Quantifying Defects in Thin Films using Machine Vision

The sensitivity of thin-film materials and devices to defects motivates extensive research into the optimization of film morphology. This research could be accelerated by automated experiments that characterize the response of film morphology to synthesis conditions. Optical imaging can resolve morphological defects in thin films and is readily integrated into automated experiments but the large volumes of images produced by such systems require automated analysis. Existing approaches to automatically analyzing film morphologies in optical images require application-specific customization by software experts and are not robust to changes in image content or imaging conditions. Here we present a versatile convolutional neural network (CNN) for thin-film image analysis which can identify and quantify the extent of a variety of defects and is applicable to multiple materials and imaging conditions. This CNN is readily adapted to new thin-film image analysis tasks and will facilitate the use of imaging in automated thin-film research systems.


INTRODUCTION
Film morphology optimization is important for reducing the detrimental impacts of defects on the performance of thin-film devices such as photovoltaics 1,2 and light-emitting diodes 3 . Images of thin films carry information about common morphological defects, such as cracking 4 and dewetting 5,6 , which are controlled by film synthesis conditions. While automated experiments can generate images of thin films synthesized under numerous distinct conditions, existing approaches to automatically analyzing film morphologies in such images typically require application-specific customization by software experts and are not robust to changes in image content or imaging conditions 7,8 . Here we present a versatile convolutional neural network (CNN) for thin-film image analysis which can identify and quantify the extent of a variety of defects, is applicable to multiple materials and imaging conditions, and is readily adapted to new thin-film image analysis tasks.
The severity of film defects such as thickness variations, cracks, precipitates, or dewetting can often be identified by the naked eye or with optical microscopy 4,9,10 . For this reason, rapid, nondestructive optical inspection of thin films is often carried out in the place of more expensive, more destructive, or more timeconsuming methods such as stylus profilometry, atomic force microscopy, or electron microscopy. Quantitative defect analysis enables researchers to identify potentially subtle trends in film morphology as a function of experimental conditions. Researchers frequently perform quantitative image analyses using semimanual software tools, such as measuring film coverage with ImageJ 11 , or surface roughness with Gwyddion 12 . Semi-manual analysis becomes impractical, however, when applied to highthroughput experiments or high-speed manufacturing where images of thin films are generated at high frequency or in large numbers. In such cases, automated image analysis is necessary. Automated analyses of images of thin-film materials and devices are often performed using image-processing algorithms that are specific to the material, morphology, and imaging modality of interest 13 . An example of this type of approach is the matrix-based analysis of orientational order in AFM images of P3HT nanofibers 7 . This traditional type of computer vision includes applicationspecific feature extraction subroutines with numerous adjustable parameters, such as imaging condition-dependent thresholds, which can make them difficult to adapt to new applications 14 , such as new materials, morphologies, or imaging modalities. Here, we describe a new approach to image-based thin-film defect quantification which uses a CNN to overcome many limitations of previous approaches. The CNN we developed for this purpose, which we call DeepThin, quantifies the extent of several types of common morphological defects (e.g., particles, cracks, scratches, and dewetting) in images of thin films. We show that DeepThin works with different imaging modalities (darkfield imaging and brightfield microscopy), different magnifications and different materials (a small-molecule organic glass and a metal oxide) and can readily be retrained to detect new defect types.
CNNs are a family of machine learning algorithms that have been applied to image classification 15 , feature detection 16 , image segmentation 17 , and object recognition problems 18 . CNNs have achieved classification accuracy comparable to human experts in computer vision challenges 19,20 . The performance and robustness demonstrated by CNNs make them appealing for thin-film defect analysis. An additional benefit of CNNs is that they can be easily trained using examples provided by a domain expert (e.g., a materials scientist) rather than through involved algorithm customization by a computer vision expert 14 . CNNs are an established approach to electron microscopy image analysis tasks, with examples in the materials sciences including mechanical property estimation 21 , nanoparticle segmentation 22 , nanostructure classification 23 , and the study of atomic-scale defects [24][25][26] . However, CNNs have only recently been applied for the analysis of optical images of thin films in two highly-application-specific ways: classifying the corrosion conditions under which surface films formed on metal surfaces 27,28 and determining the thickness of exfoliated 2D crystals 29 . The DeepThin CNN reported here is a general-purpose CNN for classifying or quantifying common morphological defects in optical images of thin films.

Training dataset and model development
To develop and validate DeepThin (Fig. 1), we first created a dataset of 2600 darkfield images of organic semiconductor thin films (each 4000 × 3000 pixels) exhibiting varying extents of cracking and dewetting due to differences in film composition and annealing conditions. These films were deposited by spincoating, annealed, and imaged by a flexible robotic platform equipped with a darkfield photography system (see "Methods" section, ref. 30 ). The images in this darkfield dataset were labeled with respect to the extent of dewetting and of cracking by materials scientists with expertise in thin-film materials research (see "Methods" section). Labeling was on a subjective integer scale from zero (no defects observed) to ten (extremely defected) for both defect types. This labeled dataset was first randomly divided into training, validation, and test sets to facilitate the development of a CNN for image-based thin film defect analysis. These datasets were then augmented by applying rotations and mirroring to the labeled images to obtain a total of 17,374 labeled images. Finally, some images of non-defected films were removed to improve the balance of the datasets, with the final breakdown as detailed in Table S1. This balancing was done to avoid biasing the model towards labeling images as non-defected. We evaluated the suitability of several state-of-the-art CNNs architectures 31,32 for this task before choosing to develop a new architecture for DeepThin (Methods) inspired by the VGG16 CNN (see "Methods" section). We trained DeepThin using five-fold cross-validation and the Adam optimizer (see "Methods" section). After this optimization, DeepThin quantified the extent of cracking, and of dewetting, in each of the darkfield dataset images with >93 % accuracy (Table  S2). With the largest possible quantification error being 10, the root-mean-square-errors between the model's scores and the ground truth were 0.086609 for crack quantification and 0.090362 for dewetting quantification.
Model validation against a known, monotonic morphological trend To further validate DeepThin we carried out an experiment where an organic semiconductor film was imaged as it underwent thermally-activated dewetting 9 (Fig. 2a). This experiment provided a series of images in which the extent of dewetting was known to increase monotonically with respect to time. We then used DeepThin to quantify the extent of dewetting in each image. The resulting dewetting scores also increased monotonically with respect to time (Fig. 2b), showing that DeepThin can correctly order a set of images of thin films based on a one-dimensional trend in the film morphology.
Resolution of a two-dimensional film-morphology response surface To illustrate the applicability of our method to thin film optimization, we used DeepThin to resolve a 2-dimensional filmmorphology response surface in a set of experiments where both film composition and processing were varied. Following our previous work 30 , thin films of spiro-OMeTAD doped with varying amounts of FK102 Co(III) TFSI salt and annealed for varying durations were prepared and then imaged using a robotic platform (see "Methods" section). These experiments provided an array of images exhibiting morphological trends as a function of both film composition and processing. The analysis of these images using DeepThin automatically provided a response surface  quantifying the extent of dewetting as a function of the film composition and annealing time (Fig. 3). From this surface, two trends can readily be identified: (i) the extent of dewetting increased as the dopant-to-spiro-OMeTAD molar ratio increased from 0 to 0.4, then decreased at higher dopant levels; (ii) longer annealing times produced more dewetted films across all dopant-to-spiro-OMeTAD ratios, with the exception of undoped films which did not exhibit dewetting regardless of annealing time. The ability to automatically obtain composition-processing-morphology response surfaces such as the one shown in Fig. 3 using rapid, inexpensive, and non-destructive imaging is a benefit of our approach.
Applicability of DeepThin to multiple materials, defect types and imaging modalities To demonstrate the versatility of DeepThin, we next applied it to a different imaging modality (bright-field microscopy) at different magnifications (×5 and ×20), to additional defect types (scratches, particles, and thickness non-uniformities) and to films of a different material (a metal oxide) (Fig. 4). For these demonstrations, three new image datasets were manually obtained using a bright-field microscope (see "Methods" section): a set of 129 images of organic semiconductor films at ×5 magnification and two sets of images of TiO x films (81 images at ×5 magnification and 82 at ×20 magnification). These microscope images, originally 1024 × 768 pixels, were divided into 100 × 100 pixels patches, manually labeled based on the types of defects present and then subjected to reflections and rotations to obtain augmented datasets of adequate size for retraining and testing DeepThin (Tables S3-S5). These images were classified based on the presence or absence of cracking, dewetting, and additional defect types not considered in the darkfield dataset originally used for model development (scratches, particles, and thickness non-uniformities). After a separate retraining for each of the three microscopy datasets, DeepThin was able to accurately detect the presence or absence of the five labeled defect types (cracks, dewetting, particles, scratches, and thickness non-uniformities) wherever they appeared in the datasets for the different materials and magnifications (Fig. 4). The model could classify a given brightfield image as having no defects or any combination of one or more defects. Confusion matrices, which highlight the model's ability to discriminate between defect-types, are also provided in Tables S6-S8. These results demonstrate that CNNs such as DeepThin may be applied to a broad scope of thin-film materials, defect morphologies, and imaging conditions.
Benchmarking against concrete defect detection literature To assess the performance of DeepThin for defect detection in a domain other than thin films, we benchmarked DeepThin against previously reported state-of-the-art algorithms for crack detection 33 and segmentation 34,35 in images of concrete and road surfaces. To benchmark the road-surface crack detection ability of DeepThin, we used the training and testing datasets provided by Zhang and coworkers 33 to first retrain and then test DeepThin. The accuracy statistics given in Table S9, architecture comparison given in Table S10, and the receiver operating characteristic (ROC) curves in Fig. S1 show that DeepThin outperforms the three crack detection algorithms used by Zhang and coworkers 33 . Next, we benchmarked DeepThin against the road-surface crack segmentation algorithms described by Shi et al. 34 and Fan et al. 35 using the 118 image CFD dataset provided by Shi et al. We used 72 of these images for training and 46 images for testing as was done by  Shi et al. and again found that DeepThin again achieves state-of-art performance (Tables S11 and S12). The state-of-the-art performance of DeepThin in these benchmarks likely arises from our use of a CNN architecture based on one of the best available (VGG16) and further optimized for crack detection. These results suggest that DeepThin may also have utility in areas of materials science other than thin films.

DISCUSSION
We have shown that a CNN can accurately identify several different types of morphological defects in images of organic and inorganic thin films acquired under a variety of imaging conditions. The versatility of this approach to defect detection arises due to the ease with which it can be adapted to new defect types using labeled example images. The labeling of images containing examples of materials defects provides a straightforward mechanism for materials scientists to encode their domain expertise into an image analysis algorithm. As this example-based process for algorithm customization does not require software engineering expertise, we expect CNN-based approaches to material defect analysis to increase the accessibility of automated image analysis to the materials science community. Our DeepThin CNN provides the ability to rapidly and automatically identify trends in film morphology arising from manipulations of composition and process variables. We anticipate that capabilities of this kind, particularly in combination with automated experimentation, will accelerate thin film materials science research by facilitating the optimization of materials in design spaces where the morphological response to the experimental parameters is initially unknown.

METHODS
Robotic platform for film deposition, annealing, and imaging Deposition, annealing, and darkfield imaging of all the organic thin films included in the database were performed using a flexible robotic platform configured for thin-film experiments described in detail in ref. 30 . Briefly, the robotic platform consists of a multi-purpose robotic arm that can handle fluids and planar glass substrates, as well as a variety of other modules that enable other tasks to be performed. The modules relevant to this study include: trays of stock solutions and mixing vials which enable the formulation of spin-coating inks with various compositions; a spincoater for depositing inks on substrates to form thin films; an annealing station for variable-time annealing of thin films; a darkfield imaging station for imaging the thin films.
Fused silica wafers and microscope slides were cleaned prior to thin film deposition. A solution of 1% v/v Extran 300 in deionized water was prepared. The substrates were sonicated successively in the diluted Extran 300, deionized water, acetone, and 2-propanol. Before each sonication step, the substrates were rinsed in the following solvent. Substrates were stored submersed in 2-propanol. Prior to use, the substrates were dried with filtered, compressed air and inspected by eye for defects.  Fig. 4 Accuracy of DeepThin under a variety of conditions. In the top row, the accuracy for reproducing the human-labeled scores for the extent of cracking and the extent of dewetting in an image is shown. In all other rows, the accuracy for correctly classifying the images based on the presence or absence of different morphological defects is shown. Empty cells in the figure are associated with defects that were not present in the datasets or were not labeled for this study. Images in each row have the same scale. Scale bars from top to bottom are 500 µm, 50 µm, 50 µm, and 12.5 µm.
Organic thin film deposition Stock solutions of spiro-OMeTAD, FK102 Co(III) TFSI salt, Zn(TFSI) 2 , and 4tert-butylpyridine were prepared at 50 mg mL −1 in 1:1 v/v acetonitrile/ toluene. These stock solutions were combined using the robotic platform described above to form 150 µL of ink. 100 µL of ink was deposited by the robotic platform onto a microscope substrate rotating at 1000 rpm; rotation was maintained for 60 s following ink injection. The resulting thin films were then annealed for 0 to 250 s using a custom forced air annealer (an aluminum enclosure around heat gun, Model 750 MHT Products, Inc.). All of these procedures are described in more detail in ref. 30

Robotic darkfield imaging
All darkfield images taken with the robot were captured with a FLIR Blackfly S USB3 (BFS-U3-120S4C-CS) camera using a Sony 12.00 MP CMOS sensor (IMX226) and an Edmund Optics 25 mm C Series Fixed Focal Length Imaging Lens (#59-871). The C-mount lens was connected to the CS-mount camera using a Thorlabs CS-to C-Mount Extension Adapter, 1.00"-32 Threaded, 5 mm Length (CML05). The sample was illuminated from the direction of the camera using an AmScope LED-64-ZK ring light. For imaging, the lens was opened to f/1.4, and black flocking paper (Thorlabs BFP1) was placed 10 cm behind the sample.

Bright-field microscopy
All brightfield images were collected using an OLYMPUS LEXT OLS 3100 microscope operating in bright-field reflection mode using ×5 and ×20 objectives.

Monotonic dewetting experiment
To collect images of an organic thin film monotonically dewetting over time, a thin film of Spiro-OMeTAD and FK102 Co(III) TFSI salt was deposited (but not annealed) using the robotic platform as described above. A camera and lightsource were positioned above the sample in the same way as they were for the robotic darkfield imaging setup. A heat gun (Model 2363333, Wagner) was positioned to heat the sample from below at a 45°degree angle so as not to obscure the black background from the camera. To perform the experiment, the heat gun was turned on high and images were acquired every second for 100 s.
Image labeling procedure to define ground truth for model development The extent of dewetting in the dark-field images was scored by up to 3 experts on an integer scale from 0 to 9. The extent of cracking in these images was, separately, scored in the same way. In both cases, the average of the available scores was used as the ground truth. All experts used the same graphical user interface to perform the labeling. The darkfield images and the associated scores, as well as the labeling GUI can be found online (see "Data availability" section) For the brightfield images, a vector of binary values was assigned by a single researcher to each image. Each element of the vector indicated the presence or absence of one type of defect from the following: cracks, dewetting, particles, scratches, non-uniformities. In this way, images could be labeled as having no defects, one defect (of a specified type) or more than one defect (with the types present specified). The brightfield images and the associated labels are also available online (see "Data availability" section).

Development of the DeepThin network
The DeepThin CNN architecture (Fig. 1) was developed for the thin-film image analysis tasks described here and is inspired by the VGG16 CNN architecture 36 . Initially, DeepThin was trained using only one convolutional layer. The model complexity was iteratively increased until the model accuracy stopped improving. We employed five-fold cross-validation 37 to find a high-performance model before evaluating the model on the unseen validation data.
The input layer to DeepThin is an image with 3 RGB color channels. DeepThin has several convolutional and pooling layers as detailed in Fig. 1. The first convolutional layer uses 32 filters with a 3 × 3 × 3 kernel to convolve over the image, creating an output of size 50 × 50 × 32. Zero padding is performed so that the resulting image size is identical to the input image size. The output of the convolutional layer is passed into a ReLU activation layer. This convolutional layer is repeated, as in the VGG16 model.
Next, a maximum pooling layer of kernel size 2 × 2 is convolved over the output of the previous layer to generate a 25 × 25 × 32 output, returning the maximum value for a kernel. The two convolution layers and the pooling layer are repeated a second time. The output of the second maximum pooling layer is flattened to a 2000 × 1 vector. This output is followed by two fully connected layers of 20 neurons with ReLU activation functions and a final layer that outputs defects classes by applying a sigmoid activation function. DeepThin is trained by minimizing an error function through backpropagation using the stochastic gradient descent method. L2 (Gaussian) and Dropout regularization was used to reduce interdependent learning amongst the neurons. Regularization reduces overfitting by adding a penalty to the loss function.
DeepThin was trained using the Adam optimizer 38 , with an initial learning rate of 0.001 and a batch size of 100. Training loss and validation loss converged after 11 epochs.

DATA AVAILABILITY
The labeled image datasets and a spreadsheet giving the individual expert labels for the darkfield images as well as the labeling application and the code used to develop the model are all available at https://github.com/berlinguette/ada. All other data supporting the findings of this study are available from the corresponding authors upon request.