PHYSICS OF SEMICONDUCTOR DEVICES

Transcription

1 PHYSICS OF SEMICONDUCTOR DEVICES

2 PHYSICS OF SEMICONDUCTOR DEVICES by J. P. Colinge Department of Electrical and Computer Engineering University of California, Davis C. A. Colinge Department of Electrical and Electronic Engineering California State University KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

3 ebook ISBN: Print ISBN: Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print 2002 Kluwer Academic Publishers Dordrecht All rights reserved No part of this ebook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's ebookstore at:

4 CONTENTS Preface 1. Energy Band Theory 1.1. Electron in a crystal Two examples of electron behavior Free electron The particle-in-a-box approach Energy bands of a crystal (intuitive approach) Krönig-Penney model Valence band and conduction band Parabolic band approximation Concept of a hole Effective mass of the electron in a crystal Density of states in energy bands 1.2. Intrinsic semiconductor 1.3. Extrinsic semiconductor Ionization of impurity atoms Electron-hole equilibrium Calculation of the Fermi Level Degenerate semiconductor Alignment of Fermi levels 2. Theory of Electrical Conduction 2.1. Drift of electrons in an electric field 2.2. Mobility 2.3. Drift current Hall effect 2.4. Diffusion current 2.5. Drift-diffusion equations Einstein relationships 2.6. Transport equations 2.7. Quasi-Fermi levels xi

5 vi Contents 3. Generation/Recombination Phenomena 3.1. Introduction 3.2. Direct and indirect transitions 3.3. Generation/recombination centers 3.4. Excess carrier lifetime 3.5. SRH recombination Minority carrier lifetime 3.6. Surface recombination 4. The PN Junction Diode 4.1. Introduction 4.2. Unbiased PN junction 4.3. Biased PN junction Current-voltage characteristics Derivation of the ideal diode model Generation/recombination current Junction breakdown Short-base diode PN junction capacitance Transition capacitance Diffusion capacitance Charge storage and switching time 4.6. Models for the PN junction Quasi-static, large-signal model Small-signal, low-frequency model Small-signal, high-frequency model 4.7. Solar cell 4.8. PiN diode 5. Metal-semiconductor contacts 5.1. Schottky diode Energy band diagram Extension of the depletion region Schottky effect Current-voltage characteristics Influence of interface states Comparison with the PN junction 5.2. Ohmic contact

6 Contents 6. JFET and MESFET 6.1. The JFET 6.2. The MESFET 7. The MOS Transistor 7.1. Introduction and basic principles 7.2. The MOS capacitor Accumulation Depletion Inversion Current in the MOS transistor Channel length modulation Threshold voltage Ideal threshold voltage Flat-band voltage Threshold voltage Influence of substrate bias on threshold voltage Simplified model Surface mobility Carrier velocity saturation Subthreshold current - Subthreshold slope Continuous model Numerical modeling of the MOS transistor Short-channel effect Hot-carrier degradation Scaling rules Hot electrons Substrate current Gate current Degradation mechanism Terminal capacitances Particular MOSFET structures Non-Volatile Memory MOSFETs SOI MOSFETs Advanced MOSFET concepts Polysilicon depletion High-k dielectrics Drain-induced barrier lowering (DIBL) Gate-induced drain leakage (GIDL) Reverse short-channel effect Quantization effects in the inversion channel vii

7 viii 8. The Bipolar Transistor 8.1. Introduction and basic principles Long-base device Short-base device Fabrication process Amplification using a bipolar transistor Ebers-Moll model Emitter efficiency Transport factor in the base Regimes of operation Transport model Gummel-Poon model Current gain Recombination in the base Emitter efficiency and current gain 8.7. Early effect 8.8. Dependence of current gain on collector current Recombination at the emitter-base junction Kirk effect 8.9. Base resistance Numerical simulation of the bipolar transistor Collector junction breakdown Common-base configuration Common-emitter configuration Charge-control model Forward active mode Large-signal model Small-signal model 9. Heterojunction Devices 9.1. Concept of a heterojunction Energy band diagram Photonic Devices Heterojunction bipolar transistor (HBT) High electron mobility transistor (HEMT) Light-emitting diode (LED) Laser diode Contents

8 Contents 10. Quantum-Effect Devices Tunnel Diode Tunnel effect Tunnel diode Low-dimensional devices Energy bands Density of states Conductance of a 1D semiconductor sample D and 1D MOS transistors Semiconductor Processing Doping techniques Single-electron transistor Tunnel junction Double tunnel junction Single-electron transistor Semiconductor materials Silicon crystal growth and refining Ion implantation Doping impurity diffusion Gas-phase diffusion Oxidation Chemical vapor deposition (CVD) Silicon deposition and epitaxy Dielectric layer deposition Photolithography Etching Metallization Metal deposition Metal silicides CMOS process NPN bipolar process 12. Annex Al. A2. A3. A4. A5. A6. A7. Index Physical Quantities and Units Physical Constants Concepts of Quantum Mechanics Crystallography Reciprocal Space Getting Started with Matlab Greek alphabet Basic Differential Equations ix

9 PREFACE This Textbook is intended for upper division undergraduate and graduate courses. As a prerequisite, it requires mathematics through differential equations, and modern physics where students are introduced to quantum mechanics. The different Chapters contain different levels of difficulty. The concepts introduced to the Reader are first presented in a simple way, often using comparisons to everyday-life experiences such as simple fluid mechanics. Then the concepts are explained in depth, without leaving mathematical developments to the Reader's responsibility. It is up to the Instructor to decide to which depth he or she wishes to teach the physics of semiconductor devices. In the Annex, the Reader is reminded of crystallography and quantum mechanics which they have seen in lower division materials and physics courses. These notions are used in Chapter 1 to develop the Energy Band Theory for crystal structures. An introduction to basic Matlab programming is also included in the Annex, which prepares the students for solving problems throughout the text. Matlab was chosen because of its ease of use, its powerful graphics capabilities and its ability to manipulate vectors and matrices. The problems can be used in class by the Instructor to graphically illustrate theoretical concepts and to show the effects of changing the value of parameters upon the result. We believe it is important for students to understand and experience a "hands-on" feeling of the consequences of changing variable values in a problem (for instance, what happens to the C-V characteristics of a MOS capacitor if the substrate doping concentration is increased? - What happens to the band structure of a semiconductor if the lattice parameter is increased? - What happens to the gain of a bipolar transistor if temperature increases?). Furthermore,

10 xii Preface some Matlab problems make use of a basic numerical, finite-difference technique in which the "exact" numerical solution to an equation is compared to a more approximate, analytical solution such as the solution of the Poisson equation using the depletion approximation. Chapters 1 to 3 introduce the notion of energy bands, carrier transport and generation-recombination phenomena in a semiconductor. End-ofchapter problems are used here to illustrate and visualize quantum mechanical effects, energy band structure, electron and hole behavior, and the response of carriers to an electric field. Chapters 4 and 5 derive the electrical characteristics of PN and metalsemiconductor contacts. The notion of a space-charge region is introduced and carrier transport in these structures is analyzed. Special applications such as solar cells are discussed. Matlab problems are used to visualize charge and potential distributions as well as current components in junctions. Chapter 6 analyzes the JFET and the MESFET, which are extensions of the PN or metal-semiconductor junctions. The notions of source, gate, drain and channel are introduced, together with two-dimensional field effects such as pinch-off. These important concepts lead the Reader up to the MOSFET chapter. Chapter 7 is dedicated to the MOSFET. In this important chapter the MOS capacitor is analyzed and emphasis is placed on the physical mechanisms taking place. The current expressions are derived for the MOS transistor, including second-order effects such as surface channel mobility reduction, channel length modulation and threshold voltage rolloff. Scaling rules are introduced, and hot-carrier degradation effects are discussed. Special MOSFET structures such as non-volatile memory and silicon-on-insulator devices are described as well. Matlab problems are used to visualize the characteristics of the MOS capacitor, to compare different MOSFET models and to construct simple circuits. Chapter 8 introduces the bipolar junction transistor (BJT). The Ebers- Moll, Gummel-Poon and charge-control models are developed and second-order effects such as the Early and Kirk effects are described. Matlab problems are used to visualize the currents in the BJT. Heterojunctions are introduced in Chapter 9 and several heterojunction devices, such as the high-electron mobility transistor

11 Preface xiii (HEMT), the heterojunction bipolar transistor (HBT), and the laser diode, are analyzed. Chapter 10 is dedicated to the most recent semiconductor devices. After introducing the tunnel effect and the tunnel diode, the physics of low-dimensional devices (two-dimensional electron gas, quantum wire and quantum dot) is analyzed. The characteristics of the single-electron transistor are derived. Matlab problems are used to visualize tunneling through a potential barrier and to plot the density of states in lowdimensional devices. Chapter 11 introduces silicon processing techniques such as oxidation, ion implantation, lithography, etching and silicide formation. CMOS and BJT fabrication processes are also described step by step. Matlab problems analyze the influence of ion implantation and diffusion parameters on MOS capacitors, MOSFETs, and BJTs. The solutions to the end-of-chapter problems are available to Instructors. To download a solution manual and the Matlab files corresponding to the end-of-chapter problems, please go to the following URL: This Book is dedicated to Gunner, David, Colin-Pierre, Peter, Eliott and Michael. The late Professor F. Van de Wiele is acknowledged for his help reviewing this book and his mentorship in Semiconductor Device Physics. Cynthia A. Colinge California State University Jean-Pierre Colinge University of California