Neurofuzzy modeling of chemical vapor deposition processes

The modeling of semiconductor manufacturing processes has been the subject of intensive research efforts for years. Physical-based (first-principle) models have been shown to be difficult to develop for processes such as plasma etching and plasma deposition, which exhibit highly nonlinear and complex multidimensional relationships between input and output process variables. As a result, many researchers have turned to empirical techniques to model many semiconductor processes. This paper presents a neurofuzzy approach as a general tool for modeling chemical vapor deposition (CVD) processes. A five-layer feedforward neural network is proposed to model the input-output relationships of a plasma-enhanced CVD deposition of a SiN film. The proposed five-layer network is constructed from a set of input-output training data using unsupervised and supervised neural learning techniques. Product space data clustering is used to perform the partitioning of the input and output spaces. Fuzzy logic rules that describe the input-output relationships are then determined using competitive learning algorithms. Finally, the fuzzy membership functions of the input and output variables are optimally adjusted using the backpropagation learning algorithm. A salient feature of the proposed neurofuzzy network is that after the training process, the internal units are transparent to the user, and the input-output relationship of the CVD process can be described linguistically in terms of IF-THEN fuzzy rules. Computer simulations are conducted to verify the validity and the performance of the proposed neurofuzzy network for modeling CVD processes     

Efficient establishment of a fuzzy logic model for process modelingand control

Fuzzy logic modeling using internal and membership functions is a promising technique for the modeling and control of semiconductor manufacturing and packaging processes. To simplify its implementation procedure, a fuzzy logic model needs to be established with the minimum user interference. An algorithm with two major steps has been proposed and demonstrated for the efficient model establishment The first step develops intermediate fuzzy logic models with different numbers of membership functions assigned to each input variable. The number is one for the simplest model, and is increased one by one according to the pre-defined sequence and pathfinding criteria for more complex models, The second step stops the incremental procedure when the stopping criteria are met. The criteria are the multiple correlation factors R ² based on the training and the testing data. The algorithm's accuracy and efficiency have been demonstrated by testing it with five two-variable, nonlinear functions     

Fuzzy logic models for thermally based microelectronicmanufacturing processes

This paper presents fuzzy logic models (FLM) to simulate two thermally based microelectronic manufacturing processes: the “pool boiling” in vapor phase soldering and silicon deposition process in a horizontal chemical vapor deposition (CVD) reactor. After a brief discussion of the various input-output models, we present our general approach to the development of FLM's, followed by their application to the two case studies. For the pool boiling, experimental data are used to develop the fuzzy logic model. Results show that the FLM not only simulates the different regions of the pool boiling curve satisfactorily, but also faithfully represents the two transitions. For the CVD process, pseudo-analytical equations from Eversteyn's paper are used to generate data under simulated production conditions. Results show that the model can describe the process very well. The physico-fuzzy model, incorporating the physical understanding of the process, is shown to improve the model's extrapolation capability     

Generating optimal adaptive fuzzy-neural models of dynamicalsystems with applications to control

The paper describes an approach to generating optimal adaptive fuzzy neural models from I/O data. This approach combines structure and parameter identification of Takagi-Sugeno-Kang (TSK) fuzzy models. We propose to achieve structure determination via a combination of modified mountain clustering (MMC) algorithm, recursive least squares estimation (RLSE), and group method of data handling (GMDH). Parameter adjustment is achieved by training the initial TSK model using the algorithm of an adaptive network based fuzzy inference system (ANFIS), which employs backpropagation (BP) and RLSE. Further, a procedure for generating locally optimal model structures is suggested. The structure optimization procedure is composed of two phases: 1) locally optimal rule premise variables subsets (LOPVS) are identified using MMC, GMDH, and a search tree (ST); and 2) locally optimal numbers of model rules (LONOR) are determined using MMC/RLSE along with parallel simulation mean square error (PSMSE) as a performance index. The effectiveness of the proposed approach is verified by a variety of simulation examples. The examples include modeling of a nonlinear dynamical process from I/O data and modeling nonlinear components of dynamical plants, followed by tracking control based on a model reference adaptive scheme (MRAC). Simulation results show that this approach is fast and accurate and leads to several optimal models     

Fast and Automated Electromigration Analysis for CMOS RF PA Design

This paper presents fast and automated electromigration (EM) reliability modeling by using automated modeling generation (AMG) algorithm. The AMG converts human based EM modeling into an automated modeling and simulation process with the help of ANSYS parametric design language (APDL) program. For automating the neural model training process, training-driven adaptive sampling is applied to integrate data generation, data distributions determination, model structure adaptation, training and testing into a unified framework. Fully automated reliability model construction and simulation is achieved for the first time. This method effectively shortens the period of EM modeling by using dynamic sampling method. Furthermore, the heat generation from active devices has been considered to describe the heat effect on the interconnect reliability. Through the proposed technique, the allowable sizes, temperature and output power of a CMOS radio frequency power amplifier (RF PA) are derived to give reliability criteria for PA designer.     

Statistical equipment modeling for VLSI manufacturing: anapplication for LPCVD

An equipment characterization and modeling methodology has been developed. The methodology is based on the development of generic first-principle process models. These models are subsequently refined and fitted to specific manufacturing equipment by using a multistage D-optimal experimental design. The methodology has been successfully applied to a low-pressure chemical vapor deposition (LPCVD) furnace for undoped polysilicon deposition. A two-stage D-optimal experiment with 24 runs has yielded fitted models for the film growth rate and film residual stress. The calibrated models agree well with the experimental data and account for the observed variations     

An equipment model for polysilicon LPCVD

An equipment model has been developed for the low pressure chemical vapor deposition (LPCVD) of polycrystalline silicon in a horizontal tube furnace using a methodology which combines physical modeling with statistical experimental design. The model predicts the wafer to wafer deposition rate down the length of the tube and is intended to aid the process engineer in the operation of equipment, including the selection of optimum process parameters and process control based on measured deposition thicknesses. Kinetic and injection parameters in the model were calibrated using a series of nine statistically designed experiments which varied four parameters over three levels. The model accurately predicts the axial deposition profile over the full range of experimentation, and demonstrates good extrapolation beyond the range of experimental calibration     

基于递阶原理的非均匀采样非线性系统的模糊辨识

针对非均匀多采样率非线性系统的建模问题,提出了基于递阶原理的模糊辨识方法.首先,分析了非线性系统在输入信号非均匀周期刷新,输出信号周期采样的情况下,非线性系统可以通过提升技术,利用多个局部线性模型加权组合的模糊模型来描述.在此基础上,利用GK模糊聚类确定模糊模型前件结构,利用基于递阶原理的递推最小二乘辨识算法辨识模糊模型后件参数.同时,通过鞅定理对辨识算法的收敛性进行了研究.最后,通过仿真实例证明了本文方法的有效性.     

Advantages of plasma etch modeling using neural networks overstatistical techniques

Due to the inherent complexity of the plasma etch process, approaches to modeling this critical integrated circuit fabrication step have met with varying degrees of success. Recently, a new adaptive learning approach involving neural networks has been applied to the modeling of polysilicon film growth by low-pressure chemical vapor deposition (LPCVD). In this paper, neural network modeling is applied to the removal of polysilicon films by plasma etching. The plasma etch process under investigation was previously modeled using the empirical response surface approach. However, in comparing neural network methods with the statistical techniques, it is shown that the neural network models exhibit superior accuracy and require fewer training experiments. Furthermore, the results of this study indicate that the predictive capabilities of the neural models are superior to that of their statistical counterparts for the same experimental data     

基于模糊逻辑的两级运算放大器宏模型

运算放大器是最常用的模拟集成电路功能块,本文提出了一种基于模糊逻辑建立的运算放大器宏模型。基于运放电路结构分解的模糊逻辑建模方法利用了电路内部的结构特点与工作特性等先验知识。根据电路的结构知识确定模型整体结构;根据电路的工作特性确定模糊逻辑模型的规则（包括条数、前提与结论函数的形式）及初始参数。这就大大简化了模型构造过程,使一开始构造出来的初始模型就有较好的逼近精度,后续模型参数的学习训练只需经过少量的迭代,相对于传统的系统辨识方法具有很大的优势。     

基于模糊多特征递归分组算法的隐树结构图模型学习

隐树结构图模型通过引入了隐藏节点来描述变量之间的潜在关系,因而可以更好地对变量之间的相关性进行建模。树模型学习过程中,从变量观测数据所提取的有用特征数量,决定了该模型对变量间深层关系的建模能力;而现有学习算法都是对观测数据直接计算统计量来进行模型学习,未能按观测数据中的特征分类处理。针对现有算法对观测数据中信息利用不充分的不足,该文提出基于模糊多特征递归分组算法的隐树模型学习方法。首先,将变量的原始观测数据通过反映其特征的模糊隶属度函数转化成多个模糊特征,并构造多维模糊特征向量;其次,计算两两变量模糊特征向量之间的距离,并将其综合得到所有变量之间的模糊特征向量距离矩阵;最后,基于该距离矩阵,利用递归分组算法学习隐树模型。该文还将所提算法应用于股票收益数据和气温数据建模,验证了该文算法的实用性和有效性。     

Modeling and simulation of combinational CMOS logic circuits by ANFIS

In this paper, application of adaptive neuro-fuzzy inference system (ANFIS) in modeling of CMOS logic gates as a tool in designing and simulation of CMOS logic circuits is presented. Structures of the ANFIS are developed and trained in MATLAB 7.0.4 program. We have used real hardware data for training the ANFIS network. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training. Influence of the structure of the proposed ANFIS model on accuracy and network performance has been analyzed through some combinational circuits. For the comparison of the ANFIS simulation results, we have simulated the circuits in HSPICE environment with 0.35 μm process nominal parameters. The comparison between ANFIS, HSPICE, and real hardware shows the feasibility and accuracy of the proposed ANFIS modeling procedure. The results show the proposed ANFIS simulation has much higher speed and accuracy in comparison with HSPICE simulation and it can be simply used in software tools for designing and simulation of complex CMOS logic circuits.     

A neuro fuzzy logic approach to material processing

A new application of fuzzy systems to the processing of materials is presented. The relationships between temperature, time, and the impact strength of an austempered ductile iron (ADI) part are adaptively modeled. Four fuzzy and neuro fuzzy approaches have been used to build predictive models. These are: a fuzzy based model, a backpropagation based neuro fuzzy model, a clustering based model, and a clustering backpropagation based neuro fuzzy model. The clustering approach, using the subclustering method, yielded the best predictive results when all models had been given the same input-output training data. The backpropagation based neuro fuzzy approach suffers from the lack of a higher number of input-output data training sets. All preliminary results obtained suggest the adequacy of the fuzzy based and neuro fuzzy based modeling techniques to tackle those types of problems in the material processing areas     

基于模糊分组和监督聚类的RBF回归性能改进

为了提高RBF回归建模的精度,该文提出了一种基于模糊分组和监督聚类的RBF回归建模的新方法。基本思想是:首先利用监督聚类将训练样本模糊划分为若干子集,然后分别针对各个子集的样本分布情况进行RBF回归建模,最后利用加权组合得到最终的输出。实验表明,该方法对于目标模型的局部细节具有更好的逼近精度。     

Human recognition system for outdoor videos using Hidden Markov model

Human recognition is an essential requirement for human-centric surveillance, activity recognition, gait recognition etc. Inaccurate recognition of humans in such applications may leads to false alarm and unnecessary computation. In the proposed work a robust background modeling algorithm using fuzzy logic is used to detect foreground objects. Three distinct features are extracted from the contours of detected objects. An unique aggregated feature vector is formed using a fuzzy inference system by aggregating three feature vectors. To minimize computation in recognition using Hidden Markov model (HMM), the length of final feature vector is reduced using vector quantization. The proposed method is explained using five basic phases; background modeling and foreground object detection, features extraction, aggregated feature vector calculation, vector quantization, and recognition using Hidden Markov model.     

Use of influence diagrams and neural networks in modelingsemiconductor manufacturing processes

An adaptive learning architecture for modeling manufacturing processes involving several control variables is described. The use of this architecture to process modeling and recipe synthesis for deposition rate, stress, and film thickness in low-pressure chemical vapor deposition (LPCVD) of undoped polysilicon is discussed. In this architecture the model for a process is generated by combining the qualitative knowledge of human experts, captured in the form of influence diagrams, and the learning abilities of neural networks for extracting the quantitative knowledge that relates the parameters of a process. To evaluate the merits of this methodology, the accuracy of these new models is compared to that of more conventional models generated by the use of first principles and/or statistical regression analysis. The models generated by the integration of influence diagrams and neural networks are shown to have half the error or less, even though given only half as much information in creating the models. Furthermore, it is shown that, by employing the generalization ability of neural networks in the synthesis algorithm, new recipes can be produced for the process. Two such recipes are generated for the LPCVD process. One is a zero-stress polysilicon film recipe; the second is a uniform deposition rate recipe which is based on the use of a nonuniform temperature distribution during deposition     

Identification of pneumatic artificial muscle manipulators by a MGA-based nonlinear NARX fuzzy model

This study investigates the technique of modeling and identification of a new dynamic NARX fuzzy model by means of genetic algorithms. In conventional identification techniques, there are difficulties such as poor knowledge of the process, inaccurate process or complexity of the resulting mathematical model. All these factors deteriorate the identification performance when dealing with dynamic nonlinear industrial processes. To overcome these difficulties, this paper proposes a novel approach by using a modified genetic algorithm (MGA) combined with the predictive capability of nonlinear ARX (NARX) model for generating the dynamic NARX Takagi–Sugeno (TS) fuzzy model. The MGA algorithm processes the experimental input–output training data from the real system and optimizes the NARX fuzzy model parameters. This is referred to as fuzzy identification, which automatically generates the appropriate fuzzy if-then rules to characterize the dynamic nonlinear features of the real plant. The prototype pneumatic artificial muscle (PAM) manipulator, being a typical nonlinear and time-varying system, is used as a test system for this novel approach. This result shows that, with this MGA-based modeling and identification, the novel NARX fuzzy model identification approach to the PAM manipulator achieved highly outstanding performance and high precision as well. The accuracy of the proposed MGA-based NARX fuzzy model proves excellent in comparison with the MGA-based TS fuzzy model and the conventional GA-based TS fuzzy model.     

Parameter identification and vibration control in Modular manipulators

The joint parameters of modular manipulators are prerequisite data for effective dynamic control. A method for identifying these parameters using fuzzy logic was devised to study modular redundant robots. Experimental modal analysis and finite element modeling were exploited to model the dynamics. The joint parameters of a nine degrees-of-freedom (9-DOF) modular robot have been identified. In addition, active vibration control based on a neural network and a genetic algorithm were investigated. Ideal control simulation results for a reduced dynamic model of the 9-DOF modular robot were then derived.     

Modeling, optimization and control of spatial uniformity inmanufacturing processes

Spatial uniformity, or the uniformity of product output characteristics at different locations in a batch of product is modeled, optimized, and controlled using a methodology called multiple response surfaces, which may be used to characterize the results of an experimental design. Multiple, low-order polynomial models are used to model the output characteristics at each of several sites within a batch of product. The uniformity model is then obtained by manipulating these multiple models. The approach is compared to the traditional method of fitting a single high-order polynomial to the calculated uniformity. Experimental results confirm that similar or improved modeling accuracy is obtained with fewer data points using the new method due to the use of low-order models. Characteristics of the approach are examined both analytically and in application to plasma etching, silicon epitaxy, tungsten chemical vapor deposition (CVD) and the simulation of polysilicon low-pressure CVD (LPCVD)