Charge collection in silicon imaging sensors
01 Jan 2016-
TL;DR: In this paper, a method of physically modelling charge collection within the detector using analytical solutions to Poisson's equation is described, which is shown to qualitatively reproduce many features of measured dynamic charge collection effects.
Abstract: The subject of this thesis is the analysis of instrumental effects caused by the interaction between collected signal charge and electric fields within precision CCD imaging sensors typically used for astronomy. These phenomena cause aberrations in the measured spatial distribution of subsequently collected signal, which may present a major error for upcoming astronomy projects which rely heavily on accurately determining shapes of compact sources. Examples are the Large Synoptic Survey Telescope and the Euclid space telescope. The size of dynamic collection effects may be subtly affected by the operating conditions and design parameters of the device. Dynamic charge collection effects differ in origin from many other errors introduced by imaging detectors in that they are attributable to changes in the confinement of charge carriers during the collection phase of operation, rather than the readout phase. The fact that the exact aberration implied by dynamic charge collection effects depends exactly on the incident light field’s spatial distribution also makes them comparatively difficult to correct for.
A method of physically modelling charge collection within the detector using analytical solutions to Poisson’s equation is described, which is shown to qualitatively reproduce many features of measured dynamic charge collection effects. Since the model is derived from device physics, it differs in approach in a complementary way from previous efforts which are empirically based. Experimental charge collection measurements from two different CCDs both affected by dynamic collection effects are presented, and shown in large part to be consistent with the predictions from the theoretical model.
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1,146 citations
Journal Article•
TL;DR: In this paper, the free charge transfer characteristics of charge-coupled devices (CCD's) are analyzed in terms of the charge motion due to thermal diffusion, self-induced drift, and fringing field drift.
Abstract: The free charge-transfer characteristics of charge-coupled devices (CCD's) are analyzed in terms of the charge motion due to thermal diffusion, self-induced drift, and fringing field drift. The charge-coupled structures considered have separations between the gates equal to the thickness of the channel oxide. The effect of each of the above mechanisms on charge transfer is first considered separately, and a new method is presented for the calculation of the self-induced field. Then the results of a computer simulation of the charge-transfer process that simultaneously considers all three charge-motion mechanisms is presented for three-phase CCD's with gate lengths of 4 and 10 µ. The analysis shows that while the majority of the charge is transferred by means of the self-induced drift that follows a hyperbolic time dependence, the last few percent of the charge decays exponentially under the influence of the fringing field drift or thermal diffusion, depending on the design of the structure. The analysis shows that in CCD's made on relatively high resistivity substrates, the transfer by fringing-field drift can be very fast, such that transfer efficiencies of 99.99 percent are expected at 5- to 10- MHz bit rates for 10-µ gate lengths and at up to 100 MHz for 4-µ gate lengths.
121 citations
Journal Article•
TL;DR: In this article, the authors reexamine the prescriptions currently used in the modeling of X-ray CCD detectors to provide analytic expressions for the charge distribution over the CCD pixels which are suitable for use in numerical simulations of CCD response.
Abstract: Critical to the detection of X-rays by CCDs, is the detailed process of charge diffusion and drift within the device. We reexamine the prescriptions currently used in the modeling of X-ray CCD detectors to provide analytic expressions for the charge distribution over the CCD pixels which are suitable for use in numerical simulations of CCD response. Our treatment results in models which predict charge distributions which are more centrally peaked and have flatter wings than the Gaussian shapes predicted by previous work and adopted in current CCD modeling codes.
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Book•
01 Feb 1996
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Abstract: Preface 1. Introduction. Problems to be considered Characteristics of 'real-world' problems Finite-precision arithmetic and measurement of error Exercises 2. Nonlinear Problems in One Variable. What is not possible Newton's method for solving one equation in one unknown Convergence of sequences of real numbers Convergence of Newton's method Globally convergent methods for solving one equation in one uknown Methods when derivatives are unavailable Minimization of a function of one variable Exercises 3. Numerical Linear Algebra Background. Vector and matrix norms and orthogonality Solving systems of linear equations-matrix factorizations Errors in solving linear systems Updating matrix factorizations Eigenvalues and positive definiteness Linear least squares Exercises 4. Multivariable Calculus Background Derivatives and multivariable models Multivariable finite-difference derivatives Necessary and sufficient conditions for unconstrained minimization Exercises 5. Newton's Method for Nonlinear Equations and Unconstrained Minimization. Newton's method for systems of nonlinear equations Local convergence of Newton's method The Kantorovich and contractive mapping theorems Finite-difference derivative methods for systems of nonlinear equations Newton's method for unconstrained minimization Finite difference derivative methods for unconstrained minimization Exercises 6. Globally Convergent Modifications of Newton's Method. The quasi-Newton framework Descent directions Line searches The model-trust region approach Global methods for systems of nonlinear equations Exercises 7. Stopping, Scaling, and Testing. Scaling Stopping criteria Testing Exercises 8. Secant Methods for Systems of Nonlinear Equations. Broyden's method Local convergence analysis of Broyden's method Implementation of quasi-Newton algorithms using Broyden's update Other secant updates for nonlinear equations Exercises 9. Secant Methods for Unconstrained Minimization. The symmetric secant update of Powell Symmetric positive definite secant updates Local convergence of positive definite secant methods Implementation of quasi-Newton algorithms using the positive definite secant update Another convergence result for the positive definite secant method Other secant updates for unconstrained minimization Exercises 10. Nonlinear Least Squares. The nonlinear least-squares problem Gauss-Newton-type methods Full Newton-type methods Other considerations in solving nonlinear least-squares problems Exercises 11. Methods for Problems with Special Structure. The sparse finite-difference Newton method Sparse secant methods Deriving least-change secant updates Analyzing least-change secant methods Exercises Appendix A. A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations (by Robert Schnabel) Appendix B. Test Problems (by Robert Schnabel) References Author Index Subject Index.
6,831 citations
Book•
01 Jan 1985TL;DR: Bjarne Stroustrup makes C even more accessible to those new to the language, while adding advanced information and techniques that even expert C programmers will find invaluable.
Abstract: From the Publisher:
Written by Bjarne Stroustrup, the creator of C, this is the world's most trusted and widely read book on C.
For this special hardcover edition, two new appendixes on locales and standard library exception safety have been added. The result is complete, authoritative coverage of the C language, its standard library, and key design techniques. Based on the ANSI/ISO C standard, The C Programming Language provides current and comprehensive coverage of all C language features and standard library components.
For example:
abstract classes as interfaces class hierarchies for object-oriented programming templates as the basis for type-safe generic software exceptions for regular error handling namespaces for modularity in large-scale software run-time type identification for loosely coupled systems the C subset of C for C compatibility and system-level work standard containers and algorithms standard strings, I/O streams, and numerics C compatibility, internationalization, and exception safety
Bjarne Stroustrup makes C even more accessible to those new to the language, while adding advanced information and techniques that even expert C programmers will find invaluable.
6,795 citations
TL;DR: In this article, the electromotive force due to thermal agitation in conductors is calculated by means of principles in thermodynamics and statistical mechanics, and the results obtained agree with results obtained experimentally.
Abstract: The electromotive force due to thermal agitation in conductors is calculated by means of principles in thermodynamics and statistical mechanics. The results obtained agree with results obtained experimentally.
2,762 citations