Process optimization of gravure printed light-emitting polymer layers by a neural network approach

Organic Electronics 10 (2009) 1495–1504

Contents lists available at ScienceDirect

Organic Electronics journal homepage: www.elsevier.com/locate/orgel

Process optimization of gravure printed light-emitting polymer layers by a neural network approach Jasper J. Michels *, Suzanne H.P.M. de Winter, Laurence H.G. Symonds Holst Centre, High Tech Campus 31, P.O. Box 8550, 5605 KN Eindhoven, The Netherlands

a r t i c l e

i n f o

Article history: Received 29 April 2009 Received in revised form 6 August 2009 Accepted 18 August 2009 Available online 23 August 2009 PACS: 07.05.Mh 85.60.Jb 42.79.Kr 87.19.rh Keywords: Organic electronics Lighting Printing Neural networks

a b s t r a c t We demonstrate that artificial neural network modeling is a viable tool to predict the processing dependence of gravure printed light-emitting polymer layers for flexible OLED lighting applications. The (local) thickness of gravure printed light-emitting polymer (LEP) layers was analyzed using microdensitometry, after which the data was used to train a multi-layer neural network using error back propagation. Cell engraving depth, printing speed, and polymer concentration were used as input parameters of the neural network. Mean printed layer thickness, relative RMS roughness and feature anisotropy were defined as output parameters. The inhomogeneity of the gravure printed LEP layers was defined by two parameters, being the normalized standard deviation from the mean layer thickness, as well as the anisotropy or ‘directionality’ of the roughness features. Despite the limited number of input parameters, a fair prediction accuracy was obtained once new input data was fed into the trained network. The prediction error for the three output parameters was of the order: anisotropy > roughness > mean layer thickness. Calculating the magnitude of the output parameters as a function of the total space determined by the input parameters can be used as a way to find optimal printing conditions. These ‘landscape’ plots also reveal qualitative information on the rheological behavior of the inks during the printing process. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Besides display technology, flexible large area lighting and signage is nowadays considered to be a major application area for organic light-emitting diodes (OLEDs) and organic electronics. A shift in research focus is taking place from the fundamental aspects of material- and device optimization to issues related to processability and manufacturing. The demanding cost-price constraints enforced by the lighting market can only be met if these devices can be produced in a fast and cheap fashion. For this reason roll-to-roll printing, known from graphics industry, is receiving much attention as a potential manufacturing technology for flexible electronics and lighting. OLED devices contain several functional organic conductive and * Corresponding author. Tel.: +31 0 40 277 4045. E-mail address: [email protected] (J.J. Michels). 1566-1199/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.orgel.2009.08.015

light-emitting layers, each with a thickness of about 100 nm [1]. These materials, either polymeric or small molecule-based, may be printed from solvent- or waterbased solutions, upon which integral layers form during drying. Any defects or irregularities in these layers will lead to inhomogeneous light-output due to local variation of the current density. In the worst case, irregularities lead to short circuited (dark) devices. The general thickness constraint for light-emitting polymer (LEP) layers is 100 nm ± 2%. For printing processes this forms a tough challenge which, for large area applications, has not yet been met on a pilot- or a (semi)-industrial scale. One of the printing methods under consideration for the production of large area lighting and electronics is direct (roto-)gravure printing [2]. This process is characterized by fluid transfer from an ink-loaded micro-engraved hard roller (gravure roll) directly onto a (flexible) substrate. Direct gravure printing, as opposed to gravure-off set

1496

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

printing, combines robustness, speed and proven roll-toroll compatibility with a good accuracy [3]. Another advantage compared to gravure-off set and flexographic printing is the absence of a rubber transfer plate, which lacks sufficient resilience against the organic solvents typically used for LEP inks (e.g. toluene, anisole, xylene, etc.) to allow for a robust and stable printing process. Furthermore, gravure printing does not suffer from plate or screen wear, typically observed for off-set lithography and screen printing. Roll-to-roll inkjet printing is generally believed to be insufficiently fast and robust, despite advantages relating to non-contact fluid transfer and digital free-form flexibility. To avoid time consuming trial-and-error experimentation, it is desirable to model the printing process in order to be able to predict optimal process conditions for printed layer formation. Since gravure printing is a complex process involving many non-linearly interrelated parameters, statistical modeling, despite its ‘black-box’ nature, is often preferred over physical modeling. Artificial neural networks (ANN) have proven to be useful predictive statistical models for a wide range of applications [4]. ANNs are capable of modeling any linear or non-linear relationship between sets of input and output parameters. ANNs applied in manufacturing technology are often based on a supervised learning protocol during which the network is repetitively exposed to input data with a known (e.g. measured) response. During this process a cost function is minimized by adapting the network’s coefficients. Once properly trained, the network is capable of calculating the correct response to new values and combinations of the input parameters, not previously included in the training data set. In the field of the graphic arts, artificial neural networks have shown to be viable tools in process control and development. Well-known examples are color processing and proofing [5], inkjet printing [6], and off-set lithography [7]. Also in fields related to graphical printing, such as solder paste printing for printed circuit boards, the use of neural networks for process optimization has been reported [8]. Ding et al. [9] recently reported on the use of a fuzzy neural network to establish the link between process parameters and gravure printed dot features. The gravure printing process has to some extent also been modeled physically. One should discriminate here between forward gravure printing [10–12] (image transfer, as is the case for this work), whereby the web and the gravure roll move in the same direction, and reverse gravure [13], which is essentially a coating technique, as gravure roll and web move in opposite directions. The forward gravure printing models, though elegant, generally oversimplify the real life situation as they only describe single cell withdrawal events in two dimensions. These models could, for instance, be used to predict the ratio of transferred to contained ink as a function of the separation velocity between gravure roll and substrate. However, their limited geometrical scope renders them unsuitable for the actual prediction of printed layer thickness and homogeneity in large area applications. The overall process is yet too complex to be modeled reliably in a physical manner using state of the art computing facilities. In this paper, we show for the first time the application of ANN modeling in printed organic electronics. The net-

work models the characteristics of forward, direct rotogravure printed layers of LEP on a non-porous, conductive poly-(ethylenedioxythiophene)/poly(styrene sulfonate)covered poly(ethylene terephthalate) substrate (PET-PEDOT/PSS). The network is set-up and trained to predict the relation between three input parameters: (i) gravure cell engraving depth, (ii) printing speed, and (iii) LEP concentration, and three output parameters: (i) mean printed layer thickness, (ii) relative root mean square (RMS) roughness, and (iii) printed layer anisotropy. We clarify the selection of these parameters and show how fairly accurate predictions can be made once the network has been properly trained. We give a quantitative definition of printed layer anisotropy, since we believe that root mean square deviation by itself insufficiently describes printed layer homogeneity, especially for printed OLED lighting applications. Finally, we show how the trained network can be used to map the input parameter space for each output parameter in order to find optimum values and to gain qualitative insight in the behavior of the ink during the printing process.

2. Materials and methods The LEP gravure printing inks were based on an inhouse developed light-emitting polymer. This LEP had a weight-averaged molecular weight of 628 kDa and a polydispersity index of 2.1. The sample solutions were prepared by dissolving the LEP in a 30/70 (w/w) mixture of toluene and anisole under nitrogen (Table 2 lists the used LEP concentrations). In order to increase the optical absorptivity of the printed layers in the visible wavelength range we added Oil Blue N as a low molecular weight dye to the formulations. What’s more, the addition of the dye fully quenched the polymer’s fluorescence, thus ruling out possible disturbing optical factors stemming from the polymer’s intrinsic emissive properties. The amount of dye (by weight) was kept twice as low as the polymer quantity. Owing to its low molecular weight and concentration, the dye was assumed to not influence the rheological properties of the inks. Prints were made using an IGT Testing Systems F1 labscale printability tester running in direct forward gravure mode. Commercial Orgacon EL-350 PEDOT/PSS-coated PET foil (Agfa-Gevaert) with a total thickness of 125 lm was used as substrate. The PEDOT/PSS layer has been applied by slot coating, which gives very homogenous layers with low amplitude undulations (typically a few %) extending over several tens of centimeters. The Orgacon foil was mounted onto the backing roller of the gravure printer and cleaned by gentle wiping with a non-scratching cloth containing 2-propanol. For making a print, typically about 0.5 mL LEP/dye ink was applied onto the gravure roll in the nip between the doctor blade and the roller, after which the ink was printed in one pass at a given speed setting and a constant gravure roll-to-substrate force setting of 250 N. The gravure roll used in this study contained patterned areas of square pyramidal cells, stylus engraved (120° stylus angle) under a screen angle of 53° at a density of 70 lines/cm. The total engraved pattern contained ten patches,

1497

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

each having a surface area of about 6 cm2. Each patch corresponds to a different cell engraving depth in the range 11–48 lm, roughly corresponding to an ink containment volume of 0.2–12 mL/m2. The printed layers were left to dry under ambient conditions in a matter of seconds. The printed LEP/dye layers were characterized using a microdensitometer (Joyce-Loebl MDM-6), fitted with a Philips halogen lamp, type 7012 (12 V, 50 W). The microdensitometer measured and recorded the integrated optical density of a sample layer as a function of X, Y-coordinate, on a scale with a cut-off value of 4096. The printed layers were scanned at a lateral resolution of 20 lm using a wavelength range of 300 < k < 800 nm. The total measured optical density of the printed layers (i.e., the summed values for the LEP, the dye, and the PET-PEDOT/PSS substrate), was typically in the range 1800–2100, considerably below the cut-off threshold. The crude optical density data was corrected for the optical density of the 125 lm thick PETPEDOT/PSS substrate, as recorded at the site of each printed patch. Correction occurred by subtraction of the substrate’s optical density from the total measured value. The thus corrected optical density of the printed LEP/dye layers was in the range 50–200. The scanning software was adapted as to scan exclusively within the printed patches corresponding to the various cell engraving depth levels. The edges of the prints were not included in the scans to avoid artifacts related to incomplete engraving, often observed at the edges of engraved patterns on gravure rolls. When printing an OLED, one would make sure that such edge artifacts would fall outside the active (emissive) area of the device. The scanning data was filtered, normalized, and processed using MATLAB R2008a. In order to convert the measured optical density values into actual printed layer thickness information, we recorded the optical density of reference LEP/dye layers of known thickness, spin-coated from toluene solution on glass slides. This solution contained 10 mg/mL of LEP and 5 mg/mL Oil Blue N, giving the same LEP-to-dye ratio as used for the gravure printing inks involved in the neural network study. The measured values were corrected by subtracting the optical density of the glass substrate. The absolute thickness of the reference samples was determined using a Veeco DekTac M6 stylus profilometer. Neural network analyses were performed using a home-built algorithm in C++. The ANN used in this study (Fig. 1) was a double layer Perceptron (MLP) neural net, using feed forward of input data and back propagation of error information [4]. The output of the hidden (V) and output units (Y) was calculated using logistic sigmoidal and linear transfer functions (Eqs. (1) and (2), respectively).

f ðxÞ ¼

ab þa 1 þ expðsxÞ

f ðxÞ ¼ sx:

ð1Þ ð2Þ

Here, x and f(x), respectively, represent the neuron’s input and output; a and b are the lower and upper asymptotic values of the logistic sigmoid, and s is the steepness. During training the synaptic weights (wi,j and zj,k) and bias values (b) were optimized in an iterative procedure, minimizing the cost function expressed by Eq. (3).

b

b w1,1

Z1 V

cell depth X A1

z1,1 Z2 V

speed X A2

Y1 mean layer thickness Z3 V

concentration X A3

Y2

w2,n w3,n zn,2

RMS

Y3 anisotropy

zn,3 Zn V

Fig. 1. Neural network architecture used in this study; input, hidden, and output units are denoted X, V, and Y, respectively; synaptic weights are denoted wi,j and zj,k for the first and second layer, respectively; the bias units are denoted b.

E¼

X ðt i  yi Þ2 :

ð3Þ

i

Here, ti and yi represent the target (measured) response and calculated output corresponding to a certain set of input parameters (input vector). Usually, a neural net is not allowed to reach maximum convergence to avoid over-fitting, as an over-fitted network will be better at memorizing its training data set than predicting output to new input data. To avoid over-fitting a separate testing data set was used to check the network’s predictive capability during training. Prior to training all input data was normalized in a bipolar fashion: 1 6 n 6 1. This allowed faster training and ensured the error information terms calculated for the output parameters to be of comparable magnitude. Relating to this, we chose the asymptotic values of the sigmoid activation function of the hidden units (Eq. (1)) to be a = 1.2 and b = 1.2, slightly extending beyond the largest and smallest target values [4]. For presentation the calculated data was denormalized. The steepness of both activation functions (s in Eqs. (1) and (2)) was set to 0.5.

3. Results and discussion We start with defining the ANN’s input and output parameters. The input parameters are settings relating to the printing process (printing parameters), whereas the output parameters are quantifiable characteristics of the printed LEP/dye layers. The printing parameters may be categorized as gravure roll-, process-, ink-, or substrate-related. Table 1 lists the most important parameters in this categorized fashion. Naturally, these parameters do not all influence the printed layer characteristics equally strongly. We selected (i) cell engraving depth (d), (ii) printing speed (v), and (iii) LEP concentration (c) as a limited, but highly relevant set of input parameters for the neural network model. These input parameters represent three of the four categories defined above. Their selection is partly based on prior experience with LEP printing. We also note that several of the parameters defined in Table 1 can be expressed as functions of the selected parameters. For example, rheological parameters such as zero shear viscosity and fluid elasticity, are strongly related to the solute

1498

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

Table 1 Summary of the gravure printing parameter space. Gravure roll

Process

Ink

Substrate

Cell engraving depth Cell shape Screen angle Stylus angle Surface energy Radius

Pressure/force Printing speed

Viscosity Elasticity Surface tension Volatility Solvent composition Polymer concentration Molecular weight

Material Surface energy Roughness Pre-treatment Cleaning method

concentration. Other parameters, such as surface tension and evaporation rate, are not included in the model, as we used the same solvent system throughout the study. In this context, we assumed the polymer (and dye) concentration not to have an appreciable effect on the surface tension and evaporation, especially in the early stages of drying during which solute transport is most likely to occur. Naturally, if one would want the neural network to also predict the solvent characteristics, a more extended model is necessary. By using the same gravure roll which is cleaned the same way prior to printing, we did not vary the parameters in the gravure roll category, except for cell engraving depth. We found a gravure roll force exceeding 150 N to be of little influence on the thickness and appearance (homogeneity) of the prints. Forces below this value did not allow full (web wide) transfer of the ink. From the substrate category no parameters were selected. The reason for this is the limited number of available possibilities to vary the nature of the rather delicate PEDOT/PSS layer. We settled down on the mild cleaning method described in the Experimental Section as a suitable nondestructive pre-treatment that still allows proper wetting of the LEP ink. Three output parameters were defined (see Fig. 1): (i) mean printed layer thickness, (ii) roughness, and (iii) ‘stripiness’ or anisotropy. In order to obtain reasonable estimates of the mean printed layer thickness, optical density scans produced by the microdensitometer were converted into actual thickness matrices using the calibration curve depicted in Fig. 2. This line was constructed by recording the optical density of spin-coated LEP/Oil Blue N layers (same ratio as for the gravure printing inks) on glass substrates (the inset illustratively showing the absorption spectrum of the LEP/Oil Blue N blend). The layers were coated at different spinning velocities, giving a range of thicknesses. The absolute thickness of these reference layers was determined using profilometry. These values were then plotted as a function of the measured optical density. As the graph shows, the data suggest a linear relationship between thickness and optical density, at least within the window of the measurement. Despite this (partial) linearity, the curve does not seem to obey the Beer– Lambert law, as the suggested straight line does not pass through the origin of the graph. In stead, it would abscise the horizontal axis at an optical density of about 45. However, physically, the origin itself should lie on the curve, as a zero optical density is recorded when no material is present at all. Unfortunately, it proved difficult to obtain homogeneous layers with a thickness in the range 0–75 nm. We

Fig. 2. Layer thickness as a function of integrated optical density for spincoated reference layers of the 2:1 LEP/Oil Blue N mixture on glass slides. The line is a fit to the measured values, including the origin as an extra data point. The curve has been extrapolated into the upper range of the optical density values measured by the microdensitometer on the gravure printed layers. For illustration: the inset depicts the absorption spectrum of the LEP/dye mixture in the range 300 < k < 800 nm.

therefore included the origin as one extra data point and, as an approximation, fitted a calibration curve using a continuous, fully differentiable mathematical function capable of passing through the origin as well as describing the linear behavior observed for higher optical densities, as suggested by the measurement. The mean printed layer thickness was obtained simply by calculating the average value of the thickness matrix. The (relative root-meansquare) roughness of the printed layers was defined as the standard deviation from the mean taken as a fraction (or percentage) from the mean value. Below we will mostly use the term ‘roughness’ to denote the relative RMS roughness. The third output parameter, the printed layer anisotropy, requires a little more clarification. In general, printed layer irregularities may occur during three stages of the gravure printing process: (i) ink transfer (e.g. due to fluid film or ligament instabilities), (ii) leveling on the substrate (e.g. due to incomplete merging or leveling of deposited fluid dots from separate engraved cells), and (iii) drying (surface tension-driven flow of solute during solvent evaporation). The latter cause was assumed to be strongly suppressed by the relatively high viscosity of the LEP inks (around 30 mPas at t = 0, as determined by separate measurements), as well as the rapid viscosity increase due to

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

the high volatility of the solvent mixture. This assumption was supported by the fact that the printed LEP layers did not show signs of the well-known ‘coffee stain effect’ [14] or other drying patterns that can be attributed to surface tension-induced solute transport [15]. For this, we suggest that the irregularities encountered in the gravure printed LEP layers predominantly originated from instabilities during fluid transfer or incomplete merging and leveling, or a combination of both. The appearance of the print depends on which of the two causes prevails. Fig. 3 depicts photographs of four exemplary gravure printed layers fabricated with the same LEP ink, printed at different cell engraving depths. Although this ink was based on a different LEP (a poly(p-phenylenevinylene) derivative) than the one used in the neural network study, the printed layer appearance as a function of gravure roll engraving depth is qualitatively similar. At a low engraving depth (22– 30 lm) the amount of ink transferred to the substrate is

Fig. 3. Light emitting polymer gravure printed (v = 0.9 m/s, c = 10 mg/mL) onto PET-ITO foil at different cell engraving depths (stylus angle 120°, screen angle 53°, 70 lines/cm): 22 lm (top left: separate dots of ink corresponding to engraved cells), 30 lm (top right: dots start to merge), 34 lm (bottom left: merging leads to an integral layer), 38 lm (bottom right: ridges and trenches appear parallel to the printing direction). The grainy appearance of the prints is caused by the fact that they have been photographed against a white paper background.

1499

simply too low to give integral printed layers (see Fig. 3, top left and top right). The print corresponding to a 22 lm cell depth does not show merging of the fluid dots at all. The dots only start merging once more fluid is applied, and give an integral layer at an engraving depth of 34 lm (Fig. 3, bottom left). At larger cell depths (e.g. 38 lm) too much ink is applied, which leads to the formation of ridges of polymer running parallel to the printing direction (Fig. 3, bottom right). Notably, regions adjacent to the ridges show considerable ink depletion. The formation of these ridges may be explained by a collapse of multiple fluid ligaments pulled from adjacent cells. The irregularity of these layers is anisotropic, as the ridges appear exclusively parallel to the printing direction. It immediately becomes clear that although the roughness as defined above gives a good indication of general layer homogeneity, it does not provide any information about the appearance or anisotropy of the irregularities encountered in the printed layers. This is illustrated by Fig. 4. This figure shows optical density scans of LEP layers printed using different sets of input parameters (left: d = 46 lm, v = 0.5 m/s, c = 22 mg/mL; right: d = 42 lm, v = 1.5 m/s, c = 22 mg/mL). Similar roughness values were obtained (6.2% and 6.5%, respectively), despite the large difference in appearance of the prints. Fig. 4 (right) shows isotropically distributed irregularities, whereas print Fig. 4 (left) has a much more stripy appearance due to ridge formation parallel to the printing direction. For OLED production it is desirable to be able to predict printed LEP layer roughness in general terms, as well as in terms of anisotropy or directionality. This is explained as follows. Scattering renders intensity variations in the emitted light due to highly frequent, isotropically distributed layer thickness variations to be much less obvious than variations stemming from a relatively small number of ridges in an essentially smooth layer (see Fig. 5). Furthermore, as mentioned, a deficiency of printed material is encountered adjacent to the ridges, giving the risk of shorts. The question now raises how to quantify the anisotropy. In tribology, the kurtosis (Ku) of a distribution is often used to discriminate between a layer with an isotropic (Gaussian) distribution of many irregularities (low Ku) and one that is essentially flat, except for a few

Fig. 4. Color-height images of gravure printed LEP layers corresponding to different input parameter sets: left, d = 46 lm, v = 0.5 m/s, c = 22 mg/mL; right, d = 42 lm, v = 1.5 m/s, c = 22 mg/mL. The prints have roughness and anisotropy values of 11.9% and 42.9, and 12.7% and 3.8, respectively.

1500

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

Fig. 5. Gravure printed flexible OLED devices (33  15 mm): left, printed LEP layer containing ridges of polymer in the printing direction; right, printed LEP layer containing highly frequent, isotropically distributed irregularities, apart from two dust particle-induced spots.

large deviations (high Ku). The kurtosis is defined by Eq. (4).

Ku ¼

m X n 1 X Zði:jÞ4 : mnr4 i¼1 j¼1

ð4Þ

Here, the layer is represented by an m  n matrix of local height values Z(i, j), and r is the standard deviation of the height distribution. Unfortunately, due to the nature of the scanning data and the high noise-sensitivity relating to the 4th power Z- and r-dependency, Ku did not discriminate properly between gravure printed layers with high and low anisotropy: the prints represented by Fig. 4 have a kurtosis of 3.5 and 3.9, respectively. For this reason, we wrote an algorithm dedicated to recognize and quantify the anisotropy. This algorithm, which is essentially represented by Eq. (5), performs separate row- and column-wise summations of the elements of binary representations of the scanning data matrices. Amplification factors were implemented which magnitudes increase with the longitudinal extent of the ridges (represented by ‘‘ones”) and trenches (represented by ‘‘zeros”). Hypothetically, if comparable numbers of ridges would run both parallel and perpendicular to the printing direction, the anisotropy (A) will be low:

Pm Pn i¼1

b vrow i;j ui;j : column b ui;j i¼1 vi;j j¼1

A ¼ Pn Pm j¼1

ð5Þ

Here, vrow and vcolumn are the amplification factors for the i;j i;j row and column summations, respectively, and ubi;j are the binarized optical density values (0 or 1). The amplification factor was increased stepwise as long as the value of a matrix element did not differ from that of the previous neighboring element in the same row or column. In case the next neighboring element did have a different value the amplification factor was reset to one, effectively indicating the end of a ridge or trench. The necessary binary representations of the scans were obtained using Eq. (6).

 U b ði; jÞ ¼ HðZði; jÞ  ZÞ:

ð6Þ

 the mean Here, H is the Heaviside step function and Z height (or optical density). Eq. (5) proved much less discriminative when applied to non-binarized data, resulting

Table 2 Levels of the input parameters used to build up the total data set. Level

Cell depth (lm)

Printing speed (m/s)

Concentration (mg/mL)

1 2 3 4 5 6

30 34 38 42 44 46

0.5 0.8 1.0 1.2 1.5 –

22 27 30 – – –

Fig. 6. Binarized versions of the prints presented by Fig. 4; white represents thickness values exceeding the mean, whereas black represents areas with a thickness lower than the mean.

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

in a loss of information on anisotropy. Fig. 6 represents binarized versions of the scans depicted in Fig. 4. We note that the print corresponding to Fig. 4 (right) and Fig. 6 (right) shows an anisotropy in a different sense in that the layer thickness is generally higher on top of the print

1501

than at the bottom. This effect, which is observed for a minority of the prints, is explained by partial incomplete filling of the engraved cells during inking of the gravure roll. This hardly avoidable issue relates to the operational limitations of the gravure printer in combination with

Fig. 7. Measured (closed/solid) and predicted (open/dashed) values for mean printed layer thickness (left), relative RMS roughness (left), and feature anisotropy (right) for the validation data set (prints corresponding to d = 44 lm).

Fig. 8. Calculated mean layer thickness plotted in color grades as a function of cell depth (d) (in lm) and printing speed (v) (in m/s) at c = 22.0, 25.0, 27.5, and 30.0 mg/mL (top left to bottom right).

1502

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

the manual operation, and will be absent in an industrial gravure printing environment owing to automated inking. These fluctuations are not accounted for by the neural network and will to some extent impart uncertainty in the prediction accuracy. On the other hand, we note that the algorithm expressed by Eq. (5) is relatively insensitive to this kind of printed layer anisotropy. Using Eqs. (5) and (6), the anisotropy of the prints represented by Fig. 4 was determined to be 42.9 and 3.8, respectively, clearly discriminating between the two prints. Unfortunately, the quality of the scanning data was not sufficient to include quantitative information about the height of the ridges as well. To build up an input–output data set for training and validation of the neural net, we performed prints and scans varying the input parameters at preset levels (Table 2). Three LEP concentration levels were chosen in a realistic range (22, 27, and 30 mg/mL), corresponding to a suitable dry LEP layer thickness, without the viscosity becoming too high or too low for proper printing. Five levels of printing speed were selected, effectively covering the whole speed range setting of the gravure printer (0.5, 0.8, 1.0, 1.2, and 1.5 m/s). As for cell engraving depth, six levels were used in the range 30–46 lm (i.e. 30, 34, 38, 42, 44, and 46 lm). By experience we know that LEP layers printed with gravure cell depths in this range typically give working OLEDs. Prints produced at lower cell depth values do not give integral layers due to incomplete merging of the depos-

ited ink dots. Cell depth values exceeding the indicated range usually give highly irregular, rather messy prints having areas containing hardly any material and areas in which material is accumulated into very thick patches. Both extremes usually lead to short circuited devices. As the total cell depth range expressed by Table 2 has been patch-wise engraved onto the same gravure roll, we were able to acquire all cell depth information within one single print (per level of LEP concentration and speed setting). Practically, the whole study required only 15 prints (three concentration levels  5 speed levels) and 4 scans, as the set-up allowed us to scan four printed strips of substrate in one session. Thus we collected a total data set of 3  5  6 = 90 three-element input-target vector pairs. Of this total data set all vector pairs corresponding to a 44 lm cell depth (15 in total) were kept aside for validation of the trained network. Of the remaining 75 vector pairs ten were randomly selected to form the testing set. The 65 vector pairs left formed the actual training data set. During training, the network was iteratively exposed to the 65 training vectors, during which the synaptic weight and bias values were optimized to reduce the cost function (Eq. (3)). At set times during training the predictive power of the network was assessed by calculating the total squared error of the predicted output to the testing data set. Once this value did not further decrease, training was aborted and the optimized weight and bias values were saved.

Fig. 9. Calculated relative RMS roughness plotted in color grades as a function of cell depth (d) (in lm) and printing speed (v) (in m/s) at c = 22.0, 25.0, 27.5, and 30.0 mg/mL (top left to bottom right).

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

As for the hidden layer it is well known that a large number of units may lead to fast convergence of the net, which is an advantage if computational time is a limiting factor. However, many hidden units and fast convergence impart the risk of over-fitting. The optimal number of hidden units was determined to be around 12 by trial-and-error. We varied the actual contents of the training and testing sets to check whether the selection of testing vectors had a significant effect on the prediction error of the testing set. We found that this was not the case as long as the testing set was randomly chosen. After training to optimal convergence, the validation vector set, corresponding to the 44 lm cell engraving depth, was fed into the neural net. Fig. 7 shows that the net is indeed capable of predicting the output to this new input set with a very reasonable accuracy. The prediction error is generally around 10%, 20%, and 25% for mean layer thickness, roughness, and anisotropy, respectively. Especially for roughness and anisotropy, though, some values were predicted with an error that falls outside the range indicated by this ‘typical’ prediction error. The number of these outliers, as well as their deviation from the error distribution, somewhat depends on the distribution of the training data over the training and testing data sets. General trends in the printed layer characteristics as a function of the input parameters are very well distinguished by the neural net. Issues such as mechanical play of parts of the

1503

printer’s engine, and experimental errors induced by fluctuations in manual operation may lead to experimental deviations that are not easily captured by any (statistical) model. We further note that all output parameters are less accurately calculated when any one of the input parameters is left out during training. One could, for instance, imagine that the mean layer thickness is predominantly determined by concentration and cell depth, the printing speed being of little or no influence. However, leaving out printing speed as an input parameter led to significantly larger prediction errors. In general, the mean printed layer thickness may seem somewhat higher than ideal for the fabrication of OLEDs, but we note that these layers contain 30 vol.% dye (assuming a density of 1 g/ cm3 for both LEP and dye). Omitting the dye would indeed give LEP layers with a thickness in the desired range. As mentioned above, the optimized synaptic weight and bias values were stored after training. This allowed us to systematically calculate the output of the trained net as a function of the full space determined by the three input parameters. Figs. 8–10 represent color-height plots of the mean layer thickness, roughness and anisotropy as a function of cell engraving depth and printing speed, calculated at four different polymer concentration levels. Fig. 8 clearly shows a general increasing trend of the mean layer thickness with concentration. This is to be expected, but the effect is not linear: no large changes are observed

Fig. 10. Calculated anisotropy plotted in color grades as a function of cell depth (d) (in lm) and printing speed (v) (in m/s) at c = 22.0, 25.0, 27.5, and 30.0 mg/mL (top left to bottom right).

1504

J.J. Michels et al. / Organic Electronics 10 (2009) 1495–1504

for a polymer concentration in the range c = 22.0 – 27.0 mg/mL, whereas a pronounced increase of the mean thickness is predicted for higher concentrations. This may be indicative of a non-linear increase in fluid elasticity due to an increasing polymer entanglement density with concentration. Separate viscosity measurements showed the overlap concentration of this LEP to be around 25 mg/mL in toluene/anisole 30/70 (w/w), which falls within the tested concentration range (see Table 2). In contrast, no strong dependency of the mean layer thickness on printing speed is observed. Expectedly, a general increase of layer thickness with cell engraving depth is predicted. The non-linearity of this increase, however, becomes more pronounced at high LEP concentrations. This is indicative of an increasingly non-Newtonian behavior with polymer concentration. As for the roughness (Fig. 9), at low polymer concentrations (22.0 < c < 24.5 mg/mL) an optimum (minimum) is predicted for intermediate speed and cell engraving depth settings (0.9–1.2 m/s and 36–40 lm, respectively). This optimum seems to shift towards higher engraving depths for higher LEP concentrations (c > 26.0 mg/mL). Besides this optimum, the roughness shows a trend-wise decrease with increasing cell engraving depth for the entire LEP concentration range. Interestingly, this relation changes from non-linear at low concentrations to more linear at high concentrations. This is indicative of a difficulty in the leveling of the printed dots at low cell engraving depths, despite the fact that integral layers are obtained. Expectedly, this effect becomes more pronounced if the viscosity increases due to a rise in LEP concentration. It is further noted that for any LEP concentration the roughness is highest when a low cell depth is used in combination with a high printing speed. This is especially the case for low LEP concentrations. Together with the low mean layer thickness obtained under these conditions, this is explained by a very low fluid transfer volume. A high anisotropy at any concentration is obtained by combining a high cell engraving depth with a low printing speed (Fig. 10), the effect being most pronounced at high concentrations (30.0 mg/mL). Gradually going down in polymer concentration, it decreases to a minimum around c = 26.0 mg/mL, but increases again at lower concentrations. A minimum in anisotropy is obtained for intermediate concentrations (23.5 < c < 25.5 mg/mL) in combination with intermediate to low printing speed and cell engraving depth settings (0.5–1.1 m/s and 30–42 lm, respectively). Clearly, for the whole concentration range a much stronger speed-dependence is observed for the anisotropy than for the mean layer thickness and the roughness. This indicates that the directionality of the irregularities in a print is strongly related to the rheology of the ink. 4. Conclusions We have shown that artificial neural network modeling may be used as a viable tool to predict gravure printed light-emitting polymer layer characteristics for flexible OLED lighting applications. The gravure printed LEP layers were analyzed using microdensitometry, after which the

scanning data was converted into (local) layer thickness information and used to train a multi-layer neural network using error back propagation. Polymer concentration, printing speed and cell engraving depth were used as input parameters. Mean layer thickness, roughness, and feature anisotropy were defined as output parameters of the neural net. Despite the limited number of input parameters a reasonable to fair prediction accuracy was obtained once new input data was fed into the trained network. The prediction error for the three output parameters was of the order anisotropy > roughness > mean layer thickness. Calculating the magnitude of the output parameters as a function of the total space determined by the input parameters can be used as a way to find optimal printing conditions. The plots also express the highly non-linear dependency of the output on the input parameters. References [1] For more information on OLED devices see: K. Müllen, U. Scherf (Eds.), Organic Light Emitting Devices, Wiley-VCH Verlag, Weinheim, 2006. [2] (a) 3rd Press Release OLLA Project, 14 May 2007; (b) M. Tuomikoski, R. Suhonen, M. Välimäki, T. Maaninen, A. Maaninen, M. Sauer, P. Rogin, M. Mennig, S. Heusing, J. Puetz, M.A. Aegerter, Proc. SPIE – Int. Soc. Opt. Eng., 2006, p. 6192 (art. no. 619204); (c) M. Tuomikoski, R. Suhonen, M. Välimäki, A. Maaninen, IEEE/LEOS Opt. MEMS 2005: Int. Conf. Opt. MEMS Appl., 2005, pp. 141–142 (art. no 1540118). [3] E. Jewell, T.C. Claypole, G. Davies, Proc. Tech. Assoc. Graph. Arts, TAGA (2006) 419–429. and references cited therein. [4] L. Fausett, Fundamentals of Neural Networks, Prentice Hall, New Jersey, 1994. [5] (a) E. Köse, T. Sßahinbasßkan, I. Güler, Exp. Syst. Appl. 36 (2009) 745– 754; (b) X. Su, Y. Wang, T. Zhang, High Tech. Lett. 9 (2003) 39–43; (c) G. Wermuth, Farbe Lack 110 (2004) 30–37; [d] Rose, Oded, US Patent 5200816, 1991; [e] Rose, Oded, US Patent 5285297, 1992. [6] (a) R. Schettini, D. Bianucci, G. Mauri, S. Zuffi, Proc. CGIV (2004) 393– 397; (b) S.-C. Chen, Y.-C. Yeh, W.-L. Chen, Int. J. El. 89 (2002) 19–34; (c) J.R.G. Evans, M.J. Edirisinghe, P.V. Coveney, J. Eames, J. Eur. Ceram. Soc. 21 (2001) 2291–2299. [7] (a) C. Englund, A. Verikas, Int. J. Adv. Man. Tech. 39 (2008) 919–930; (b) L. Bergman, A. Verikas, Proc. IASTED (2004) 173–178; (c) C. Englund, A. Verikas, Eng. Appl. Art. Intell. 18 (2005) 759–768. [8] (a) T. Yang, T.-N. Tsai, J. Yeh, Eng. Appl. Art. Intell. 18 (2005) 335– 341; (b) N. Morad, H.K. Yii, M.S. Hitam, C.P. Lim, Proc. IEEE Region 10 Ann. Int. Conf. 3 (2000) III-479–III-483; (c) S.L. Ho, M. Xie, L.C. Tang, K. Xu, T.N. Goh, IEEE Trans. El. Pack. Man. 24 (2001) 323–332. [9] L. Ding, P.E. Bamforth, M.R. Jackson, R.M. Parkin, Proc. Control (2004). [10] C.A. Powell, M.D. Savage, J.T. Guthrie, Int. J. Num. Meth. Heat Fluid Flow 12 (2002) 338–355. [11] X. Yin, S. Kumar, Phys. Fluid 17 (2005) 063101. [12] X. Yin, S. Kumar, Chem. Eng. Sci. 61 (2006) 1146–1156. [13] (a) R.W. Hewson, N. Kapur, P.H. Gaskell, Chem. Eng. Sci. 61 (2006) 5487–5499; (b) N. Kapur, Chem. Eng. Sci. 58 (2003) 2875–2882; (c) L.W. Schwartz, J. Eng. Math. 42 (2002) 243–253; (d) C.A. Powell, M.D. Savage, P.H. Gaskell, Trans. IChemE 78 (2000) 61–67; (e) L.W. Schwartz, P. Moussalli, P. Campbell, R.R. Eley, Trans. IChemE 76 (1998) 22–28; (f) H. Benkreira, R. Patel, Chem. Eng. Sci. 48 (1993) 2329–2335. [14] (a) R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Phys. Rev. E 62 (2000) 756–765; (b) R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Nature 389 (1997) 827–829. [15] R.D. Deegan, Phys. Rev. E 61 (2000) 475–485.