CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No.

63/183,911 filed May 4, 2021, the contents of which are hereby incorporated by reference in their entirety.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with Government support under Grant No.

HR001118C0036 awarded by the Defense Advanced Research Projects Agency (DARPA), and under Grant No. 1931065 awarded by the National Science Foundation (NSF). The Government has certain rights in the invention.

BACKGROUND OF THE INVENTION

[0003] This invention relates to high-throughput printing of materials for a material composition discovery process.

[0004] Prior approaches to discovery of material compositions (e.g., semiconductor material compositions) have combined machine learning algorithms with experimental synthesis to discover new material compositions with desirable properties. Some of those approaches have used Bayesian optimization to accelerate convergence to a material composition with an optimal desired material property.

SUMMARY OF THE INVENTION

[0005] Modem materials (e.g., high-performance semiconductor optoelectronics such as perovskites) have high-dimensional and vast composition spaces that govern the performance properties of the material. Aspects described herein relate to a system for cost-effectively searching these composition spaces by rapidly printing arrays of material “patches,” each patch including one or more discrete droplets of material and associated with a unique material composition.

[0006] As the speed of printing the arrays of patches increases, some conventional printer systems have difficulty maintaining uniformity of the deposited droplets — the shape of the droplets and the spacing between the droplets begin to lose uniformity. Aspects described herein use a computer vision-driven Bayesian optimization framework to find optimized printer parameters that can be used to rapidly deposit highly uniform arrays of discrete droplets in a high-throughput system.

[0007] In a general aspect, a method for depositing material on a surface includes receiving objective specification data characterizing a material deposition objective, depositing, from a printhead, material regions, each region deposited according to corresponding printer parameters, wherein the printer parameters include two or more of a material pressure parameter, a printhead translation parameter, and an actuator frequency parameter, imaging the regions to form images of the material regions, determining the deposition objectives for respective regions from the images, determining a relationship between the determined deposition objectives and printer parameters, selecting printer parameters for depositing target material properties using the determined relationship, and depositing the material with the selected printer parameters.

[0008] Aspects may include one or more of the following features.

[0009] Selecting the printer parameters may include using a Bayesian optimization scheme. Each material region may include one or more droplets of material. At least some of the droplets of material in different material regions may have different material compositions. Determining the deposition objectives for respective regions from the images may include computing a loss score for the material regions. The loss score may be based at least in part on a geometry of material deposited in the material regions. The loss score may be based at least in part on a measure of how closely droplets of material deposited on the surface match a desired circular shape. The loss score may be based at least in part on a ratio of an area of the regions occupied by deposited material to a total area of the regions. The loss score may be based at least in part on a spacing between droplets of material deposited in the material regions.

[0010] In another general aspect, a system for depositing material on a surface includes an input for receiving objective specification data characterizing a material deposition objective, a printhead for depositing a material regions, each region deposited according to corresponding printer parameters, wherein the printer parameters include two or more of a material pressure parameter, a printhead translation parameter, and an actuator frequency parameter, an imaging device for imaging the regions to form images of the material regions, one or more processors configured to: determine the deposition objectives for respective regions from the images, determine a relationship between the determined deposition objectives and printer parameters, and select printer parameters for depositing target material properties using the determined relationship, and a controller for controlling the printhead to deposit the material with the selected printer parameters.

[0011] In another general aspect, a method for depositing material on a surface includes receiving objective specification data characterizing a material deposition objective, depositing, from a printhead, material regions, each region having corresponding material parameters and deposited according to corresponding printer parameters, imaging the regions to form images of the material regions, determining the deposition objectives for respective regions from the images, determining a relationship between the determined deposition objectives and material parameters and printer parameters, selecting printer parameters for depositing target material properties using the determined relationship, and depositing the material with the selected printer parameters.

[0012] Aspects may include one or more of the following features.

[0013] The material parameters may represent physical characteristics of a target material property of the material. The physical characteristics may include a viscosity of the material. The viscosity of the deposited material may vary between at least some material regions. The material parameters may include a ratio of two or more precursor materials corresponding to the target material properties. Determining the relationship between the determined deposition objectives and material parameters and printer parameters may include using a Bayesian optimization scheme. Determining the relationship between the determined deposition objectives and material parameters and printer parameters may include3 using the Bayesian optimization scheme to learn a loss function and using the learned loss function to determine the printer parameters. Each material region may include one or more droplets of material. At least some of the droplets of material in different material regions may have different material compositions.

[0014] In another general aspect, a system for depositing material on a surface includes an input for receiving objective specification data characterizing a material deposition objective, a printhead for depositing material regions, each region having corresponding material parameters and deposited according to corresponding printer parameters, an imaging device for imaging the regions to form images of the material regions, one or more processors configured to, determine the deposition objectives for respective regions from the images, determine a relationship between the determined deposition objectives and material parameters and printer parameters, and select printer parameters for depositing target material properties using the determined relationship, and a controller configured to cause the printhead to deposit the material with the selected printer parameters.

[0015] Aspects may have one or more of the following advantages.

[0016] Advantageously, aspects described herein minimize the time and resources spent in configuring a system for material discovery applications. In particular, the Bayesian optimization framework finds the optimized printer parameters in a short amount of time and requires printing of only a few sample arrays of droplets.

[0017] Aspects generate uniform arrays of droplets (e.g., in geometry and spacing), which advantageously results in fewer material composition analysis errors.

[0018] Aspects advantageously maximize a yield of the printer for material composition analysis purposes by optimizing printer parameters to maximizing a density of the droplet arrays while maintaining droplet uniformity.

[0019] Other features and advantages of the invention are apparent from the following description, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. l is a material composition discovery system.

[0021] FIG. 2 is a flow diagram for a method of material composition discovery.

[0022] FIG. 3 is a training data collection step.

[0023] FIG. 4 is a model training and printer parameter discovery step.

[0024] FIG. 5 is a second embodiment of a material composition discovery system.

[0025] FIG. 6 is a front-view of a printhead.

[0026] FIG. 7 is a perspective view of a printhead.

[0027] FIG. 8 shows a mixing manifold of a printhead.

[0028] FIG. 9 is a cross-sectional view of a mixing manifold.

[0029] FIG. 10 is a printhead valve and nozzle. DETAILED DESCRIPTION

1 OVERVIEW

[0030] Referring to FIG. 1, a material composition discovery system 100 is configured for rapid discovery of a material a composition that meets a desired material characteristic. Very generally, the system 100 does so by performing an iterative optimization process that is initialized by first printing a set of “patches” of material, where the patches together have a number of different material compositions. For example, each material composition is characterized by material properties defining volumetric ratios of a set of precursor materials. The printed patches are analyzed to determine how closely they match the desired material characteristic. The optimization process then performs a number of iterations. At each iteration, a process controller 116 uses the result of the analysis of prior compositions to determine material compositions for a subsequent set of patches to print, with the goal of converging to the desired material characteristic. The system 100 repeats this process until a patch with the material composition, / that meets the desired material characteristic is discovered. In some implementations, the selection of the set of compositions to evaluate at each iteration is performed using a Bayesian Optimization (BO) approach.

[0031] It should be appreciated that in order to analyze the patches, it is desirable that a well-formed set of patches is deposited in the printing process. However, because different precursor materials and/or difference compositions (e.g., ratios) of those precursor materials may behave differently in the printing process, for example, with the printing not forming separate patches, forming irregularly shaped patches, and/or forming irregularly spaced patches. It is desirable that printing parameters that control the printer are selected to match the materials or compositions, as described with reference to one or more embodiments below, to form patches that are uniform and have desired geometry.

[0032] The system 100 includes a printhead 102 that is controlled by a printer controller 104 to print N patches 106 on a substrate 108 that is placed on a platen 109, where each patch includes one or more droplets 107 with a particular material composition. The printer controller 104 receives printer parameters y* and N material compositions

(/[l],/[2],.../[V]) corresponding to the N patches as inputs. As is described in greater detail below, the printer parameters, y* are used to configure aspects of the printhead 102 such as fluid pressure, valve actuation frequency, and a relative velocity of the printhead to the substrate 108. The N material compositions specify the material compositions of droplets 107 in each of the patches 106.

[0033] In operation, the printer controller 104 controls the printhead 102 and the platen 108 to cause deposition of the N patches 106 on the platen, with each patch being formed by a discrete drop emitted from the printhead (i.e., expelled as a discrete drop, or formed into discrete drops during the transit from the printhead to the platen). Very generally, a particular material composition (e.g., a particular volumetric ratio) is deposited by causing two or more precursor materials (e.g., ¾, and p ₃ ) to mix at a mixing point 101 in the printhead 102.

Pressure is applied to the mixed material according to the fluid pressure printer parameter.

For example, the rate that the precursor materials are passed into the printhead at the selected ratio controls the pressure in the printhead, where a faster rate results in higher pressure and a lower rate results in lower pressure. A valve 103 in the printhead 102 opens and closes according to the valve actuation frequency printer parameter. For example, the frequency of the valve corresponds to the frequency at which drops are formed from the printhead. When the valve 103 is open, the pressurized material is ejected as a droplet from a nozzle 105 of the printhead 102 onto the platen 108. The ejected material falls onto the platen 108 as it moves relative to the printhead 102, forming the patches 106 on the substrate 108.

[0034] While FIG. 1 is illustrated in cross-section with a single row of patches, in generally, the printing process forms a two-dimensional array of patches on the substate by offsetting the platen between passes and forming multiple adjacent rows of patches. For the sake of discussion below, the two-dimensional arrangement of patches is not illustrated, and should not be considered essential.

[0035] The substrate 108 with the N patches 106 deposited thereon is then removed from the platen 109 and measured by a measurement device 112 and a utility function, m( f ) is computed to generate material utilities 114 for the patches, /??[]],. .,/??[A ^f ] (where , the measurement/material utility for the n ^th material composition). In some examples, the measurement device 112 includes an optical device such as a camera, but it is noted that any other suitable device for measuring properties of the deposited materials may be used.

[0036] As introduced above, the material utilities 114 are provided to a process controller 116 that uses Bayesian optimization techniques to process the material utilities 114 to determine a next set of N material compositions that are closer to the desired material characteristic. The system 100 repeats the above-described printing, measurement, and optimization procedure until the optimal material composition, / is discovered.

[0037] Due to the potentially very large number of possible material compositions that need to be evaluated in the material optimization process, the system 100 should be capable of very quickly depositing large numbers of patches 106 (and corresponding droplets 107).

To achieve high-speed deposition of the patches 106, the printer parameters, y* of the printhead 102 are closely controlled.

2 PRINTER PARAMETERS

[0038] In order to print well-formed patches, printer parameters (illustrated as y in FIG. 1 configuring the printer controller 104) are selected to match the material compositions that are evaluated in the material optimization process. For example, a set of printer parameters appropriate for a range of material compositions to the evaluated may be determined prior to the material optimization and kept fixed during the material optimization iterations. In other examples, printer parameters may be varied from iteration to iteration, for example, with all the patches printed on a substrate in an iteration using one set of printer parameters, but the printer parameters potentially changing between material optimization iteration. In yet other examples, different printer parameters may be used within one iteration for example, with different rows being printed with different printer parameters that match the compositions being deposited in those rows, or in the case of an iteration using multiple substrates, for different substrates printed in one iteration. Yet other variation of printer parameters may be used to match the material compositions being deposited.

[0039] In one or more examples described herein, three printer parameters govern the structure of deposited droplets: jetting pressure, valve actuation frequency, and printhead translation speed. The jetting pressure parameter essentially determines how fast the material stream is ejected from the nozzle 105 of the printhead 102. By changing the pressure within the printhead a rate of material flow rate changes (or vis a versa where the rate is controllable and the pressure results from the rates). For example, as the pressure increases, the amount of material ejected from the nozzle 105 increases per unit time. In some examples, the jetting pressure ranges between 0.02MPa-0.15MPa.

[0040] The valve actuation frequency parameter controls a rate of droplet formation from the printhead 102. In some examples, the valve 103 of the printhead 102 is controlled to actuate at the valve actuation frequency. For at least some materials, actuation of the valve breaks the stream of material flowing through the nozzle 105, creating droplets at a rate controlled by the valve actuation frequency parameter — as the valve actuation frequency increases, droplets are created at a faster rate. In some examples, the valve actuation frequency is in a range of 20Hz-40Hz.

[0041] The nozzle translation speed parameter controls a relative velocity between the nozzle 105 of the printhead 102 and the substrate 108. As the nozzle translation speed increases, the droplets are deposited further apart. Furthermore, as the speed increases, there may be more irregularity (e.g., entropy) in the shape of the patch, for example, with slower speed resulting in more circular patches had high speed results in elliptical and/or irregular patch shapes. In some examples, the nozzle translates parallel to the deposition site on the platen in two-dimensions at speeds ranging between 300mm/s- 900mm/s.

[0042] In general, to increase the rate of deposition of patches, the printer parameters may each be increased to achieve higher material rate, higher drop frequency and/or more rapid printing over a given area of substrate. But increasing the printer parameters can cause problems with formation of the patches 106. For example, the droplets 107 of the patches may be too sparsely distributed, resulting in a loss of efficiency. Or the droplets of the patches may be too densely distributed, resulting in droplets merging and making measurement of the patches difficult or impossible. Finally, the shapes of the droplets in the patches may diverge from an ideal (e.g., circular) shape, making accurate measurement of the patches difficult.

2.1 Printer Parameter Optimization

[0043] In a first printer parameter optimization process, printer parameters are determined for a particular material composition or range of material compositions or for a particular material property (e.g., viscosity or range of viscosity). For example, the printer parameters may be selected prior to and then fixed during the material optimization process.

[0044] Referring to FIG. 2, a printer parameter optimization method 200 uses Bayesian optimization to quickly identify optimal printer parameters, y * for printing uniform, densely distributed patches for a particular material composition, / .

[0045] Very generally, the method 200 prints sample arrays of droplets, captures images of the printed sample arrays, and uses image segmentation and processing methods to detect droplet structures in the images of each sample array. In some examples, a two-level model is used to segment and then score each droplet structure based on a defined objective function to (1) maximize droplet uniformity and (2) maximize droplet yield. Bayesian optimization (BO) is then utilized to efficiently search for printer parameters that minimize the loss score of the droplet structures. New printer parameters are synthesized iteratively in a loop seeking to identify the optimal printer parameters until the method converges on printer parameters that reliably generate optimized droplet structures.

[0046] As is described in greater detail below, the method 200 includes an initial training data generation step 220 where training data 222 is generated. A model training step 224 processes the training data 222 to train an initial Bayesian optimization model 226 for the printing process. A Bayesian optimization step 228 uses the initial Bayesian optimization model 226 to generate predicted printer parameters, y _precj that are used to print a sample,

S _pred (e.g., an array of patches of material composition / ) in a printing and measurement step 230. The sample, s _pred is measured (e.g., imaged) and used by the Bayesian optimization step 228 to update the model of the printing process (e.g., maintained in the

Bayesian optimization module 228) and generate a new predicted set of printer parameters, y _pred using the updated model. This process repeats until the optimal printer parameters, y* are discovered (as is described in greater detail below).

2.1.1 Training Data Generation

[0047] Referring to FIG. 3, in some examples, in the initial training data generation step 220, the printer controller 104 receives M different sets of printer parameters, a material composition, / (or in some embodiments a representative range of material compositions). In some examples, the M different sets of printer parameters, Y = [TI,T2 _> ··· _> TM ] ^are determined in a way that minimizes a variability of the printer parameters in as few samples as possible. For example, the initial sets of printer parameters can be determined using Latin Hypercube Sampling of the pressure, frequency, and translation speed parameters. In some examples, Latin Hypercube Sampling (LHS) minimizes the variance along each parameter vector. For example, LHS splits a D dimensional parameter space (in this case 3D: (pressure, frequency, speed}) into k striations, where each striation is of equal volume. A random point is selected within that D- dimensional volume. By creating these striations, variance is minimized to ensure that all regions of the D-dimensional space are represented in the initialization dataset, unlike how random sampling would work (selecting points randomly in D-dimensions usually does not capture the entire space well). [0048] For each set of printer parameters, y _m , the printer controller 104 controls the printhead 102 to print a sample set of patches using the printer parameters, resulting in M printed samples. For example, setting of the printing parameters may be used to print a different row on one of the substrates used in the initial training stage. A camera 232 collects image data for each of the printed samples to generate a sample image data set, Atraining data collector 234 combines the M different sets of printer parameters, Y = the sample image data set, to form the training data 222.

2.1.2 Initial Model Training

[0049] Referring to FIG. 4, the initial training data set 222 is processed by the initial model training module 224 to generate the initial Bayesian optimization model 226 for the printing process. In some examples, the initial model training module 224 first detects and scores the droplet structures in the patches of each of the samples. For example, each sample image, s _m is processed using a watershed image segmentation method to segment pixels of the image associated with droplets from pixels of the image associated with the platen 108. The droplet structures are then scored by computing a linear combination of scalarized losses. A first component of the score is a geometric loss characterizing how circular each droplet is. In some examples, the geometric loss for the m ^th sample image is quantified by a normalized sum of pixels that do not fit to perfect circles mapped onto centroids of the droplets in the sample: where P _dropiet represents the pixels of the droplet and P _circie represents the pixels of a circle mapped to the droplet.

[0050] A second component of the score is a yield loss that is quantified by a ratio of all non-droplet pixels in the sample image to the total number of pixels in the sample image: where P _dropiet represents the pixels of a droplet and P _totai represents the total number of pixels in the m ^th sample. [0051] A loss score, L _m for the m ^th sample is then computed as: where are the geometric and yield loss scores for each image, respectively and o _{g ,} o _e are geometric and yield-component weights, respectively.

[0052] The printer parameters and corresponding loss scores associated with samples (i.e., - _> LM ) ^are then used to update the initial Bayesian optimization model 226. In some examples, Bayesian optimization uses a surrogate model and acquisition function to efficiently sample a complex A-dimensional parameter space by updating prior hypotheses with incoming new data to converge to an optimum. Through efficient sampling and hyperparameter tuning, Bayesian optimization elicits rapid convergence to the optimum using few samples, thus promoting high-throughput experimentation and reducing waste material in the process.

[0053] In some examples the Bayesian optimization model includes a Gaussian process surrogate model, expected improvement (El) acquisition function, a Matern 5/2 kernel with automatic relevance detection, and a jitter value of 0.01. In general, the El acquisition function balances model exploration and exploitation and is defined as: where x is the improvement of f* - f (x) and /* is the current minimum value of the evaluated function / (x) .

2.1.3 Optimal Printer Parameter Prediction

[0054] The Bayesian optimization module 228 uses the current Bayesian optimization model 226 to select printer parameters in the printer parameter space where the acquisition value is high, meaning that the prediction uncertainty of the objective is high and the mean of the objective is low, corresponding to a low loss score.

[0055] To begin the parameter space search, the Bayesian optimization module 228 computes posterior probabilities for each of the M sets of printer parameters associated with the M samples using their corresponding loss scores. A predicted optimum set of printer parameters, y _precj is suggested where the acquisition value, x, is maximized (and the loss score is minimized). The predicted optimum set of printer parameters, y _prej is used by the printer controller 104 to configure the printhead 102. The printhead is then controlled to print a new sample according to the printer parameters, y _{pr ed .} The camera 232 captures an image,

S _pred °f the new sample, which is fed back to the process optimization module 228. The process optimization module 228 performs image segmentation and computes a loss score for s _pre , then updates its Bayesian optimization model to incorporate y _prej and the loss score,

^L pred associated with s _{pred .}

[0056] The process optimization module 228 determines a subsequent set of predicted printer parameters using the updated Bayesian optimization model, and the process repeats until the loss score for the predicted printer parameters is less than a predetermined convergence threshold. The predicted printer parameters associated with the loss score less than the convergence threshold are output as the optimal printer parameters, y * .

[0057] To the extent that the material composition is representative of the material compositions that will be used in the material optimization process (e.g., illustrated in FIG.

1), the patches of the various compositions being evaluated will be well formed, and the material optimization can proceed efficiently.

[0058] To the extent that it is known that a wide range of material compositions may be encountered in the material optimization procedure, the range of compositions may be used in the training, thereby achieving a good “average” printer parameters that is usable over the range.

2.2 Printer Parameter Mapping Function

[0059] While in some material optimization procedures, the printer parameters may be kept fixed for the range of compositions, in another embodiment, rather than fixing the printer parameters, the printer parameters are selected based on a learned mapping from material parameters to optimal printer parameters.

[0060] Referring to FIG. 5, in some examples, different printer parameters are required for uniformly printing materials with different material compositions because those materials have different physical properties (e.g., different viscosities). For example, the process controller 116 receives N material compositions /[l],/[2],.../[/V] corresponding to N patches that to be deposited on the platen 108 by the printhead 102. Each material composition is a different combination of the precursors p , p , and p and, in this example, has a different viscosity than some or all of the other material compositions. The different viscosities cause the material compositions to behave differently when deposited by the printhead by, for example, requiring more pressure to eject a droplet or spreading differently upon contact with the platen 108.

[0061] To ensure uniform deposition of the patches 106 on the platen 108 when depositing material compositions with varying physical characteristics, another embodiment of a material composition discovery system 500 includes a mapping function 515 that maps a particular material composition, f[n\ to a corresponding set of printer parameters, >¾(//) .

[0062] A variety of approaches may be used to learn the mapping of material parameters ( / ) to corresponding optimal printer parameters y* =M(f) . One such approach uses a variant of the Bayesian optimization process described in Section 2.1 above. The Bayesian Optimization process can be considered to be a process of learning a (loss) function L(y) for the process of learning the optimal y* = argmin^ (y ) under certain assumptions of correlation of /.(jq ) and L(y ₂ ) for different pairs (jq , y ₂ ) . The printer parameters that are chosen in the printer optimization are selected to efficiently find y * . One approach to learning the mapping is to formulate the Bayesian Optimization problem as learning a function L(f , y) and using the learning function to determine the optimal printer parameters for particular material parameters / as y* = M{f) = argmin _v, L(f y) In optimizing the learning of the loss function, a range of material parameters are sampled rather than merely seeking the global optimum over both material and printer properties.

[0063] The system 500 illustrated in FIG. 5 uses such a trained mapping from material parameters to printer properties to perform a Bayesian optimization scheme (similar to the process in FIG. 1) to iteratively converge to a material composition that meets the desired material characteristic. For each set of N patches to be printed, the process controller 116 provides corresponding A material compositions /[l],/[2],.../[A] and to the mapping function 515 and to the printer controller 104. The mapping function 515 processes the material composition for each patch, f[n\ in turn to determine the optimal printer parameters, y*{ri) for the material composition. The optimal printer parameters, y*(n) and the corresponding material composition f[n\ are provided to the printer controller 104, which deposits droplets for the n ^th patch according to y*(n) and /[//] . As a result, the printer parameters are controlled to maintain uniform printing of the patches as physical properties of the materials in the patches changes.

[0064] There are a number of alternative approaches to determining the mapping from material parameters to printer parameters including the following. [0065] In some examples, rather than learning a joint loss function, optimal printer parameters are determined separately for different material parameters. In operation, the printer parameters for particular material parameters f[n\ are selected, for example, by using the printer parameters for the closest corresponding material parameters used in the printer parameter training, or using an interpolation procedure (e.g., linear or polynomial interpolation, learning parameterized non-linear mapping) of the mapping function y * =M(f ) . In some examples, the function space between material parameters may be too complex for a naive linear or polynomial interpolation. Other common fitting methods are Gaussian Process (essentially a multidimensional regression) or a neural network (which may requires a significant amount of training data).

[0066] In some examples, the mapping is specific for a set of precursor materials, and the material parameters may represent for example, the volumetric ratios of those precursors. In some examples, properties of the precursors may be used in the mapping, for example, with the viscosities of the precursors being provided as input to the mapping. In this way, a more “universal” mapping may be determined that can be used for different precursor materials.

[0067] In some examples, other approaches than Bayesian Optimization are used. For example, gradient descent of mapping parameters may be used. For instance, a neural network that maps from material parameters (e.g., ratios, material identities, material properties) to printer parameters may be optimized using a backpropagation approach. In some such approaches, a Reinforcement Learning approach may be used to determine a best policy that maps from material parameters to printer parameters may be used.

3 PRINTHEAD CONFIGURATION

3.1 Radial arrangement of inkjet material reservoirs and pumps

[0068] In some conventional printers, print heads traverse a one-dimensional or two- dimensional path. The print heads are plumbed via flexible tubing to one or more reservoirs, which remain fixed, relative to a printer’s frame, while the print head moves. The flexible tubing is necessarily relatively long, leading to long resident transport times through the tubing.

[0069] However, in many cases, the length of the plumbing between an inkjet reservoir and an inkjet nozzle should be minimized, particularly if multiple materials, from respective reservoirs, are mixed prior to ejection from a nozzle. Minimizing the distances between precursor material storage and the ejection point reduces transport time and reduces material waste when changing materials.

[0070] The reservoirs occupy some volume, as do respective drive motors, lead screws and other apparatus (collectively “reservoir hardware”) that support the reservoirs and motivate material in the reservoirs toward the nozzle. Competing requirements of short plumbing and packing several reservoirs and their attendant reservoir hardware into a small space pose problems.

[0071] These and other problems are solved by disposing the reservoirs and reservoir hardware in a radial arrangement, and attaching the reservoirs and reservoir hardware to the print head, so they all travel together. An example of such a multi-reservoir system 900 is shown in Figs. 6-8. This example includes four reservoirs 902, 904, 906 and 908. However, in other embodiments, other numbers of reservoirs may be included.

[0072] As shown in Fig. 6, the four reservoirs 902-908 are disposed in a fan shape, each reservoir 902-908 being oriented generally toward a common nozzle 910. Each reservoir 902-908 may include a hollow body, exemplified by body 912, a piston, exemplified by piston 914, disposed within a hollow defined by the body 912, where each piston 914 is mechanically coupled to a lead screw, exemplified by lead screw 916, driven by a respective motor, exemplified by motor 918.

[0073] In the embodiment shown in Figs. 6-8, an end of each body 912 distal from the piston 914 is connected via a tube, exemplified by tube 920, so as to be in fluid communication with the nozzle 910. In the embodiment shown in Figs. 6-8, each tube terminates at a common manifold 922, where materials from the respective reservoirs 902- 908 are mixed, prior to being delivered to the nozzle 910. Thus, the manifold 922 is upstream of the nozzle 910. The manifold 922 includes a number of input ports, one for each reservoir 902-908, and the manifold includes only one output port, which is coupled in fluid communication to the nozzle 910. Thus, the tubes 920 are in fluid communication with the nozzle 910 via the manifold 922. In other embodiments (not shown), the manifold 922 is omitted, and each reservoir 902-908 is fluidically coupled to a separate nozzle.

[0074] Each motor 918 is separately controlled, such as by a processor, to motivate material from the respective body 912 toward the nozzle 910. Essentially, each reservoir 902-908 is a syringe which, in combination with the lead screw and motor, for a pump. However, in other embodiments, other pumping mechanisms may be used, such as squeezing a flexible body. In some examples, this separate motor control is what generates either a high or low fluid pressure, which determines the ejection rate of the respective fluid.

[0075] As noted, the four reservoirs 902-908 are disposed in a fan shape. The fan shape minimizes lengths of the tubes 920 extending from the distal ends of the bodies 912 to the manifold 922. In the fan shaped arrangement, the reservoirs 902-908 are co-planar. In some examples, minimizing the length of tube is important to minimize the latency of signal from the motor input to the ejected droplet composition. Additionally, when changing syringes & tubing to swap in a new material precursor, minimizing tube length decreases accumulated waste.

3.2 Mixing manifold

[0076] As noted with respect to Figs. 6-8, in some embodiments, each tube from a respective reservoir 902-908 terminates at a common manifold 922, where materials from the reservoirs 902-908 mix, prior to being delivered to the nozzle 910. Fig. 9 is a cross- sectional view of the manifold 922 of Figs. 6-8. The manifold 922 has four input ports 1500, 1502, 1504 and 1506, in fluid communication with a common channel 1507, and one output port 1508. However, a manifold for an inkjet printer according to the present invention can have any number of input ports greater than one.

[0077] Although some prior art inkjet print heads include manifolds, these prior art manifolds branch so as to deliver a single material from a single input port to multiple nozzles via multiple output ports. In contrast, a manifold 922 according to the present invention mixes several material for delivery to a single nozzle. Thus, a manifold 922 according to the present invention branches to a larger number of ports in a direction upstream of the single output port, and upstream relative to the nozzle, whereas a prior art manifold branches to a larger number of ports in the opposite direction, i.e., downstream toward the nozzles.

[0078] In the manifold 922, the input ports 1500-1506 should join the common channel 1507 at right angles, exemplified by angle 1510, to maximize turbulent mixing of the materials delivered via the input ports 1500-1506. Optionally (not shown), the input port 1500 furthest upstream from the output port 1508 need not join the common port 1507 at a right angle. In some embodiments, the input ports 1500-1506 join the common channel 1507 at angles of about 90° ±1°. In some embodiments, the input ports 1500-1506 join the common channel 1507 at angles of about 90° ±5°. In some embodiments, the input ports 1500-1506 join the common channel 1507 at angles of about 90° ±10°. In some embodiments, the input ports 1500-1506 join the common channel 1507 at angles of about 90° ±20°.

[0079] Amount of deviation from 90°, at which a given input port 1500-1506 joins the common channel 1507, that is acceptable for adequate mixing depends on several factors, including viscosity of material to be fed into the input port 1500-1506 and viscosity of material to be fed into the common channel 1507 upstream of the input port 1500-1506. Similarly, maximum radius of comers formed at intersections of the input ports 1500-1506 and the common channel 1507, exemplified by comer 1512, should be chosen to ensure adequate mixing. The maximum radius of the corners 1512 that is acceptable for adequate mixing depends on several factors, as noted with respect to the deviation from 90°. The amount of deviation of the angles 1510 from 90°, and the maximum radii 1512, may be determined empirically or using well-known fluid dynamic methods.

[0080] The manifold 922 can be made of any suitable material. One embodiment is made of polyetherimide (PEI) resin, for example ULTEM brand polyetherimide (PEI), a commercially available amorphous thermoplastic resins that retains its mechanical integrity at high temperatures.

3.3 Positive displacement pumping of inkjet materials

[0081] As noted with respect to Figs. 6-8, in some embodiments, piston-based pump is used for each reservoir 902-908. Advantageously, a piston-based pump provides positive displacement pumping of inkjet material in the reservoirs 902-908. Since the materials are essentially incompressible, positive displacement pumping enables dispensing the materials in precise amounts. In contrast, simply drawing material from a tank at atmospheric pressure, or pressurized, leads to poorly determined amounts of material being dispensed, in part because gas in the tank is compressible.

[0082] In some embodiments, stepper motors are used for the motors 918 that drive the lead screws 916 that advance the pistons 914. Stepper motors can be precisely controlled, when enables advancing the pistons 914 precise distances, leading to dispensing precise amounts of material from the reservoirs 902-908. Optionally or alternatively, each lead screw 916 may be mechanically coupled to a respective rotary encoder (not shown) to measure rotation of the lead screw. Rotation of the lead screw, together with knowledge of the pitch of the lead screw 916, enables precise calculation of displacement of the piston 914. Optionally or alternatively, each piston 914 may be mechanically coupled to a respective linear encoder (not shown) to directly measure displacement of the piston 914.

3.4 Multi-fluid Displacement Controller

[0083] To mix several precursor solutions in real-time, an accurate method of dispensing several solutions in parallel from storage vials in preferred. The volumetric flow rate of precursor material out of the vial should be measured for every step of unit time, such that the composition of the deposited droplet is back-computed. Aspects described herein use a motor-controlled fluid displacement system from which measurements of the precursor volumetric flow rate can be accurately obtained using the motor inputs.

[0084] In some examples, a stepper-motor actuated plunger, is designed to displace the precursor fluid from a vial. Utilizing a stepper motor in this construction allows for accurate mechanical control of the plunger by sending electrical pulses to the motor. Using the frequency of these electrical pulses, the angular velocity w of the stepper motor is known: where Q is the step angle of the motor and f is the frequency of the applied electrical signal in Hz.

[0085] In some examples, precursor material is ejected from a vial at some velocity v2 by accurately controlling the angular velocity w of a stepper motor M. The linear velocity vl of the plunger attached to a threaded motor shaft is computed using w and the count of threads per inch (TPI) on the plunger lead screw. The value v2 is accurately calculated using the continuity equation of fluid flow given vl at some unit time.

[0086] The volumetric flow rate of precursor material out of the vial is computed by converting the angular velocity w of the motor to linear velocity of the plunger n _c in addition to applying fundamental principles of fluid mechanics. To convert the angular motion of the stepper to linear motion of the plunger, the motor shaft is designed with threads that feed into a stationary threaded cap on top of the precursor vial. The stepper motor translates vertically on rails as it rotates the shaft and threads it into the cap to push the plunger down. The linear velocity n _c is computed using from the geometry of the threading and w.

Lead = Starts \m rev ^~1 ]

V = — 2TC x Lead, [ms ^-1 ] where TPI is the threads per inch on the shaft and cap treading (Pitch = 1/TPl) and Starts is the number of start threads. The flow of precursor material throughout the vial is governed by the linear speed of the plunger and the cross-sectional area of which the fluid flows though. The cross-sectional area of the precursor vial A1 is different from the cross-sectional area of vial tip A2 where the fluid will be dispensed. Thus, the volumetric flow rate of precursor out of the vial Qout is computed using the continuity equation of fluid flow.

ViAi = V ₂ A ₂ , [m ³ s ^-1 ]

= Qout. [m ³ s ^~1 ]

[0087] The fluid flow of precursor solutions are generally incompressible, i.e., V u = 0, thus, accurately models the volumetric flow of precursor material out of the vial.

[0088] Multiple fluids are dispensed in parallel by controlling the angular velocity w of stepper motor via a microprocessor. The percent composition %C of each precursor C E C that comprises a deposited droplet is back-computed from the known Qout: where %(2(W) is the percent composition of precursor C in a droplet deposited between the time interval [t _a t _b ], given the set of precursor stepper motor angular velocities W and the set of precursors C. For example, if there are three precursor vials {A, B, X} e C deposited at volumetric flow rates using angular velocities

{w _A , w _B w _c ) e W, respectively, between [t _a t _b ], the chemical composition of the droplet is (%A, %B, %X).

3.5 Dual series-connected mechanical and piezo valves before nozzle for inkjet printing

[0089] Some conventional inkjet printers employ piezoelectric elements to generate droplets. A nozzle of such an inkjet printer ejects a continuous stream of material. However, typically only some of the droplets should be directed toward a substrate to be printed, and the remainder of the droplets must be prevented reaching the substrate. The unwanted droplets are typically either directed to a gutter and thence to a waste container or recycled back to a supply reservoir. This selective direction of droplets is achieved in the prior art by electrically charging the droplets and then electrostatically deflecting the unwanted droplets toward the gutter. [0090] Embodiments of the present invention avoid complexities associated with the prior art electrostatic deflection scheme by including two valves in series. Fig. 10 is a cross- sectional, partially schematic, view of such a dual -valve system 1600, according to an embodiment of the present invention. Droplets are ejected from an orifice 1602 of a nozzle 1604. A piezoelectric element 1606 is disposed adjacent or surrounding a resilient tube 1607 made of a suitable material, such as polytetrafluoroethylene (PTFE). The piezoelectric element 1606 operates at a high frequency, causing generation of the droplets, in a conventional manner. However, a mechanical ON-OFF valve 1608, such as a solenoid- actuated valve, is in fluid communication with the nozzle 1604, but plumbed upstream of the piezoelectric element 1606. Thus, a supply 1610 of material, such as from a reservoir or manifold, can be turned on when droplets are needed and off when droplets are not needed. Although the mechanical ON-OFF valve 1608 may not be able to operate at as high a frequency as the piezoelectric element 1606, compliance in plumbing upstream and/or downstream of the mechanical valve 1608 accommodates volumetric variations caused by the difference in operating frequencies.

[0091] The piezoelectric element 1606 is separated, and therefore protected, from the material flowing from the supply 1610 by walls of a tube. Materials of the mechanical valve 1608 should be selected to prevent, or at least reduce, chemical reaction with materials expected to flow from the supply 1610.

4 ALTERNATIVES

[0092] In embodiments described above, the optimization of printer parameters may be performed prior to performing a material parameter optimization. Alternatively, the printer parameters and/or a mapping from material parameters to printer parameters may be updated during the material optimization process. For example, in the case of using a parameterized non-linear mapping (e.g., a neural network), a Reinforcement Learning approach may be used to adapt the mapping during the material optimization process. In some such approaches, some of the patches printed during the material optimization may be used to “explore” the printer parameter space to permit effective updating of the mapping.

[0093] In some alternatives, a “prior” loss function may be known based on general properties of the precursor materials, thereby providing a good starting point for optimization for specific materials. [0094] In some alternatives, rather than optimizing printer parameters after groups of one or more substrates are printed, an adaptive process is used by imaging the patches while a substrate is being printed. For example, the imaging of a row of patches on a substrate may inform the printer parameters used for a subsequent row on that substrate.

[0095] In some alternatives, a series of patches represents a trajectory in the space of material parameters, and the printer parameters are varied accordingly such that different patches in the series are printed with different printer parameters. For example, the printer parameters may be varied during the printing of a single row of dots on a substrate.

[0096] It is noted that, in some examples, the measurement device 112 and the process controller 116 are capable of analyzing and scoring patches with irregular geometries and densities. While such scores may be far from the ideal / , the measurement data still provides useful information about the quality of a particular set of printing conditions.

[0097] In some examples, rather than imaging the droplets as they are deposited as patches on the substrate, one can image the droplets mid-flight from the side of the device with a high-speed camera to get measurements of the droplet volume, number of droplets per unit length, elongation, and angle of flight — all which are influenced by the motor pressure, actuation frequency, and traverse speed.

[0098] In some examples, additional measurement tools can be used to quantify the material compositions, such as hyperspectral camera for ab sorb ance/reflectance/b and gap, 4- point probe for electrical conductance, controlled environmental chamber for stability/degradation.

5 IMPLEMENTATIONS

[0099] The approaches described above can be implemented, for example, using a programmable computing system executing suitable software instructions or it can be implemented in suitable hardware such as a field-programmable gate array (FPGA) or in some hybrid form. For example, in a programmed approach the software may include procedures in one or more computer programs that execute on one or more programmed or programmable computing system (which may be of various architectures such as distributed, client/server, or grid) each including at least one processor, at least one data storage system (including volatile and/or non-volatile memory and/or storage elements), at least one user interface (for receiving input using at least one input device or port, and for providing output using at least one output device or port). The software may include one or more modules of a larger program, for example, that provides services related to the design, configuration, and execution of dataflow graphs. The modules of the program (e.g., elements of a dataflow graph) can be implemented as data structures or other organized data conforming to a data model stored in a data repository.

[0100] The software may be stored in non-transitory form, such as being embodied in a volatile or non-volatile storage medium, or any other non-transitory medium, using a physical property of the medium (e.g., surface pits and lands, magnetic domains, or electrical charge) for a period of time (e.g., the time between refresh periods of a dynamic memory device such as a dynamic RAM). In preparation for loading the instructions, the software may be provided on a tangible, non-transitory medium, such as a CD-ROM or other computer-readable medium (e.g., readable by a general or special purpose computing system or device), or may be delivered (e.g., encoded in a propagated signal) over a communication medium of a network to a tangible, non-transitory medium of a computing system where it is executed. Some or all of the processing may be performed on a special purpose computer, or using special-purpose hardware, such as coprocessors or field-programmable gate arrays (FPGAs) or dedicated, application-specific integrated circuits (ASICs). The processing may be implemented in a distributed manner in which different parts of the computation specified by the software are performed by different computing elements. Each such computer program is preferably stored on or downloaded to a computer-readable storage medium (e.g., solid state memory or media, or magnetic or optical media) of a storage device accessible by a general or special purpose programmable computer, for configuring and operating the computer when the storage device medium is read by the computer to perform the processing described herein. The inventive system may also be considered to be implemented as a tangible, non-transitory medium, configured with a computer program, where the medium so configured causes a computer to operate in a specific and predefined manner to perform one or more of the processing steps described herein.

[0101] A number of embodiments of the invention have been described. Nevertheless, it is to be understood that the foregoing description is intended to illustrate and not to limit the scope of the invention, which is defined by the scope of the following claims. Accordingly, other embodiments are also within the scope of the following claims. For example, various modifications may be made without departing from the scope of the invention. Additionally, some of the steps described above may be order independent, and thus can be performed in an order different from that described.