CHEM01200604009 Sreejith Kaniyankandy - Homi Bhabha ...

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7 As seen from the schematic, potential barrier height is V 0 and barrier width is ‘a’. Potential repeats itself with a period of x=a+b=c. Since potential is periodic, wave function also has the same periodicity. Width of region II is ‘b’. The Schrödinger’s equation can be set up for a single electron trapped in this periodic potential as follows, 2 2 d H V( x) E 2 2mdx (1.1) Since the potential varies in two different regions we can set up Schrödinger’s equation for the two regions as given below, 2 d 2m 2 2 E V 0 0 Region I dx 2 d 2m 0 Region II 2 2 E dx (1.2) The general solution for the above equations can be represented as 1/2 ix ix 2 mE ( V0 ) I Ae Be , 2 1/2 ix ix 2mE II Ce De , 2 (1.3) The coefficients A , B ,C and D can be determined by boundary conditions and normalization procedure. The boundary conditions are both and d dx are continuous functions of x at the boundaries. Applying boundary conditions and Bloch function as given below we arrive at,
8 ( x) u ( x) e k k ikx cos( kc) F 2 2 F cos( b)cos( a) sin( b)sin( a) 2 (1.4) The above equations show that real solutions only exist for F 1 and the solution is wavelike. The gaps between these discontinuities are forbidden regions where no real solution exists. This treatment while being instructive as a paradigm for evolution of electronic structure in a periodic lattice, it does not include various complications that arise in the case of a charge carrier in solids. For example potential is not square well, electron at one lattice site interacts with nearby electrons and lattice site, furthermore electron- electron correlations introduces more complications. In a bulk semiconductor the potential varies along different directions. Therefore the dispersion of electrons along different directions is expected to be different. These complications were innovatively resolved in bulk semiconductors by using effective mass model. This model uses an approximation where the electrons and holes are assumed as free particles with different masses as compared to free electron mass or in other words the dispersion is assumed to be parabolic near k=0 or at zone center. The effective mass of charge carriers is a combined effect of all interaction of charge carriers in the crystal lattice. 1.2.2 Effective Mass Approximation As mentioned previously Bloch functions are taken as Eigen functions to solve Schrodingers Equation for a solid [1.14]. Therefore wave function in a 3-D solid is given by
Page 1: Charge Transfer Dynamics in Quantum
Page 7: DECLARATION I, hereby declare that
Page 11: ACKNOWLEDGEMENTS It is my privilege
Page 14 and 15: 1.3.5. Defect Mediated Relaxation 2
Page 16 and 17: 2. 8. 4. White Light Generation- 45
Page 18 and 19: 6.2. Experimental 6.2.1.Synthesis o
Page 20 and 21: devices based on QDs it has been sh
Page 22 and 23: Furthermore generation of pump (~40
Page 24 and 25: shell). This clearly indicated that
Page 26 and 27: 12. V. I. Klimov, J. Phys. Chem. B,
Page 28 and 29: 1.13 Reactant and Product Potential
Page 30 and 31: light. Inset: Kinetic traces monito
Page 32 and 33: 6.5 Transient decay kinetics of gra
Page 34 and 35: at 670 nm after exciting at 400 nm
Page 37 and 38: ABBREVIATIONS BET BQ CB CCD CdS CdT
Page 39: 1 Chapter 1
Page 42 and 43: 3 size dependent optical properties
Page 44 and 45: 5 1.2. Physics of Semiconductors 1.
Page 48 and 49: 9 Substituting this in Schrödinger
Page 50 and 51: 11 ( r, r ) ( r ) ( r ) (1.13) e
Page 52 and 53: 13 E E E 2 2 2 EX ne, le nh,
Page 54 and 55: 15 spherical symmetry of field. The
Page 56 and 57: 17 gE ( ) 2Em 2 3 3 (1.25) For a
Page 58 and 59: 19 1.3.2. Electron-Hole energy tran
Page 60 and 61: 21 Impact Ionization Figure 1.7. Sc
Page 62 and 63: 23 understanding on mechanistic asp
Page 64 and 65: 25 carriers are unable to sample th
Page 66 and 67: 27 CB VB QD Metal Figure. 1. 10. Sc
Page 68 and 69: 29 energy barrier. Therefore it is
Page 70 and 71: 31 1 f q 2 A qB (1.30) 2 In equa
Page 72 and 73: 33 Vibrational contribution can be
Page 74 and 75: 35 1. 7. 1. Electron Injection ET i
Page 76 and 77: 37 Under assumption of invariance o
Page 78 and 79: 39 distribution. To achieve good si
Page 80 and 81: 41 initially achieved monodispersit
Page 82 and 83: 43 and rate of charge transfer acro
Page 84 and 85: 45 1.32 P. V. Kamat, J. Phys. Chem.
Page 87: 47 Chapter 2
Page 90 and 91: 49 chemical species. Since a partic
Page 92 and 93: 51 fluorescence forms an important
Page 94 and 95: 53 eliminated by use of standard wh
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55 sample. Raman spectroscopy is ba
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57 will appear bright and region wi
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59 volatile solvent is drop casted
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61 spots arise from diffraction fro
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63 The electrical signal is then ch
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65 delayed and inverted. The two si
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67 Pump-probe technique is one of t
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69 Amplifier Jade Stretcher fs Osci
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71 Figure 2.6. Optical layout of Ti
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73 Grating Convex Mirror Concave Mi
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75 changes the polarization from ho
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77 Grating Output Input Mirror Grat
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79 μJ has a very high peak power.
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81 2.6. Dynamical Theory of X-Ray D
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83 Chapter 3
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85 Therefore the study of interfaci
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87 3. 2. Experimental Section 3.2.1
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89 and intensity show absence of ot
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91 which is also neutral; therefore
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93 electron transfer times. This re
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95 r B a * 0 3.1 me / me Now the
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97 nonadiabatic case the electron t
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99 drastically reduced leading to a
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101 While the study of injection dy
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103 study. Based on the injection d
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105 17. L. E. Brus, J. Phys. Chem.
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107 Chapter 4
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109 of the QDs. As a result surface
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111 4.2.2. Synthesis: The CdTe QDs
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113 lower hole state. In CdSe the l
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115 4.2 inset. The kinetic traces a
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117 growth of the bleach kinetics (
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119 previous section we have discus
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121 lived charge transfer complex w
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123 100 times concentration of the
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125 4.5. References 4.1. Efros, Al.
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127 Chapter 5
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129 been made in the synthesis of t
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131 metallic synthesis by arrested
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133 5.3. Result and discussion: 5.3
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135 indicating a confinement induce
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137 absorption studies that on form
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139 1000 c b PL Intensity 100 10 a
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141 samples due to a very weak exci
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143 dynamical spectrum is negligibl
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145 Earlier authors [5.4] reported
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147 Sample t r(ps) t 1(ps) t 2(ps)
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149 In addition to the cooling dyna
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151 pulse-width time scale followed
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153 5.20. Sreejith Kaniyankandy, Sa
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155 CHAPTER 6 Charge Separation in
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157 Studies by Wang et. al. [6.15]
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159 graphene in a 1M NaOH solution.
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161 Intensity (a.u.) 5 4 3 2 1 CdTe
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163 dynamics of graphene oxide and
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165 GO as shown in the Figure 3 rev
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167 electron acceptor for Graphene.
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169 governs the recombination dynam
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171 Sample τ 1 (ps) τ 2 (ps) τ 3
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173 A (mO.D) 10.0 0.0 -10.0 -20.0 0
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175 involved in the relaxation may
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177 Electron quencher (benzoquinone
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179 Scheme 6.1. Schematic of Electr
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181 6.6. Reina, A.; Jia, X.; Ho, J.
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183 6.26. Kaiser, A. B.; Navarro, C
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185 assigned to injection into diff
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187 transfer from CdSe core to ZnTe
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189 However the position of bands i
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