AN ELECTRO-THERMAL APPROACH TO ACTIVE THERMOGRAPHY RAJESH GUPTA

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1 AN ELECTRO-THERMAL APPROACH TO ACTIVE THERMOGRAPHY by RAJESH GUPTA Centre for Applied Research in Electronics Submitted in fulfillment of the requirements of the degree of DOCTOR OF PHILOSOPHY to the INDIAN INSTITUTE OF TECHNOLOGY, DELHI NEW DELHI , INDIA December 2004

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3 Dedicated to Mankind

4 CERTIFICATE This is to certify that the thesis entitled "An Electro-Thermal Approach to Active Thermography", which is being submitted by Mr. Rajesh Gupta to the Indian Institute of Technology, Delhi, for the award of the degree of Doctor of Philosophy, is a record of bonafide research work carried out by him under my supervision. In my opinion, this thesis has reached the standard fulfilling the requirements of the regulations relating to the degree. The results contained in it have not been submitted, in part or full, to any other university or institute for the award of any degree or diploma. Dr. Suneet Tuli Associate Professor Centre for Applied Research in Electronics Indian Institute of Technology, Delhi New Delhi , India

5 ACKNOWLEDGEMENTS To the Ministry of Human Resource Development, Govt. of India, for providing financial assistance during the course of this work. To Dr. Suneet Tuli (my supervisor), for his invaluable encouragement, inspiration, guidance and for providing an excellent working environment during the course of this work. Apart from academics, I have personally gained a lot from his thoughts and the way of thinking. To Dr. G. Bose, for his valuable technical support, advice, encouragement and for providing facilities of microelectronics laboratory. To Director, IIT Delhi, Prof. D. Nagchoudhary (EE), Head and faculty members of CARE, for providing facilities and valuable suggestions from time-to-time. To Prof. V. Vavilov, Tomsk Polytechnic University, Russia, for technical discussions and Prof. X. Maldague, University Laval, Canada, for his continued interaction and support. To the technical and non-technical staff of CARE: Mr. Govind Ram, Mr. Pardeep, Mrs. Sneh Kapoor, Mr. Chana, Mr. Joseph, Mrs. Ravinder Kaur, Mr. Sethi, Mr. Purushottam, Mr. Govind and others for readily providing support and services during my research work. To my research colleagues and fellow workers: Prem, Jyotsana, Sudha, Venkatesh, Swami, Ravi, Jyoti, Vivekanand, Gagan, Nagendra, Ravindra, Priyanka and Preeti for discussions and sharing light moments. To my parents, and other family members for their support and patience. To my friends: Rupesh, Pallav, Pramod and Ravi for their encouragement. Raj esh Gupta

6 ABSTRACT Active infrared thermography is a nondestructive evaluation technique in which a material is thermally stimulated by a heat source, and the resulting thermal transient at the surface of material is recorded, generally by an infrared camera. As the heat diffuses inside the material, it get perturbed by the presence of sub-surface defects, causing a temperature contrast at the surface, which is then used for defect detection. The technique is relatively fast, safe, non-contact and easy to use for large area scans. It is also applicable to a wide range of materials and can be employed for single side inspection of complex geometries without any significant difficulty. Active infrared thermography is generally used for qualitative inspections. Quantitative analysis based on this technique tends to be quite complex, especially when inverse solutions are required for estimation of defect parameters. In the present work, a simplified electro-thermal approach has been introduced in this field, for obtaining novel analytical inverse solutions for stepped infrared thermography, independent of material thermal properties. Electro-thermal modeling and simulation has also been used for obtaining direct active thermography solutions, which are important in the study of surface temperature evolution under the effect of various parameters. Analytic. inverse solutions related to the estimation of thermal properties of materials from the surface temperature evolution have also been presented in the thesis based on the same electro-thermal approach.

7 In the electro-thermal approach, active thermography problems have been modeled in terms of electrical equivalent circuits and solved with the help of circuit simulator and network analysis techniques for obtaining direct and inverse solutions, respectively. This approach simplifies the thermal problem by constructing approximate analogous electrical models of the problems, thereby reducing many complexities of the purely analytical thermal approach. Electrothermal approach has been widely used and well established in other fields (e.g. thermal investigation of integrated circuits and system, thermal modeling of buildings, thermal software's etc). However, such an approach has not yet been introduced in the field of active infrared thermography for obtaining simplified solutions and analysis of active thermography problems. In the present work, this approach has been exploited in the interest of some active infrared thermography problems. work. The thesis consists of six chapters, each dealing with a specific aspect of this Chapter-1 introduces nondestructive testing and various techniques of active infrared thermography with brief overview of earlier solutions. Basic introduction and motivation behind the electro-thermal approach for the active thermography solution has been explained along with the objectives behind the thesis. Chapter-2 describes the electrical equivalence of heat conduction by direct comparison of differential equations describing, voltage variation in a lossy transmission line, with temperature variation in one-dimensional (1D) heat II

8 conduction. Based on that, 1D, 2D and 3D electro-thermal models have been proposed for obtaining direct solutions of active thermography. These models can be simulated and solved by a wide variety of circuit simulators, without the need for dedicated thermography software. In the present work, a 3D electro-thermal model of samples has been generated and simulated by commonly available SPICE (Simulation Program with Integrated Circuit Emphasis) family of circuit simulator. Some studies related to optimization of heating parameters have been undertaken on mild-steel and silicon samples from the prediction of surface temperature evolution by this method. Experiments have also been performed in support of simulated results. Application of active thermography for nondestructive evaluation of silicon structure has also been explored in this chapter. Active infrared thermography has also been proposed for detection and estimation of voids in bonded wafers, which are used in fabrication of microelectronic and optoelectronic devices, and micromechanical systems. A lumped 1D electrical model of transient heat conduction has been used for deriving an analytical expression of the void thickness from surface temperature evolution over the bonded wafers. The estimated void thickness obtained from this expression has been verified by simulated results. Chapter-3 presents the electro-thermal modeling, analysis and validation for estimation ofdefect depth by stepped infrared thermography. A one-dimensional electrical analysis based on the Laplace transform technique of network analysis and delay time in resistance-capacitance (RC) ladder network, is adopted for depth estimation. Defect depth is evaluated based on the time instants at which the iii

9 surface temperature evolution, over the defect and non-defect regions of the material, deviates from its constant initial slope corresponding to the response of a semi-infinite material, under similar condition of step heating. The method is applicable to materials with unknown thermal properties. Experimental and simulated results validate the proposed method and give good estimation of defect depth. Chapter-4 presents a RC model of transient heat conduction for the estimation of defect area from single point surface temperature evolutions over the defect and non-defect regions of a material subjected to step heating. For estimation of defect area, a lumped RC model is the basis for obtaining an analytical expression of defect area from the later part of surface temperature evolution. The derived analytical expression, estimates the defect area from the defect depth (obtained in the earlier chapter), the saturation value of absolute thermal contrast and the initial and final slopes of surface temperature evolution curve. The presented method does not require knowledge of material thermal properties and incident value of heat flux. The method has been validated, by estimating the defect areas of various sizes and at different depths, from the experimental and simulated surface temperature evolutions. Chapter-5 presents the electro-thermal modeling, analysis and validation for estimation of thermal conductivity and thermal diffusivity of materials through contact and non-contact fashion. The analysis of stepped thermography presented in Chapters 3 and 4, has further been used for obtaining the analytical expressions of thermal diffusivity and thermal conductivity for the estimation of these iv

10 properties through non-contact fashion. However, for the estimation of these properties by contact fashion, the material is heated from one side by making physical contact with another hot body and temperature evolution at other side of the material is recorded by placing a temperature sensor in contact. For this purpose, silicon spreading resistance temperature sensor and its associated electronics has been designed and developed for measurement of temperature. Delay time analysis of 1D distributed RC ladder network has been exploited for the analysis of this problem, and analytical expressions for thermal properties have subsequently been derived. All the derived expressions for thermal properties are for non-steady state conditions, which is advantageous for fast measurements. Experiments and simulations have been preformed for validating the proposed expressions. Chapter-6 summarises the work in the thesis and concludes by highlighting scope of further work.

11 CONTENTS, Abstract List of Figures List of Tables Nomenclature vi xiii xiv CHAPTER-1 INTRODUCTION Nondestructive Testing Infrared Thermography Literature Survey Electro-thermal Approach Thesis Motivation and Objective Outline of Thesis 1.15 CHAPTER-2 ELECTRO-THERMAL MODELING AND SPICE SIMULATION FOR ACTIVE THERMOGRAPHY Introduction Electro-thermal Modeling for Active Thermography SPICE Simulated and Experimental Results Mild-steel Sample Silicon Sample Electro-thermal Analysis for Characterization of Bonded Wafers Conclusions 2.35 CHAPTER-3 DEFECT DEPTH ESTIMATION BY STEPPED INFRARED THERMOGRAPHY Introduction Electro-thermal Modeling and Analysis for Defect Depth Estimation Simulated and Experimental Results Conclusions 3.27

12 CHAPTER-4 DEFECT AREA ESTIMATION BY STEPPED INFRARED THERMOGRAPHY 4.1 Introduction 4.2 Electro-thermal Modeling and Analysis for Defect Area Estimation 4.3 Simulated and Experimental Results 4.4 Conclusions CHAPTER-5 ESTIMATION OF MATERIAL THERMAL PROPERTIES 5.1 Introduction 5.2 Estimation of Thermal Properties through Non-contact Stepped Infrared Thermography Analysis of Thermal Properties Results and Discussion 5.3 Estimation of Thermal Properties by Contact Method with Step Temperature Rise Analysis of Thermal properties Design and Development of Silicon Spreading Resistance Thermometer Results Discussion 5.4 Conclusions CHAPTER-6 CONCLUSION 6.1 Conclusions 6.2 Scope of Future Work References R.1-R.12