices of the organic semiconductor Spiro-MeO-TAD were determined by spectroscopic ellipsometry by BASF SE, Germany. The indices of the other materials were taken from the materials library which was delivered with the spectroscopic reflectometry tool from Mikropack.
4. Results and discussion
4.1. SiO2 on silicon wafer
An image of the first sample, the silicon wafer, captured by the modified scanner is shown in Fig. 5. We determined the thickness map of the silicon dioxide (one layer, hence q = 1) using the proposed imaging color reflectometry based on this image. For the reference RGB values which were required for the contrast calculation in Eq. (14) we averaged over an area of the bottom field 6 of Fig. 5. This field was not coated with silicon dioxide and therefore, possessed a thickness close to zero apart from a native oxide layer under ambient conditions of 1.2 nm, as determined by the manufacturer (Table 1). Furthermore, to apply Eq. (15) for the list of theoretical contrast values, we set the lower limit of the thickness range d1,r of the silicon dioxide to d1,1 = 0 nm and the upper limit to d1,601 = 600 nm. This was prior knowledge of the sample we had to add at this point. The theoretical contrast values ck for this sample within the specified thickness range d1,r, r ∈ [1, 601] are depicted in Fig. 6 for the three color channels. Using Eq. (16) to find the best match between measured and theoretical contrast values yielded the final thickness map of the silicon dioxide shown in Fig. 7. Extracting average profiles along the vertical axis of Fig. 7 and measuring the thicknesses within the profiles showed very good agreement with the values specified by spectroscopic ellipsometry summarized in Table 1. The maximum difference between the measurements techniques is only 2.5 nm.
4.2. Organic semiconductor on ITO/glass substrate
The second sample, Spiro-MeO-TAD/ITO/glass (two thin layers, hence q = 2), was treated differently according to the reference RGB values. Here, we just scanned the substrate before printing with Spiro-MeO-TAD to obtain a complete reference image. The scanned image of an area of 76.9 mm × 132.9 mm of the printed sample is shown in Fig. 8 which contains eight full and seven partly printed squares with vertical lines in it. We swiped lines after printing to perform topography thickness measurements using phase shifting interferometry (PSI) as mentioned before. The resulting thicknesses with PSI for the six fields labeled in Fig. 8 are summarized in Table 2.
From known printing parameters and composition of the ink we expected the film thickness of the organic semiconductor to stay below 60 nm and the thicknesses of the fields to fulfill the relationsFig. 9. The least square (LS) minimization of the distance between the pixel based contrast values and the theoretic ones (see Eq. (16)) led to the thickness map for the printed organic semiconductor shown in Fig. 10. Instead to phase shifting interferometry which measured the thickness only at some positions at the swiped lines, we could analyze the complete printed fields of Fig. 10. The results for the six labeled fields according to Fig. 10 are compared in Table 2. Although the limited-area measurements of the phase shifting interferometry did not represent the whole printed fields, we found only a maximum difference of 4.6 nm between the two measurement methods. Additionally, comparing the thicknesses summarized in Table 2 with the relations mentioned in Eq. (18), we can conclude that the ICR method produced more reliable results in matching the expectations defined by the printing process parameters than PSI.
The two different samples which we analyzed with the proposed method showed very good agreement with the reference methods. The thicknesses and the refractive indices of the layers and the substrates play an important role to achieve reasonable results. If the refractive indices were too close or the thicknesses are too thin, we would strongly lose the information to distinguish between different thicknesses. For example, the difference of the real part of the refractive indices of silicon and SiO2 of the first sample is around 2.5 nm. To show the importance of this difference, we assume to have coated SiO2 on glass instead of on silicon. Now, the mean difference of the real parts of the refractive indices of SiO2 and glass is only 0.02. Then, the maximum range of the theoretic contrast values ck of Fig. 6 would drop from 0.6 to 0.05. In this case, the least square minimization between the measured and the theoretic values would produce more noisy, unreliable results. Unfortunately, the dependencies are too complicated to present a simple rule when the method will work and when it will not. We could estimate that we need a significant maximum range of the theoretic contrast values of at least 0.1.
We presented a measurement method for the thickness determination of the top qth layer of a semi-transparent, large-area thin film stack. Based on optical thin film interference, we analyzed the resulting RGB colors using a modified commercial flatbed scanner. We characterized the optical system of the scanner and applied a physical model to estimate the thickness based on a scanned image of the sample and reference values. The reference values were either obtained by image areas of known thickness or by capturing the sample before printing the layer of interest. Contrast values were determined theoretically and from the image data and compared to minimize the distance between them in contrast space. Corresponding thickness values were found pixel by pixel resulting in an overall thickness map. With prior knowledge of the refractive indices of the corresponding materials and the thicknesses of the (q − 1)th layers, we analyzed two different samples with our method and compared the results to different methods. We found good agreement between them and drew the conclusion that within specific boundary conditions imaging color reflectometry is a reliable technique for large-area thin film determination. The boundaries of this method are mainly defined by the resulting range of possible contrast values for the different color channels which should exceed 0.1. Those, on the other hand, are affected by considerable differences of the refractive indices and the thicknesses of the films.
The present analysis method could also be applied to small samples as for example shown by Roddaro et al. . They used an optical microscope for acquiring high color contrast images of graphene layers on SiO2/Si samples to actually count the number of layers. The critical aspect for enabling a microscope to this type of measurement is its numerical aperture (NA) which defines the opening angle of the optical system. For hight NA, the deviation from the assumed normal angle of incidence and refection is high and arbitrary opening angles could not be neglected any more. Then, one should modify the optical model by including the polarization states of the light and integrate over the possible opening angles.
Although we optically characterized our system by “only” 35 interference band filters, ignored possible arbitrary opening angles of the optical setup and neglected noise and errors of the hardware parts, we obtained very reliable and accurate results. This circumstance and the fact that the optical system setup is very simple open the interesting possibility to implement the proposed imaging color reflectometry (ICR) as part of a color vision inspection in in-line systems for printing or coating applications.
We thank Philipp Urban, Hans Martin Sauer and Peter Neuroth for fruitful discussions. We are also grateful to Ingo Münster, BASF SE Ludwigshafen, and Klaus Bonrad, Merck KGaA Darmstadt, and their research groups for the supply of the organic semiconductors, the ellipsometric measurements and the substrate materials. This work has been funded by the Bundesministerium für Bildung und Forschung, Germany, under Grant No. 13N10760 (PrintOLED).
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