Nanotechnology-Enabled Sensors

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6.2 Density and Number of States 287 Fig. 6.2 The time-independent Schrödinger equation solutions for a twodimensional infinite potential well. 6.2.4 Definition of Density of States The electrical, mechanical, optical and magnetic properties of materials depend strongly on how the energies are distributed. To assess these properties, we need to consider the NOS and DOS. We define the number of free particles having an energy of E as N(E). The density of states is then defined as D(E) = dN(E)/dE. DOS is then expressed as D(E)dE, which is the number of allowed energy levels per unit volume of the material, within the energy range E to E + dE. 6.2.5 DOS in Three-Dimensional Materials In three-dimensional k space, the points of vectors of equal magnitude in all directions form a spherical shell. These vectors represent equal energy states, proportional to k 2 = kx 2 +ky 2 +kz 2 , given by: E 2 � 2 2 2 2 � ( kx + k y + k z ) = 2 k = . (6.10) 2m 2m If we consider the free particles being contained in a cube of length L, the total volume will be equal to V = L 3 , while the difference between kspace points will be equal to 2π/L.
288 In three-dimensional reciprocal space, the volume of a cubic unit cell is defined as: V3D 3 ⎛ 2π ⎞ = ⎜ ⎟⎠ , (6.11) ⎝ L which is the volume of a single energy state. The vector k encompasses a volume of 4/3 πk 3 . As a result, with reference to (Fig. 6.3), the volume between the two shells which are infinitely close to each other, at a distance of k from the centre is found to be: ⎛ 4 3 ⎞ 2 d⎜ π k ⎟ = 4πk dk . (6.12) ⎝ 3 ⎠ ky Chapter 6: Inorganic Nanotechnology Enabled Sensors kz Fig. 6.3 The k-space (reciprocal space) in 3D. Calculation of the NOS for a wavenumber between k and k+dk. By dividing this volume by the volume of a single energy state (Eq. (6.11)), the density of states, D(k), in reciprocal space can be obtained as: 2 2 3 4πk dk k L dk D( k) dk = 2 × = . (6.13) 2 V π 3D k dk kx
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Nanotechnology-Enabled Sensors
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Kourosh Kalantar-zadeh RMIT Univers
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Acknowledgments We have been fortun
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viii Contents Chapter 3: Transducti
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x Contents 5.7.1 Scanning Electron
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xii Contents 7.5 Nano-sensors based
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2 Chapter 1: Introduction Nobel lau
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4 Chapter 1: Introduction Fig. 1.2
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6 Chapter 1: Introduction ensure th
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8 Chapter 1: Introduction ments, th
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10 Chapter 1: Introduction aim is t
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12 Chapter 1: Introduction Referenc
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14 Chapter 2: Sensor Characteristic
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64 Chapter 3: Transduction Platform
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100 Chapter 3: Transduction Platfor
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136 Chapter 4: Nano Fabrication and
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212 Chapter 5: Characterization Tec
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Page 248 and 249: 236 Chapter 5: Characterization Tec
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337 ing ballistic transport of elec
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339 Fig. 6.36 Nanoresonators made o
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6.5 Nanotechnology Enabled Mechanic
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6.6 Nanotechnology Enabled Optical
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6.7 Magnetically Engineered Spintro
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ferromagnetic haematite (a form of
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References 365 21 E. Comini, G. Fag
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References 367 58 D. E. Williams an
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References 369 96 J. J. Shi, Y. F.
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Chapter 7: Organic Nanotechnology E
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7.2 Surface Interactions 373 can be
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7.2 Surface Interactions 375 Carbox
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7.2 Surface Interactions 377 Fig. 7
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7.2 Surface Interactions 379 There
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Fig. 7.12 The schematic of physical
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Fig. 7.13 Formation of SAMs. 7.2 Su
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7.2 Surface Interactions 385 ple, t
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7.3 Surface Materials and Surface M
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7.4 Proteins in Nanotechnology Enab
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7.4.4 Using Proteins as Nanodevices
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Fig. 7.36 The general structure of
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+ 7.4 Proteins in Nanotechnology En
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7.5 Nano-sensors based on Nucleotid
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Fig. 7.57 The structure of DNA stra
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7.6 Sensors Based on Molecules with
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7.6 Sensors Based on Molecules with
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7.8 Biomagnetic Sensors 7.8 Biomagn
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7.9 Summary 471 metal oxides, carbo
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References 473 19 T. Kunitake, Ange
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63 J. X. Huang, S. Virji, B. H. Wei
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References 477 105 M. Plomer, G. G.
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References 479 145 R. F. Service, S
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7.8 References 481 185 J. Wang, D.
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Remote plasma enhanced CVD (RPECVD)
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Thin film equivalent circuit ... 32
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Optical waveguides ................
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Semiconductor-semiconductor junctio
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About the Authors Dr. Kourosh Kalan
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Nanotechnology-Enabled Sensors

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