List of Tables

List of Tables
3.1
Parametrization details of the pairwise repulsive potentials for Cd-X, Se-X and
Te-X interactions (X = H, C, N, O, S, Se, Te and Cd). . . . . . . . . . . . . . . . . 65
3.2
Structural and energetic properties of bulk phases of Cd, Se and Te, calculated
using SCC-DFTB and PP-PBE. The experimental values are also given. . . . . . . 68
3.3
Structural and energetic properties of rock-salt CdO, zb and wz phases of CdS,
CdSe and CdTe, calculated using SCC-DFTB and PP-PBE. The experimental values are also given. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.4
Calculated geometry (bond lengths are in Å and bond angles are in degrees) and
surface energy γ in [J/m2 ] of both (1010) and (1120) surfaces of cadmium chalcogenides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.5
Calculated geometry (bond lengths are in Å and bond angles are in degrees) and
formation energy E f in [eV/pair] of both (1010) and (1120) faceted hexagonal
nanowires of cadmium chalcogenides. . . . . . . . . . . . . . . . . . . . . . . . . 82
3.6
Atomic spin dependent constants (WAll′ in a.u.) of Se and Te. . . . . . . . . . . . . 86
3.7
Comparison between SCC-DFTB, PP-PBE and B3LYP results on the binding energy (in eV) and equilibrium bond length (in Å) of simple diatomic molecules. s,
d, t, q denote as singlet, doublet, triplet, quartet spin state, respectively. . . . . . . . 87
iv
LIST OF TABLES
3.8
v
Comparison between SCC-DFTB, PP-PBE (SIESTA), B3LYP (G03) and experimental results on the binding energy (in eV), equilibrium bond angle (in degrees)
and length (in Å) of AB2 type molecules. All molecules have been calculated in
the singlet state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1
The details of the structural relaxation of bare and passivated wurtzite Cd56 Te56
clusters. M, stands for the mean value and N is the number of the bond lengths
and bond angles; bond length are in Å and angles are in degrees. . . . . . . . . . . 102
4.2
HOMO-LUMO gap (Eg in eV) of both zinc-blende and wurtzite derived thiolcapped Cdn Ten QDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.1
Structural relaxation of (1010) CdTe surface and (1010) CdTe nanowire (bond
lengths are in Å and bond angles are in degrees.) . . . . . . . . . . . . . . . . . . 121
6.1
¯ faceted
Bond lengths (in Å) and bond angles (in degree) of relaxed CdTe (1010)
nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
List of Figures
1.1
The evolution (shown schematically) of a three-dimensional systems to two-, oneand zero-dimensional systems, correlating with the continuing discretization of the
energy states [These are the DOS of the valence band near Fermi region of the one
representative CdX semiconductor]. . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
6
Absorption (upper) and fluorescence (lower) spectra of CdSe semiconductor nanocrystals showing quantum confinement and size tunability [64]. . . . . . . . . . . . . . 10
1.3
Impact of shape on the electronic and surface properties of semiconductor nanocrystals. (A) Band gaps of CdSe quantum wells, wires, and dots are plotted against the
length of the confined dimension. The bulk band gap and exciton diameter are
noted on the axes. (B) Fractions of atoms on the nanocrystal surface are plotted
against the total number of atoms. The wires (purple) are 1 µm in length, the disks
(green) are 20 nm in length, and the rods (red) are 4 nm in diameter [64]. (C) Transmission electron micrographs depicting CdSe dots [64], rods [65], tetrapods [66],
and disks [67]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1
First Brillouin Zone for hexagonal lattices and its high symmetry points. . . . . . . 45
2.2
DFT tot shows the (shifted) total energy versus Cd-S distances (in a.u.) for zincblende
CdS, DFT Belec , the same for the electronic part (Eq. 2.65) and Erep is the difference of these two curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
vi
LIST OF FIGURES
3.1
vii
Electronic band structure of hcp-Cd (a, b), trigonal-Se (c, d) and trigonal-Te (e,
f), calculated by SCC-DFTB (left panel) and PP-PBE (right panel) methods. For
hcp-Cd, ǫ f denotes the Fermi level for each case. For Se and Te the zero of energy
is set at the top of the valence band. . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2
Electronic band structure of bulk rock-salt CdO, calculated by (a) SCC-DFTB and
(b) PP-PBE methods. The zero of energy is set at the top of the valence band. . . . 72
3.3
Electronic band structure of zb-CdS (a, b), zb-CdSe (c, d) and zb-CdTe (e, f),
calculated by SCC-DFTB (left panel) and PP-PBE (right panel) methods. The
zero of energy is set at the top of the valence band for each case. . . . . . . . . . . 73
3.4
Electronic band structure of wz-CdS (a, b), wz-CdSe (c, d) and wz-CdTe (e, f),
calculated by SCC-DFTB (left panel) and PP-PBE (right panel) methods. The
zero of energy is set at the top of the valence band for each case. . . . . . . . . . . 75
3.5
Optimized structure of one representative CdX (a) (1010) and (b) (1120) surfaces
(side view). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.6
The electronic band structures of CdX [X = S (a, b), Se (c, d) and Te (e, f)] (1010)
surfaces, calculated with SCC-DFTB (left panel) and PP-PBE (right panel) methods. The zero of energy is set at the top of the valence band for each case. . . . . . 79
3.7
The electronic band structures of CdX [X = S (a, b), Se (c, d) and Te (e, f)] (1120)
surfaces, calculated with SCC-DFTB (left panel) and PP-PBE (right panel) methods. The zero of energy is set at the top of the valence band for each case. . . . . . 80
3.8
Optimized structure of one representative CdX (a) (1010) and (b) (1120) faceted
hexagonal nanowires (top view). . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.9
Electronic band structure of (1010) faceted nanowires for CdS (a, b), CdSe (c,
d), CdTe (e, f), calculated with SCC-DFTB (left panel) and PP-PBE (right panel)
methods. The zero of energy is set at the top of the valence band for each case. . . 83
LIST OF FIGURES
viii
3.10 Electronic band structure of (1120) faceted nanowires for CdS (a, b), CdSe (c,
d), CdTe (e, f), calculated with SCC-DFTB (left panel) and PP-PBE (right panel)
methods. The zero of energy is set at the top of the valence band for each case. . . 84
3.11 Schematic view of few small molecules together with their equilibrium geometric
parameters obtained with SCC-DFTB, PP-PBE in parenthesis and B3LYP/SBK+631G(d,p) in third bracket;The bond lengths are in Å and angles are in degree. . . . 90
4.1
Variation in binding energy per atom as a function of cluster size for zinc-blende
(blue line) and wurtzite (red line) derived Cdn Ten (SH)m Hm clusters. . . . . . . . . 98
4.2
Radial relaxations for the (a) bare Cd56 Te56 wurtzite cluster and (b) thiol capped
Cd56 Te56 wurtzite cluster. Points those fall on the dotted line correspond to atoms
that have not relaxed radially.
4.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Density of States of the (a) bare Cd56 Te56 wurtzite cluster and (b) thiol capped
Cd56 Te56 wurtzite cluster. Zero energy is set as the Fermi energy (dotted line).
4.4
. . 103
Total Density of States (DOS) for zinc-blende (left panel) and wurtzite (right panel)
derived Cdn Ten (SH)m Hm clusters of different n. (a, b, c, d represents n = 10, 55,
119, 143, respectively and e, f, g, h represents n = 10, 56, 117, 148, respectively).
The vertical dash lines denote the Fermi level.
4.5
. . . . . . . . . . . . . . . . . . . 105
Radial distribution of the Mulliken charges in the zinc-blende (left panel) and
wurtzite (right panel) derived Cdn Ten (SH)m Hm clusters of different n. (a, b, c,
d represent n = 10, 55, 119, 143, respectively and e, f, g, h represents n = 10, 56,
117, 148, respectively). The horizontal dash lines mark the values for the neutral
atoms, i.e., 0 charge for all atoms. The Mulliken charges of the Cd, Te, S and H
atoms are depicted in black, red, green and blue, respectively.
4.6
. . . . . . . . . . . 108
The optimized structure (both top (right) and side (left) view) of one representative
Cd65 Te65 QD-CNT (10, 0) nanohybrid system. . . . . . . . . . . . . . . . . . . . 110
LIST OF FIGURES
4.7
ix
The band structure of (a) CNT [zig-zag (10, 0)] and CdTe QD-CNT [zig-zag (10,
0)] nanohybrids with CdTe QDs of different size (b) Cd34 Te34 , (c) Cd55 Te55 , (d)
Cd65 Te65 and (e) Cd98 Te98 , The zero energy is set at the top of the valence band. . 111
4.8
The Density of States (DOS) of CdTe QD-CNT [zig-zag (10, 0)] nanohybrids
with CdTe QDs of different size (a) Cd34 Te34 , (b) Cd55 Te55 , (c) Cd65 Te65 and
(d) Cd98 Te98 . The zero energy is set at Fermi level. . . . . . . . . . . . . . . . . . 113
5.1
Optimised structure of (a) CdTe (1010) faceted nanowire (top view) and (b) CdTe
(1010) surface (side view). Cd and Te atoms are represented by grey (dark) and
yellow (light), respectively.
5.2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Evolution of formation energies as a function of (a) diameter and (b) surface atom
ratio of the CdTe (1010) faceted nanowires. Blue solid line represents the NWs of
hexagonal cross sections and the red solid line represents the NWs of triangular
cross sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.3
Electronic band structures of bare triangular [top (a, b, c, d, e)] and hexagonal
[bottom (f, g, h, i, j)] (1010) faceted CdTe nanowires of five different sizes. a, b,
c, d, e represents the band structure of WT 1 , WT 2 , WT 3 , WT 4 and WT 5 triangular
nanowires, respectively. f, g, h, i, j represents the same for WH1 , WH2 , WH3 , WH4
and WH5 hexagonal nanowires, respectively. The zero of energy is set at the fermi
energy for each case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.4
Variation of band gaps with the wire (a) diameter and (b) surface atom ratio of
the CdTe (1010) faceted nanowires. Blue solid line represents the unpassivated
hexagonal NWs, blue dotted line represents the H-passivated hexagonal NWs, the
red solid line represents the unpassivated triangular NWs and the red dotted line
represents the H-passivated triangular NWs. . . . . . . . . . . . . . . . . . . . . . 126
LIST OF FIGURES
5.5
x
The charge densities at (a) CBM (blue) and (c) VBT (red) for the unpassivated
nanowire WH1 and (b) CBM (blue) and (d) VBT (red) for the H-passivated nanowire
WH1 . The isosurface value 0.0004 e Å−3 was used. . . . . . . . . . . . . . . . . . 127
5.6
Optimized structure of the dihydrogen dicarboxylic acid (DHDC) derivative adsorbed on CdTe nanowire (WH1 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.7
Total density of states (shaded area) for (a) clean CdTe nanowire, (b) NW-DHDC
interface, (c) NW-DMDC interface, (d) NW-DCDC interface and (e) NW-DNDC
interface. The zero of energy is set at the Fermi energy. . . . . . . . . . . . . . . . 132
5.8
The Projected local Density of States of NW-DNDC hybrid system showing the
contribution from different orbitals. The zero energy is set at Fermi energy. . . . . 133
5.9
VBT/HOMO (red) and CBM/LUMO (blue) energy alignment for the considered
NW-molecule hybrid systems (bold) and molecules in the gas phase. The region
inside the dotted lines identifies the band gap of clean CdTe nanowire (WH1 ). The
zero energy is set at the VBT of the clean nanowire. . . . . . . . . . . . . . . . . . 134
6.1
¯ surface (side view), (b) CdTe (1010)
¯ faceted
Relaxed geometry of (a) CdTe (1010)
¯ faceted double-walled nanotube (top
nanowire (top view) and (c) CdTe (1010)
view). Cd and Te atoms are represented by grey and orange spheres, respectively. . 142
6.2
¯
Variation of formation energies with surface atom ratios for various CdTe (1010)
faceted nanowires and nanotubes. The inset indicates the evolution of formation
¯ faceted nanowires and nanotubes.144
energies as a function of radius of the CdTe (1010)
LIST OF FIGURES
6.3
xi
¯ faceted nanotubes of five different wall
Electronic band structures of CdTe (1010)
thickness along the Γ(0,0,0) 2π/c → A(0,0,1/2) 2π/c direction, where c is the lattice constant along the axial direction. From left to right (a-e) the figures represent the band structures of 2WNT, 3WNT, 4WNT, 5WNT and 6WNT, respectively
(wall thickness increased (2WNT to 6WNT) keeping the inner tube radius fixed).
The zero of the energy is set at the Fermi energy in each case. . . . . . . . . . . . . 146
6.4
¯ faceted nanVariation of band gap with surface atom ratios for the CdTe (1010)
¯
otubes. The inset indicates the band gaps as a function of radius of the CdTe (1010)
faceted nanotubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.5
Isosurface plots of the charge densities (squared wave-functions) at (a) valence
band top (VBT) and (b) conduction band minimum (CBM) of CdTe nanotube
(2WNT) at the Γ point. The isosurface value 0.0002 e Å−3 was used. . . . . . . . . 149
6.6
The Projected local Density of States of the (a) 2WNT and (b) 2WNT-C60 showing
the contributions from different orbitals. The value of Gaussian smearing, used to
plot the DOS, is 0.1. The zero of the energy is set at the Fermi energy in each case. 151
6.7
The Projected local Density of States of 2WNT, 3WNT, 4WNT and C60 in the NTC60 hybrid systems. The value of Gaussian smearing, used to plot the DOS, is 0.1.
The zero of the energy is set at the Fermi energy. . . . . . . . . . . . . . . . . . . 152
6.8
The Total Density of States (DOS) of the 2WNT-1C60 (red), 2WNT-2C60 (green)
and 2WNT-3C60 (violet) nanohybrids. The value of Gaussian smearing, used to
plot the DOS, is 0.1. The zero of the energy is set at the Fermi energy. . . . . . . . 153
LIST OF FIGURES
6.9
xii
Isosurface plots of the charge densities (squared wave-functions) at (a) valence
band top (VBT) and (b) conduction band minimum (CBM) for 2WNT-C60 hybrid
system at the Γ point. (c) Isosurface plots of the charge density difference distribution for the 2WNT-C60 hybrid system at the Γ point. The green indicates an
increase in charge density. The isosurface value used for (a) and (b) 0.0002 e Å−3
and for (c) 0.01 e Å−3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.10 (a), (b), (c), (d), (e) and (f) represent the electronic band structures (left panel) and
the density of states (DOS) (right panel) of the 2WNT-C60 , 2WNT-C68 , 2WNTC70 , 2WNT-C76 , 2WNT-C80 and 2WNT-C84 nanohybrids, respectively. The blue
shaded area in DOS reflects the Projected local Density of States of CdTe NT of
the hybrid systems and the red peaks are the Projected local Density of States of
fullerene derivatives of the hybrid systems. The value of Gaussian smearing, used
to plot the DOS, is 0.02. The zero of the energy is set at the Fermi energy in each
case.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.11 Valence band top (HOMO for molecule) (red) and conduction band minimum
(LUMO for molecule) (blue) energy alignment for the considered 2WNT-Cn (n
= 60, 68, 70, 76, 80 and 84) hybrid systems (bold) and Cn -thiol molecules (n = 60,
68, 70, 76, 80 and 84) in the gas phase. The dotted region identifies the band gap
of the clean CdTe nanotube (2WNT).
. . . . . . . . . . . . . . . . . . . . . . . . 158

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