Introduction to Nanotechnology

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A.l. INTRODUCTION APPENDIX A FORMULAS FOR DIMENSIONALITY We saw in Chapter 9, on quantum wells, quantum wires and quantum dotes, that the dimensionality of the system has a pronounced effect on its properties. This is one of the dramatic new factors that makes nanoscience so interesting. In this appendix we gather together some of the important formulas that summarize the role played by dimensionality. A.2. DELOCALIZATION The regions occupied by a system of conduction electrons delocalized in one-, two-, and three-dimensional coordinate space are the length, area, and volume given in the Introduction to Nanotechnology, by Charles P. Poole Jr. and Frank J. Owens. ISBN 0-471-07935-9. Copyright 0 2003 John Wiley & Sons, Inc. 357
358 FORMULAS FOR DIMENSIONALITY Table A.l. Properties of coordinate and k space in one, two, and three dimensions Coordinate k-Space Fermi Value Region Unit Cell Region of kz Dimensions Length L 24L 2kF k; One Area A = L2 (2./LI2 nkz k: + k$ Two Volume v = L~ (27l/LI3 47lk,/3 k,? + k; + k$ Three first column of Table A. 1. Column 2 of the table gives the size of the unit cell in reciprocal or k space, and column 3 gives the size of the Fermi region that is occupied by the delocalized electrons, where the Fermi energy EF has the value EF = fi2k,/2m, and in this region E < EF. Column 4 gives expressions for I? in the three systems. The numbers of electrons N in the occupied regions of column 3 at the temperature of absolute zero, as well as the density of states D(E) defined by the expression D(E) = dN(E)/dE, are given in Table A.2. We see from this table that the density of states decreases with the energy for one dimension, is constant for two dimensions, and increases with increasing energy for three dimensions. Thus the number of electrons and the density of states as functions of the energy have quite different behaviours for the three cases, as indicated by the plots of Figs. 9.9, 9.10, and 9.15. A.3. PARTIAL CONFINEMENT The conduction electrons in nanostructures can be partially confined and partially delocalized, depending on the shape and the dimensions of the structure. One limiting case is a quantum dot in which they are totally confined, and the other Table A.2. Number of electrons N(€) and density of states Q€)= dN(E)/d€as function of energy €for electrons delocalized in one, two, and three spatial dimensions, where A = L2 and V= L3 Number of Density of Delocalization Electrons N States D(E) Dimensions N(E) = - = N(E) = D(E) = A (”) 271 h2 D(E) =- 2E2 (:)3’2E112 - 1
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INTRODUCTION TO NANOTECHNOLOGY Char
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CONTENTS Preface xi 1 Introduction
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5.2 Carbon Molecules 103 5.2.1 Natu
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9.4 Excitons 244 9.5 Single-Electro
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PREFACE In recent years nanotechnol
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INTRODUCTION The prefix nano in the
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INTRODUCTION 3 he recognized the ex
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1000 (I) a 900 4 800 a 900 I 6 700
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INTRODUCTION 7 developed before the
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2.1. STRUCTURE 9 mechanics, the res
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X T 2.1. STRUCTURE 11 Figure 2.4. C
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2.1. STRUCTURE 13 Figure 2.6. Thirt
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Sodium Nanoparticle Na, Magic Numbe
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2.1. STRUCTURE 17 of the large anio
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2.1. STRUCTURE 19 other, and high-f
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2.2. ENERGY BANDS 21 Conduction Ban
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2.2. ENERGY BANDS 23 Figure 2.13. S
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2.2. ENERGYBANDS 25 band at point T
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A X ' Wavevector A Si c z 2.2. ENER
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2.2. ENERGY BANDS 29 bands of Figs.
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2.3. LOCALIZED PARTICLES 31 add ele
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1 meV 10 meV 100 meV FJ E W 1 eV 10
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3 METHODS OF MEASURING PROPERTIES 3
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3.2. STRUCTURE 37 Table 3.1. Crysta
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3.2. STRUCTURE 39 Figure 3.2. Two-d
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3.2. STRUCTURE 41 The widths of the
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44 METHODS OF MEASURING PROPERTIES
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3.3. MICROSCOPY 51 types of transit
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3.3. MICROSCOPY 53 Actual diverging
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Tunneling current Tunneling current
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3.3. MrCAOSCOPY 57 and the latter m
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3.4. SPECTROSCOPY 59 From Eq. (3.8)
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1 Average Panicle FWHM Size (nm) in
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CdSe colloidal NCs a = 1.2 nrn 3.4.
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El X-RAY TUBE 8000 - A 6000 - 4000
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2 N I w 3.0 2.5 2.0 1.5 1 .o 0.5 3.
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i 3.4. SPECTROSCOPY 69 NMR involves
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T=220K - 2G H FURTHER READING 71 Fi
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NUMBER OF ATOMS RADIUS (nm) 1 10 1
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I L 7 3 5 7 9 11 13 15 17 NUMBER OF
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JELLIUM MODEL OF CLUSTERS ATOMS CLU
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1.02 { 1.01 - 1 - 0.99 - 4.2. METAL
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4.2. METAL NANOCLUSTERS 81 Figure 4
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4.2. METAL NANOCLUSTERS 83 Figure 4
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-0 100 200 300 400 500 600 MASSICHA
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a 42. METAL NANOCLUSTERS 87 Figure
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. . . .. . - . D 111111111111111111
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3 4 2.5 0 cn g 2 0 z d 1.5 t a 9 1
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4.3. SEMICONDUCTING NANOPARTICLES 9
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4.4. RARE GAS AND MOLECULAR CLUSTER
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4.5. METHODS OF SYNTHESIS 97 d Figu
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4.5. METHODS OF SYNTHESIS 99 isopro
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PULSED LASER BEAM 1 1 1 1 1 I ROTAT
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5.1. INTRODUCTION CARBON NANOSTRUCT
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5.2. CARBON MOLECULES 105 methane d
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5.3. CARBON CLUSTERS 107 -0 20 40 6
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PHOTON ENERGY (electron volts) 5.3.
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Figure 5.6. Structure of the CEO fu
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1 30 0 14.1 14.2 14.3 14.4 14.5 LAT
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(c) 5.4. CARBON NANOTUBES 115 Figur
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5.4. CARBON NANOTUBES 1 17 The mech
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5.4. CARBON NANOTUBES 11 9 investig
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5.4. CARBON NANOTUBES 121 energy gr
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5.4. CARBON NANOTUBES 123 stretch c
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5.5. APPLICATIONS OF CARBON NANOTUB
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- v) 450 : 400 3 350 1 300 : 5 250
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BULK NANOSTRUCTURED MATERIALS In th
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h 8 0 6.1. SOLID DISORDERED NANOSTR
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6.1. SOLID DISORDERED NANOSTRUCTURE
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6.2. NANOSTRUCTURED CRYSTALS 153 qu
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6.2. NANOSTRUCTURED CRYSTALS 155 Fi
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158 BULK NANOSTRUCTURED MATERIALS 6
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160 BULK NANOSTRUCTURED MATERIALS w
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162 BULK NANOSTRUCTURED MATERIALS 0
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164 BULK NANOSTRUCTURED MATERIALS n
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166 NANOSTRUCTURED FERROMAGNETISM f
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168 NANOSTRUCTURED FERROMAGNETISM i
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170 NANOSTRUCTURED FERROMAGNETISM M
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172 NANOSTRUCTURED FERROMAGNETISM h
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174 NANOSTRUCTURED FERROMAGNETISM d
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176 NANOSTRUCTURED FERROMAGNETISM o
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4 h $ 3 7.5. NANOCARBON FERROMAGNET
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7.6. GIANT AND COLOSSAL MAGNETORESI
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1.4 N 1 1.2 z " 1 0 v 5 h 0.8 0 0.6
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7.6. GIANT AND COLOSSAL MAGNETORESI
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7.7. FERROFLUIDS 187 Figure 7.22. M
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7.7. FECIROFLUIDS 189 Figure 7.25.
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7.7. FERRQFLUlOS 191 FerroRuids can
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FURTHER READING FURTHER READING 193
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10- IR f IA -1 8.1. INTRODUCTION 19
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8.2. INFRARED FREQUENCY RANGE 197 1
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8.2. INFRARED FREQUENCY RANGE 199 d
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s C CTI e 8 9 4( 8.2. INFRARED FREQ
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8.2.3. Raman Spectroscopy 8.2. INFR
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8.2. INFRARED FREQUENCY RANGE 205 a
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- r I 520 51 8 v 6 516 a" 51 4 51 2
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8.2. INFRARED FREQUENCY RANGE 209 i
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v) - C 3 8 600 400 100 0 e e 10 20
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i E (cm-’ ) 20 c I 1 ID 0 4x107 8
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- ? m v .- - z In C a, c C - .. . .
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Excitatior I [eV]: 2.175 2.214 2.25
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6 100 200 300 Time (ns) 8.3. LUMINE
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400 nm Laser / Free excitons Trappe
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8.4. NANOSTRUCTURES IN ZEOLITE CAGE
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FURTHER READING 225 P. Milani and C
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9.2. PREPARATION OF QUANTUM NANOSTR
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i 9.2. PREPARATION OF QUANTUM NANOS
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9.3. SIZE AND DIMENSIONALITY EFFECT
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w n 3 2 1 9.3. SIZE AND DIMENSIONAL
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WE) Quantum Dot Number of Electrons
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9.5. SINGLE-ELECTRON TUNNELING 245
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9.5. SINGLE-ELECTRON TUNNELING 247
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1 pair section ;- COT. .; . . I. .
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o.6 LWIR: T = 77 K 45" incidence AD
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9.7. SUPERCONDUCTIVITY 253 horizont
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9.7. SUPERCONDUCTIVITY 255 applied
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10.1. SELF-ASSEMBLY 10 SELF-ASSEMBL
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10.1. SELF-ASSEMBLY 259 factor of 2
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(a) (LI (dl 10.1. SELF-ASSEMBLY 261
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10.1. SELF-ASSEMBLY 263 atoms, as n
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- c v) ._ C 3 2 9 40 c - .- e m v w
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10.2. CATALYSIS 267 where the lengt
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10.2. CATALYSIS 269 are also other
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1600 2 1200 t p - Bi2M020, 10.2. CA
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7 - I 2,330 m .- c r 0 2 2,300 - u)
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10.2. CATALYSIS 275 with a top and
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10.2. CATALYSIS 277 based on the pr
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10.2. CATALYSIS 279 CnHlnfl, which
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I1 ORGANIC COMPOUNDS AND POLYMERS 1
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11.2. FORMING AND CHARACTERIZING PO
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1 1.3. NANOCRYSTALS 285 This expres
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-1 5 0) C a, -1 1 000 300 100 30 10
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11.3. NANOCRYSTALS 289 Table 11.1.
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11.3. NANOCRYSTALS 291 R’ groups
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11.4. POLYMERS 293 Figure 11.9. Ske
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11.5. SUPRAMOLECULAR STRUCTURES 295
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M Et3P OTf M=Pd M=Pt M=Pd, 41 % M=P
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11.5. SVPRAMOLECUUAR STRUCTURES 2s
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11.5. SUPRAMOLECULAR STRUCTURES 301
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11 5. SUPRAMOLECULAR STRUCTURES 303
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Page 318 and 319: BiodegradaWe surface 4 Functional g
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Page 329 and 330: 318 BIOLOGICAL MATERtALS i J / Flgu
Page 331 and 332: 320 BIOLOGICAL MATERIALS Pyrimidine
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Page 339 and 340: 328 BIOLOGICAL MATERIALS tions they
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Page 359 and 360: 348 NANOMACHINES AND NANODEVICES -
Page 361 and 362: 350 NANOMACHINES AND NANODEVICES re
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Page 365 and 366: 354 NANOMACHINES AND NANODEVICES -1
Page 370 and 371: A.3. PARTIAL CONFINEMENT 359 limiti
Page 372 and 373: APPENDIX B TABULATIONS OF SEMICONDU
Page 374 and 375: TABULATIONS OF SEMICONDUCTING MATER
Page 376 and 377: Table B.8. Effective masses m+ rela
Page 378 and 379: TABULATIONS OF SEMICONDUCTING MATER
Page 380: TABULATIONS OF SEMICONDUCTING MATER
Page 383 and 384: 372 INDEX amoeba, 3 16 amphiphilic,
Page 385 and 386: 374 INDEX CdS, 9, 130, 213, 216, 36
Page 387 and 388: 376 INDEX dispersion, 277 disulfide
Page 389 and 390: 378 INDEX Ga (gallium) (continued)
Page 391 and 392: 380 INDEX length (continued) critic
Page 393 and 394: 382 INDEX multiple ionization, 93 r
Page 395 and 396: 384 INDEX pi-conjugation, 282, 292
Page 397 and 398: silica, 269 silica-alumina, 269, 27
Page 399: 388 INDEX wavefimction (continued)
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