DOCSLIB.ORG

Study of Stress in Microelectronic Materials by Photoelasticity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Study of Stress in Microelectronic Materials by Photoelasticity New Jersey Institute of Technology Digital Commons @ NJIT Dissertations Electronic Theses and Dissertations Fall 1996 Study of stress in microelectronic materials by photoelasticity Hancheng Liang New Jersey Institute of Technology Follow this and additional works at: https://digitalcommons.njit.edu/dissertations Part of the Electrical and Electronics Commons Recommended Citation Liang, Hancheng, "Study of stress in microelectronic materials by photoelasticity" (1996). Dissertations. 1017. https://digitalcommons.njit.edu/dissertations/1017 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at Digital Commons @ NJIT. It has been accepted for inclusion in Dissertations by an authorized administrator of Digital Commons @ NJIT. For more information, please contact [email protected]. Copyright Warning & Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be “used for any purpose other than private study, scholarship, or research.” If a, user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of “fair use” that user may be liable for copyright infringement, This institution reserves the right to refuse to accept a copying order if, in its judgment, fulfillment of the order would involve violation of copyright law. Please Note: The author retains the copyright while the New Jersey Institute of Technology reserves the right to distribute this thesis or dissertation Printing note: If you do not wish to print this page, then select “Pages from: first page # to: last page #” on the print dialog screen The Van Houten library has removed some of the personal information and all signatures from the approval page and biographical sketches of theses and dissertations in order to protect the identity of NJIT graduates and faculty. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 UMI Number: 9618582 Copyright 1996 by Liang, Hancheng All rights reserved. UMI Microform 9618582 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 ABSTRACT STUDY OF STRESS IN MICROELECTRONIC MATERIALS BY PHOTOELASTICITY by Hancheng Liang The study of stress is playing an important role in microelectronic technology. In comparison with other techniques, the photoelasticity technique has the advantages of having high spatial resolution and high sensitivity. It can be used in qualitative observation in real-time and quantitative determination of stress distribution in the microelectronic materials and devices. This dissertation presents a systematic study of photoelastic stress analysis in microelectronic materials and devices, ranged from theoretical study to practical system setup, from measurement methods to their applications. At first, based on the detailed survey on the piezo-optic properties of the crystals used in microelectronics, we apply the stress-optic law of engineering mechanics to study the stress in crystals, such as silicon, gallium arsenide, and diamond. We, for the first time, derive the relationship between the stress ellipsoid and the refractive index ellipsoid, and, derive the matrix forms of piezo­ optic coefficient tensor for several commonly used coordinates. These theoretical results have laid a firm ground for the photoelastic stress analysis of microelectronic materials and devices. Second, based on exclusive experiments, we develop several effective methods of photoelastic analysis to determine the stress state in the samples. Some of them are successfully borrowed from the classic photoelastic mechanics, such as the Semarmont compensation which is used to determine the decimal fringe of the isochromatic line, and the shearing stress difference method which is used to separate two principal stresses and obtain the stress distribution of a sample. We also provide our origination to the photoelastic techniques, such as the three-direction observation method which is used to abstract the principal stresses from the secondary principal stresses; the Fourier analysis method and the intensity analysis method, both of which are especially suitable for precisely and automatically determining the principal stress distribution in a large area. Combining computer and digital image processing techniques with photoelastic techniques, we set up a photoelastic measurement system, which has the capability of qualitative observation of the photoelastic patterns and quantitative measurement of the stress distribution. We apply the photoelasticity principles and methods to investigate the stress state in microelectronic materials, including developing a series of feasible methods to measure the stress distribution of the microelectronic materials and devices, investigating the mechanisms of stress induction and stress change. For example, we investigate the stress distribution of a synthetic diamond substrate, study the stress induced during the typical impurity diffusion processes for manufacturing power diodes, and analyze the stress induced in the thin film/substrate structures. We also develop some models to explain the measurement results and provide theoretical discussions of the results. STUDY OF STRESS IN MICROELECTRONIC MATERIALS BY PHOTOELASTICITY by Hancheng Liang A Dissertation Submitted to the Faculty of New Jersey Institute of Technology Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Department of Electrical and Computer Engineering January 1996 Copyright © 1996 by Hancheng Liang ALL RIGHTS RESERVED APPROVAL PAGE STUDY OF STRESS IN MICROELECTRONIC MATERIALS BY PHOTOELASTICITY Hancheng Liang Dr. Ken K. Chin, Dissertation Adviser Date Professor of Physics, NJIT Dr. John C. Hensel, Committee Member Date Distinguished Research Professor of Physics, NJIT Dr. Robert B. Marcus, Committee Member Date Research Professor of Electrical and Computer Engineering, NJIT Dr. William N. Carr, Committee Member Date Professor of Electrical and Computer Engineering, NJIT Professor of Physics, NJIT Dr. Yun-Qing Shi, Committee Member Date Associate Professor of Electrical and Computer Engineering, NJIT BIOGRAPHICAL SKETCH Author: Hancheng Liang Degree: Doctor of Philosophy in Electrical Engineering Date: January 1996 Education: • Doctor of Philosophy in Electrical Engineering New Jersey Institute of Technology, Newark, New Jersey, 1996 • Master of Science in Applied Physics South China Institute of Technology, Guangzhou, P. R. China, 1985 • Diploma of Electrical Engineering South China Institute of Technology, Guangzhou, P. R. China, 1980 Major: Electrical Engineering Presentations and Publications: Hancheng Liang, Yongxiong Pan, Shounan Zhao, Ganming Qin, and K. Ken Chin, "Two-Dimensional State of Stress in a Silicon Wafer", J. Appl. Phys. 71 (1992): 2863-2870. Hancheng Liang, Shounan Zhao, and K. Ken Chin, "A New Method of Determining the Stress State in Microelectronic Materials", Measurement Science and Technology, 6 (1995): 1-4. Hancheng Liang, Shounan Zhao, Ganming Qin, and K. Ken Chin, "Thin Film- induced Stress in Substrate/Thin Film Structure", Procedings of the Fourth International Conference on Solid-State and Integrated-Circuit Technology, Publishing House of the Electronics Industry, Beijing (1995): 272-274. Hancheng Liang, Andrei Vescan, Erhard Kohn, and K. Ken Chin, "Measurement of Stress in a Synthetic Diamond Substrate by Using Photoelastic Method", The Sixth European Conference on Diamond, Diamond-Like and Related Materials, Barcelona, Spain, 1995. Also accepted for publication in Diamond and Related Materials. iv To my beloved family v ACKNOWLEDGMENT The author wishes to express his sincere gratitude to his advisor, Dr. Ken K. Chin, for his encouragement,
Load more

Recommended publications
  • Processor U.S
    USOO5926295A United States Patent (19) 11 Patent Number: 5,926,295 Charlot et al. (45) Date of Patent: Jul. 20, 1999 54) HOLOGRAPHIC PROCESS AND DEVICE 4,602,844 7/1986 Sirat et al. ............................. 350/3.83 USING INCOHERENT LIGHT 4,976,504 12/1990 Sirat et al. .. ... 350/3.73 5,011,280 4/1991 Hung.............. ... 356/345 75 Inventors: Didier Charlot, Paris; Yann Malet, 5,081,540 1/1992 Dufresne et al. ... ... 359/30 Saint Cyr l’Ecole, both of France 5,081,541 1/1992 Sirat et al. ...... ... 359/30 5,216,527 6/1993 Sharnoff et al. ... 359/10 73 Assignee: Le Conoscope SA, Paris, France 5,223,966 6/1993 Tomita et al. .......................... 359/108 5,291.314 3/1994 Agranat et al. ......................... 359/100 21 Appl. No.: 08/681,926 22 Filed: Jul. 29, 1996 Primary Examiner Jon W. Henry Attorney, Agent, or Firm Michaelson & Wallace; Peter L. Related U.S. Application Data Michaelson; John C. Pokotylo 62 Division of application No. 08/244.249, filed as application 57 ABSTRACT No. PCT/FR92/01095, Nov. 25, 1992, Pat. No. 5,541,744. An optical device for generating a signal based on a distance 30 Foreign Application Priority Data of an object from the optical device. The optical device includes a first polarizer, a birefringent crystal positioned Nov. 27, 1991 FR France ................................... 91. 14661 optically downstream from the first polarizer, and a Second 51) Int. Cl. .............................. G03H 1/26; G01B 9/021 polarizer arranged optically downstream from the birefrin 52 U.S. Cl. ................................... 359/30; 359/11; 359/1; gent crystal.
    [Show full text]
  • William T. Rowe
    Bao Shichen: An Early Nineteenth-Century Chinese Agrarian Reformer William T. Rowe Johns Hopkins University Prefatory note to the Agrarian Studies Program: I was greatly flattered to receive an invitation from Jim Scott to present to this exalted group, and could not refuse. I’m also a bit embarrassed, however, because I’m not working on anything these days that falls significantly within your arena of interest. I am studying in general a reformist scholar of the early nineteenth century, named Bao Shichen. The contexts in which I have tended to view him (and around which I organized panels for the Association for Asian Studies Annual Meetings in 2007 and 2009) have been (1) the broader reformist currents of his era, spawned by a deepening sense of dynastic crisis after ca. 1800, and (2) an enduring Qing political “counter discourse” beginning in the mid-seventeenth century and continuing down to, and likely through, the Republican Revolution of 1911. Neither of these rubrics are directly concerned with “agrarian studies.” Bao did, however, have quite a bit to say in passing about agriculture, village life, and especially local rural governance. In this paper I have tried to draw together some of this material, but I fear it is as yet none too neat. In my defense, I would add that previously in my career I have done a fair amount of work on what legitimately is agrarian history, and indeed have taught courses on that subject (students are less interested in such offerings now than they used to be, in my observation).
    [Show full text]
  • Lab 8: Polarization of Light
    Lab 8: Polarization of Light 1 Introduction Refer to Appendix D for photos of the appara- tus Polarization is a fundamental property of light and a very important concept of physical optics. Not all sources of light are polarized; for instance, light from an ordinary light bulb is not polarized. In addition to unpolarized light, there is partially polarized light and totally polarized light. Light from a rainbow, reflected sunlight, and coherent laser light are examples of po- larized light. There are three di®erent types of po- larization states: linear, circular and elliptical. Each of these commonly encountered states is characterized Figure 1: (a)Oscillation of E vector, (b)An electromagnetic by a di®ering motion of the electric ¯eld vector with ¯eld. respect to the direction of propagation of the light wave. It is useful to be able to di®erentiate between 2 Background the di®erent types of polarization. Some common de- vices for measuring polarization are linear polarizers and retarders. Polaroid sunglasses are examples of po- Light is a transverse electromagnetic wave. Its prop- larizers. They block certain radiations such as glare agation can therefore be explained by recalling the from reflected sunlight. Polarizers are useful in ob- properties of transverse waves. Picture a transverse taining and analyzing linear polarization. Retarders wave as traced by a point that oscillates sinusoidally (also called wave plates) can alter the type of polar- in a plane, such that the direction of oscillation is ization and/or rotate its direction. They are used in perpendicular to the direction of propagation of the controlling and analyzing polarization states.
    [Show full text]
  • Chronology of Chinese History
    Chronology of Chinese History I. Prehistory Neolithic Period ca. 8000-2000 BCE Xia (Hsia)? Trad. 2200-1766 BCE II. The Classical Age (Ancient China) Shang Dynasty ca. 1600-1045 BCE (Trad. 1766-1122 BCE) Zhou (Chou) Dynasty ca. 1045-256 BCE (Trad. 1122-256 BCE) Western Zhou (Chou) ca. 1045-771 BCE Eastern Zhou (Chou) 770-256 BCE Spring and Autumn Period 722-468 BCE (770-404 BCE) Warring States Period 403-221 BCE III. The Imperial Era (Imperial China) Qin (Ch’in) Dynasty 221-207 BCE Han Dynasty 202 BCE-220 CE Western (or Former) Han Dynasty 202 BCE-9 CE Xin (Hsin) Dynasty 9-23 Eastern (or Later) Han Dynasty 25-220 1st Period of Division 220-589 The Three Kingdoms 220-265 Shu 221-263 Wei 220-265 Wu 222-280 Jin (Chin) Dynasty 265-420 Western Jin (Chin) 265-317 Eastern Jin (Chin) 317-420 Southern Dynasties 420-589 Former (or Liu) Song (Sung) 420-479 Southern Qi (Ch’i) 479-502 Southern Liang 502-557 Southern Chen (Ch’en) 557-589 Northern Dynasties 317-589 Sixteen Kingdoms 317-386 NW Dynasties Former Liang 314-376, Chinese/Gansu Later Liang 386-403, Di/Gansu S. Liang 397-414, Xianbei/Gansu W. Liang 400-422, Chinese/Gansu N. Liang 398-439, Xiongnu?/Gansu North Central Dynasties Chang Han 304-347, Di/Hebei Former Zhao (Chao) 304-329, Xiongnu/Shanxi Later Zhao (Chao) 319-351, Jie/Hebei W. Qin (Ch’in) 365-431, Xianbei/Gansu & Shaanxi Former Qin (Ch’in) 349-394, Di/Shaanxi Later Qin (Ch’in) 384-417, Qiang/Shaanxi Xia (Hsia) 407-431, Xiongnu/Shaanxi Northeast Dynasties Former Yan (Yen) 333-370, Xianbei/Hebei Later Yan (Yen) 384-409, Xianbei/Hebei S.
    [Show full text]
  • Principles of Retarders
    Polarizers PRINCIPLES OF RETARDERS etarders are used in applications where control or Ranalysis of polarization states is required. Our retarder products include innovative polymer and liquid crystal materials. Crystalline materials such as quartz and Retarders magnesium fluoride are also available upon request. Please call for a custom quote. A retarder (or waveplate) is an optical device that resolves a light wave into two orthogonal linear polarization components and produces a phase shift between them. The resulting light wave is generally of a different polarization form. Ideally, retarders do not polarize, nor do they induce an intensity change in the Crystals Liquid light beam, they simply change its polarization form. state. The transmitted light leaves the retarder elliptically All standard catalog Meadowlark Optics’ retarders are polarized. made from birefringent, uniaxial materials having two Retardance (in waves) is given by: different refractive indices – the extraordinary index ne = ␤tր␭ and the ordinary index no. Light traveling through a retarder has a velocity v where: dependent upon its polarization direction given by ␤ = birefringence (ne - no) Spatial Light ␭ Modulators v = c/n = wavelength of incident light (in nanometers) t = thickness of birefringent element where c is the speed of light in a vacuum and n is the (in nanometers) refractive index parallel to that polarization direction. Retardance can also be expressed in units of length, the By definition, ne > no for a positive uniaxial material. distance that one polarization component is delayed For a positive uniaxial material, the extraordinary axis relative to the other. Retardance is then represented by: is referred to as the slow axis, while the ordinary axis is ␦Ј ␦␭ ␤ referred to as the fast axis.
    [Show full text]
  • Yue Liang Department of Human Development and Family Studies the University of North Carolina at Greensboro Greensboro, NC, 27403 (336) 500-9596 Y [email protected]
    Yue Liang Department of Human Development and Family Studies The University of North Carolina at Greensboro Greensboro, NC, 27403 (336) 500-9596 [email protected] EDUCATION 2012-2014 Beijing Normal University, Beijing, China School of Psychology M.S. Developmental Psychology, June 2014 Major Field: Developmental Psychology Minor Fields: Cognitive Neuroscience Thesis: Dual processing in creative thinking: The role of working memory 2008-2012 China University of Political Science and Law, Beijing, China Department of Psychology B.S. June 2012 Thesis: Research on relationship between family cohesion and implicit aggression of adolescents with externalizing behaviors AREAS OF SCIENTIFIC INTEREST Social development of child and adolescent, moral development, parenting behaviors PUBLICATIONS Cao, H., Zhou, N., Mills-Koonce, W. R., Liang, Y., Li, J., & Fine, A. M. (Under review). Minority Stress and Relationship Outcomes among Same-sex Couples: A Meta-Analysis. Journal of Family Theory and Review. Kiang, L., Mendonça, S. E, Liang, Y., Payir, A., , Freitas, L. B. L., O’Brien, L., & Tudge, J. R. H. (Under review). If Children Won Lotteries: Materialism, Gratitude, and Spending in an Imaginary Windfall. Social Development. Tudge, J. R. H., Payir, A., Merçon-Vargas, E., Cao, H., Liang, Y., & Li, J. (Under review). Still misused after all these years? A re-evaluation of the uses of Bronfenbrenner’s bioecological theory of human development. Journal of Family Theory and Review. MANUSCRIPTS IN PROGRESS Liang, Y., Zhou, N. & Cao, H. (In progress). Maternal provision of learning opportunities in early childhood and externalizing behaviors in early adolescence: The mediation role of executive functioning. Mokrova, I., Liang, Y., & Tudge, J.
    [Show full text]
  • Optical and Thin Film Physics Polarisation of Light
    OPTICAL AND THIN FILM PHYSICS POLARISATION OF LIGHT An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular to each other; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field. In linear polarization, the fields oscillate in a single direction. In circular or elliptical polarization, the fields rotate at a constant rate in a plane as the wave travels. The rotation can have two possible directions; if the fields rotate in a right hand sense with respect to the direction of wave travel, it is called right circular polarization, while if the fields rotate in a left hand sense, it is called left circular polarization. On the other side of the plate, examine the wave at a point where the fast-polarized component is at maximum. At this point, the slow-polarized component will be passing through zero, since it has been retarded by a quarter-wave or 90° in phase. Moving an eighth wavelength farther, we will note that the two are the same magnitude, but the fast component is decreasing and the slow component is increasing. Moving another eighth wave, we find the slow component is at maximum and the fast component is zero. If the tip of the total electric vector is traced, we find it traces out a helix, with a period of just one wavelength. This describes circularly polarized light. Left-hand polarized light is produced by rotating either the waveplate or the plane of polarization of the incident light 90° .
    [Show full text]
  • In China: Why Young Rural Women Climb the Ladder by Moving Into China’S Cities
    “Making It” In China: Why Young Rural Women Climb the Ladder by Moving into China’s Cities By Lai Sze Tso A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Women’s Studies and Sociology) in the University of Michigan 2013 Doctoral Committee: Professor Mary E. Corcoran, Co-Chair Professor Fatima Muge Gocek, Co-Chair Professor Pamela J. Smock Associate Professor Zheng Wang © Lai Sze Tso 2013 DEDICATION I dedicate this dissertation to Mom, Danny, Jeannie, and Dad. I could not have accomplished this without your unwavering love and support. During the toughest times, I drew strength from your understanding and resilience. ii ACKNOWLEDGEMENTS I would like to recognize the invaluable guidance of my dissertation committee, Pam Smock, Muge Gocek, Wang Zheng, and Mary Corcoran. I also learned a great deal about China as a member of James Lee's research team. Thank you James and Cameron Campbell for teaching me the ropes in Chinese academe, and Zhang hao for helping me adjust to fieldwork in North River. I am also indebted to Xiao Xing for digitizing complex hukou files, and Wang Laoshi and Yan Xianghua for helping me navigate the administrative culture at Peking University, Weiran Chen, her family, and Gao Zuren will always have a special place in my heart for the help and hospitality shown me while during the first phase of my research endeavors. Preliminary field work in North River and early drafts of dissertation chapters benefitted immensely from keen insight provided by fellow research team members Danching Ruan, Wang Linlan, Li Lan, Shuang Chen, Li Ji, Liang Chen, Byung-Ho Lee and Ka Yi Fung.
    [Show full text]
  • Stokes Polarimetry
    photoelastic modulators Stokes Polarimetry APPLICATION NOTE by Dr. Theodore C. Oakberg beforehand. The polarimeter should be aligned so that the James Kemp’s version of the photoelastic modulator was passing axis of the modulator is at 45 degrees to the known invented for use as a polarimeter, particularly for use in linear polarization direction, as shown. The polarizer is oriented astronomy. The basic problem is measuring net polarization at right angles to the plane of the incident linear polarization components in what is predominantly an unpolarized light component. source. Dr. Kemp was able to measure a polarization The circular polarization component will produce a signal at the component of light less than 106 below the level of the total modulator frequency, 1f. If the sense of the circular polarization light intensity. is reversed, this will be shown by an output of opposite sign The polarization state of a light source is represented by four from the lock-in amplifi er. This signal is proportional to Stokes numerical quantities called the “Stokes parameters”.1,2 These Parameter V. correspond to intensities of the light beam after it has passed The linear polarization component will give a signal at twice the through certain devices such as polarized prisms or fi lms and modulator frequency, 2f. A linearly polarized component at right wave plates. These are defi ned in Figure 1. angles to the direction shown will produce a lock-in output with I - total intensity of light beam opposite sign. This signal is proportional to Stokes Parameter U. y DETECTOR y A linear component of polarization which is at 45 degrees to the I x x I x x direction shown will produce no 2f signal in the lock-in amplifi er.
    [Show full text]
  • Beyond Buddhist Apology the Political Use of Buddhism by Emperor Wu of the Liang Dynasty
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Ghent University Academic Bibliography Beyond Buddhist Apology The Political Use of Buddhism by Emperor Wu of the Liang Dynasty (r.502-549) Tom De Rauw ii To my daughter Pauline, the most wonderful distraction one could ever wish for and to my grandfather, a cakravartin who ruled his own private universe iii ACKNOWLEDGEMENTS Although the writing of a doctoral dissertation is an individual endeavour in nature, it certainly does not come about from the efforts of one individual alone. The present dissertation owes much of its existence to the help of the many people who have guided my research over the years. My heartfelt thanks, first of all, go to Dr. Ann Heirman, who supervised this thesis. Her patient guidance has been of invaluable help. Thanks also to Dr. Bart Dessein and Dr. Christophe Vielle for their help in steering this thesis in the right direction. I also thank Dr. Chen Jinhua, Dr. Andreas Janousch and Dr. Thomas Jansen for providing me with some of their research and for sharing their insights with me. My fellow students Dr. Mathieu Torck, Leslie De Vries, Mieke Matthyssen, Silke Geffcken, Evelien Vandenhaute, Esther Guggenmos, Gudrun Pinte and all my good friends who have lent me their listening ears, and have given steady support and encouragement. To my wife, who has had to endure an often absent-minded husband during these first years of marriage, I acknowledge a huge debt of gratitude. She was my mentor in all but the academic aspects of this thesis.
    [Show full text]
  • Achieving High Coverage for Floating-Point Code Via Unconstrained Programming
    Achieving High Coverage for Floating-Point Code via Unconstrained Programming Zhoulai Fu Zhendong Su University of California, Davis, USA [email protected] [email protected] Abstract have driven the research community to develop a spectrum Achieving high code coverage is essential in testing, which of automated testing techniques for achieving high code gives us confidence in code quality. Testing floating-point coverage. code usually requires painstaking efforts in handling floating- A significant challenge in coverage-based testing lies in point constraints, e.g., in symbolic execution. This paper turns the testing of numerical code, e.g., programs with floating- the challenge of testing floating-point code into the oppor- point arithmetic, non-linear variable relations, or external tunity of applying unconstrained programming — the math- function calls, such as logarithmic and trigonometric func- ematical solution for calculating function minimum points tions. Existing solutions include random testing [14, 23], over the entire search space. Our core insight is to derive a symbolic execution [17, 24], and various search-based strate- representing function from the floating-point program, any of gies [12, 25, 28, 31], which have found their way into many whose minimum points is a test input guaranteed to exercise mature implementations [16, 39]. Random testing is easy to a new branch of the tested program. This guarantee allows employ and fast, but ineffective in finding deep semantic is- us to achieve high coverage of the floating-point program by sues and handling large input spaces; symbolic execution and repeatedly minimizing the representing function. its variants can perform systematic path exploration, but suf- We have realized this approach in a tool called CoverMe fer from path explosion and are weak in dealing with complex and conducted an extensive evaluation of it on Sun’s C math program logic involving numerical constraints.
    [Show full text]
  • The Later Han Empire (25-220CE) & Its Northwestern Frontier
    University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2012 Dynamics of Disintegration: The Later Han Empire (25-220CE) & Its Northwestern Frontier Wai Kit Wicky Tse University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Asian History Commons, Asian Studies Commons, and the Military History Commons Recommended Citation Tse, Wai Kit Wicky, "Dynamics of Disintegration: The Later Han Empire (25-220CE) & Its Northwestern Frontier" (2012). Publicly Accessible Penn Dissertations. 589. https://repository.upenn.edu/edissertations/589 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/589 For more information, please contact [email protected]. Dynamics of Disintegration: The Later Han Empire (25-220CE) & Its Northwestern Frontier Abstract As a frontier region of the Qin-Han (221BCE-220CE) empire, the northwest was a new territory to the Chinese realm. Until the Later Han (25-220CE) times, some portions of the northwestern region had only been part of imperial soil for one hundred years. Its coalescence into the Chinese empire was a product of long-term expansion and conquest, which arguably defined the egionr 's military nature. Furthermore, in the harsh natural environment of the region, only tough people could survive, and unsurprisingly, the region fostered vigorous warriors. Mixed culture and multi-ethnicity featured prominently in this highly militarized frontier society, which contrasted sharply with the imperial center that promoted unified cultural values and stood in the way of a greater degree of transregional integration. As this project shows, it was the northwesterners who went through a process of political peripheralization during the Later Han times played a harbinger role of the disintegration of the empire and eventually led to the breakdown of the early imperial system in Chinese history.
    [Show full text]