THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

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The Black Swan: The Impact of the Highly Improbable

A projection exposure apparatus including an irradiation optical system including a light source and irradiating a mask with irradiation light beams, a projection optical system for projecting an image of a pattern of the mask on a substrate, a plurality of first fly-eye type optical integrators each having an emission side focal plane disposed on a Fourier transformed surface with respect to the pattern of the mask in the irradiation optical system or on a plane adjacent to the same and having a center located at a plurality of positions which are eccentric from the optical axis of the irradiation optical system, a plurality of second fly-eye type optical integrators each having an emission side focal plane disposed on a Fourier transformed plane with respect to the incidental end of each of a plurality of the first fly-eye type optical integrators or on a plane adjacent to the same and being disposed to correspond to a plurality of the first fly-eye type optical integrators, and a light divider for dividing and causing the irradiation light beams from the light source to be incident on each of a plurality of the second fly-eye type optical integrators.

Projection exposure apparatus

The phase-shifting mask consists of a normal transmission mask that has been coated with a transparent layer patterned to ensure that the optical phases of nearest apertures are opposite. Destructive interference between waves from adjacent apertures cancels some diffraction effects and increases the spatial resolution with which such patterns can be projected. A simple theory predicts a near doubling of resolution for illumination with partial incoherence σ < 0.3, and substantial improvements in resolution for σ < 0.7. Initial results obtained with a phase-shifting mask patterned with typical device structures by electron-beam lithography and exposed using a Mann 4800 10× tool reveals a 40-percent increase in usuable resolution with some structures printed at a resolution of 1000 lines/mm. Phase-shifting mask structures can be used to facilitate proximity printing with larger gaps between mask and wafer. Theory indicates that the increase in resolution is accompanied by a minimal decrease in depth of focus. Thus the phase-shifting mask may be the most desirable device for enhancing optical lithography resolution in the VLSI/VHSIC era.

Improving resolution in photolithography with a phase-shifting mask

The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

Preface. 1. Introduction to Semiconductor Lithography. 1.1 Basics of IC Fabrication. 1.2 Moore's Law and the Semiconductor Industry. 1.3 Lithography Processing. Problems. 2. Aerial Image Formation - The Basics. 2.1 Mathematical Description of Light. 2.2 Basic Imaging Theory. 2.3 Partial Coherence. 2.4 Some Imaging Examples. Problems. 3. Aerial Image Formation - The Details. 3.1 Aberrations. 3.2 Pupil Filters and Lens Apodization. 3.3 Flare. 3.4 Defocus. 3.5 Imaging with Scanners Versus Steppers. 3.6 Vector Nature of Light. 3.7 Immersion Lithography. 3.8 Image Quality. Problems. 4. Imaging in Resist: Standing Waves and Swing Curves. 4.1 Standing Waves. 4.2 Swing Curves. 4.3 Bottom Antirefl ection Coatings. 4.4 Top Antirefl ection Coatings. 4.5 Contrast Enhancement Layer. 4.6 Impact of the Phase of the Substrate Refl ectance. 4.7 Imaging in Resist. 4.8 Defi ning Intensity. Problems. 5. Conventional Resists: Exposure and Bake Chemistry. 5.1 Exposure. 5.2 Post-Apply Bake. 5.3 Post-exposure Bake Diffusion. 5.4 Detailed Bake Temperature Behavior. 5.5 Measuring the ABC Parameters. Problems. 6. Chemically Amplifi ed Resists: Exposure and Bake Chemistry. 6.1 Exposure Reaction. 6.2 Chemical Amplifi cation. 6.3 Measuring Chemically Amplifi ed Resist Parameters. 6.4 Stochastic Modeling of Resist Chemistry. Problems. 7. Photoresist Development. 7.1 Kinetics of Development. 7.2 The Development Contrast. 7.3 The Development Path. 7.4 Measuring Development Rates. Problems. 8. Lithographic Control in Semiconductor Manufacturing. 8.1 Defi ning Lithographic Quality. 8.2 Critical Dimension Control. 8.3 How to Characterize Critical Dimension Variations. 8.4 Overlay Control. 8.5 The Process Window. 8.6 H-V Bias. 8.7 Mask Error Enhancement Factor (MEEF). 8.8 Line-End Shortening. 8.9 Critical Shape and Edge Placement Errors. 8.10 Pattern Collapse. Problems. 9. Gradient-Based Lithographic Optimization: Using the Normalized Image Log-Slope. 9.1 Lithography as Information Transfer. 9.2 Aerial Image. 9.3 Image in Resist. 9.4 Exposure. 9.5 Post-exposure Bake. 9.6 Develop. 9.7 Resist Profi le Formation. 9.8 Line Edge Roughness. 9.9 Summary. Problems. 10. Resolution Enhancement Technologies. 10.1 Resolution. 10.2 Optical Proximity Correction (OPC). 10.3 Off-Axis Illumination (OAI). 10.4 Phase-Shifting Masks (PSM). 10.5 Natural Resolutions. Problems. Appendix A. Glossary of Microlithographic Terms. Appendix B. Curl, Divergence, Gradient, Laplacian. Appendix C. The Dirac Delta Function. Index.

Fundamental principles of optical lithography : the science of microfabrication

The 1959 invention of the planar silicon transistor led to the development of the integrated circuit (IC) and the growth trend in IC complexity known as Moore's Law While Moore's observation came in 1965, his original trend line showing a doubling of components per chip each year began with one component in 1959 Thus, we have now experienced 50 years of Moore's Law This paper provides a history of Moore's Law through its many changes and reinterpretations, containing possibly a few new ones as well

Fifty Years of Moore's Law

1.3. Mask Illumination Purpose: The purpose of this section is to describe how masks are illuminated in lithographic imaging systems and how this illumination affects image formation. Objectives: Upon completion of this section, you will be able to:  Describe the effect of illumination angle on the diffraction pattern  Define partial coherence  Describe the impact of illumination on resolution  Define Kohler illumination

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Fundamental principles of optical lithography

A mechanism for the development of positive optical photoresists is proposed, leading to the derivation of a development rate equation. This rate equation compares favorably with experimentally determined development rates. Typical values of the rate constants involved are given. Empirical models are given for the surface induction and substrate adhesion effects. An overall positive resist processing model requires a mathematical representation of the development process. Previous attempts have taken the form of empirical fits to development rate data as a function of exposure (1, 2). The model formulated below begins on a more fundamental level, with a postulated reaction mechanism which then leads to a development rate equation. The rate constants involved can be determined by comparison with experimental data. Deviations from the expected development rates have been reported under certain conditions at the surface of the resist and near the resist-substrate interface. These effects, called the surface induction and substrate adhesion effects, respectively, can be related empirically tothe expected development rate, i.e., to the bulk development rate as predicted by a kinetic model. Bulk Development Model In order to derive an analytical development rate expression, a kinetic model of the development process will be used. This approach involves proposing a reasonable mechaffism for the development reaction and then applying standard kinetics to this mechanism in order to derive a rate equation. We shall assume that the development of a diazo-type positive photoresist involves three processes: diffusion of developer from the bulk solution to the surface of the resist, reaction of the developer with the resist, and diffusion of the product back into the solution. For this analysis, we shall assume that the last step, diffusion of'the dissolved resist into solution, occurs very quickly so that this step may be ignored. Let us now look at the first two steps i n the proposed mechanism. The diffusion of developer to the resist surface can be described with the simple, diffusion rate equation rD = k,~(D - Ds) [1] where rD = rate of diffusion of the developer to the resist surface,. D = bulkdeveloper concentration, Ds = developer concentration at the resist surface, and kD = rate constant. We shall now propose a mechanism for the reaction of developer'with theresist. The resist is composed of large macromolecules of resin R along with a photoactive compound M, which converts to product P upon exposure to UV light. The resin is quite soluble in the developer solution, but the presence of the PAC (photoactive compound) acts as an. inhibitor to dissolution, making the development rate very slow. The product P, however, is very solubie in developer, enhancing the dissolution rate of the resin. Let us assume that n molecules of product p react with the developer to dissolve a resin mo'lecule. The rate of the reaction is rR = - kRDsP '~ [2] where rR = the rate of reaction of the developer with the resist and kR = rate constant. From the stoichiometry of the exposure reaction P = M,, - M [3]

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Development of Positive Photoresists

A method for determining one or more process parameter settings of a photolithographic system is disclosed.

Chris A. Mack

Papers

Fundamental principles of optical lithography : the science of microfabrication

Fifty Years of Moore's Law

Fundamental principles of optical lithography

Development of Positive Photoresists

Method for determining lithographic focus and exposure