SEMICONDUCTORS R. A. SMITH CAMBRIDGE AT THE UNIVERSITY PRESS. M.A., PH.D. Head of the Physics Department Royal Radar Establishment Malvern J 959

Transcription

1 SEMICONDUCTORS BY R. A. SMITH M.A., PH.D. Head of the Physics Department Royal Radar Establishment Malvern CAMBRIDGE AT THE UNIVERSITY PRESS J 959

2 CONTENTS Chapter 1. The Elementary Properties of Semiconductors I.I Early work on semiconductors i I.I.I 'Excess'and'defect'semiconductors The alkali halides Surface and bulk effects Applications of semiconductors Elementary theory of semiconductors Conduction processes Control of carrier density 19 Chapter 2. Energy Levels in Crystalline Solids 2.1 Wave mechanics of free electrons Motion in a periodic potential Form of the energy bands Positive holes Motion of electrons and holes in a crystal under the infiuence of an external field of force Energy-level diagrams Resistance to motion of electrons and holes in a crystal 44 Chapter 3. Impurities and Imperfections in Crystals 3.1 Types of imperfection I.I Impurities Interstitial atoms and vacancies Dislocations Polygonization and dislocation walls 49

3 X CONTENTS 3.2 Chemical binding in semiconductors Ionic bonds Homopolar bonds Mixed bonds Substitutional impurities in group IV semiconductors Energy levels of group III or group V impurities in group IV semiconductors Energy levels of other impurities in group IV semiconductors Impurities in polar semiconductors Impurities in the groups III-V semiconductors Excitons 68 Chapter 4. Carrier Concentrations in Thermal Equilibrium 4.1 Distribution of electrons between the various energy levels Intrinsic semiconductors Semiconductors with impurity levels 82 Chapter 5. Electron Transport Phenomena 5.1 Collisions with crystalline imperfections relaxation time, T Constant relaxation time T Electrical conductivity The Hall effect Transverse magneto-resistance Relaxation time a function of E or v Boltzmann's equation Electrical conduction Variation of T with energy E Hall effect for semiconductor with spherical constant-energy surfaces Hall effect for semiconductor with multiple energy maxima or minima 120

4 CONTENTS XI Magneto-resistance of semiconductor with spherical constant-energy surfaces Magneto-resistance of semiconductor with constant-energy surfaces in the form of ellipsoids S catter ing mechanisms Scattering by lattice vibrations Phonons Relaxation time for lattice scattering Impurity scattering Scattering by dislocations Other types of scattering High-field effects 156 Chapter 6. Thermal Effects in Semiconductors 6.1 Thermal conductivity Thermo-electric power Thermomagnetic effects The Ettingshausen effect The Nernst effect The Righi-Leduc effect Condition of degeneracy Strong magnetic fields Relative magnitudes of the magnetic effects 187 Chapter 7. Optical and High-frequency Effects in Semiconductors 7.1 Optical constants of semiconductors The fundamental absorption Direct transitions, k min = k max Direct transitions, ß mln #= ß max, Indirect transitions, k min 4= Ä mtt 201 Indirect transitions, k m, = %,.,. 210

5 XÜ CONTENTS 7.3 Exciton absorption Photo-conductivity The photo-magnetic effect Free-carrier absorption Plasma resonance High-frequency effects in a magnetic field Cyclotron resonance Magnetic quantization The magnetic band shift The oscillatory magneto-absorption effect Impurity absorption Spin resonance due to impurities Lattice absorption Infra-red emission from semiconductors 233 Chapter 8. Diffusion of Electrons and Positive Holes 8.1 Inhomogeneous semiconductors Einstein's relationship Departures from thermal equilibrium Electron-hole recombination Diffusion and conduction in extrinsic material (n ^> p or p^> n) The equation of continuity Small electric field Carrier injection (ßsmall) Carrier extraction { small) Large electric field (^ > o) General Solution (p <4 n) Drift of a pulse of minority carriers in an electric field 250

6 CONTENTS 8.7 Near-intrinsic material 251 XÜi Small field condition Carrier exclusion Carrier accumulation Comparison of contact phenomena The p-n junction Barrier-layer capacity Current-voltage characteristic f High-frequency behaviour oiap-n junction The n + -n and p + -p junctions Surface properties of semiconductors The field effect Metal-semiconductor contacts Recombination mechanisms Radiative recombination Recombination through traps Recombination at dislocations Recombination with donors or acceptors at low temperatures Surface recombination Mean lifetime in filaments and thin strips Photo-conductivity Uniform absorption rate Effect of trapping Effect of surface recombination Non-uniform absorption rate The transverse photo-voltage The photo-magnetic effect 314 Chapter 9. Methods of Determining the Characteristic Properties of Semiconductors 9.1 Band structure The minimum energy gap, AE 320

7 XIV CONTENTS 9.3 Mobility of electrons and holes Carrier concentration Effective mass Energy levels in the ' forbidden' band due to impurities Thermal method Impurity band conduction Impurities with more than one level Optical methods Minority carrier lifetime Injection ratio 342 Chapter 10. The Element Semiconductors 10.1 Germanium and Silicon General physical properties Crystal structure Energy-band structure Electron and hole mobility Value of n i and cr i 358 IO.I.Ö Hall coemcient Magneto-resistance Impurity energy levels Optical properties Pressure effects 368 IO.I.II Thermo-electric power Molten Ge Other properties of Si and Ge Crystal growth and purification Ge-Si alloys Diamond and gray tin Type II b diamond 379

8 CONTENTS Electron and hole mobility in high-resistivity diamond Properties of gray tin Selenium Tellurium Hall effect in Te Electrical conductivity of Te Forbidden energy gap, A.E Optical properties of Te Electron and hole mobility, and value of n i Thermal effects in Te Minority carrier lifetime in Te Liquid Te Te-Se alloys Boron Other 1 Dossible dement semiconductors XV i S 38S Chapter 11. Compound Semiconductors II.I Groups, IH-V intermetallic Compounds InSb Hall coefficient and conductivity of InSb Electron and hole mobility Value of w^ for InSb Optical properties Effective masses Forbidden energy gap, AE Minority carrier lifetime Impurity levels Crystal growth and purification Other properties of InSb

9 XVi CONTENTS 11.3 Other groups III-V Compound semiconductors InAs, InP GaSb, GaAs, GaP A1Sb Alloys of groups III-V semiconductors Summary of properties of groups III-V semiconductors Other intermetallic Compound semiconductors Groups I-V Compound semiconductors Groups II-IV Compound semiconductors Groups II-V Compound semiconductors Polar Compound semiconductors PbS, PbSe, PbTe Methods of crystal growth Hall coefficient and conductivity Electron and hole mobilities Optical properties Band structure Minority carrier lifetime Value of «^ Impurities and deviations from stoichiometric composition Other properties of PbS, PbSe, PbTe CdS, CdSe, CdTe Other semiconducting Compounds of S, Se, Te Bi 2 Te Ternary and quaternary Compounds Oxide semiconductors Cu ZnO, Ti Fe 3 0 4) NiO Silicon carbide 441

10 CONTENTS XVÜ Chapter 12. Some Applications of Semiconductors 12.1 Use of semiconductors in electrical technology Rectifiers High-frequency and switching diodes Zener or avalanche-breakdown diodes Avalanche-injection diodes Methods of making junction diodes Transistors The point-contact transistor The filamentary transistor The junction transistor Equivalent circuits of the junction transistor Energy-level diagram for the junction transistor structure Methods of manufacturing junction transistors High-frequency and switching transistors Other types of transistor The photo-diode The photo-electric power generator Photo-cells Infra-red detectors PbS detectors ' PbTe detectors PbSe detectors InSb detectors Doped Ge detectors Infra-red and microwave modulators Applications of the Hall effect in semiconductors Thermopiles and thermo-electric refrigerators Thermistors, varistors and other non-linear resistors 479 Appendix. Some recent review articles on semiconductors 482 Index 483