A method for optimizing inkjet printing parameters based on machine learning algorithms to fabricate high-efficiency solar cells and optoelectronic devices

Abstract

This paper presents a method for optimizing inkjet printing parameters based on machine learning algorithms to fabricate high-efficiency solar cells and optoelectronic devices, belonging to the field of optoelectronic devices. During piezoelectric inkjet printing, parameters such as rise time Rt, hold time Dt, fall time Ft, and driving voltage Dv are parameterized. Droplet velocity v, droplet volume V, droplet roundness R, droplet continuity CV, droplet number Ns, and film surface roughness Ra are collected. Nozzle pressure and droplet formation data obtained from two-phase flow-solid-liquid coupling-piezoelectric coupling multiphysics simulations are combined. A stacked ensemble learning model consisting of a multilayer perceptron regression model, a support vector regression model, a random forest regression model, and a k-nearest neighbor regression model is used to establish the mapping relationship between waveform parameters, nozzle pressure characteristics, and droplet behavior indices. An objective function is constructed, and a genetic algorithm is used to search for the optimal waveform parameters, achieving droplet suppression and uniform film formation, thereby improving device performance and consistency.

Description

Technical Field

[0001] This invention, based on machine learning technology, studies a data-driven optimization method for the driving waveform and inkjet conditions during piezoelectric inkjet printing, used to fabricate thin films of various functional layers in solar cells and optoelectronic devices. This invention belongs to the field of optoelectronic device fabrication technology, specifically involving inkjet printing, droplet formation control, multiphysics simulation, and machine learning modeling. Background Technology

[0002] Solar cells and optoelectronic devices include organic solar cells, perovskite solar cells, quantum dot solar cells, organic light-emitting diodes (OLEDs), and organic field-effect transistors (FETs). The key functional layer films of these devices are sensitive to thickness uniformity, surface roughness, and interface defect density. Traditional spin-coating and vacuum deposition processes have limitations in material utilization, large-area fabrication, and roll-to-roll manufacturing.

[0003] Inkjet printing, as a non-contact digital manufacturing process, enables on-demand material deposition and patterned film formation, making it suitable for flexible substrates and large-area manufacturing. The core challenge of inkjet printing lies in droplet ejection stability. When the driving waveform, nozzle pressure, and ink rheological properties are mismatched, satellite droplets are generated during the ejection process. The secondary landing of these satellite droplets can cause surface texture, pinholes, and thickness fluctuations in the film, thereby reducing device performance and consistency.

[0004] Existing methods typically reduce the probability of satellite droplet formation by empirically adjusting solvent systems, viscosity, or waveform parameters. This approach relies on human experience, making it difficult to rapidly migrate across different material systems, printhead structures, and environmental conditions, and also hindering online compensation during printing. Therefore, an optimization method is needed that can quantitatively map printhead drive waveforms, nozzle pressure profiles, and ink properties to droplet behavior, and can be updated in a closed-loop manner during printing. Summary of the Invention

[0005] This invention differs from existing inkjet printing parameter optimization methods by proposing a waveform optimization method oriented towards droplet behavior and film quality, utilizing machine learning modeling and multiphysics simulation. This method takes driving waveform parameters, nozzle pressure curve characteristics, and ink properties as inputs to establish predictive models for droplet velocity, volume, roundness, continuity, and satellite droplet formation. Under constraints, it solves for the optimal waveform and performs online fine-tuning of the waveform during the printing process through a feedback mechanism.

[0006] The main process of this method can be divided into the following three steps: constructing an inkjet droplet behavior dataset, training a machine learning model, optimizing the driving waveform online, and fabricating optoelectronic devices.

[0007] This invention achieves rapid optimization and online compensation of inkjet printing waveforms through a data-driven approach, reducing the probability of satellite ink droplet formation, improving film thickness uniformity and surface smoothness, and enhancing parameter migration efficiency under different material systems and printhead conditions. Attached Figure Description

[0008] Figure 1 The inkjet principle of piezoelectric ceramic printheads.

[0009] Figure 2 Multiphysics simulation of piezoelectric ceramic nozzles (two-phase flow-solid-liquid coupling-piezoelectric coupling).

[0010] Figure 3 Multiphysics simulation of inkjet process (two-phase flow-solid-liquid coupling).

[0011] Figure 4 A schematic diagram of the Pearson correlation coefficient matrix.

[0012] Figure 5 Vibration of piezoelectric ceramics as observed by a Doppler vibration meter.

[0013] Figure 6 Images of droplets flying and falling, as observed by the ink droplet observation system.

[0014] Figure 7 Current-voltage characteristic curves of small-area and large-area devices. Detailed Implementation

[0015] Based on the above description, a specific implementation process is given below. This implementation process is used to explain the principles and implementation methods of the present invention: This implementation process takes a piezoelectric inkjet printhead as the object, constructs an inkjet droplet behavior dataset, trains a stacked ensemble learning prediction model, and performs offline global optimization and online closed-loop fine-tuning with the support of the prediction model to obtain driving waveform parameters that satisfy the target droplet behavior; after obtaining the optimal waveform parameters, the inkjet printing fabrication of multilayer stacked optoelectronic devices is completed using these waveform parameters.

[0016] Step 1: Define symbols and variables

[0017] Step 1.1: Waveform Definition. The driving waveform parameter vector is denoted as u=[Rt,Dt,Ft,Dv,f], where Rt is the rise time, Dt is the hold time, Ft is the fall time, Dv is the driving voltage, and f is the injection frequency. The value range of Rt is 1.5–3.5 μs; the value range of Dt is 2.0–3.5 μs; the value range of Ft is 4.5–6.0 μs; the value range of Dv is 10–20 V; and the value range of f is 200–3000 Hz.

[0018] Step 1.2: Ink Definition. The ink operating parameter vector is denoted as m=[η,γ,ρ,pH,c_i,k_d], where η is viscosity, γ is surface tension, ρ is density, c_i is ion concentration, and k_d is drying rate parameter; the nozzle structure parameter vector is denoted as s=[d_n,V_c], where d_n is nozzle diameter and V_c is ink cavity volume. Preferably, η is 1–30 mPa·s, γ is 20–60 mN / m, ρ is 0.8–1.3 g / cm³, pH is 2–12, c_i is 0–1.0 mol / L, k_d is 0.01–5 s⁻¹, d_n is 10–60 μm, and V_c is 0.1–10 μL.

[0019] Step 1.3: Pressure definition at the nozzle. The pressure characteristic vector is denoted as p=[PP1,PP2,PP3], where PP1 is the positive pressure peak value within the 0–20 μs time window, PP2 is the first negative pressure valley value within the 20–50 μs time window, and PP3 is the second negative pressure valley value within the 50–80 μs time window.

[0020] Step 1.4: Definition of droplet behavior. The droplet behavior index vector is denoted as y=[v,V,R,CV,Ns], where v is velocity, V is volume, R is roundness, CV is continuity, and Ns is the number of satellite droplets.

[0021] Step 2: Construction of Inkjet Droplet Behavior Dataset

[0022] Step 2.1: Definition of printhead and drive waveform parameters. A piezoelectric inkjet printhead is used, and the drive waveform is a pulse trapezoidal waveform. The waveform parameters are defined as rise time Rt, hold time Dt, fall time Ft, drive voltage Dv, and ejection frequency f, and Rt, Dt, Ft, Dv, and f are each limited to the value ranges described in Step 1.

[0023] Step 2.2: Jetting Experiment and Droplet Behavior Indicators. A high-speed imaging system was used to record continuous images of the droplet from its ejection from the nozzle to its stable flight phase. The high-speed imaging frame rate was 20,000 fps, and the sampling time interval Δt was 50 μs. Threshold segmentation was performed on each frame to obtain a binary image of the droplet, yielding the droplet's projected area A, perimeter P, and centroid position x. The droplet velocity v was calculated using formula (1), the equivalent diameter D using formula (2), the droplet volume V using formula (3), and the droplet roundness R using formula (4).

[0024] (1)

[0025] (2)

[0026] (3)

[0027] (4)

[0028] To evaluate the jetting stability, M droplets were continuously jetted under the same set of waveform parameters, with M set to 100. The volume V_i of each droplet was calculated, and the droplet continuity CV was calculated according to formula (5):

[0029] (5)

[0030] Where σ_V is the standard deviation of {V_i}, and μ_V is the mean of {V_i}. The satellite droplet identification rule is as follows: when an additional ink droplet other than the main ink droplet is detected in a single ejection event, and the equivalent diameter of the additional ink droplet is less than 0.3D and the distance between the centroid of the main ink droplet and the centroid of the main ink droplet is greater than 0.5D, it is counted as a satellite ink droplet, and the number of satellite ink droplets Ns is accumulated.

[0031] Step 2.3: Nozzle Pressure Curve Acquisition and Pressure Feature Extraction. A pressure sensor is positioned 1.0 mm from the nozzle outlet to acquire the pressure-time curve P(t) at the nozzle, with a sampling frequency of 1–10 MHz. P(t) is divided into three time windows: 0–20 μs, 20–50 μs, and 50–80 μs, and pressure features PP1, PP2, and PP3 are extracted for each window. PP1 is defined as the maximum value within the first time window, PP2 as the minimum value within the second time window, and PP3 as the minimum value within the third time window.

[0032] Step 2.4: Multiphysics Simulation Feature Construction and Dataset Fusion. The finite element method is used to jointly solve for piezoelectric coupling, solid-liquid coupling, and two-phase flow, obtaining the simulated pressure curve P_s(t) at the nozzle and the droplet breakage time t_b. The simulated peak and valley values ​​of P_s(t) are extracted and combined with t_b to form the simulation feature p_s=[PP1_s,PP2_s,PP3_s,t_b]. The jetting experimental data and simulation features are merged in a one-to-one correspondence manner to form a training dataset for model training.

[0033] Step 3: Training the machine learning prediction model

[0034] Step 3.1 Sample Feature and Label Construction. For each set of candidate waveform parameters u (Dt, Rt, Ft, Dv), under the constraints of Rt=1.5–3.5 μs, Dt=2.0–3.5 μs, Ft=4.5–6.0 μs, Dv=10–20 V, and f=200–3000 Hz, jetting experiments are conducted to sample and obtain droplet behavior indices y=[v,V,R,CV,Ns] and pressure features p=[PP1,PP2,PP3]. Simultaneously, ink condition parameters m=[η,γ,ρ,pH,c_i,k_d] and nozzle structure parameters s=[d_n,V_c] are recorded. The input feature vector of the sample is defined as X=[u,m,s,p], where p can be replaced by the simulation feature p_s or concatenated with p; the output label is defined as Y=y=[v,V,R,CV,Ns]. In this embodiment, 10,000 sets of samples are constructed and divided into a training set of 7,000 sets, a validation set of 1,500 sets, and a test set of 1,500 sets.

[0035] Step 3.2 Construction of stacked ensemble learning model. For each target quantity y_k∈{v,V,R,CV,Ns} in the droplet behavior index, a stacked ensemble regression predictor F_k(X) is constructed to achieve separate prediction of multiple target quantities. Each predictor contains four base learners and one meta learner, and the input of the four base learners is X, and the output is the predicted value of the corresponding target quantity. (1) Base learner one: Multilayer perceptron regression model MLP, input is X, output is ŷ_k,MLP. MLP contains 4 hidden layers, with the number of neurons being 128, 64, 32 and 16 respectively, the activation function is ReLU, the optimizer is Adam, the initial learning rate is 0.001, the batch size is 64, and the maximum number of training rounds is 500; when the validation set MAE does not decrease for 30 consecutive rounds, training is stopped and the model parameters with the minimum number of rounds of validation set MAE are adopted. (2) Base learner two: Support vector regression model SVR, input is X, output is ŷ_k,SVR. SVR uses a radial basis kernel function with a penalty coefficient C of 10, a kernel parameter γ of 0.1, and an ε-insensitive interval parameter ε of 0.01. (3) Base learner three: Random forest regression model RF, input is X, output is ŷ_k,RF. The number of random forest trees is 300, and the maximum depth is 20. (4) Base learner four: k-nearest neighbor regression model KNN, input is X, output is ŷ_k,KNN. The number of nearest neighbors k is 7. (5) Meta-learner: Ridge regression model as a stacking layer, input is Z_k=[ŷ_k,MLP, ŷ_k,SVR, ŷ_k,RF, ŷ_k,KNN], output is the final predicted value ŷ_k. During stacked training, the base learner first fits on the training set; on the validation set, the base learner predicts the values ​​to form the secondary feature Z_k, and then trains the ridge regression meta-learner, thereby avoiding information leakage and improving generalization ability.

[0036] Step 3.3 Model Evaluation and Interpretability Analysis. The prediction accuracy of each predictor is evaluated using the Mean Absolute Error (MAE). The MAE is calculated using the following formula:

[0037] (6)

[0038] Where y_i is the true value, ŷ_i is the predicted value (y_i is ŷ_k of input Z_k; ŷ_i is output ŷ_k), and n is the number of test samples. To explain the model's decision-making basis, Pearson correlation coefficient analysis is performed on the input feature X and a correlation coefficient matrix is ​​plotted. At the same time, SHAP values ​​are calculated for the stacked ensemble predictor and the feature importance ranking is output.

[0039] Step 4: Drive waveform optimization and optoelectronic device fabrication.

[0040] Step 4.1 Objective Function Construction. The target droplet behavior is defined as follows: the number of satellite droplets Ns is minimized, the velocity v is close to the target velocity v0, the volume V is close to the target volume V0, the roundness R is maximized, and the continuity CV is minimized. The objective function J is constructed as follows:

[0041] (7)

[0042] Where w1, w2, w3, w4, and w5 are weighting coefficients, v0 is the target velocity, V0 is the target volume, and CV0 is the target continuity threshold. In this embodiment, v0 = 6 m / s, V0 = 30 pL, CV0 = 0.05, w1 = 10, w2 = 1, w3 = 1, w4 = 5, and w5 = 5.

[0043] Step 4.2 Offline Global Optimization. In the offline stage, a genetic algorithm is used to perform a global search on the waveform parameters u=[Rt,Dt,Ft,Dv,f]. For any candidate individual u, under given conditions m and s, an input feature X=[u,m,s,p_s] is constructed, and [v, V, R, CV, Ns] are calculated using the five predictors obtained in step S2. The predicted values ​​are substituted into the objective function to obtain Ĵ(u). The genetic algorithm uses 1 / (Ĵ+Ω) as the fitness function, where Ω is 1×10^−9. The parameters of the genetic algorithm are set as follows: population size 64, maximum number of iterations 100, crossover probability 0.8, and mutation probability 0.1. Fitness is evaluated for 64 individuals in each generation, and a total of 6400 candidate waveform parameters are evaluated over 100 generations, outputting the optimal offline waveform parameter u*.

[0044] Step 4.3 Online Closed-Loop Fine-Tuning. In the online phase, using the offline optimal waveform parameter u* as the initial value, droplet behavior indicators y=[v,V,R,CV,Ns] and pressure characteristics p=[PP1,PP2,PP3] are collected in real time during inkjet printing using high-speed imaging and pressure sensing, and the objective function J is minimized in a closed loop. Online fine-tuning employs a coordinate search strategy to update Rt, Dt, Ft, Dv, and f one by one. A single iteration of online fine-tuning is defined as: performing one coordinate update in the order of Rt, Dt, Ft, Dv, and f, for a total of 5 sub-updates; after each sub-update, B jet events are printed and the objective function is recalculated, where B is set to 10, velocity v, volume V, and roundness R are taken as the average values ​​of the batch, and the number of satellite droplets Ns is taken as the total number within the batch; the continuity CV is calculated using a rolling window of the most recent 100 jet events. The update step size for each parameter is as follows: 0.1 μs for Rt, Dt, and Ft; 0.1 V for Dv; and 10 Hz for f. For any parameter α∈{Rt,Dt,Ft,Dv,f} to be updated, the objective function value is calculated under both α+ and α− step perturbations, and compared with the current value. The parameter that minimizes J is selected as the update result. If neither perturbation reduces J, the current parameter remains unchanged. The updated parameters always satisfy the range constraints of Rt, Dt, Ft, Dv, and f. The maximum number of iterations for online closed-loop fine-tuning is 20, i.e., a maximum of 100 sub-updates. If the objective function decreases by less than 1% for three consecutive iterations, the process stops early and the optimal online waveform parameter u** is output; or if Ns=0 and CV≤CV0, and both |v−v0| and |V−V0| fall within the process tolerance range, the process stops early and u** is output.

[0045] Step 4.4 Optoelectronic Device Fabrication. After waveform optimization, multilayer stacked optoelectronic devices were fabricated using inkjet printing with the final waveform parameters u**. The hole transport layer, light absorption layer, electron transport layer, and electrode layer were printed sequentially. After printing, solvent evaporation and heat treatment were performed, and the film thickness uniformity, surface roughness, and device electrical performance were tested. In one embodiment, the photoelectric conversion efficiency of the small-area organic solar cell reached 20%, and the photoelectric conversion efficiency was 17.10% on a module with an area of ​​23.6 cm².

Claims

1. A method for optimizing inkjet printing parameters based on machine learning algorithms to fabricate solar cells and optoelectronic devices, characterized in that, The steps include: (1) providing a flexible or rigid substrate and determining the functional layer structure to be printed by inkjet printing; (2) setting the driving waveform of the piezoelectric inkjet printhead to a pulse trapezoidal waveform and defining the driving waveform parameter vector. Where Rt is the rise time, Dt is the hold time, Ft is the fall time, Dv is the driving voltage, and f is the injection frequency; generate N sets of candidate waveform parameters u in the preset parameter space; (3) define the ink condition parameter vector. and nozzle structure parameter vector Where η is viscosity, γ is surface tension, ρ is density, c_i is ion concentration, k_d is drying rate parameter, d_n is nozzle diameter, and V_c is ink cavity volume; (4) Spraying experiments were conducted under each group of candidate waveform parameters u and corresponding ink liquid conditions m and nozzle structure s: droplet flight images were obtained using a high-speed imaging system and ink droplet behavior index vectors were calculated. Where v is velocity, V is volume, R is roundness, CV is continuity, and Ns is the number of satellite ink droplets; simultaneously, a pressure sensor is used to acquire the pressure-time curve P(t) at the nozzle, and the pressure feature vector is extracted. PP1 is the positive pressure peak value within the 0-20 μs time window, PP2 is the first negative pressure valley value within the 20-50 μs time window, and PP3 is the second negative pressure valley value within the 50-80 μs time window; (5) The jetting experimental data obtained in step (4) are merged with the pressure and droplet formation data obtained from the two-phase flow-solid-liquid coupling-piezoelectric coupling multiphysics simulation to construct a training dataset; wherein, the input features of the training dataset are The output labels of the training dataset are (6) Train a stacked ensemble learning model based on the training dataset. The stacked ensemble learning model includes a pressure prediction sub-model and a droplet behavior prediction sub-model. The pressure prediction sub-model takes X as input and PP1, PP2, and PP3 as output. The droplet behavior prediction sub-model takes X and pressure features, i.e., the predicted pressure features output by the pressure prediction sub-model or the pressure features measured in real time by the pressure sensor, as input and v, V, R, CV, and Ns as output. (7) Construct an objective function J for waveform parameter optimization and use a genetic algorithm to perform a global search for u in the preset parameter space. The genetic algorithm is used to perform the global search for u in the preset parameter space. The population size is 64, the maximum number of iterations is 100, the crossover probability is 0.8, the mutation probability is 0.1, and the optimal waveform parameter u* is obtained through iteration; (8) The optimal waveform parameter u* is loaded into the inkjet printing device and inkjet printing is performed. During the inkjet printing process, the real-time collected y and P(t) are used as feedback, and the coordinate search strategy is used to update Rt, Dt, Ft, Dv, and f online; one online iteration is defined as updating Rt, Dt, Ft, Dv, and f once in the order of Rt, Dt, Ft, Dv, and f, and the upper limit of the number of online iterations is 20; the inkjet printing of the functional layer is completed and the solar cell and optoelectronic device are prepared.

2. The method according to claim 1, characterized in that: The inkjet printhead is a piezoelectric inkjet printhead. The inkjet printhead drives the piezoelectric actuator to deform through a driving waveform, changing the ink cavity volume and forming a pressure wave, causing ink to be ejected from the nozzle. The pulse trapezoidal waveform consists of a rising segment, a holding segment, and a falling segment. The duration of the rising segment is Rt, the duration of the holding segment is Dt, the duration of the falling segment is Ft, and the peak value of the driving voltage is Dv.

3. The method according to claim 1, characterized in that: The rise time Rt is 1.5 μs to 3.5 μs, the hold time Dt is 2.0 μs to 3.5 μs, the fall time Ft is 4.5 μs to 6.0 μs, the drive voltage Dv is 10 V to 20 V, and the ejection frequency f is 200 Hz to 3000 Hz; and during the ejection experiment or inkjet printing process, the pressure characteristics satisfy: the positive pressure peak PP1 is 4 MPa to 6 MPa, the first negative pressure valley PP2 is -4 MPa to -2 MPa, and the second negative pressure valley PP3 is -4.5 MPa to -3.5 MPa.

4. The method according to claim 1, characterized in that: The droplet velocity v is calculated using the difference in the centroid position Δx between two consecutive frames and the shooting time interval Δt. The equivalent diameter D of the droplet is calculated from the binary droplet projected area A. The droplet volume V is calculated from the droplet's equivalent diameter D. The droplet roundness R is calculated from the binarized droplet projected area A and perimeter P. The droplet continuity CV is the coefficient of variation of the volume of M continuously ejected droplets. Where M is 100, σ_V is the standard deviation, and μ_V is the mean.

5. The method according to claim 1, characterized in that: The number of satellite ink droplets Ns is obtained by the high-speed imaging system. When an additional ink droplet other than the main ink droplet is detected in a single ejection event, and the equivalent diameter of the additional ink droplet is less than 0.3D and the distance between the centroid of the main ink droplet and the centroid of the main ink droplet is greater than 0.5D, it is counted as a satellite ink droplet and added to Ns.

6. The method according to claim 1, characterized in that: The sampling frequency of the pressure-time curve P(t) is from 1 MHz to 10 MHz; the positive pressure peak PP1 is the maximum value of P(t) within the time window of 0 μs to 20 μs, the first negative pressure valley PP2 is the minimum value of P(t) within the time window of 20 μs to 50 μs, and the second negative pressure valley PP3 is the minimum value of P(t) within the time window of 50 μs to 80 μs.

7. The method according to claim 1, characterized in that: The multiphysics simulation uses the finite element method to solve the piezoelectric coupling equation, the solid-liquid coupling equation, and the two-phase flow volume function equation, outputting the pressure-time curve P_s(t) at the nozzle and the droplet breakage time t_b. The simulation pressure features PP1_s, PP2_s, and PP3_s are extracted from P_s(t). The simulation pressure features and the droplet breakage time t_b are used together with the pressure features and droplet behavior indicators obtained from the jetting experiment to expand the training dataset.

8. The method according to claim 1, characterized in that: The stacked ensemble learning model consists of a multilayer perceptron regression model, a support vector regression model, a random forest regression model, and a k-nearest neighbor regression model, and outputs the prediction results using a stacked regression approach. For any output q, the four base learners take the corresponding input features as input and output the predicted value, while the meta-learner takes the predicted values ​​of the four base learners as input and outputs the final predicted value of the output q.

9. The method according to claim 1, characterized in that: The stacked ensemble learning model undergoes interpretability analysis after training, which includes Pearson correlation coefficient analysis, SHAP value analysis, and feature importance ranking.

10. The method according to claim 1, characterized in that: The solar cells and optoelectronic devices mentioned are organic solar cells, perovskite solar cells, quantum dot solar cells, organic light-emitting diodes, or organic field-effect transistors.

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