Direct Energy, 2018a

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6 PHOTOVOLTAICS 117 Figure 6.6: <strong>Energy</strong> gap versus interatomic spacing for multiple semiconductors. Used with permission from [71]. Some solar cells are made from layered material with the largest energy gap material on the top. For example, a solar cell could be made from a top layer of ZnS, a middle layer of ZnSe, and a bottom layer of ZnTe. Photons with energy E > 3.6 eV would be absorbed in the ZnS layer. Photons with energy 2.7 eV
118 6.3 Semiconductors and <strong>Energy</strong> Level Diagrams Figure 6.7: The dark mineral embedded in the rock is naturally occurring zinc sulde. level by the name chemical potential, μ chem . In a pure semiconductor at T =0K, all electrons occupy the lowest possible states. The valence band is completely lled, and the conduction band is completely empty. The Fermi level, E f , is the energy level at the middle of the energy gap. No electrons are found at energy E f because no electrons can have an energy inside the energy gap. However, the Fermi level is a useful measure to describe the material. In a pure semiconductor at T > 0 K, some electrons are excited into higher energy levels. As the temperature increases, more electrons are likely to be found at higher energy levels more often. The probability that an electron is in energy level E varies with temperature as e −E/k BT [9] [10]. The quantity k B is the Boltzmann constant. k B =1.381 · 10 −23 J K =8.617 · 10−5 eV K (6.13) The Fermi level for a material with T > 0 K is slightly higher than the Fermi level for a material with T =0K because more electrons are likely to be excited. The probability of nding an electron at energy level E at temperature T is F (E,T)= 1 1+e (E−E f )/k B T . (6.14) Equation 6.14 is called the Fermi Dirac distribution, and like any probability, it ranges 0 ≤ F ≤ 1. For energy levels far above the conduction band, (E − E f ) is large and positive, so electrons are quite unlikely to be found, F ≈ 0. For energy levels far below the valence band, (E − E f ) is large and negative, so electrons are quite likely to be found, F ≈ 1.
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Direct Energy Conversion by Andrea
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CONTENTS i Contents Contents i 1 In
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CONTENTS iii 6.3.2 Energy Levels in
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CONTENTS v 9.6 Fuel Cells . . . . .
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Acknowledgements I would like to th
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2 1.2 Preview of Topics to connect
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4 1.2 Preview of Topics Math throug
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6 1.2 Preview of Topics Process Spo
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8 1.2 Preview of Topics drodynamic
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10 1.4 Measures of Power and Energy
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12 1.5 Properties of Materials 1.5
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14 1.5 Properties of Materials most
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16 1.6 Electromagnetic Waves −→
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18 1.6 Electromagnetic Waves Relate
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20 1.6 Electromagnetic Waves A unif
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22 1.7 Problems
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24 2.2 Capacitors 2.2 Capacitors 2.
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26 2.2 Capacitors 2.2.3 Permittivit
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28 2.2 Capacitors â z â y â x No
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30 2.2 Capacitors Figure 2.3: Natur
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32 2.3 Piezoelectric Devices Piezoe
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34 2.3 Piezoelectric Devices Lattic
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36 2.3 Piezoelectric Devices Herman
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38 2.3 Piezoelectric Devices Figure
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40 2.3 Piezoelectric Devices c a β
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42 2.3 Piezoelectric Devices In cer
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44 2.3 Piezoelectric Devices made m
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46 2.3 Piezoelectric Devices tions.
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48 2.4 Problems 2.5. A piezoelectri
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50 2.4 Problems 2.13. Consider a pi
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52 2.4 Problems 2.16. The gure belo
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54 3.2 Pyroelectricity Material Che
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56 3.3 Electro-Optics KH 2 PO 4 [25
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58 3.3 Electro-Optics The rst two t
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60 3.3 Electro-Optics used as an el
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62 3.4 Notation Quagmire Notation i
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64 3.5 Problems 3.5 Problems 3.1. F
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Page 79 and 80: 68 4.1 Introduction Center-fed half
Page 81 and 82: 70 4.2 Electromagnetic Radiation In
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Page 85 and 86: 74 4.3 Antenna Components and Denit
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Page 93 and 94: 82 4.4 Antenna Characteristics 4.4.
Page 95 and 96: 84 4.4 Antenna Characteristics 5 Li
Page 97 and 98: 86 4.5 Problems Figure 4.6: A snow
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Page 103 and 104: 92 5.2 Physics of the Hall Eect The
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Page 107 and 108: 96 5.3 Magnetohydrodynamics This am
Page 109 and 110: 98 5.5 Applications of Hall Eect De
Page 111 and 112: 100 5.6 Problems 5.6 Problems 5.1.
Page 113 and 114: 102 6.2 The Wave and Particle Natur
Page 115 and 116: 104 6.3 Semiconductors and Energy L
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Page 131 and 132: 120 6.4 Crystallography Revisited L
Page 133 and 134: 122 6.5 Pn Junctions E Indirect Sem
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Page 137 and 138: 126 6.5 Pn Junctions V x - + Energy
Page 139 and 140: 128 6.6 Solar Cells to day and loca
Page 141 and 142: 130 6.6 Solar Cells dot based mater
Page 143 and 144: 132 6.7 Photodetectors Solar Panel
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Page 148 and 149: 6 PHOTOVOLTAICS 137 6.3. The gure i
Page 150 and 151: 7 LAMPS, LEDS, AND LASERS 139 7 Lam
Page 152 and 153: 7 LAMPS, LEDS, AND LASERS 141 Photo
Page 154 and 155: 7 LAMPS, LEDS, AND LASERS 143 Absor
Page 156 and 157: 7 LAMPS, LEDS, AND LASERS 145 We ca
Page 158 and 159: 7 LAMPS, LEDS, AND LASERS 147 If we
Page 160 and 161: 7 LAMPS, LEDS, AND LASERS 149 tube
Page 162 and 163: 7 LAMPS, LEDS, AND LASERS 151 easil
Page 164 and 165: 7 LAMPS, LEDS, AND LASERS 153 Power
Page 166 and 167: 7 LAMPS, LEDS, AND LASERS 155 Two L
Page 168 and 169: 7 LAMPS, LEDS, AND LASERS 157 but n
Page 170 and 171: 7 LAMPS, LEDS, AND LASERS 159 of ec
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Page 174 and 175: 7 LAMPS, LEDS, AND LASERS 163 Ti:Sa
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7 LAMPS, LEDS, AND LASERS 167 Gas D
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7 LAMPS, LEDS, AND LASERS 169 categ
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7 LAMPS, LEDS, AND LASERS 171 7.8.
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8 THERMOELECTRICS 173 8 Thermoelect
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8 THERMOELECTRICS 175 Symbol Name V
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8 THERMOELECTRICS 177 per unit volu
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8 THERMOELECTRICS 179 kPa, and the
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8 THERMOELECTRICS 181 Seebeck Effec
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8 THERMOELECTRICS 183 gradient acro
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8 THERMOELECTRICS 185 thermocouples
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8 THERMOELECTRICS 187 The gure of m
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8 THERMOELECTRICS 189 or mass invol
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8 THERMOELECTRICS 191 temperatures?
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8 THERMOELECTRICS 193 Figure 8.4: L
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8 THERMOELECTRICS 195 8.9 Problems
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8 THERMOELECTRICS 197 8.8. A thermo
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8 THERMOELECTRICS 199 Figure 8.5 8.
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202 9.2 Measures of the Ability of
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212 9.3 Charge Flow in Batteries an
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214 9.3 Charge Flow in Batteries an
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216 9.4 Measures of Batteries and F
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224 9.5 Battery Types specic energi
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226 9.5 Battery Types at the anode
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228 9.5 Battery Types Figure 9.8: T
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230 9.6 Fuel Cells Fuel cell compon
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232 9.6 Fuel Cells 9.6.3 Practical
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234 9.7 Problems 9.7 Problems 9.1.
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236 9.7 Problems A E - + I B D H 2
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238 10.3 Radiation Detectors high e
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240 10.5 Resistive Sensors capacito
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242 10.6 Electrouidics However, ene
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244 10.6 Electrouidics
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246 11.2 Lagrangian and Hamiltonian
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248 11.3 Principle of Least Action
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250 11.4 Derivation of the Euler-La
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252 11.5 Mass Spring Example not in
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254 11.5 Mass Spring Example Path 1
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256 11.5 Mass Spring Example We can
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258 11.6 Capacitor Inductor Example
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260 11.6 Capacitor Inductor Example
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262 11.7 Schrödinger's Equation 11
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264 11.8 Problems 11.4. Figure 11.2
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266 11.8 Problems a famous result k
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268 11.8 Problems (c) Find the gene
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270 12.2 Electrical Energy Conversi
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276 12.3 Mechanical Energy Conversi
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282 12.4 Thermodynamic Energy Conve
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284 12.4 Thermodynamic Energy Conve
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286 12.5 Chemical Energy Conversion
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288 12.6 Problems 12.6 Problems 12.
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290 12.6 Problems 12.6. Match the d
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292 13.1 Introduction • Describe
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294 13.2 Preliminary Ideas Assuming
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296 13.3 Derivation of the Lagrangi
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306 13.4 Deriving the Thomas Fermi
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308 13.5 From Thomas Fermi Theory t
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310 13.6 Problems (a) Write the Ham
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312 14.1 Introduction damental equa
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314 14.2 Types of Symmetries be wri
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316 14.3 Continuous Symmetries and
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322 14.4 Derivation of the Innitesi
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330 14.5 Invariants and we end up w
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332 14.5 Invariants in the limit ε
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334 14.5 Invariants Next use Eq. 14
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336 14.6 Summary 14.6 Summary In th
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338 14.7 Problems 14.6. The equatio
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340 14.7 Problems
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342 Appendices Symbol Quantity Unit
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350 Appendices Prex name Symbol Val
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352 Appendices for voltage. (As an
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354 Appendices Material or Device S
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356 REFERENCES [15] E. C. Jordan an
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358 REFERENCES [45] V. K. Tikhomiro
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360 REFERENCES [73] M. G. Thomas, H
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362 REFERENCES [100] A. Ishibashi,
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364 REFERENCES [125] D. Wright, Req
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366 REFERENCES [150] J. P. Owejan,
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368 REFERENCES [175] G. K. Woodgate
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Index Absorption, 139 Action, 247 A
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372 INDEX Nernst equation, 220 Neur
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Direct Energy, 2018a

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