Semiconductor Statistics

International Series of Monographs on Semiconductors

1st Edition - January 1, 1962

Author: J. S. Blakemore

Editor: Heinz K. Henisch

eBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 4 8 9 4 - 6

Semiconductor Statistics presents statistics aimed at complementing existing books on the relationships between carrier densities and transport effects. The book is divided into… Read more

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Semiconductor Statistics presents statistics aimed at complementing existing books on the relationships between carrier densities and transport effects. The book is divided into two parts. Part I provides introductory material on the electron theory of solids, and then discusses carrier statistics for semiconductors in thermal equilibrium. Of course a solid cannot be in true thermodynamic equilibrium if any electrical current is passed; but when currents are reasonably small the distribution function is but little perturbed, and the carrier distribution for such a ""quasi-equilibrium"" condition is inappreciably different from that of thermal equilibrium itself. Thus the results of Part I are not invalidated when the properties of a semiconductor are measured using small current densities. Part II considers non-equilibrium statistics for semiconductors with appreciable excess carrier densities. The various kinds of recombination mechanism are examined, and the consequences discussed for steady state and transient situations. The subject matter of this book was deliberately restricted in scope in order to be of maximum value to scientists with an active interest in the basic properties of semiconducting materials.

Preface

Part I. Semiconductors in Thermal Equilibrium

Chapter 1. Basic Concepts in the Electron Theory of Solids

1.1 Classical Theories of Metallic Conduction

1.2 Quantum Statistics and the Free Electron Theory

1.3 The Band Theory of Solids

1.4 The Effective Mass of Charge Carriers

1.5 Band Shapes for Some Representative Semiconductors

1.6 Some Varieties of Impurity Center (Flaw)

Chapter 2. The Fermi Level—electron Density Equilibrium

2.1 The Fermi-Dirac Integrals

2.2 Interrelation of Free Electron Density and Fermi Level

2.3 Intrinsic Semiconductors

2.4 The Product nopo and ö for Intrinsic and Extrinsic Situations

2.5 Spatial Fluctuations of Carrier Density

Chapter 3. Semiconductors Dominated by impurity levels

3.1 Occupancy Factor for Impurity Levels

3.2 Semiconductors Controlled by a Single Monovalent Donor Species

3.3 Semiconductors Dominated by Several Localized Levels

3.4 The Influence of Lattice Defects

3.5 Impurity Bands and the Behavior of an Impurity Metal

Part II. Semiconductors Containing Excess Carriers

Chapter 4. Factors Affecting Carrier Transition Rates

4.1 Reciprocity of Transition Probabilities

4.2 The Continuity Equations

4.3 Band-to-Band and Band-to-Flaw Transitions

Chapter 5. Radiative and Radiationless Recombination

5.1 The Physics of The Two Processes

5.2 Behavior of the Radiative Lifetime

Chapter 6. Band-to-band Auger Recombination

6.1 Electron-Electron and Hole-Hole Collisions

6.2 Behavior of the Auger Lifetime when mc < mv

Chapter 7. Free Carrier Capture by Flaws

7.1 Flaw Capture Mechanisms

7.2 Behavior of the Extrinsic Lifetime

7.3 Interaction with Both Bands

Chapter 8. Recombination Through a Set of Monovalent Flaws

8.1 The Two Continuity Equations

8.2 The Criteria of Trapping

8.3 Lifetime for a Small Flaw Density (The S-R Model)

8.4 Steady State Conditions for Arbitrary Flaw Density

8.5 Transient Decay for Arbitrary Flaw Density

Chapter 9. More Complicated Examples of Flaw Recombination

9.1 Multivalent Flaws

9.2 More Than One Kind of Flaw

9.3 The Haynes-Hornbeck Trapping Model

9.4 Recombination and Trapping at Dislocations

Chapter 10. Spatial Distribution of Excess Carriers

10.1 Approach to the Space-dependent Problem

10.2 Situations Involving Junctions and Contacts

10.3 Residual Spatial Influences in Homogeneous Samples

10.4 Lifetime in Filaments

Appendixes

Appendix A. The Fermi-dirac Distribution Law

Appendix B. Tables of the Fermi-dirac Integrals

Appendix C. Some Applications and Properties of the Fermi-dirac Integrals

C.1. Fermi-Dirac Integrals and Transport Properties

C.2. Fermi-Dirac Integrals for Non-standard Bands

C.3. Analytic Properties of the Fermi Integrals, and Asymptotic Expansions for Non-degenerate and Degenerate Cases

References

Index