FMEA-TSTM-NNGA: A Novel Optimization Framework Integrating Failure Mode and Effect Analysis, the Taguchi Method, a Neural Network, and a Genetic Algorithm for Improving the Resistance in Dynamic Random Access Memory Components

Abstract

Dynamic random access memory (DRAM) serves as a critical component in medical equipment. Given the exacting standards demanded by medical equipment products, manufacturers face pressure to improve their product quality. The electrical characteristics of these products are based on the resistance value of the DRAM components. Hence, the purpose of this study is to optimize the resistance value of DRAM components in medical equipment. We proposed a novel FMEA-TSTM-NNGA framework that integrates failure mode and effect analysis (FMEA), the two-stage Taguchi method (TSTM), neural networks (NN), and genetic algorithms (GA) to optimize the manufacturing process. Moreover, the proposed FMEA-TSTM-NNGA framework achieved a substantial reduction in experimental trials, cutting the required number by a factor of 85.3 when compared to the grid search method. Our framework successfully identified optimal manufacturing condition settings for the resistance values of DRAM components: Depo time = 27 s, Depo O2 flow = 151 sccm, ARC-LTO etch time = 43 s, ARC-LTO etch pressure = 97 mTorr, Ox-SiCO etch time = 91 s, Ox-SiCO gas ratio = 22%, and Polish time = 84 s. The results helped the case company improve the resistance value of DRAM components from 191.1 × 10⁻³ Ohm to 176.84 × 10⁻³ Ohm, which is closer to the target value of 176.5 × 10⁻³ Ohm. The proposed FMEA-TSTM-NNGA framework is designed to operate efficiently on resource-constrained, facilitating real-time adjustments to production attributes. This capability enables DRAM manufacturers to swiftly optimize product quality.

1. Introduction

The overall usage of DRAM has been greatly improved, particularly in applications like telemedicine, as the health sector increasingly relies on digital solutions. This trend is expected to continue, with the pandemic accelerating the intensified use of technology in healthcare settings, thereby raising the demand for DRAM components in medical applications [1]. As the demand for high-performing memory tools capable of handling large volumes of data and performing tasks quickly and reliably grows, medical devices are increasingly utilizing DRAM components. As medical technologies advance, DRAM plays a significant role in optimizing devices used for diagnosis, sensing the presence of illnesses, and various other healthcare purposes [2].

Healthcare equipment and appliances require enhanced precision and reliability, and the same is true for the DRAM components used in these devices. This underscores the need for DRAM to meet the stringent demands of complex medical applications that require high performance and data authenticity. The evolution of medical technology requirements indicates a growing need for DRAM with greater stability and performance characteristics [3,4].

These devices are critical instruments in diagnosis and in the monitoring of various physiological parameters, which are crucial for clinical assessment. For example, information from an accurate analysis of olfactory evoked potentials may greatly aid in understanding neurological functions and diagnosing related disorders [5]. Similarly, advancements in deep learning algorithms, such as ResUNet for liver and tumor segmentation in CT images, enhance the level of detail in medical imaging, thereby improving the diagnosis of medical conditions [6]. These technologies ensure that accurate and efficient medical equipment relay information that facilitates informed decision making by healthcare practitioners in patient management.

Regarding a sustainable smart healthcare system, regulations focus on efficacy, dependability, and risk assessment for smart healthcare technology. These stringent requirements arise because healthcare applications are typically mission-critical, where errors can be costly. It is crucial to ensure that all medical devices and systems meet these standards to safeguard patient well-being and deliver dependable healthcare solutions. The COVID-19 pandemic has amplified the need for these criteria, rendering durable and reliable health IT essential to the system [7].

DRAM components are embedded in various types of medical analysis and application devices, including ventilators, medical tablets, medical computers, and physiological monitoring systems. These components provide the memory storage and speed needed to handle substantial amounts of critical data processed in real time, enabling the smooth and effective functioning of medical devices. Integrating DRAM into these systems is crucial for meeting the performance and stability requirements of medical applications [8,9].

Therefore, the difference between the theoretical resistance of DRAM components and the intended value should be as small as possible to ensure optimal results. Significant resistance deviations in DRAM components can lead to disruptions in electronic signals and a reduction in the quality and yield of medical products. This study is set in a semiconductor firm in the Hsinchu Science Park in Taiwan, which specializes in producing DRAM components. During production, the firm encountered issues with electronic signals in DRAM parts, and a further examination revealed that the resistance fluctuations in the DRAMs with signal problems were beyond tolerance. To facilitate timely shipping and meet customer demand, this study will assist the company in analyzing and enhancing these aspects.

During production, if the yield rate is too low, production engineers need to constantly monitor the production situation. Low production yield rates can affect the shipping schedule, so customers often request rapid improvements in production yield rates. To improve product yield rates, production engineers often use previous production data for predictive improvement. Although there is a lot of production data, most of it falls within the specification tolerance range, which can only be predicted within that region, not beyond it. Because of these limitations, the results of yield rate improvements are often not very significant. In addition, when production engineers conduct product improvement experiments, they often use trial-and-error methods, which consume a large amount of experimental resources. Moreover, these trial-and-error experiments often result in imbalanced data, which increases the prediction error.

In order to improve the resistance values of DRAM components in medical equipment, it is necessary to first collect a high-quality dataset for predicting the resistance values of DRAM components. Therefore, there is a need to introduce a fast and effective data collection method. Before collecting data, it is necessary to identify the important production attributes on the production line. Thus, this study will use the FMEA and Taguchi method to identify the important production attributes with the minimum number of experiments and help the case company obtain the most valuable production data. Then, the Taguchi experimental data will be integrated with artificial neural network for modeling, in order to find the best attribute setting of production attribute to assist the case study in improving the resistance values of DRAM components.

2. Motivation for Problem Description

The resistance values of DRAM components in medical equipment can vary due to different production attributes settings. As the manufacturing process becomes more complex, improving the resistance value of DRAM components requires considering multiple possible production attributes. During production, production engineers often rely on past engineering experience to make improvements, which can be time-consuming and delay product shipping schedules. Companies often find that their equipment schedules are overloaded, customers require tight improvement times, and experiment resources are limited, among other constraints. Therefore, in order to meet shipping schedule as quickly as possible, the best production attribute level setting must be determined within a short period of time.

The semiconductor manufacturing processes affecting the resistance of DRAM components include deposition, photolithography, etching, and polishing [10,11,12,13] and are described below:

(1)

Thin film deposition operates by building up structures on a wafer using different types of materials in a layered manner. The first deposition method is chemical vapor deposition (CVD), which involves the use of corrosive gasses and chemicals which provide a thin covering to the wafers upon a chemical reaction. First of all, the gas containing target material is injected into the reaction chamber, and the wafer is located in this chamber. After that, by adjusting parameters such as the temperature and pressure, the gas molecules are prompted to chemically react with the aim of depositing the correct thin film material. These materials are deposited at the surface of the wafer, and after some time, they stack up and develop a film-like structure. The second deposition technique is physical vapor deposition (PVD), which is an advanced technology that transfers physical state materials into a gas or plasma state and deposits them on the surface of the wafer. Some PVD technologies are sputter deposition and evaporation deposition. Often, the material that is going to be deposited in any PVD technique becomes heated or is bombed first so that it can evaporate in the form of gas or plasma. These high-energy particles are then directed to the surface of the wafer, and in the process of collision, it is transformed into a thin film structure.

(2)

A microfabrication technique that is closely related to the manufacturing of a semiconductor is photolithography, where fine semiconductor circuit patterns are printed. The four sub-process operations are cleaning, photoresist application, exposure, and development, which the wafers undergo in the main process. Before photolithography is carried out, there is always a need to cleanse the wafer to remove any particles which may hinder the photolithography process. The cleaning methods which are employed for the wafers are solution washing, high-pressure water cleaning, and ultrasonic cleaning. Then, a layer of material known as the photoresist, a polymer that can be dissolved by exposure to light of a specific wavelength, is formed on the wafer’s surface. The photoresist is typically used and can be dispensed uniformly on the surface of the wafer by the spin-coating method. Incidentally, the photomask may be exposed to a light source of a given wavelength with the intention of projecting some patterns on the surface of the wafer. These light rays will only pass through the parts of the photo res dose where the thickness of the photo res dose will be consistent with that of the underlying layer, and they will not pass through areas where the layers of the photo res dose will have to be stripped off. Finally, the wafer is put into a developer solution where the other parts of the photoresist layer exposed to light are dissolved. This method is called positive photoresist development, where the exposed layer of the photoresist becomes the pattern in the shape and size of the required design.

(3)

In the etching process, the un-masked areas in the wafer are chemically or physically etched to make the circuit structure of the required semiconductor materials by erasing the unwanted areas. Dry etching can be described as the technique of taking material on a wafer’s surface by means of gas plasma or reactive plasma. In the course of the dry etching process, the wafer is located in the vacuum chamber, and a gas flow containing the reactive gas is used. Finally, the gas experiences a reaction under plasma excitation, which allows the removal of material deposited on the surface of the wafer. Wet etching also involves the process of removing material on the wafer’s surface by an actual chemical process which occurs in a liquid medium. In the wet etching process, the wafer is completely submerged in a bath which contains an etching solution. The etching solution decomposes chemically with the materials on the wafer, and this results in their removal.

(4)

The polishing process is employed in the manufacturing process to planarize the wafer. The steps include coarse polishing, fine polishing, cleaning, and inspection. First, the wafer is placed on the rotating polishing disk, and then, with the polishing particles, a preliminary polish is performed to minimize surface roughness, protrusions, and depressions on the wafer. However, an additional step of planarization is required to further smooth the wafer’s surface. This step uses the smallest polishing particles and the highest pressure to achieve the desired flatness. During the polishing process of ion-implanted silicon wafers, polish debris and dirt are extensively produced. Therefore, it is necessary to perform chemical or physical cleaning on the wafer’s surface to meet the required cleanliness and smoothness conditions, as the presence of high amounts of polishing powder and dirt may hinder this. After polishing and cleaning, there may still be slight roughness or scratches on the wafer’s surface in terms of flatness. To further enhance the flatness and surface quality of the wafer, other methods like chemical mechanical polishing or even conventional mechanical polishing can be employed. Lastly, the wafers are required to undergo a final cleaning step to ensure that the entire surface is free of any dirt and polishing residue and to verify that the wafer’s flatness meets the required standards.

3. Methodology

3.1. Taguchi Method

The Taguchi method (TM) is an experimental design method which can be used to improve the product quality of manufacturing processes [14,15]. One of the key characteristics of the Taguchi method is the use of orthogonal arrays (OA). OA can make the experiment more efficient [16].

Table 1. Orthogonal array L₁₂(2¹¹).

No	A	B	C	D	E	F	G	H	I	J	K
1	1	1	1	1	1	1	1	1	1	1	1
2	1	1	1	1	1	2	2	2	2	2	2
3	1	1	2	2	2	1	1	1	2	2	2
4	1	2	1	2	2	1	2	2	1	1	2
5	1	2	2	1	2	2	1	2	1	2	1
6	1	2	2	2	1	2	2	1	2	1	1
7	2	1	2	2	1	1	2	2	1	2	1
8	2	1	2	1	2	2	2	1	1	1	2
9	2	1	1	2	2	2	1	2	2	1	1
10	2	2	2	1	1	1	1	2	2	1	2
11	2	2	1	2	1	2	1	1	1	2	2
12	2	2	1	1	2	1	2	1	2	2	1

shows the Taguchi orthogonal array L₁₂(2¹¹). The letters A~K in the OA represent different production attributes, while the numbers 1 and 2 represent the two different levels for each production attribute. Each column in OA represents a specific production attribute. L₁₂(2¹¹) has a total of 11 columns, which means that up to 11 production attributes can be arranged. The number of columns in OA corresponds to the number of experiments, so the number of experiments in the L₁₂(2¹¹) orthogonal array is 12.

Genichi Taguchi developed SN (signal-to-noise) to assess the impact of manufacturing process attributes on product quality. SN is a measure of the quality of a signal relative to the background noise. In manufacturing, SN can be used to identify key attributes that significantly affect product quality. A higher SN indicates greater process stability and higher product quality. Conversely, a lower SN indicates process instability, which may require corrective measures. The SN can be categorized into three types based on quality requirements [17]: Nominal The Better (NTB), Smaller The Better (STB), and Larger The Better (LTB), each with a corresponding Formula (1)–(3). The SN has become an essential tool in quality control and improvement, widely applied by industries worldwide.

In this context, $\overline{y}$ denotes the average value of a group of experiments; while m represents the target quality value; S² represents the variance of each group of experiments. It is calculated as the sum of the squared deviations from the mean, divided by the degrees of freedom; The value of the i^th experiment is denoted by y_i, and n represents the total number of experiments conducted.

$${SN}_{NTB}=-10\mathit{log}\left[{\displaystyle \frac{{\sum }_{i=1}^n(y_i-m{)}^2}{n}}\right]=-10\mathit{log}\left({\displaystyle \frac{S^2}{{\overline{y}}^2}}\right)$$

(1)

$${SN}_{STB}=-10\mathit{log}{\displaystyle \frac{{\sum }_{i=1}^n{y}_i^2}{n}}=-10\mathit{log}({\overline{y}}^2+S^2)$$

(2)

$${SN}_{LTB}=-10\mathit{log}{\displaystyle \frac{{\sum }_{i=1}^n\frac{1}{y_i^2}}{n}}$$

(3)

The algorithmic process of the Taguchi method is as follows:

(1)

Problem Definition and Objective Setting: The output attributes and the inputs related to the performance, for instance, the quality of the product, are determined. When writing down the specifications, it is necessary to state the target performance issues of the system as well as define its target values or response curves if any.

(2)

Experimental Design: The control factors that define the system’s performance are chosen and their possible levels are defined. As noted in the Taguchi method, it is possible to test more than one input factor. It is recommended to apply Taguchi’s orthogonal array to build an experimental matrix that would cover all possible combinations of the factor level settings.

(3)

Experimentation and Data Collection: Experiments are performed on the basis of designed specifications of the input and output characteristics. For each run of the experiment, the response values (the output characteristics) are documented.

(4)

Data Analysis: Regarding quality characteristics, the SN is used in order to determine the stability of the system. On that basis, the key factors that play a crucial role in shaping the output characteristics are defined, and their importance is assessed.

(5)

Optimization and Validation: Multiple comparison is performed using the post hoc test to define the best level of the factor on the basis of the mean value of the SN ratio and the ANOVA. Using a practical test or more precise factor confirmation experiments, the advantages of the selected factor setting are confirmed.

The pseudo code of the Taguchi method is determined as follows:

(1)

Define the Problem

−

To ensure clarity on what the experiment would set out to achieve, the following is carried out:

−

The output (response) characteristics, which should be optimized, are identified.

−

The relations between the input factors (variables) and output are determined.

(2)

Select Factors and Levels

−

The research objectives and questions or hypotheses are formulated for the control factors for the study.

−

The method used to measure each factor is described.

(3)

Design the Experiment

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An appropriate orthogonal array is chosen depending on the factor number and level number.

−

The experimental matrix is developed through the choice of orthogonal array, chosen above.

(4)

Conduct the Experiments

−

The experiments are carried out as per the design matrix laid out above.

−

A record of the final output values obtained at the end of each of the experimental runs is made.

(5)

Analyze the Data

−

The signal-to-noise (SN) ratio values of each experimental runs are determined.

−

The trends in the SN ratios could be analyzed in order to obtain an idea about the performance of the system.

−

An analysis of variance (ANOVA) test is performed to determine the contribution of each factor.

(6)

Optimize the Process

−

The combination of factor levels is determined, which could be considered as optimal according to the analysis.

−

All of the process parameters are changed to the best possible values.

3.2. Artificial Neural Network

Artificial neural networks (ANNs) are among the most popular tools used for data analysis. This approach involves the creation of a model through the use of statistics from a given dataset of input attributes and output variables. The model identifies the interdependence of variables and can be used for prediction, decision making, and diagnosing engineering problems, as pointed out in [18].

In fact, to train a neural network, the weights of the links between neurons must be changed iteratively. An important fact is that weights determine the probabilities of activation in connected neurons and affect the output variable. Neural networks are formed by integrating several neurons; this can be explained by the following reasons [19]. In Figure 1 below, we provide a three-layer neural network architecture. The training process in the network has to be performed multiple times so that the input attributes are mapped correctly to the right output variable. The primary goal of training is to minimize error and ensure the output value of the neural network is as close as possible to the engineering target. This means that training is considered complete once the error rate no longer fluctuates, thus suggesting that the network has completely converged. It then requires evaluation on a set of samples that were never used in training to ensure that the predicted value matches the output variable in the sample set [20]. With respect to training neural networks, the learning rate is generally a hyperparameter that determines the speed at which the network converges. The advantage of a higher learning rate is that it results in convergence at a much faster rate than a lower learning rate [21,22].

The pseudo code of an artificial neural network is determined as follows:

(1)

Initialize the Network

−

The number of neurons in the input layer, hidden layer, and output layer is decided.

−

Initial values of the weights and biases are assigned with respect to each neuron (these may preferably be assigned randomly).

(2)

Forward Propagation

−

The following is carried out for each input sample:

• Input Layer:

  −

  Let the input layer take in the input data.

• Hidden Layer:

  −

  The following is carried out for each hidden layer neuron:

  −

  The weighted sum of inputs is found, and bias is added to them.

  −

  An activation function, such as ReLU, sigmoid, or other, is applied to the sum.

• Output Layer:

  −

  The following is carried out for each output neuron:

  −

  The sum of the products of the weight in the connection between two neurons and the hidden layer’s output plus the bias term are found.

  −

  An activation function is applied to the sum to come up with the final output.

(3)

Calculate Loss

−

The difference between the predicted output and the target output is found by using a loss function, e.g., mean squared error or cross entropy.

(4)

Backpropagation

−

The backpropagation algorithm is used to determine the gradient with respect to all of the weights and biases of the network.

−

The following is carried out for each layer:

• The derivative of the activation function is determined.
• The first-order derivative of the loss with the weights and the biases is calculated.
• The weights and the biases are updated according to the gradients calculated at the beginning of the current iteration.

(5)

Iterate

−

Steps 2–4 are repeated for a certain number of epochs or until the loss function falls within an acceptable range.

(6)

Output the Results

−

Once training is complete, the network can be used to predict the outputs of other inputs.

−

The effectiveness of the network is assessed using a testing dataset.

3.3. Genetic Algorithm

Holland J. developed the genetic algorithm (GA) in 1975. Since then, the GA has undergone extensive development. The GA has been shown to be an effective search algorithm, especially in the proposed model, as it can locate the global optimal solution rather than just a local one. Through natural selection, the GA identifies the fittest set of individuals to survive, forming an adaptive optimization technology capable of searching the high-dimensional solution space.

The GA is widely used in work related to hyperparameter tuning in machine learning models and engineering parameter optimization [23]. The evolutionary process of the GA consists of three main steps: chromosome replication or duplication, crossover, and mutation. The GA operates in the solution space of engineering problems, and after multiple iterations, it finds the most adaptable solution that satisfies all constraint conditions. This is the chromosome with the highest fitness function value, which is the global optimal solution [24]. The algorithmic process of the GA is as follows:

(1)

Initialize population: First, a set of potential solutions is randomly created, which forms the first generation of the population.

(2)

Evaluate population: The performance value of each possible solution is measured, and it is referred to as the fitness function value.

(3)

Select parents: Some solutions with high fitness function values are chosen as parents. In most cases, roulette wheel selection or the elite preservation strategy is employed for the selection of parents.

(4)

Crossover: Two parents are randomly chosen to crossover in order to create two new chromosomes.

(5)

Mutation: Sometimes, it is necessary to mutate the offspring with some certain probability in order to avoid falling into local optima.

(6)

Select next generation: Numbers of offspring and parents are chosen as the next generation of the population.

(7)

Iteration steps 2 to 6 are performed over and over until either the condition for convergence is reached or the maximum number of iterations has been exhausted.

(8)

Finally, the candidate with the highest objective value is chosen as the global optimal solution to the presented mathematical model.

The pseudo code of the genetic algorithm is determined as follows:

(1)

Initialize Population

−

The first generation of the candidate solutions, commonly known as the chromosomes, is produced.

−

Each chromosome is a candidate solution, and most commonly, these chromosomes are stored as binary strings of numbers and real numbers, amongst other formats.

(2)

Evaluate Fitness

−

The following is carried out for each chromosome in the population:

• The chromosome is translated into the solution on the chromosome it represents.
• Another measure of the solution obtained is determined by considering the goal or objective function of the problem.

(3)

Selection

−

Parent chromosomes in the current population are chosen using the fitness measure defined.

−

Higher fitness enhances the likelihood of selection, for example, by means of roulette wheel and tournament selections.

(4)

Crossover

−

The following is carried out for each pair of selected parents:

• The crossover point(s) is selected as a victim.
• Equal segments of the parent’s chromosomes are exchanged at crossover point(s) to form the offspring commonly referred to as children.

−

With a certain crossover probability, a crossover operation should be performed in order to generate new offsprings.

(5)

Mutation

−

The following is carried out for each offspring:

• A possibility of mutation is created that will cause some arbitrary change to some genes in the chromosome.
• It must be ensured that mutation contributes to the creation of diversity but does not interfere with searching.

(6)

Create New Population

−

The waiting list state is populated by replacing the old population with the new population, which is the offspring.

−

Optionally, some of the chromosomes with good quality are transferred to the old population in order to guarantee the existence of good solutions.

(7)

Iterate

−

Steps 2–6 are repeated for a specified number of generations or until a termination condition is met (e.g., the fitness threshold or maximum number of generations).

(8)

Output the Best Solution

−

After the final generation, the chromosome with the highest fitness is identified and output as the best solution found by the algorithm.

4. The Proposed Methodology

To improve the quality of DRAM components in medical equipment within a limited timeframe, this study employed a novel FMEA-TSTM-NNGA framework, which integrates Failure mode and effect analysis (FMEA), two stage Taguchi method (TSTM), artificial neural network (NN), and genetic algorithm (GA). The primary objective is to aid the case company in enhancing product yield despite resource and time limitations. Using these methods, the research aims to improve the resistance value of DRAM components, thereby achieving a higher yield rate.

To ensure high-quality data, Taguchi method can be a beneficial approach. Unlike trial-and-error or one-factor-at-a-time experiments, Taguchi method allows for the simultaneous consideration of multiple production attributes on the resistance value of DRAM components under different experimental level settings. This Taguchi method also helps balance data, using the characteristics of orthogonal arrays. Moreover, Taguchi method can aid in identifying important production attributes that affect the resistance of DRAM components. Traditionally, companies have relied on work experience to select important production attributes for experiments. However, this approach can result in the testing of insignificant effects, wasting valuable experimental resources. By determining the important attributes of the product before initiating quality improvement efforts and then optimizing and adjusting them, companies can more efficiently achieve the best quality performance of the product.

Taguchi method is a useful for finding an optimal production attribute setting under a specific experimental setting level. However, Taguchi method may only identify a local optimal solution rather than the best global production attribute setting for the entire experimental region. To address this limitation, artificial intelligence algorithms such as artificial neural network and genetic algorithms can be used to further optimize product quality.

Artificial neural networks are particularly well-suited for performing nonlinear modeling on the complex relationship between input production attributes and the resistance of DRAM components. The predictive model can then be used to help identify the best production attribute setting across the entire experiment region. By incorporating these AI techniques into the design and optimization process, companies can achieve even better product quality while minimizing the amount of time and resources spent on experimentation.

The proposed methodology of this study can be divided into seven steps, as shown in Figure 2. A schematic diagram of the methodology is provided in Figure 3.

• Defining the problem: In this step, the existing abnormal phenomena and their yield loss rate of defects in the case study are described. The manufacturing process that may be causing the abnormalities is identified based on the adverse phenomena observed.
• Using FMEA to assess production attributes: FMEA was used to assess the production attributes affecting memory component resistance in thin film deposition, etching, plating, and polish processes. Relevant production attribute setting is then identified to improve the average resistance of DRAM components in the medical equipment through the optimization of these production attributes.
• Applying first stage Taguchi method to find important attributes: In this step, we will use the Taguchi method L₁₂(2¹¹) orthogonal array to collect experimental data. We will then use attribute response tables, attribute response charts, and ANOVA (analysis of variance) tables to analyze the data and identify important production attributes that affect the average resistance of DRAM components. At present, many researchers have used Taguchi method to assist in the optimization and improvement of engineering problems. Gao and Zhou (2024) employs the Taguchi Method to conduct sensitivity analysis on operating parameters for a proton exchange membrane fuel cell (PEMFC) combined heat and power (CHP) cogeneration system in variable climate regions, proposing cost-effective strategies for electricity- and heat-dominated outputs [25]. Xie et al. (2024) used the Taguchi method to explore key parameters in pure waterjet surface treatment of Ti6Al4V specimens, emphasizing the significance of operation pressure for biomaterial surface fine-tuning [26]. Tanürün et al. (2024) employed the Taguchi method to optimize Vertical Axis Wind Turbine (VAWT) performance with an adaptive flap design, achieving a 74.01% increase in power coefficient (CP) compared to conventional VAWTs, with flap position identified as the most influential factor [27]. Lu et al. (2024) used the Taguchi method to optimize CO₂ laser polishing of fused silica, revealing laser beam scanning speed as a crucial factor, resulting in a substantial reduction in surface roughness from Ra = 0.157 μm to 0.005 μm [28]. Yang et al. (2024) utilized the Taguchi method and Gray relation analysis to identify the optimal design parameters (perforation length, height, and tilt angle) for slit fins with lateral perforations, achieving the highest j-factor and lowest f-factor [29]. Based on the empirical evidence presented in the literature, it is clear that Taguchi’s experimental design can effectively assist researchers in identifying important parameters across various fields and finding optimal parameter settings for different engineering problems.
• Applying second stage Taguchi method to recollect data and find out the optimal attribute setting: To collect experimental data, we used the Taguchi method L₁₈(2¹ × 3⁷) orthogonal array. We conducted a second Taguchi method in the production attribute region, with the aim of recollecting experimental data that could potentially contain optimal solutions using the L₁₈(2¹ × 3⁷) orthogonal array. We analyzed the collected data using attribute response tables, attribute response charts, and ANOVA table to determine the optimal attribute setting in the region.
• Using artificial neural networks to build a model: To construct the relationship between the important production attributes and the resistance value of DRAM components of medical equipment in the L₁₈(2¹ × 3⁷) orthogonal array, an artificial neural network can be used. Recent studies frequently use neural networks to establish relationships between production attributes and response variables, and subsequently use these models to determine the optimal attribute settings and enhance product quality. Acharjee et al. (2024) developed two artificial neural network based models (W-ANN and H-ANN) for predicting dynamic modulus in Colombian hot-mix asphalt mixtures, outperforming previous models and providing practical tools for pavement design with reduced testing requirements [30]. Liu (2024) presents a sensor array based on noble metal-doped In₂O₃, employing a back propagation neural network (BPNN) integrated with the whale optimization algorithm (WOA) for anti-interference detection of mixed NOX, achieving quantitative prediction of components in the presence of cross interference [31]. Mudawar et al. (2024) employed artificial neural networks to predict heat transfer and critical heat flux (CHF) in both microgravity and Earth gravity [32]. Sayed et al. (2024) applied artificial intelligence (ANN and FBI) to optimize yeast and wastewater concentrations in a microalgae microbial fuel cell, achieving significant improvements in power density and COD removal [33]. Sanni et al. (2024) employed an adaptive neuro-fuzzy inference system (ANFIS) to model the corrosion rate of AISI 316 stainless steel under various inhibitor dosages and schedules, achieving superior prediction accuracy [34].
• Adopting genetic algorithm to identify the best production attribute setting: The genetic algorithm will be used to identify the best setting of production attribute levels across the entire production attribute region. Many researchers have also confirmed the feasibility of the genetic algorithm. Park et al. (2024) integrated genetic algorithms and deep learning to enhance the I-V modeling of DRAM transistors, addressing limitations of the BSIM model and accurately modeling devices with hot-carrier degradation effects [35]. Mukhanov et al. (2020) introduced DStress, a framework using genetic algorithms to identify worst-case DRAM error patterns, enhancing testing by detecting critical reliability issues and improving testing mechanisms [36]. Leu et al. (2021) used genetic algorithms to reduce thickness deviation in DRAM manufacturing. The approach successfully decreased deviation from 45.0 to 12.9 Å [37]. Babu et al. (2024) proposed a novel IoT network optimization strategy using a genetic algorithm (GA) for energy efficiency and mixed integer linear programming (MILP) for node deployment, with blockchain enhancing data privacy; outperforming existing models in network lifetime and throughput [38]. Nigam et al. (2024) accelerated molecular design using a genetic algorithm and an artificial neural network, identifying over 10,000 potential organic emitters with inverted singlet-triplet gaps (INVEST) and appreciable fluorescence rates for potential use in new-generation organic light-emitting diodes [39]. Wang et al. (2024) applied an improved genetic algorithm for optimal scheduling in hybrid energy ship power systems, reducing costs and environmental impacts [40]. Bhat et al. (2024) enhanced aluminum alloy design using machine learning, incorporating data-driven classes and genetic algorithms for feature optimization, achieving improved tensile strength and elongation predictions [41]. Ildarabadi et al. (2024) applied a genetic algorithm with elitism mechanism to optimize the cost of restoring power to a distribution network after disasters by building Tie-lines between damaged and healthy sections [42]. GA is an optimization technique that can be applied to a wide range of engineering problem areas. Therefore, it is favored by researchers who want to find optimal solutions to complex problems.
• Performing confirmation experiments and comparisons: After identifying the optimal settings for production attributes, confirmation experiments are carried out to confirm the efficacy of the suggested methodology., and the results are compared with the average resistance of DRAM components before improvement to confirm the effectiveness of the improvements.

The pseudo code of the proposed methodology is determined as follows:

(1)

Define the problem.

−

The various abnormal phenomena and the yield loss rate of defects that is associated with it are explained.

−

The manufacturing processes that is responsible for the formation of such abnormalities is determined.

(2)

Examine the possibility of failure in the future and identify product attributes in the FMEA.

−

The FMEA is used to assess the production characteristics that impact memory component resistance.

−

The critical production attributes of thin film deposition, etching and plating, and polishing are determined.

−

The optimal settings of the production attributes that will cause the DRAM components to have an average resistance greater than past records are determined.

(3)

Use the first stage of the Taguchi method.

−

The L₁₂(2¹¹) orthogonal array is chosen to plan the experiments.

−

Research is conducted and information is obtained.

−

The analysis of attribute data can be carried out with the help of attribute response tables, response chars, and an ANOVA in order to determine important production attributes influencing DRAM component resistance.

(4)

Use the second stage of the Taguchi method.

−

Further experimentation should be carried out using the L₁₈(2¹ × 3⁷) orthogonal array.

−

More tests should be conducted in order to gather information on the area of important attributes.

−

This means that one has to perform the analysis of the obtained data to identify the appropriate values of production attributes.

(5)

Develop a model employing artificial neural networks.

−

An artificial neural network is performed with the dependent variable of resistance values of DRAM components, with the independent variables being the important production attributes.

−

The neural network model should be trained and validated using the experimental data collected from the second stage of the Taguchi method.

(6)

Optimize the production attribute settings with the genetic algorithm.

−

A genetic algorithm search is performed regarding the overall attribute region of the production attribute in order to obtain the global optima of the attribute settings.

−

The suitability of several contexts is analyzed and the most appropriate one is determined.

(7)

Confirmation experiments and comparison.

−

Confirmation experiments are carried out using the best production attribute settings which were found.

−

The findings are assessed with pre-change data to ensure that the above proposed methodology has a powerful impact.

−

Details, especially the outline of the results of their work, are determined with an emphasis on increases in the average resistance of DRAM parts.

5. Case Study

Details Content of the Proposed Methodology

There are seven steps involved in the proposed methodology:

(1)

Problem Definition

This case study is based on a DRAM manufacturing company located in Hsinchu Science Park, Taiwan. In 2023, it was discovered that abnormal resistance values occurred in the DRAM manufacturing processes. By the second half of 2023, the number of abnormal wafers had reached 360, and the yield loss rate had increased to 1.89%, significantly impacting the DRAM quality. To address the abnormality of the DRAM components, the company analyzed the production data from 2023 and created a trend chart of weekly average resistance values, as shown in Figure 4. The chart indicates a gradual increase in the resistance values of the DRAM components, with the abnormal position occurring at RM5_01 in a memory component, as shown in Figure 5. The primary reason for the abnormal resistance value was not optimized production attributes in the deposition, etching, plating, and polishing processes. This study analyzes the production data of DRAM components from 2023 and finds that the average resistance value is 191.1 × 10⁻³ Ohm, which exceeds the target value of 176.5 × 10⁻³ Ohm specified by the customer. These findings are shown in Figure 6. Therefore, the purpose of this study is to optimize the production attributes of these DRAM components to improve their average resistance value and meet the customer’s specification target in a short period.

(2)

Using FMEA to assess production attributes

The semiconductor manufacturing processes that impact the resistance of DRAM components in medical equipment primarily include thin film deposition, etching, plating, and polishing processes. These processes have specific names, namely SiCO TF depo, ARC-LTO etch, Oxide-SiCO etch, Cu ECP, and Cu polish, as shown in Figure 7. The abbreviations used in Figure 7 are SiCO for Silicon-OxyCarbide, ARC for Anti-Reflective Coating, LTO for Low Temperature Oxide, and ECP for Electro-Chemical Plating.

To assess the production attributes that may affect the resistance of DRAM components in the thin film deposition, etching, plating, and polish processes, the case company formed a group of production engineers to improve the relevant production attributes for these processes. The production engineers evaluate three indicators, Severity (S), Occurrence (O), and Detection (D), based on the criteria of failure mode and effect analysis (FMEA). Severity (S) presents the magnitude of the impact of a failure. Severity is assessed on a scale of 1 to 10, where 1 indicates a minor impact and 10 indicates a very severe impact. Occurrence (O) shows the probability of a failure occurring. The probability is evaluated on a scale of 1 to 10, where 1 indicates a very low probability and 10 indicates a very high probability. Detection (D) presents how easily a failure can be detected when it occurs. Detection is assessed on a scale of 1 to 10, where 1 indicates detection is easy and 10 means detection is very difficult.

The corresponding S, O, and D values are assessed for each production attribute, and the risk priority number (RPN) is calculated as the process of S, O, and D. A higher RPN value indicates a higher risk, requiring the implementation of more control measures to mitigate the risk. The results of this evaluation are shown in

Table 2. Relevant attributes in the production process of DRAM components.

No	Process	Attributes	Severity	Occurrence	Detection	RPN
1	SiCo TF-depo	HtrSpace1/HtrSpace2	3	4	4	48
2		Pressure (Torr)	4	3	3	36
3		RF1Time/RF2Time (s)	7	8	2	112
4		HighFreqRF1Pwr/HighFreqRF2Pwr (W)	3	4	3	36
5		LowFreqRF1Pwr/LowFreqRF2Pwr (W)	5	4	3	60
6		OMCTS Flow Set (mgm)	2	3	2	12
7		HE_OMCTS Flow Set (sccm)	3	4	4	48
8		O2 Flow Set (sccm)	2	4	4	32
9	ARC-LTO etch	E.Time (s)	3	4	2	24
10		Pressure (mTorr)	9	8	3	216
11		RF Power 60 MHz	3	3	4	36
12		RF Power 13.56 MHz	2	4	4	32
13		HV (-V)	3	2	3	18
14		Gas O2 (sccm)	5	3	4	60
15		Gas CF4 (sccm)	2	3	4	24
16		Gas CHF3 (sccm)	4	2	4	32
17		Gas ratio (center%)	2	3	4	24
18		Temp Top (°C)	4	4	3	48
19		Temp Wall (°C)	3	4	3	36
20		Temp Bottom (°C)	3	4	3	36
21	Oxide-SiCO etch	E.Timt (s)	7	7	3	147
22		Pressure (mTorr)	3	5	3	45
23		RF Power (W) 60 MHz	3	4	4	48
24		RF Power (W) 13.56 MHz	3	3	4	36
25		HV (-V)	3	3	3	27
26		Gas O2 (sccm)	5	3	4	60
27		Gas CF4 (sccm)	2	4	4	32
28		Gas CHF3 (sccm)	9	5	4	180
29		Gas ratio (center%)	8	4	4	128
30		Temp Top (°C)	5	3	3	45
31		Temp Wall (°C)	2	3	3	18
32		Temp Bottom (°C)	3	3	3	27
33	Cu polish	Head States: Zone 1–5 (psi)	6	8	4	192
34		End Step Criteria: Max Time (s)	7	8	2	112

. Based on the team’s professional experience, they selected ten production attributes that may affect the DRAM components in medical equipment. These attributes include Depo time (s), Depo He flow (sccm), Depo O2 flow (sccm), ARC-LTO etch time (s), ARC-LTO etch pressure (mTorr), Ox-SiCO etch time (s), Ox-SiCO gas ratio (%), Ox-SiCO CHF3 flow (sccm), Polish time (s), and Polish pressure (psi).

(3)

Applying first stage Taguchi method to find important attributes

In the first stage of the Taguchi method, ten production attributes potentially affecting DRAM components in medical equipment were considered, and the levels of these attributes were determined based on the engineer’s experience with orthogonal arrays. The experimental setting levels for the production attributes are shown in

Table 3. Production attributes and their setting levels of L₁₂(2¹¹).

Factor	Depo Time (s)	Depo He Flow (sccm)	Depo O2 Flow (sccm)	ARC-LTO Etch Time (s)	ARC-LTO Etch Pressure (mTorr)	Ox-SiCO Etch Time (s)	Ox-SiCO Gas Ratio (%)	Ox-SiCO CHF3 Flow (sccm)	Polish Time (s)	Polish Pressure (psi)
	A	B	C	D	E	F	G	H	I	J
Level 1	29	850	160	45	55	60	30	40	90	2.2
Level 2	33	950	170	55	85	80	50	60	100	4.2

, where Level 1 shows a low setting level and Level 2 shows a high setting level. Using the Taguchi method, the L₁₂(2¹¹) orthogonal array was selected as the screening experiment to identify the important production attributes. The production attributes (A~J) are, respectively, arranged in columns 1~10 of the L₁₂(2¹¹) orthogonal array. In this phase, if we use a full factorial design to identify better setting for ten production attributes, each possessing two levels, would demand a staggering 1024 experiments (2¹⁰ = 1024). However, employing the L₁₂(2¹¹) orthogonal array, this investigation efficiently conducted a mere 12 experiments, encompassing diverse production attribute settings.

Manufacturing engineers were assigned to conduct a Taguchi method for the identified production attributes. In this design, a total of 12 experiments were carried out with different setting levels for each production attribute.

Table 4. Taguchi method L₁₂(2¹¹) and experimental data.

EXP.	Control Factors										Resistance (Ohm × 10−3)					Average Resistance (Ohm × 10−3)	Standard Deviation	SN
	A	B	C	D	E	F	G	H	I	J	N1	N2	N3	N4	N5
1	1	1	1	1	1	1	1	1	1	1	224.44	223.55	222.37	223.08	231.02	224.893	3.505	36.15
2	1	1	1	1	1	2	2	2	2	2	219.18	227.35	218.39	229.68	225.53	224.027	5.014	33.00
3	1	1	2	2	2	1	1	1	2	2	219.59	211.61	225.11	227.83	231.26	223.080	7.703	29.24
4	1	2	1	2	2	1	2	2	1	1	222.06	226.81	209.83	225.08	220.27	220.811	6.644	30.43
5	1	2	2	1	2	2	1	2	1	2	205.75	217.19	213.93	217.38	206.87	212.224	5.584	31.60
6	1	2	2	2	1	2	2	1	2	1	227.24	223.62	215.12	218.87	207.80	218.528	7.562	29.22
7	2	1	2	2	1	1	2	2	1	2	235.70	234.86	228.51	221.27	232.19	230.505	5.874	31.88
8	2	1	2	1	2	2	2	1	1	1	214.47	215.74	204.49	210.04	201.42	209.232	6.204	30.56
9	2	1	1	2	2	2	1	2	2	1	215.29	225.17	214.69	227.10	216.86	219.821	5.858	31.49
10	2	2	2	1	1	1	1	2	2	1	242.10	234.50	238.00	230.50	229.20	234.864	5.326	32.89
11	2	2	1	2	1	2	1	1	1	2	219.78	222.01	227.80	222.68	228.03	224.061	3.680	35.69
12	2	2	1	1	2	1	2	1	2	2	226.32	226.94	217.65	230.61	232.51	226.805	5.723	31.96
																222.404	5.723	32.01

shows the measured resistance values of five DRAM components for each experiment of the Taguchi orthogonal array L₁₂(2¹¹).

Table 5. Average resistance of memory component for L₁₂(2¹¹) in attribute response table.

Factor	A	B	C	D	E	F	G	H	I	J
Level 1	220.6	221.9	223.4	222.0	226.1	226.8	223.2	221.1	220.3	221.4
Level 2	224.2	222.9	221.4	222.8	218.7	218.0	221.7	223.7	224.5	223.5
Effect	3.6	1.0	2.0	0.8	7.5	8.8	1.5	2.6	4.2	2.1
Rank	4	9	7	10	2	1	8	5	3	6

shows the outcomes of the attribute response table regarding the average resistance value of DRAM components, while Figure 8 shows the results of the attribute response chart.

According to Table 5, the impact of each production attribute on the average resistance of the memory component is ranked as: F(8.8) > E(7.5) > I(4.2) > A(3.6) > H(2.6) > J(2.1) > C(2.0) > G(1.5) > B(1.0) > D(0.8). Based on Figure 8, the better settings of production attributes can be set as A = 29 s, E = 85 mTorr, F = 80 s, and I = 90 s for average resistance.

Furthermore, as the focus of this study is on improving the resistance value of DRAM components, which is a nominal-the-better (NTB) quality characteristic, the signal-to-noise ratio (SN) of each experiment was calculated using Formula (1) and the results are presented in the last column of Table 4.

Table 6. SN of memory component for L₁₂(2¹¹) in attribute response table.

Factor	A	B	C	D	E	F	G	H	I	J
Level 1	31.61	32.05	33.12	32.69	33.14	32.09	32.84	32.13	32.72	31.79
Level 2	32.41	31.96	30.90	31.32	30.88	31.93	31.17	31.88	31.30	32.23
Effect	0.80	0.09	2.22	1.37	2.26	0.16	1.67	0.25	1.42	0.44
Rank	6	10	2	5	1	9	3	8	4	7

and Figure 9 exhibit the attribute response table and attribute response chart for the SN of DRAM components, respectively.

According to the information presented in Table 6, the production attributes’ effects on the SN of DRAM components can be ranked in descending order: E(2.3) > C(2.2) > G(1.7) > I(1.4) > D(1.4) > A(0.8) > J(0.4) > H(0.3) > F(0.2) > B(0.1). Based on these findings, the better setting of production properties can be determined as A = 33 s, C = 160 sccm, D = 45 s, E = 55 mTorr, G = 30%, and I = 90 s for SN, as shown in Figure 9.

To further investigate the optimal production attribute settings for improving the resistance value of the DRAM components, a new Taguchi method L₁₈(2¹ × 3⁷) will be conducted. The study will use the analysis results of the average resistance value and SN of the DRAM components from the previous experiment, focusing on seven important production attributes: A (Depo time), C (Depo O2 flow), D (ARC-LTO etch time), E (ARC-LTO etch pressure), F (Ox-SiCO etch time), G (Ox-SiCO gas ratio), and I (Polish time). The new experiment aims to recollect relevant data within the region of experiments that may include the optimal solution and determine the optimal setting of production attribute levels suggested by Taguchi method.

(4)

Applying second stage Taguchi method to recollect data and find out the optimal attribute setting

In this step, this study adopts the Taguchi method once again to gather relevant data for the experimental region that is likely to contain the optimal solution. Based on the average resistance value of the DRAM components obtained in the previous step, the better attribute setting for average resistance is A = 29 s, E = 85 mTorr, F = 80 s, and I = 90 s. On the other hand, the best attribute setting for SN is A = 33 s, C = 160 sccm, D = 45 s, E = 55 mTorr, G = 30%, and I = 90 s. However, since there is a conflict between the levels of production attributes A and E, the production engineers decided to focus on the better attribute setting of the average resistance and finalized the attribute combination as A = 29 s, C = 160 sccm, D = 45 s, E = 85 mTorr, F = 80 s, G = 30%, and I = 90 s.

In the second stage, we adjusted the levels of the selected attributes based on the better attribute setting, as shown in

Table 7. Important attributes and setting levels of L₁₈(2¹ × 3⁷).

Factor	Depo Time (s)	Depo O2 Flow (sccm)	ARC-LTO Etch Time (s)	ARC-LTO Etch Pressure (mTorr)	Ox-SiCO Etch Time (s)	Ox-SiCO Gas Ratio (%)	Polish Time (s)
	A	C	D	E	F	G	I
Level 1	25	140	35	85	80	20	80
Level 2	27	150	40	95	90	25	85
Level 3	29	160	45	100	100	30	90

. For example, attribute A (Depo time) was initially set to 29 and 33 s in the first stage. However, the experiments revealed that A = 29 s yielded a better average resistance value. Consequently, in the second stage of the Taguchi method, we refined the attribute levels for A, adjusting them to 25, 27, and 29 s to further optimize the settings and continue identifying the best settings.

To rearrange new experimental levels, the experimental design at this step will use the L₁₈(2¹ × 3⁷) orthogonal array, where the seven important production attributes (A, C, D, E, F, G, and I) will be arranged in the L₁₈(2¹ × 3⁷) columns 2 to 8 of the orthogonal array, as shown in

Table 8. Taguchi method L₁₈(2¹ × 3⁷) and experimental data.

EXP.	Parameters							Resistance (Ohm × 10−3)					Average Resistance (Ohm × 10−3)	Standard Deviation	SN
	A	C	D	E	F	G	I	N1	N2	N3	N4	N5
1	1	1	1	1	1	1	1	178.88	179.21	176.94	175.53	175.96	177.30	1.676	40.49
2	1	2	2	2	2	2	2	172.46	170.81	176.63	172.20	172.89	173.00	2.175	38.01
3	1	3	3	3	3	3	3	166.60	165.81	171.62	168.77	175.64	169.69	4.019	32.51
4	2	1	1	2	2	3	3	184.08	177.80	179.70	180.63	180.56	180.55	2.278	37.98
5	2	2	2	3	3	1	1	166.48	168.81	173.47	166.24	173.67	169.74	3.644	33.36
6	2	3	3	1	1	2	2	179.81	190.91	182.01	185.43	188.41	185.32	4.531	32.23
7	3	1	2	1	3	2	3	182.61	179.65	186.47	183.07	186.50	183.66	2.893	36.05
8	3	2	3	2	1	3	1	187.20	181.33	178.89	178.84	181.11	181.48	3.412	34.52
9	3	3	1	3	2	1	2	174.91	184.51	178.74	179.64	178.54	179.27	3.442	34.33
10	1	1	3	3	2	2	1	163.96	167.04	168.76	167.05	172.11	167.78	2.974	35.03
11	1	2	1	1	3	3	2	176.48	175.28	175.07	174.30	174.94	175.21	0.799	46.82
12	1	3	2	2	1	1	3	178.98	186.19	184.16	177.66	189.01	183.20	4.800	31.63
13	2	1	2	3	1	3	2	178.66	175.52	181.45	183.50	179.51	179.73	3.004	35.54
14	2	2	3	1	2	1	3	179.63	184.18	189.82	188.90	178.26	184.15	5.240	30.92
15	2	3	1	2	3	2	1	169.94	171.84	168.87	173.72	170.49	170.97	1.870	39.22
16	3	1	3	2	3	1	2	185.80	176.34	176.06	174.46	174.23	177.38	4.800	31.35
17	3	2	1	3	1	2	3	185.89	183.95	189.85	183.68	182.00	185.08	3.006	35.79
18	3	3	2	1	2	3	1	186.32	174.52	177.17	180.35	180.22	179.72	4.410	32.20
													177.96	3.28	35.44

. During this phase, employing a full factorial design to pinpoint optimal setting for seven production attributes, each featuring three levels, would necessitate a substantial 2187 experiments (3⁷ = 2187). However, by using the L₁₈(2¹ × 3⁷) orthogonal array, this study conducted a streamlined set of only 18 experiments, effectively exploring a wide range of production attribute settings.

Table 8 shows the experimental results for the resistance value of DRAM components and the SN value of Taguchi’s experimental design L₁₈(2¹ × 3⁷) at different experimental level settings.

Table 9. Average resistance of memory component for L₁₈(2¹ × 3⁷) in attribute response table.

Level	A	C	D	E	F	G	I
1	174.36	177.73	178.06	180.89	182.02	178.51	174.50
2	178.41	178.11	178.17	177.76	177.41	177.63	178.32
3	181.10	178.03	177.63	175.21	174.44	177.73	181.06
Effect	6.73	0.37	0.54	5.68	7.57	0.87	6.56
Rank	2	7	6	4	1	5	3

and Figure 10 present the attribute response table and attribute response chart, respectively, for the average resistance analysis results of DRAM components. The effect of each production attribute on the average resistance value of DRAM components in descending order is shown in Table 9 as follows: F(7.57) > A(6.73) > I(6.56) > E(5.68) > G(0.87) > D(0.54) > C(0.37). As seen in Figure 10, the optimal settings of production attributes are set as A = 25 s, E = 95 mTorr, F = 100 s, and I = 85 s for average resistance.

Table 10. SN of memory component for L₁₈(2¹ × 3⁷) in attribute response table.

Level	A	C	D	E	F	G	I
1	37.42	36.07	39.11	36.45	35.03	33.68	35.80
2	34.88	36.57	34.47	35.45	34.75	36.06	36.38
3	34.04	33.69	32.76	34.43	36.55	36.60	34.15
Effect	3.37	2.88	6.35	2.03	1.81	2.91	2.23
Rank	2	4	1	6	7	3	5

and Figure 11 are the attribute response table and attribute response chart, respectively, for the SN analysis results of DRAM components. From Table 10, it can be inferred that the production attribute D has the highest contribution to the SN of DRAM components, followed by attributes A, G, C, I, E, and F in descending order of importance. In Figure 11, the optimal settings of production attributes can be set as A = 25 s, C = 150 sccm, D = 35 s, and G = 30% for SN.

Based on these analysis results of the average resistance and SN, the optimal settings of attributes for the Taguchi method are A = 25 s, C = 150 sccm, D = 35 s, E = 95 mTorr, F = 100 s, G = 30%, and I = 85 s.

To confirm the optimal production attribute setting (A = 25 s, C = 150 sccm, D = 35 s, E = 95 mTorr, F = 100 s, G = 30%, and I = 85 s) determined by the Taguchi method, the case company conducted three batches on the production line. Each batch sampled one wafer, and the resistance of five DRAM components from each wafer was measured to confirm the experimental data.

Table 11. Confirmation results of optimal production attribute setting in the second Taguchi method.

EXP.	Resistance (Ohm × 10−3)					Average Resistance (Ohm × 10−3)	Standard Deviation	SN
	N1	N2	N3	N4	N5
Wafer #1	174.11	170.99	170.55	172.35	173.45	172.289	1.531	41.03
Wafer #2	170.22	173.00	170.88	171.26	174.75	172.024	1.840	39.42
Wafer #3	173.99	170.24	171.76	171.68	172.32	171.999	1.352	42.09
						172.104	1.574	40.84

shows the measurement results. Initially, the average resistance value of the memory component was 191.1 × 10⁻³ Ohm, and the deviation from the design target value of 176.5 × 10⁻³ Ohm was 14.6 × 10⁻³ Ohm. However, after applying the Taguchi method, the average resistance value was reduced to 172.1 × 10⁻³ Ohm, and the deviation from the design target value was only 4.4 × 10⁻³ Ohm, which represents an improvement of 69.89%.

Table 12. Comparison results before and after Taguchi method.

Comparison	Depo Time (s)	Depo O2 Flow (sccm)	ARC-LTO Etch Time (s)	ARC-LTO Etch Pressure (mTorr)	Ox-SiCO Etch Time (s)	Ox-SiCO Gas Ratio (%)	Polish Time (s)	Average Resistance (Ohm × 10−3)	|Resistance-Target|
	A	C	D	E	F	G	I
Before improvement	30	160	50	70	70	30	90	191.100	14.60
TSTM	25	150	35	95	100	30	85	172.104	4.40
Improvement									69.89%

compares the results before and after the implementation of the Taguchi method, confirming that the local optimal setting of production attribute levels identified by the Taguchi method is suitable for mass production. Nevertheless, to further reduce the deviation from the design target value of 176.5 × 10⁻³ Ohm, this study plans to use an artificial neural network to construct the relationship between the production attributes and the resistance value of DRAM components in the next stage.

(5)

Using artificial neural networks to build a model

Based on results of ANOVA, we can identify the important production attributes as A (Depo time), C (Depo O2 flow), D (ARC-LTO etch time), E (ARC-LTO etch pressure), F (Ox-SiCO etch time), G (Ox-SiCO gas ratio), and I (Polish time). These attributes will be used as input variables for the artificial neural network, while the resistance value of the memory component will serve as the output variable.

To create an artificial neural network model with a rich and varied dataset, this research utilized the Monte Carlo technique to enhance the resistance data sourced from Table 8. The Monte Carlo method introduces randomness or stochastic components into its forecasts, offering varying results with each simulation. By employing a probabilistic model like Monte Carlo, diverse datasets can be generated, leading to a broader scope of outcomes [43]. In this investigation, a normal distribution probabilistic model was adopted for augmenting the data using the Monte Carlo approach. The outcomes of this data augmentation process are presented in

Table 13. Results of Monte Carlo method.

EXP.		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
Parameters	A	1	1	1	2	2	2	3	3	3	1	1	1	2	2	2	3	3	3
	C	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
	D	1	2	3	1	2	3	2	3	1	3	1	2	2	3	1	3	1	2
	E	1	2	3	2	3	1	1	2	3	3	1	2	3	1	2	2	3	1
	F	1	2	3	2	3	1	3	1	2	2	3	1	1	2	3	3	1	2
	G	1	2	3	3	1	2	2	3	1	2	3	1	3	1	2	1	2	3
	I	1	2	3	3	1	2	3	1	2	1	2	3	2	3	1	2	3	1
Resistance (Ω × 10−3)	N1	178.88	172.46	166.60	184.08	166.48	179.81	182.61	187.20	174.91	163.96	176.48	178.98	178.66	179.63	169.94	185.80	185.89	186.32
	N2	179.21	170.81	165.81	177.80	168.81	190.91	179.65	181.33	184.51	167.04	175.28	186.19	175.52	184.18	171.84	176.34	183.95	174.52
	N3	176.94	176.63	171.62	179.70	173.47	182.01	186.47	178.89	178.74	168.76	175.07	184.16	181.45	189.82	168.87	176.06	189.85	177.17
	N4	175.53	172.20	168.77	180.63	166.24	185.43	183.07	178.84	179.64	167.05	174.30	177.66	183.50	188.90	173.72	174.46	183.68	180.35
	N5	175.96	172.89	175.64	180.56	173.67	188.41	186.50	181.11	178.54	172.11	174.94	189.01	179.51	178.26	170.49	174.23	182.00	180.22
Average resistance (Ω × 10−3)		177.30	173.00	169.69	180.55	169.74	185.32	183.66	181.48	179.27	167.78	175.21	183.20	179.73	184.15	170.97	177.38	185.08	179.72
Standard deviation		1.676	2.175	4.019	2.278	3.644	4.531	2.893	3.412	3.442	2.974	0.799	4.800	3.004	5.240	1.870	4.800	3.006	4.410
P1		175.49	175.64	168.98	181.54	166.08	184.77	181.34	178.92	179.58	164.53	174.14	184.37	175.26	189.12	169.55	178.84	188.84	180.67
P2		175.57	177.75	168.86	184.14	165.04	174.95	179.59	181.78	177.59	169.11	174.11	171.38	175.46	180.28	167.70	168.27	182.54	184.95
P3		176.41	172.49	168.01	181.16	171.37	183.02	180.45	182.13	178.67	163.65	174.91	185.76	179.00	183.43	173.11	172.70	183.76	179.24
P4		178.07	176.62	172.49	184.93	169.12	184.13	177.83	184.68	178.62	166.33	174.30	187.18	181.42	180.79	171.52	175.42	183.60	183.12
P5		179.28	171.66	173.72	182.50	164.08	184.81	183.09	180.23	179.59	167.09	175.34	181.80	183.47	191.01	173.38	175.46	184.04	175.49
P6		178.62	173.16	167.40	177.90	166.32	188.50	184.34	181.04	184.53	165.41	174.92	184.90	180.94	184.55	172.23	174.54	179.67	187.32
P7		178.31	173.14	170.93	177.77	173.12	179.95	186.30	177.83	179.78	168.78	175.19	187.13	181.15	177.96	170.00	165.00	188.14	177.46
P8		179.34	173.43	173.18	182.69	175.49	184.86	185.62	177.25	174.56	167.96	173.43	182.45	176.91	195.20	172.24	172.46	189.22	187.29
P9		175.73	175.99	168.53	179.65	170.09	190.29	178.04	178.35	172.94	173.19	175.73	183.19	183.18	191.82	173.64	176.78	187.91	176.57
P10		177.82	174.22	160.50	179.52	167.78	181.07	182.16	188.91	179.26	167.84	175.19	190.43	182.58	190.26	172.03	179.76	185.53	180.65

, specifically in rows P₁ to P₁₀.

To train the network, 80% of the dataset is randomly selected as the training dataset, and the remaining 20% is used as the testing dataset. Finally, the optimal neural network architecture was identified as 7-2-6-5-1, as shown in Figure 12.

(6)

Adopting genetic algorithm to identify the best production attribute setting

In this step, the objective function for the genetic algorithm is defined as the inverse of the deviation between the predicted resistance values from the previously constructed 7-2-6-5-1 neural network architecture and the target design values.

Finally, the genetic algorithm finds that the minimum resistance deviation of the memory component is 1.2 × 10⁻⁴ Ohm, and the global optimal production attributes setting are set as follows: A (Depo time) = 27 s, C (Depo O2 flow) = 151 sccm, D (ARC-LTO etch time) = 43 s, E (ARC-LTO etch pressure) = 97 mTorr, F (Ox-SiCO etch time) = 91 s, G (Ox-SiCO gas ratio) = 22%, and I (Polish time) = 84 s.

(7)

Performing confirmation experiments and comparisons

To verify the proposed framework FMEA-TSTM-NNGA in this study, a small trial run was conducted by the case company on their production line to identify the optimal production attributes for improving the resistance value of DRAM components. The trial run involved producing 3 wafers, and 5 DRAM components were selected from each wafer. The results of the trial run are shown in

Table 14. Confirmation Results of Optimal Production Attributes in genetic algorithm.

EXP.	Resistance (Ohm × 10−3)					Average Resistance (Ohm × 10−3)	Standard Deviation	SN
	N1	N2	N3	N4	N5
Wafer #1	177.00	174.31	177.16	177.14	178.44	176.810	1.515	41.345
Wafer #2	174.88	178.07	175.27	177.20	177.52	176.586	1.424	41.871
Wafer #3	177.03	178.66	177.20	174.79	177.94	177.124	1.455	41.705
						176.840	1.465	41.640

.

Using artificial neural networks and genetic algorithms, the DRAM components of the medical equipment produced by the case company were improved. As a result, there was a significant improvement in the resistance value of the DRAM components. Specifically, the average resistance deviation of the memory element was reduced by 97.67%, from 14.6 × 10⁻³ Ohm to 0.34 × 10⁻³ Ohm, as shown in

Table 15. Comparison results before and after proposed methodology.

Comparison	Depo Time (s)	Depo O2 Flow (sccm)	ARC-LTO Etch Time (s)	ARC-LTO Etch Pressure (mTorr)	Ox-SiCO Etch Time (s)	Ox-SiCO Gas Ratio (%)	Polish Time (s)	Average Resistance (Ohm × 10−3)	|Resistance-Target|
	A	C	D	E	F	G	I
Before improvement	30	160	50	70	70	30	90	191.10	14.60
TSTM	25	150	35	95	100	30	85	172.10	4.40
FMEA-TSTM-NNGA	27	151	43	97	91	22	84	176.84	0.34
Improvement									97.67%

.

Based on the results of the trial run and the optimization process, it can be concluded that the best setting of the production attributes for DRAM components is a mass-production setting.

Additionally, the execution results of the proposed methodology can save more experimental resources compared to other existing optimization methods. The first stage of the Taguchi method employs the L₁₂(2¹¹) orthogonal array, significantly minimizing the number of experimental trials needed to identify critical production attributes that influence memory component resistance. Typically, a full factorial experiment would require 1024 tests to cover all combinations of ten production attributes across two levels. However, using the L₁₂(2¹¹) array, the number of necessary experiments is reduced to just 12, resulting in an 85.3-fold decrease in the experimental workload. The second stage of the Taguchi method applies the L₁₈(2¹ × 3⁷) orthogonal array. Normally, a complete factorial design would necessitate 2187 experiments to explore all combinations of seven production attributes at three levels. The L₁₈(2¹ × 3⁷) array reduces the number of required experiments to 18, thereby achieving a 121.5-fold reduction in experimental effort compared to the full factorial experiment. In the genetic algorithm (GA) phase, 20 initial population tests were conducted, followed by 300 iterations, resulting in a total of 6000 runs. In comparison, a grid search approach would require approximately 2.4 × 10⁷ runs (calculated as 4 × 20 × 10 × 15 × 20 × 10 × 10), demonstrating a substantial reduction in the number of model evaluations.

6. Numerical Simulations and Discussion

(a)

Analysis of variance (ANOVA)

When researchers aim to analyze multiple categorical independent variables and compare the means across different groups, an ANOVA becomes essential [44]. Specifically, when the independent variables are categorical and the dependent variable is continuous, a statistical analysis is necessary to evaluate the relationships between the groups’ means. This analysis helps determine how variations in the dependent variable are affected by the different levels of the independent variables.

For the first stage of the Taguchi method,

Table 16. ANOVA table of average resistance of DRAM components from L₁₂(2¹¹).

Item	Degree of Freedom	Sum of Square	Mean of Square	F Value	p Value
A	1	39.332	39.332	43.37	0.096
B	1	2.74	2.74	3.02	0.332
C	1	11.968	11.968	13.2	0.171
D	1	1.888	1.888	2.08	0.386
E	1	168.038	168.038	185.27	0.047
F	1	234.661	234.661	258.72	0.040
G	1	6.802	6.802	7.5	0.223
H	1	20.421	20.421	22.52	0.132
I	1	53.762	53.762	59.27	0.082
J	1	13.135	13.135	14.48	0.164
Error	1	0.907	0.907
Total	11.0	553.7
				R-Sq	R-Sq(adj)
				99.84%	98.20%

provides the analysis of variance (ANOVA) of the average resistance values of DRAM components for the orthogonal array L₁₂(2¹¹). Based on Table 16, it can be observed that the p-values for production attributes A, E, F, and I are below 0.1, indicating that these four production attributes have a significant contribution to the average resistance of DRAM components and are important production attributes that affect resistance.

Table 17. ANOVA table of SN of DRAM components from L₁₂(2¹¹).

Item	Degree of Freedom	Sum of Square	Mean of Square	F Value	p Value
A	1	1.943	1.943	103.63	0.062
B	1	0.0228	0.0228	1.22	0.469
C	1	14.8407	14.8407	791.47	0.023
D	1	5.626	5.626	300.04	0.037
E	1	15.3021	15.3021	816.08	0.022
F	1	0.0807	0.0807	4.31	0.286
G	1	8.3286	8.3286	444.17	0.030
H	1	0.1946	0.1946	10.38	0.192
I	1	6.0317	6.0317	321.68	0.035
J	1	0.577	0.577	30.77	0.114
Error	1	0.0188	0.0188
Total	11.0	53.0
				R-Sq	R-Sq(adj)
				99.96%	99.61%

provides the ANOVA results of the SN of DRAM components for the orthogonal array L₁₂(2¹¹). Table 17 shows that the p-values for production attributes A, C, D, E, G, and I are less than 0.1. Therefore, these six production attributes have a significant contribution to the SN of DRAM components and are important production attributes that affect SN.

Regarding the second stage of the Taguchi method,

Table 18. ANOVA table of average resistance of DRAM components from L₁₈(2¹ × 3⁷).

Item	Degree of Freedom	Sum of Square	Mean of Square	F Value	p Value
A	2	137.812	68.9058	28.11	0.011
C	2	0.464	0.232	0.09	0.912
D	2	0.979	0.4895	0.2	0.829
E	2	97.154	48.577	19.81	0.019
F	2	174.783	87.3916	35.65	0.008
G	2	2.752	1.3758	0.56	0.621
I	2	130.17	65.085	26.55	0.012
Error	3	7.355	2.4516
Total	17	551.468
				R-Sq	R-Sq(adj)
				98.67%	92.44%

presents the ANOVA results of the average resistance analysis of DRAM components for the Taguchi’s experimental design L₁₈(2¹ × 3⁷). Based on the information provided in Table 18, it can be observed that the p-values for production attributes A, E, F, and I are below 0.1, indicating that these four production attributes significantly contribute to the average resistance of DRAM components and are important production attributes that affect the resistance of DRAM components.

Table 19. ANOVA table of SN of DRAM components from L₁₈(2¹ × 3⁷).

Item	Degree of Freedom	Sum of Square	Mean of Square	F Value	p Value
A	2	37.06	18.53	8.05	0.062
C	2	28.44	14.22	6.18	0.086
D	2	129.389	64.694	28.1	0.011
E	2	12.303	6.152	2.67	0.216
F	2	11.325	5.663	2.46	0.233
G	2	28.833	14.416	6.26	0.085
I	2	16.138	8.069	3.5	0.164
Error	3	6.907	2.302
Total	17	270.395
				R-Sq	R-Sq(adj)
				97.45%	85.52%

shows the ANOVA results of the SN analysis of DRAM components for the orthogonal array L₁₈(2¹ × 3⁷). Table 19 indicates that the p-values for production attributes A, C, D, and G are less than 0.1, signifying that these attributes significantly contribute to the SN of DRAM components and are important factors that affect SN.

(b)

Neural networks (NN)

This study proposes an artificial neural network architecture with three hidden layers. To train the network, 80% of the dataset (Table 13) is randomly selected as the training dataset, and the remaining 20% is used as the testing dataset. The neural network model is configured with the ReLU activation function and the Adam optimizer. A grid search method is used to find the optimal settings for hyperparameters, including the learning rate, momentum rate, and number of nodes in each hidden layer. The learning rate is tested with values of [0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4], while the momentum rate is tested with values of [0.7, 0.75, 0.8, 0.85, 0.9, 0.95]. The number of nodes in each hidden layer is set as [1:10]. The initial conditions of the neural network are shown in Figure 13.

The artificial neural network is trained on 1000 iterations, and the minimum root mean square error (RMSE) of the testing dataset is used as the criterion to select the final weights. After conducting the grid search, the optimal hyperparameters settings are determined as follows: the learning rate is set to 0.1, the momentum rate is set to 0.95, and the number of nodes in the three hidden layers are set to 2, 6, and 5, respectively. Therefore, the optimal neural network architecture is 7-2-6-5-1.

To verify the convergence of the optimal hyperparameters identified by the grid search, we compare the RMSE of the training and testing datasets for the ANN model with the best hyperparameters. Figure 14 shows the convergence curve, which plots RMSE values against the number of iterations, offering essential insights into a model’s training dynamics. In the early learning phase, both the training and testing RMSE values are usually elevated, reflecting the model’s initial state with weights that are far from optimal. As training progresses, these RMSE values typically decline, signaling enhanced model performance. Around the 60th iteration, the RMSE values for both the training and testing datasets converge closely, indicating consistent learning. However, if the gap between the training and testing RMSE values begins to widen, it could indicate overfitting, where the model becomes overly adapted to the training data, thereby reducing its generalization capability. In the final stages of training, the RMSE values tend to stabilize. If the testing RMSE values stabilize near the training RMSE values, this strongly suggests that the model has achieved robustness.

(c)

Genetic algorithm (GA)

The genetic algorithm (GA) operates by first standardizing the input variables of artificial neural networks. Once standardized, the values are converted into binary code, which is then combined into a string and used in subsequent genetic processes, including reproduction, crossover, and mutation. In this study, the fitness function is defined as the reciprocal of the deviation between the memory component and the target value, as shown in Formula (4):

$$Fitness function={\displaystyle \frac{1}{\left|Resistance-Target value\right|}}$$

(4)

In this study, the initial operation of the genetic algorithm begins with the random generation of 20 populations for reproduction, Using the roulette method. The roulette wheel’s area size is determined by the fitness function value, where a larger area on the wheel indicates a higher fitness function value and easier reproduction of the next generation. Based on past experience, the crossover rate and mutation rate for the genetic algorithm have been established as 0.85 and 0.05, respectively. The stopping condition of the genetic algorithm is set to 300 iterations.

Table 20. The production attribute settings and the resistance value deviations of DRAM components after 10 times of GA.

Run	A	C	D	E	F	G	I	|Rs-Target|
#1 run	27.929	156.909	41.909	92.396	98.624	29.326	81.768	0.000131
#2 run	27.014	142.876	35.035	99.028	94.054	22.342	88.275	0.000441
#3 run	27.668	150.220	35.263	92.436	91.232	20.317	83.035	0.000900
#4 run	26.264	150.130	43.084	88.909	92.294	21.971	83.986	0.001989
#5 run	25.891	156.002	41.069	88.266	98.242	29.487	85.531	0.000139
#6 run	27.042	151.274	38.517	94.516	97.592	29.190	85.726	0.000665
#7 run	27.182	150.754	43.120	97.407	91.463	22.301	83.717	0.000120
#8 run	28.948	143.287	41.360	91.914	92.036	25.015	80.208	0.003525
#9 run	26.652	156.187	36.952	99.182	87.439	27.952	84.476	0.000272
#10 run	28.877	140.925	44.876	98.750	93.288	23.210	82.158	0.000188

shows the production attribute setting levels and the resistance value deviations of the DRAM components after each genetic algorithm. The genetic algorithm finds that the minimum resistance deviation of the memory component is 1.2 × 10⁻⁴ Ohm, and the global optimal production attribute settings are set as follows: A (Depo time) = 27 s, C (Depo O2 flow) = 151 sccm, D (ARC-LTO etch time) = 43 s, E (ARC-LTO etch pressure) = 97 mTorr, F (Ox-SiCO etch time) = 91 s, G (Ox-SiCO gas ratio) = 22%, and I (Polish time) = 84 s.

7. Conclusions

In this case study, we used FMEA to identify ten production attributes in thin film deposition, etching, plating, and polish processes. We then conducted experiments using the Taguchi method L₁₂(2¹¹) with a limited number of trials to identify key production attributes that affect memory component resistance. Using the factor response table and an ANOVA, we identified seven critical attributes: A (Depo time), C (Depo O2 flow), D (ARC-LTO etch time), E (ARC-LTO etch pressure), F (Ox-SiCO etch time), G (Ox-SiCO gas ratio), and I (Polish time). The dataset, derived from seven key attributes, was collected using the Taguchi method L₁₈(2¹ × 3⁷). This dataset was subsequently utilized as both the training and testing dataset for an artificial neural network in the following stage.

Next, we integrated the Monte Carlo method with a normal distribution probabilistic model into the L₁₈(2¹ × 3⁷) to expand the modeling dataset. During the artificial neural network modeling process, the artificial neural network in this study was fed with seven important attributes as input variables. The optimal hyperparameter setting of the artificial neural network were then found through the grid search method, with a learning rate of 0.1, momentum rate of 0.95, and three hidden layers with 2, 6 and 5 nodes, respectively. Finally, the resulting architecture was 7-2-6-5-1.

Subsequently, this study applied a genetic algorithm to determine the best production attribute setting across the entire region, resulting in the following settings: A (Depo time) = 27 s, C (Depo O2 flow) = 151 sccm, D (ARC-LTO etch time) = 43 s, E (ARC-LTO etch pressure) = 97 mTorr, F (Ox-SiCO etch time) = 91 s, G (Ox-SiCO gas ratio) = 22%, and I (Polish time) = 84 s.

After verifying the experimental results, this study found that the average resistance of the DRAM components had improved from 191.1 × 10⁻³ Ohm to 176.84 × 10⁻³ Ohm, which is very close to the target value of 176.5 × 10⁻³ Ohm. The average resistance deviation was also reduced from 14.6 × 10⁻³ Ohm to 0.34 × 10⁻³ Ohm, representing an improvement of 97.67%. The FMEA-TSTM-NNGA framework presented in this paper enables comprehensive analysis of the process and helps identify high-risk factors within it, ensuring that these key considerations are accounted for during improvement efforts.

This framework demonstrates potential for scalability and adaptability across various semiconductor manufacturing processes. However, it may require customization, including adjustments to the input and response variables, to align with the specific needs of different processes. Additionally, the training data for the ANN and the GA’s objective functions may need to be reconfigured and calibrated to match new process objectives, ensuring that the optimization outcomes remain accurate and applicable.

The key limitation of this research is the reliance on a single dataset, which may constrain the generalizability of the findings. To assess the broader applicability of the proposed FMEA-TSTM-NNGA framework, future research could investigate its effectiveness in other semiconductor fields and validate its generalizability using independent resistance datasets from multiple companies.

Our proposed framework can be seamlessly adapted to address image-based semiconductor product defect detection tasks using deep learning techniques. Notably, its design prioritizes efficient training and accurate inference, making it particularly well suited for deployment on resource-constrained edge AI devices within semiconductor manufacturing environments.