Nanotechnology-Enabled Sensors

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6.2 Density and Number of States 289 In this equation, to account for the intrinsic angular momentum of the electrons (or spin states), a factor of two has been used. For phonons this factor is 3. In order to calculate the DOS as a function of energy, by referring to Eq. (6.10) we can see that: 1 dk = mdE , (6.14) 2 2mE� and the following equation can be obtained: 3 2 3 3 3 / 2 L k dk 2L mE 1 L ⎛ 2m ⎞ 1/ 2 D( E) dE = = mdE = ⎜ ⎟ E dE . 2 2 2 2 2 2 (6.15) π π � 2mE� 2π ⎝ � ⎠ This shows that for a three-dimensional material the DOS is proportional to E 1/2 and continuous in the E space. 6.2.6 DOS in Two-Dimensional Materials The DOS can also be calculated for 2D structures, such as superlattices, where the structure is confined to quantum states in one dimension and effectively infinite in the other two. The approach is similar to the three-dimensional calculations. In this case, particles which have the same energy, occupying the same points in the reciprocal space, are have their k space points located in a ring of radius k and infinitely small width dk (Fig. 6.4). The area of this ring in two-dimensional reciprocal space is: ( πk ) 2 k dk 2 = , (6.16) d π while the area occupied by a single energy state is: V2D 2 ⎛ 2π ⎞ = ⎜ ⎟⎠ . (6.17) ⎝ L
290 Chapter 6: Inorganic Nanotechnology Enabled Sensors Fig. 6.4 k-space in 2D. The DOS in reciprocal space can therefore be calculated as: D ( k) 2π k dk k L dk dk = 2 × = , 2 ⎛ 2π ⎞ π ⎜ ⎟ ⎝ L ⎠ 2 (6.18) where again the multiplication by 2 accounts for the intrinsic angular momentum of the electrons (or 3 for phonons). Consequently, from (6.14), the 2D DOS in E space is: 2 2 L kdk L m D( E) dE = = dE . (6.19) 2 π π� It can be seen that the 2D DOS does not depend on the energy value unlike the 3D DOS. This time, the DOS takes on a staircase-function as follows: 0 ky 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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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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