Thesis (M.S.)--Rochester Institute of Technology, 1992. / Typescript. Includes bibliographical references (leaves 114-116).

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Digitized by Kansas Correctional Industries

by Kwan Wai Wing Eric. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references. / ABSTRACT / ACKNOWLEDGMENT / LIST OF FIGURES / LIST OF TABLES / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Background --- p.1-1 / Chapter 1.2 --- E-Beam testing and test generation algorithm --- p.1-2 / Chapter 1.3 --- Motivation of this research --- p.1-4 / Chapter 1.4 --- Out-of-kilter Algorithm --- p.1-6 / Chapter 1.5 --- Outline of the remaining chapter --- p.1-7 / Chapter Chapter 2 --- Electron Beam Testing / Chapter 2.1 --- Background and Theory --- p.2-1 / Chapter 2.2 --- Principles and Instrumentation --- p.2-4 / Chapter 2.3 --- Implication of internal IC testing --- p.2-6 / Chapter 2.4 --- Advantage of Electron Beam Testing --- p.2-7 / Chapter Chapter 3 --- An exhaustive method to minimize test sets / Chapter 3.1 --- Basic Principles --- p.3-1 / Chapter 3.1.1 --- Controllability and Observability --- p.3-1 / Chapter 3.1.2 --- Single Stuck at Fault Model --- p.3-2 / Chapter 3.2 --- Fault Dictionary --- p.3-4 / Chapter 3.2.1 --- Input Format --- p.3-4 / Chapter 3.2.2 --- Critical Path Generation --- p.3-6 / Chapter 3.2.3 --- Probe point insertion --- p.3-8 / Chapter 3.2.4 --- Formation of Fault Dictionary --- p.3-9 / Chapter Chapter 4 --- Mathematical Model - Out-of-kilter algorithm / Chapter 4.1 --- Network Model --- p.4-1 / Chapter 4.2 --- Linear programming model --- p.4-3 / Chapter 4.3 --- Kilter states --- p.4-5 / Chapter 4.4 --- Flow change --- p.4-7 / Chapter 4.5 --- Potential change --- p.4-9 / Chapter 4.6 --- Summary and Conclusion --- p.4-10 / Chapter Chapter 5 --- Apply Mathematical Method to minimize test sets / Chapter 5.1 --- Implementation of OKA to the Fault Dictionary --- p.5-1 / Chapter 5.2 --- Minimize test set and optimize internal probings / probe points --- p.5-5 / Chapter 5.2.1 --- Minimize the number of test vectors --- p.5-5 / Chapter 5.2.2 --- Find the optimum number of internal probings --- p.5-8 / Chapter 5.2.3 --- Find the optimum number of internal probe points --- p.5-11 / Chapter 5.3 --- Fixed number of internal probings/probe points --- p.5-12 / Chapter 5.4 --- True minimum test set and optimum probing/ probe point --- p.5-14 / Chapter Chapter 6 --- Implementation and work examples / Chapter 6.1 --- Generation of Fault Dictionary --- p.6-1 / Chapter 6.2 --- Finding the minimum test set without internal probe point --- p.6-5 / Chapter 6.3.1 --- Finding the minimum test set with optimum internal probing --- p.6-10 / Chapter 6.3.2 --- Finding the minimum test set with optimum internal probe point --- p.6-24 / Chapter 6.4 --- Finding the minimum test set by fixing the number of internal probings at 2 --- p.6-26 / Chapter 6.5 --- Program Description --- p.6-35 / Chapter Chapter 7 --- Realistic approach to find the minimum solution / Chapter 7.1 --- Problem arising in exhaustive method --- p.7-1 / Chapter 7.2 --- Improvement work on existing test generation algorithm --- p.7-2 / Chapter 7.3 --- Reduce the search set --- p.7-5 / Chapter 7.3.1 --- Making the Fault Dictionary from existing test generation algorithm --- p.7-5 / Chapter 7.3.2 --- Making the Fault Dictionary by random generation --- p.7-9 / Chapter Chapter 8 --- Conclusions / Chapter 8.1 --- Summary of Results --- p.8-1 / Chapter 8.2 --- Further Research --- p.8-5 / REFERENCES --- p.R-1 / Chapter Appendix A --- Fault Dictionary of circuit SC1 --- p.A-1 / Chapter Appendix B --- Fault Dictionary of circuit SC7 --- p.B-1 / Chapter Appendix C --- Simple Circuits Layout --- p.C-1

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Czochralski (Cz) silicon wafers are used almost exclusively for the fabrication of VLSI devices. Such silicon contains excess oxygen which precipitates as oxide particles either when the initial ingot is grown or subsequently during the wafer device fabrication. Such oxide particles can produce reduced device performance or failure if they occur within the active device regions. However, they can be used to improve the device performance by a process known as internal oxide gettering. The wafers are given a series of preanneal treatments to produce controlled precipitation in which a surface zone of the wafer to a depth of typically in the range of 10 to 50 μm is denuded of oxide particles, while the remainder of the wafer contains large numbers of well formed particles. The devices are fabricated in the surface denuded zone and harmful contaminating metal impurities are attracted during the heat treatment stages away from the device regions to precipitate at the underlying oxide particles or their associated dislocations. In this way device yields can be significantly increased. Because of the importance of these oxide particles and the oxygen precipitation process for VLSI fabrication, considerable efforts have been made to develop methods to assess the numbers and distributions of such particles within the wafers. The number density range of most interest is 10⁷ to 10¹⁰ cm^-3, and the particle size range is typically 30 to 300 nm. The method that has mostly been used is surface etching followed by optical microscopy to obtain etch pit densities. Transmission electron microscopy is a research method used for obtaining detailed information concerning a small number of individual particles. However, because these methods are destructive, much attention has been given during the last few years to the development of infra-red microscopy methods to directly image the particles within the silicon wafers. Although the particles are smaller than the resolution of these methods, individual particles can nevertheless be imaged. This is because the particles are mostly further apart than the resolution limit, and the sensitivity can be sufficient high that adequate contrast occurs. The contrast arises from scattering or absorption of the light by the particle. Infra-red imaging methods developed include infra-red microscopy (IRM), laser scattering tomography (LST), optical precipitate profiler (OPP) and scanning infra-red microscopy (SIRM), all described more fully in Chapter 2. The SIRM has been developed and used to investigate a variety of semiconductor specimens in the Materials Department, Oxford University, during the last ten years. The SIRM has a good performance and flexibility making it especially suitable as a research instrument. Although all of these infra-red imaging methods have been successful to different degrees in assessing oxide particles in Cz silicon wafers, their performance has at least initially been assessed by comparing the number densities and distributions thus obtained with the corresponding results produced by etch pit studies. Furthermore, no serious attempt has yet been made to develop a rigorous theory of the imaging process and to compare the predictions with the experimental images. One of the main objectives of the present work is to do this or at least to make a significant start to such a project based on the SIRM. The outline of an ideal project which aims at a full understanding of the imaging process and the contrast mechanisms is as follows. The performance of the present Oxford SIRM should be improved and the number of imaging modes increased. The improved performance, i.e. better lateral and depth resolutions and higher sensitivity, would enable smaller particles and higher number densities to be imaged, and hence better quantitative data obtained. The larger number of imaging modes would enable the optimum method to be used to image different types of particle. A rigorous theory should be developed that can describe the imaging process and the contrast mechanisms. First, the illumination system should be studied, and in particular the structure of the focussed probe within the specimen and how the structure changes on focussing deeper into the specimen. Second, the interaction of the light with the specimen should be investigated and especially how light is scattered by individual oxide particles in silicon for the case of the particle size being smaller than the light wavelength. Third, the detection system should be considered. For example, for the reflection confocal SIRM, how the light back scattered by the particles is collected by the probe forming lens and imaged at a pin-hole aperture placed in the front of the detector. Well designed experiments are required to determine the imaging properties of the different modes and comparisons should be made between the experimental and theoretical data. The successful conclusion of such a project would enable SIRM images of the particles to be more fully interpreted and hence more detailed information obtained concerning the particles. Furthermore, the images expected from different types of particle could be more closely predicted, e.g. whether they are detectable or not, and hence materials projects could be better planned at the outset. In this thesis we describe the methods that are presently being used to assess oxide particles in bulk silicon (Chapter 2). We review the literature on scanning optical microscopy covering both visible and infra-red light, present some considerations regarding the design of a high performance and versatile SIRM, and describe the various microscope modes that have been or could be used to image particles in semiconductors with infra-red light (Chapter 3). We give a detailed rigorous theoretical analysis of the energy distributions in the probe for the case when the light is focussed by a high numerical aperture lens from air into silicon (Chapters 4, 5). Numerically computed distributions are obtained to illustrate how the probe changes under different conditions, e.g. different focussing depths (Chapter 6). The relationship between the penetration depth of the probe and the spherical aberration coefficient arising from the silicon specimen is determined (Chapter 7). The classical theory of light scattering is applied to individual spherical silicon dioxide particles embedded in silicon. Numerical results are presented and a contrast mechanism is proposed to describe how the scattered intensity depends on particle size (Chapter 8). A formal solution relevant to the reflection confocal SIRM is given to treat the backward propagation of light using a model which takes into account the polarisation state of the incident light, the spherical aberration introduced by the silicon wafer, the polarisation state of the scattered light and the size of the pin-hole (Chapter 9). Experimental results are obtained for most of the imaging modes described in Chapter 3, specimens being selected so that the wide range of the imaging capabilities of the SIRM is shown, and experimental contrast values are compared with theoretical values (Chapter 10). Finally, overall conclusions are drawn and suggestions are made for completing the work started here (Chapter 11).

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