Understanding Luminescence Spectra and Efficiency Using Wp and Related Functions

ISBN-13: 9783642486319 / Angielski / Miękka / 2012 / 255 str.

Charles W. Struck; William H. Fonger

Opis

There are both a remote and a proximate history in the development of this book. We would like to acknowledge first the perceptiveness of the technical administrators at RCA Laboratories, Inc. during the 1970s, and in particular Dr. P. N. Yocom. Buoyed up by the financial importance of yttrium oxysulfide: europium as the red phosphor of color television tubes, they allowed us almost a decade of close cooperation aimed at understanding the performance of this phosphor. It is significant that we shared an approach to research in an industrial laboratory which allowed us to avoid the lure of "first-principles" approaches (which would have been severely premature) and freed us to formulate and to study the important issues directly. We searched for a semiquantitative understanding of the properties observed in luminescence, i. e., where energy absorption occurs, where emission occurs, and with what efficiency this conversion process takes place. We were aware that the nonradi- ative transition rates found in practice vary enormously with temperature and, for a given activator, with small changes in its environment. We traced the source of this enormous variation to the magnitude of the vibrational overlap integrals, which have strong dependences on the rearrangements occurring during optical transitions and on the vibrational number of the initial electronic state. We were willing to excise from the problem the electronic aspects - the electronic wavefunctions' and their transition integrals -by treating them as parameters to be obtained from the experimental data.

Spis treści

1 Introduction.- 1.1 Luminescence Centers and Models of Them.- 1.2 The Simplest Model: One Coordinate and Equal Force Constants.- 1.2.1 The Optical Band Shapes.- 1.2.2 The Nonradiative Rate.- 1.2.3 Six Typical Thermal Quenching Behaviors.- 1.2.3.1 Fast Bottom Crossover.- 1.2.3.2 Outside Crossover.- 1.2.3.3 Small-Offset Multiphonon Emission.- 1.2.3.4 Two-Step Quenching With a Fast Second Step.- 1.2.3.5 Two-Step Quenching with a Slow Second Step.- 1.2.3.6 Low-temperature Tunnelling Crossover.- 1.3 The Franck-Condon Principle for Nonradiative Rates.- 2 Harmonic Oscillator Wavefunctions.- 2.1 Hermite Polynomials.- 2.2 Generating Function for the Harmonic Oscillator Wavefunctions.- 3 The Manneback Recursion Formulas.- 3.1 Introduction.- 3.2 The Overlap Integral.- 3.3 The Generating Function for the Overlap Integral.- 3.4 The Recursion Formulas for the Overlap Integrals.- 3.5 Familiarity.- 3.6 The Orthonormality of the ANM Matrix.- 3.7 Additional Equal-Force-Constants Recursion Relations.- 4 The Luminescence Center: the Single-Configurational-Coordinate Model.- 4.1 The Model for the Radiative Rate.- 4.2 The Equal-Force-Constants Radiative Rate.- 4.3 The Unequal-Force-Constants Radiative Rate.- 4.4 The Model for the Nonradiative Rate.- 4.5 The Wp Recursion Formula.- 4.6 Explicit Series Expression for the Wp Function.- 4.7 Ip Modified Bessel Function Form for Wp.- 4.8 Limiting and Approximate Forms of Wp.- 4.9 The 5-Wp Formula for Wp,z.- 4.10 The p Formula.- 4.11 The Wp,d/dz Expression.- 4.12 The W-p/Wp and Related Ratios.- 4.13 Equal-Force-Constants Moments.- 4.14 Unequal-Force-Constants Moments.- 4.14.1 The Moments.- 4.14.2 Preliminaries I: The (?, m, ?).- 4.14.3 Preliminaries II: The Thermal Averages ?m?? v.- 4.14.4 Preliminaries III: The ?n?m?? uv.- 4.14.5 The Derivation of the Moment Expressions (4.109).- 5 Multiple Coordinate Models of a Luminescence Center.- 5.1 The Einstein-Huang-Rhys-Pekar Single-Frequency Multiple-Coordinate Model.- 5.2 The z and d/dz Multiple-Coordinate Nuclear Factors.- 5.2.1 Preliminaries I: the Yp Function.- 5.2.2 Preliminaries II: Xp, O±.- 5.2.3 Preliminaries III: XX Sums.- 5.2.4 Preliminaries IV: Wp, O±Wp Sums.- 5.2.5 Proof of Eq. (5.6) for Two Coordinates.- 5.3 Multiple-Frequency Models of a Luminescence Center.- 5.3.1 The Selected Model.- 5.3.2 Definition of the 1, z, and d/dz Operator Rates.- 5.3.3 The Condon-Operator Distribution.- 5.3.4 The Recursion Algebra for the z and d/dz Operators.- 5.3.4.1 The ? Functions.- 5.3.4.2 The ? Recursion Algebras.- 5.3.4.3 The ? Functions.- 5.3.4.4 The ? Recursion Algebras in terms of ? Functions.- 5.3.5 The Discretized Debye Equal S and A Model.- 6 Energy Transfer.- 6.1 The Model.- 7 Compendium of Useful Equations.- 7.1 The Wavefunctions.- 7.2 The Manneback Recursion Formulas.- 7.3 The Equal-Force-Constants Wp and Related Functions in One Dimension.- 7.4 The Unequal-Force-Constants Expressions.- 7.5 The Moments.- 7.6 Multiple Coordinate Models of a Luminescence Center.- 7.7 Energy Transfer.- 8 Contact with the Theoretical Literature.- 8.1 Unequal-Force-Constants Anm.- 8.2 Equal-Force-Constants Anm.- 8.2.1 Explicit Formulas.- 8.2.2 Laguerre Polynomial Expressions.- 8.2.3 Citations.- 8.3 The Wp Formula.- 8.4 The Wp,d/dz Formula.- 8.5 The Equal-Force-Constants Moments.- 8.6 The Unequal-Force-Constants Moments.- 8.7 The Single-Frequency-Multiple-Coordinate Derivative Operator Expressions.- 8.7.1 Huang and Rhys.- 8.7.2 Perlin.- 8.7.3 Miyakawa and Dexter.- 8.8 Multiple-Frequency Rates.- 8.8.1 Perlin’s Condon-Operator Distribution.- 8.8.1.1 The Distribution.- 8.8.1.2 Cauchy’s Integral Theorem and its Consequences.- 8.8.1.3 The Saddle Point Approximation.- 8.8.1.4 The Use of the Saddle Point Approximation Here.- 8.8.1.5 The integral of dz/z.- 8.8.1.6 Expansion of vm for Small Offset.- 8.8.1.7 Perlin’s Derivation.- 8.8.2 The Correspondence between Perlin’s and Our Multiple Frequency Expression.- 8.8.3 Perlin’s Multiple-Coordinate Derivative Operator Expression.- 8.8.4 The Correspondence between Perlin’s and Our Multiple Frequency Derivative Expression.- 8.8.5 Mostoller, Ganguly, and Wood.- 8.9 Energy Transfer.- 8.9.1 Förster and Dexter.- 8.9.2 Miyakawa and Dexter.- 9 Representative Luminescence Centers.- 9.1 Equal- and Unequal-Force-Constants Bandshapes and Nonradiative Transitions.- 9.1.1 Bandshapes.- 9.1.2 Nonradiative Rates.- 9.2 One-and NAv-Dimensional Bandshapes.- 9.3 Vibrationally-Enhanced Radiative Transitions.- 9.4 Comparisons of Nonradiative Rate Expressions.- 10 Experimental Studies.- 10.1 Eu in Oxysulfides and in Oxyhalides.- 10.1.1 The Energy Level Diagram and Qualitative Behavior.- 10.1.2 Feeding Fractions.- 10.1.3 Efficiencies under Quenching Conditions.- 10.1.4 Absorption Spectra at T > 0K.- 10.1.5 The Fit of the Absorption Data.- 10.1.5.1 LaOCl.- 10.1.5.2 Oxysulfides.- 10.1.6 Fitting the Quenching Data.- 10.1.6.1 LaOCl.- 10.1.6.2 Oxysulfides.- 10.1.6.3 Fitting the (?i)i.- 10.1.7 Fitting The Feeding Fractions.- 10.1.7.1 LaOCl.- 10.1.7.2 Oxysulfides.- 10.2 Oxysulfides: Other Rare Earths.- 10.2.1 La2O2S: Tm3+.- 10.2.1.1 The Experimental Behavior.- 10.2.1.2 Fitting with Wp Functions.- 10.2.2 Y2O2S: Yb3+.- 10.2.2.1 The Experimental Behavior.- 10.2.2.2 Fitting the Optical Spectra with SCC Model Functions.- 10.2.2.3 Fitting the Quenchings with SCC Model Functions.- 10.3 Alkali and Alkaline Earth Halides: Sm.- 10.3.1 The Model and Expectations.- 10.3.2 The Fitting Parameters.- 10.4 Ruby.- 11 Effects Beyond the Model: Oxysulfide: Eu Storage and Loss Processes.- 11.1 The Need for Enhancement of the Model.- 11.2 Synopsis of the Experiments to Probe the Model.- 11.3 The Model Equations: Notation.- 11.4 CTS Dissociation: The B0/G Behavior.- 11.5 The SCC Model for Understanding Storage-Loss Processes in Oxysulfide: Eu Phosphors.- 11.6 The Steady-State Efficiency and its Dependence on Excitation Intensity: B?/G.- 11.6.1 The Observed Behavior.- 11.6.2 The Equation for B?/G.- 11.6.3 Derivation of Nonlinear Efficiency Expression.- 11.7 The n0? Achieved.- 11.8 The Rise Time.- 11.9 The Assymetry Between Phosphorescence and Build-Up.- 11.10 An Expression for Phosphorescence.- 12 The Exponential Energy-Gap “Law” for Small-Offset Cases.- 13 Conclusions.- 14 References.- Source Code.- Source of Illustrations.