Electronic structure and bandgap engineering of CdTe nanotubes and designing the CdTe nanotube–fullerene hybrid nanostructures for photovoltaic applications

Abstract

The electronic structure of CdTe nanotube–fullerene nanocomposites has been explored. Within this context, the structural and electronic properties of isolated 101̄0 faceted CdTe nanotubes (NTs) with hexagonal cross-sections were first investigated using the self-consistent-charge density-functional tight-binding (SCC-DFTB) method. The possibility of band gap engineering of clean CdTe nanotubes is explored by varying either the size or wall thickness of the NTs. However, the efficient modification of the band gap can be attained by introducing the molecular states of fullerene into the band gap region of the CdTe NTs. The effects of the modulation of the band alignment through the variation in the wall thickness of the CdTe NTs on the electron injection rate from the NT to C₆₀ in hybrid systems have been explored and we also found that the light harvesting efficiency of these nanohybrids can be maximized by increasing the concentration of the C₆₀–thiol moieties. The position of the electronic energy levels offers information about the electronic structure of the hybrid systems such as whether it constructs type I or type II hetero-junctions, which bears key information for their application in photovoltaics. We also studied the electronic structure of CdTe–fullerene hybrid nanostructures with a series of fullerenes of different compositions.

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1 Introduction

The research on 1D crystalline solids, such as nanotubes, nanowires and nanocables has the promise of new inventions and new materials with interesting properties because of their superior electronic, optical, catalytic and mechanical properties.^1–4 The reason for the growing interest in this particular class of materials stems from the fact that in addition to the quantum size effect, the properties of these materials may also be tuned by varying their structure and morphologies. Among the various 1D nanostructures, semiconductor nanotubes are intensively investigated owing to their potential application in electronics, optoelectronics, energy storage, sensing and nanodevices due to the presence of an internal cavity which is specific to the tubular morphology with unique physical and chemical properties.^5–9 To date, emergent semiconducting nanotubes have been synthesized from II–VI group semiconductors.^10,11 As an important archetype of the II–VI semiconductor materials, CdTe nanostructures offer inherent electronic and optical properties to serve as functional building blocks for light-emitting devices (LEDs), photonic crystals, nonlinear optical devices and biological labels.^12–15 Interesting applications can be expected when nanotubes are integrated with a second material to construct heterostructure nanocomposites having a type II band offset which can induce the spatial separation of photo-generated carriers within the nanostructure itself, with the electron residing in one material and the hole in the other. These advanced dual-nanomaterials display a performance superior to those obtained with devices relying on the individual nanomaterial constituents.

As the important semiconductor for optoelectronics, the larger part of the research on CdTe has been concentrated on quantum dots,^16–20 nanowires,^21–26 tetra-pods,^27–30 nanorods^31–33 etc. However, reports on the synthesis of CdTe nanotubes are limited with success by few research groups.^13,34–36 Niu et al. synthesized diameter tunable CdTe nanotubes by templating against cadmium thiolate polymer nanowires.¹³ The hierarchical self-assembly of high aspect ratio CdTe nanotubes is generated using a water/oil reverse micelles method by Ding and co-workers.³⁴ A sacrificial template approach for the synthesis of ultra long CdTe nanotubes with high aspect ratios, from a template of Cd(OH)₂ nanowire bundles have been reported by Shinde et al.³⁵ Although there are a few number of experimental studies reporting the synthesis, characterization and optical properties of the CdTe nanotubes, theoretical studies addressing the electronic structure are still not available. However, extensive theoretical studies, in particular, the exploration of new nanostructured materials and the evolution of their electronic structure as a function of the size and morphology are of crucial importance in guiding relevant experiments, the rational explanation of experimental observations and also offering new results to be verified experimentally.

Regarding the emergent applications of hybrid nanomaterials, we here explore the possibility of designing a new hybrid nanostructure, coupling with two individual nanomaterials, one is CdTe nanotubes and other is extensively studied fullerenes. We do hope that this particular nanohybrid may find diverse applications because of the excellent exciton mobility, relatively large exciton diffusion length and high electron affinity of fullerene, which acts as the electron-acceptor and electron-transporting material and has long been employed in the construction of photovoltaic devices.^37–39 As the real world application of these nanohybrids requires the knowledge of the electronic energy levels, the understanding of the electronic structure of these materials is of paramount importance. However, theoretical studies of nanostructures composing large numbers of atoms are prohibitive because of their high computational demands. Therefore, the self-consistent-charge density-functional tight-binding (SCC-DFTB) method,^40–44 which has been successfully applied to large-scale quantum-mechanical simulations, is a suitable method for this purposes. In this work, we have employed the SCC-DFTB method to investigate the structural and electronic properties of CdTe NTs of various sizes and wall-thicknesses. Additionally, we also modified the band gaps of the CdTe NTs by coupling with thiolated fullerenes. Very recently, we have demonstrated the that the band gap of the CdTe QD–CNT nanocomposites could be controlled by the CNT⁴⁵ and our result is in good agreement with the experimental observation of Drost et al.⁴⁶ Despite the potential advantage of fullerene, it has not been yet utilized to construct hybrid nanostructures combined with CdTe NTs. Therefore the basic understanding of the electronic structures of these hybrid nanocomposites is of particular importance for their effective utilization in nanotube sensitized solar cells.

2 Computational method and modelling

In this present article, the properties of crystalline hexagonal CdTe nanotubes of various sizes have been studied using the SCC-DFTB method. The DFTB method is a parametrized density-functional method and being semi-empirical in nature can treat relatively large systems and the method has been described in detail elsewhere.^40–44 In the wurtzite phase, there are two cadmium and two tellurium atoms in a tetrahedral coordination per unit cell. At first we generated the CdTe nanowires from the optimized wurtzite crystal structure which are oriented along the [0001] direction (c axis) and are enclosed by non polar (101̄0) surfaces. These (101̄0) surfaces contain Cd and Te atoms with one dangling bond. Then, after removing the hexagonal cores of different sizes from the nanowires, multi-walled CdTe nanotubes are generated. As a result, both the inner and outer facets are enclosed by (101̄0) surfaces. The single-walled nanotubes are generated by removing all of the hexagonal cores except for the surface atoms. We considered the CdTe NTs varying their outer radii between 0.5 and 2.5 nm. Based on the experimental and theoretical studies, all of the nanotubes under consideration have approximately a cylindrical shape. All the above structures were simulated as infinite structures by using periodic boundary conditions and suitably oriented supercells. The calculations have been performed with a suitable vacuum region of 100 Å surrounding the structures, along the x and y directions, to avoid spurious interactions among consecutive periodic replicas. The conjugated gradient algorithm has been used to perform the geometry optimizations and the force convergence criteria is 0.001 eV Å⁻¹. For all calculations, the coordinates of the atoms within the supercells were fully relaxed during the geometry optimizations; the lattice constant was also optimized to minimize the total energy along the tube/wire axis. In our calculations, k-points are sampled as a (1 × 1 × 8) Monkhorst–Pack grid. The exchange–correlation energy functional of Perdew–Burke–Ernzerhof (PBE)⁴⁷ has been employed in this study. All calculations have been performed with the DFTB+ program,⁴⁴ using our recently derived set of parameters for CdTe.⁴⁸ The transferability of these parameters has been inspected by calculating and comparing the structural, electronic and energetic properties for the relevant bulk phases, surfaces, nanowires and small molecular systems. The calculated values agree well with those obtained either from experiment or ab initio calculations.⁴⁸ We have also compared the lattice constants and cohesive energies of wurtzite bulk CdTe with those calculated very recently by the bond-order potential (BOP) based molecular dynamics method of Ward et al.^49,50 and found a close agreement between the two. For instance, the lattice parameters of wurtzite bulk, a = b = 4.56 Å, c = 7.44 Å we calculated with the SCC-DFTB method are in good agreement with the experimental lattice constants (a = b = 4.55 Å and c = 7.45 Å), the lattice constants obtained by DFT calculations (a = b = 4.52 Å and c = 7.32 Å), and also with the calculated values of the BOP based molecular dynamics method (a = b = 4.84 Å and c = 7.88 Å). The cohesive energy per atom (E_c) calculated by the SCC-DFTB method is 2.92 eV which is slightly higher than the experimental value of 2.28 eV and also the value calculated by the BOP method (2.17 eV). This is due to the fact that the DFTB calculation slightly overestimates this property. We have to make this compromise to reproduce the electronic band structures of the relevant bulk phases and nanostructures of the CdTe calculated with full DFT. The band gap (E_g) of bulk wurtzite CdTe as calculated by the SCC-DFTB method is 1.89 eV and the value is slightly greater than the experimental band gap ≈1.60 eV and also the DFT value of 1.09 eV. This is due to of the use of a minimal basis set in the SCC-DFTB method which always causes the overestimation of the band gap values. We have not applied any post processing band gap correction scheme because the SCC-DFTB method is not influenced by so-called band gap error to the same extent as the standard DFT methods. The electronic properties of the CdTe–organic hybrid systems are described successfully using the SCC-DFTB method.^45,51 In our present study, we have also investigated the electronic structures of different CdTe nanotube–fullerene hybrid nanostructures. In this context, we have employed a thiol derivative of C₆₀, synthesized recently,⁵² which enables covalent linking by the S atom of the –SH group to the Cd site of the 101̄0 outer surface of the CdTe nanotubes. This kind of covalent linking of the thiol derivative of C₆₀ and the CdTe nanotube has already been demonstrated by the recent experimental work of Bang et al.⁵³ on a CdSeQD–fullerene hybrid nanocomposite. We have used 3 units of the CdTe nanotubes periodically repeated along the z-axis containing 144, 270 and 432 CdTe pairs per unit cell for 2WNT, 3WNT and 4WNT, respectively. We also extend our study to investigate the effect of different kinds of fullerene on the electronic structure of the CdTe–fullerene hybrid systems and accordingly designed the NT–C₆₈, NT–C₇₀, NT–C₇₆, NT–C₈₀ and NT–C₈₄ hybrid nanostructures. To optimize the hybrid nanostructures, we have used a (1 × 1 × 4) Monkhorst–Pack grid and the calculations have been performed with a suitable vacuum region of 100 Å surrounding the structures along the x and y directions. Geometry optimizations have been performed with the conjugated gradient algorithm, until all forces became smaller than 0.005 eV Å⁻¹.

3 Results and discussion

This section is divided into two parts. In the first part, we discuss about the structural relaxations, energetics and electronic properties of the CdTe (101̄0) faceted nanotubes. While in the other part, we discuss the electronic structure of the CdTe nanotube–fullerene hybrid nanostructures and the possibility of band gap engineering of these hybrid systems through either varying the wall thickness of the NT or attaching different types of fullerenes.

3.1 The CdTe (101̄0) nanotubes

During the calculation process, we first optimize the atomic coordinates and lattice constants along the axial direction for all of the CdTe nanotubes by allowing all atoms to move without any symmetry constraints. The interatomic topology and the wurtzite structure are retained in the CdTe nanotubes, although the bond lengths and angles change in the lateral surface of the inner and outer walls. The structural relaxations of the various CdTe nanotubes are compared with the nanowire and also the (101̄0) surfaces and is shown in Table 1. In Fig. 1 we have shown the optimized structures of CdTe (101̄0) (a) surface (side view), (b) nanowire (top view) and (c) double-walled nanotube (top view). In our previous studies, it is established that the results of the surface relaxations obtained from SCC-DFTB agree well with our PP-PBE results.^48,51 The surface relaxation normally causes the anions (Te) to displace outward from the surface while the cations (Cd) move inward, and this behaviour is in accordance with other studies.^54–57 For the (101̄0) surface of CdTe, the bond lengths d_Cd–Te are largely shortened compared with the bulk values (2.80 Å), while the bond lengths between the second and third layers are a little larger compared to the bulk values. The Te–Cd–Te angle (α) changes from the bulk value of 109° to around 120° at the top surface layer, while the same angle in the inner layers (β) shows very little change. The prediction of the surface relaxation of CdTe is similar to the results of a low energy electron diffraction (LEED) study of the related semiconductor ZnO.⁵⁸ From Table 1 it is evident that the Cd–Te bond lengths (d_Cd–Te) and (d^′_Cd–Te) of the (101̄0) faceted nanowires, are shortened compared with their bulk values. This shortening of the bond lengths occurs because the surface atoms of the nanowire with one dangling bond rehybridize from sp³ to sp². For the multi-walled NTs, similar types of surface relaxation occurred, and both the Cd–Te bond lengths (d_Cd–Te) and (d^′_Cd–Te) are shortened as compared with their bulk values but the (d^′_Cd–Te) are slightly greater than that in the NW. For the SWNT both the Cd–Te bond lengths are equal and (d^′_Cd–Te) are slightly shorter than that of the NW, because all atoms are sp² hybridized in the NT. For the (101̄0) faceted CdTe nanowires and nanotubes the Te–Cd–Te bond angles α and β are equivalent and both belong to the top surface layer of the nanowires and nanotubes. The relaxation causes a large deviation of these bond angles from the bulk value (109°). The surface Cd and Te atoms in both the inner-walls and the outer-walls of the nanotubes are all 3-fold coordinated, and the large surface strain induces structural distortions. The surface Cd and Te atoms with dangling bonds both in the inner-walls and outer-walls are all saturated with H atoms, and the H-passivated nanotubes are fully relaxed. In the relaxed H-passivated nanotubes, the surface atoms show almost the same structural features as atoms in the bulk, for example the CdTe bond lengths are about 2.84 Å close to the bulk value. Therefore passivation with H eliminates the surface strain.

Table 1 The bond lengths and bond angles of the relaxed CdTe (101̄0) faceted nanostructures

101̄0 nanostructures	dCd–Te	d^′Cd–Te	α	β
Surface	2.55	2.94	121	102
NW	2.60	2.66	121	120
SWNT	2.58	2.60	123	122
2WNT	2.59	2.68	121	120
3WNT	2.59	2.70	122	120
4WNT	2.59	2.71	122	119
5WNT	2.59	2.71	123	119
6WNT	2.59	2.71	123	119

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Fig. 1 The relaxed geometry of (a) CdTe (101̄0) surface (side view), (b) CdTe (101̄0) faceted nanowire (top view) and (c) CdTe (101̄0) faceted double-walled nanotube (top view). The Cd and Te atoms are represented by grey and orange spheres, respectively.

To estimate the stability and manufacturability of the CdTe (101̄0) 1D nanostructures, we calculated their formation energy with respect to the stable bulk wz-CdTe crystal. The formation energy (E_f/CdTe) of a given 1D nanostructure is defined by

where, E_tot is the total energy of the CdTe (101̄0) 1D nanostructures, n is the total number of the Cd–Te units in the CdTe nanostructures and E_bulk is the energy of the bulk wz-CdTe. Hence, the formation energy of bulk CdTe is corresponding to the energy zero. The E_f values of the CdTe nanowires and nanotubes as a function of surface atom ratio and radius (here we define the radius as the perpendicular distance from the center of the nanotube to the surface of the outer wall) are summarized in Fig. 2. The E_f values of the nanowires decrease with the wire radius (d/2) and they do not follow the linear relationship with the wire radius. They satisfy an inverse relationship with the radius (d/2), namely, E_f = k/d, where k is a constant. The decreasing formation energy with the wire radius indicates the higher stability of the CdTe nanowires at a relatively large size. But for the case of the CdTe nanotubes, the E_f of the nanotubes is not only determined by the radius of the tubes but also controlled by the wall thickness of the tubes. From Fig. 2, it is shown that in the nanotubes with the same wall thickness, the E_f values are close in spite of their differences in radius. This is due to the fact that the nanotubes with the same wall thickness have the same surface atom ratio. If we compare the formation energy of the nanowires and nanotubes with the same radius, Fig. 2 shows E_f(NTs) > E_f(NWs). The result can be correlated by noting that the nanotubes with the same radius as the nanowires have a larger surface atom ratio i.e. a large number of dangling bonds. In the bulk wz crystals all of the Cd and Te atoms adopt a sp³ hybridization. However, the surface atoms of the CdTe nanowires and nanotubes are sp² hybridized which is energetically unfavorable and this causes the increase in the system energy. Therefore, the small nanowires and thin walled nanotubes have a large E_f due to the high density dangling bonds (three coordinated atoms) and thus these are very difficult to synthesized experimentally. The above results indicate that the surface atom ratio (R_s) is an important factor for determining the stability of the CdTe nanostructures (where R_s is defined as the number of unsaturated Cd and Te atoms in the surface divided by the total number of Cd and Te atoms in the system). The formation energy, E_f which satisfies a linear relationship with the surface atom ratio, can be expressed as E_f = λR_s (λ is a constant). For bulk CdTe, the surface atom ratio is zero and so also the formation energy. In the case of the nanostructure of the largest diameter, the formation energy and surface atom ratio are closest to the bulk. As the surface atom ratio increases, the strain in the system increases dramatically and surface restructuring alone is not enough to eliminate the large strain and therefore the formation energy increases.^59,60

Fig. 2 The variation of formation energies with surface atom ratios for various CdTe (101̄0) faceted nanowires and nanotubes. The inset indicates the evolution of the formation energies as a function of the radius of the CdTe (101̄0) faceted nanowires and nanotubes.

The variation of the band gap of the CdTe (101̄0) nanowires and nanotubes as functions of the surface atom ratio and radii is summarized in Fig. 3. The band gaps of all of the CdTe (101̄0) nanostructures are larger than those of the bulk wurtzite CdTe. In general, the quantum size effect enlarges the band gaps; however, the band gap variation due to the quantum confinement effect is also related to the surface atom ratio and radii. The band gap exhibits a good linear relationship with the surface atom ratios. From the figure it is clear that the intercept of the linear curves is ≈1.86 eV, which is very close to the band gap of bulk wurtzite CdTe as obtained in the SCC-DFTB method. We find that the band gaps of the CdTe nanotubes decrease slightly (very close) with the increase in size when they have the same surface atom ratios. On the other hand, the band gaps decrease sharply with the decrease of the surface atom ratio of the nanotubes despite their similar diameters. With the same size, the band gaps of the CdTe (101̄0) faceted nanowires and nanotubes satisfy the relationship E_g(2WNT) > E_g(3WNT) > E_g(4WNT) > E_g(5WNT) > E_g(6WNT) > E_g(NW).

Fig. 3 The variation of the band gap with the surface atom ratios for the CdTe (101̄0) faceted nanowires and nanotubes. The inset indicates the band gaps as a function of the radius of the CdTe (101̄0) faceted nanowires and nanotubes.

Fig. 4 shows the spatial distributions of the squared wave functions (charge densities) of the valence band top (VBT) and conduction band minimum (CBM) of the CdTe (101̄0) faceted double-walled nanotubes at the Γ point. The charge density distribution at both the VBT and CBM are delocalized in the whole nanotube but the extent of the delocalization is more in the case of the VBT. Due to the delocalized character, the energy of the VBT will increase as well as energy of the CBM decrease with the increase of the wall thickness of the nanotubes. The charge density distribution at the VBT and CBM of the CdTe nanotubes is different from that of the CdTe nanowires.⁵¹ The charge densities at both the VBT and CBM of the CdTe nanowire are largely dispersed along the direction of growth while the charge densities at both the VBT and CBM of the CdTe nanotubes are dispersed perpendicular to the growth direction. A detailed analysis (shown later) of the charge densities of the VBT and CBM suggests that the VBT has major contributions from the Te p orbitals and also little contribution from the Cd p orbital while the major contribution to the CBM originates from the Te d orbitals with little contribution from the Cd p orbitals. Thus the VBT has a p-like character while the CBM has a dp mixing character. The interactions of the p states of the VBT in the CdTe nanotubes result in the dispersion of the corresponding energy level. However the interactions between the d and p states in the CdTe nanotubes result in the dispersion of the CBM. Thus, the valence and conduction bands are shifted to higher and lower energies, respectively. One can adjust both the light absorption and the energetics at the interfaces of the nanotubes with the surrounding media by controlling the size and wall thickness of the nanotubes. As the light absorption and the energetics at the interfaces depend very much on the charge densities of the VBT and CBM, a clear understanding of the spatial distribution of the charge densities of the VBT and CBM is very important in the fabrication of novel hybrid nanomaterials for use in solar cells.

Fig. 4 Isosurface plots of the charge density (squared wave functions) of (a) valence band top (VBT) and (b) conduction band minimum (CBM) of the CdTe nanotube (2WNT) at the Γ point. The isosurface value used was 0.0002 e Å⁻³.

3.2 CdTe (101̄0) nanotube–fullerene nanohybrids

The recent emergence of inorganic–organic hybrid nanostructures has stimulated serious attention because these can serve as ideal building blocks for the design of next generation solar cells.^53,61–68 These advanced nanocomposites offer to be valuable to solar energy conversion, photovoltaics, electron donor–acceptor arrays and photocurrent generation, and specifically to novel chemical- and light-driven systems.^46,53 The research on fullerene based nanohybrids has attracted much attention because of the prominent features of photo-induced charge separation and solar-energy conversion induced by fullerene. The effectiveness of these nanohybrids hinges on the excellent exciton mobility, the relatively large exciton diffusion length and the high electron affinity of fullerene, which acts as electron acceptor and electron-transporting material, thus allowing for better electron percolation to the electrodes.^71–75 In this context, nanohybrids made up from fullerenes and cadmium chalcogenide semiconductor nanoparticles, versatile electron donor–acceptor nanohybrids, are particularly promising.^53,66–68 Guldi et al.⁶⁶ have showed that the electrostatic binding of C₆₀ and CdTe nanoparticles facilitates the rapid photo-induced electron transfer and thus serves as a potent alternative in fabricating photovoltaic devices. Brown et al. have reported a novel strategy of encapsulating CdSe nanoparticles in nC₆₀ clusters which paves the way for developing new and effective strategies toward light energy harvesting.⁶⁷ They observed that the photocurrent generation efficiency with CdSe-nC₆₀ films is 2 orders of magnitude greater than for the CdSe films alone. The ability to achieve a photo-induced charge transfer between the CdSe QDs and C₆₀ is an important step in designing light harvesting systems. Recently Bang et al. have developed covalently linked donor–acceptor light harvesting nanocomposites by employing thiol-functionalized C₆₀ and CdSe QDs.⁵³ The interaction between the components plays an important role in determining the efficacy of these particular nanohybrid systems in photovoltaic applications. The basic understanding of electron transfer in hybrid nanostructures, which in turn depends on the position of the frontier energy levels of its components, therefore is crucial for their effective utilization in designing solar cells. In view of this we performed the electronic structure calculation of the CdTe nanotube–fullerene hybrid nanostructures. We would like to investigate the relative positions of the VBT and CBM energy levels of the nanohybrid systems and how the variation of the various components of the hybrid systems influence the electron transfer from the nanotube to the fullerene.

In Fig. 5 we show the density of states (DOS) of the CdTe nanotube–fullerene (2WNT–C₆₀) hybrid nanostructures and the DOS have considerably modified as compared to the clean nanotube (2WNT). The most pronounced feature is that a new peak appears above the Fermi level for the C₆₀–thiol derivative which is attributed to the LUMO of the C₆₀–thiol derivative. To have a detailed understanding of the different orbital contributions of the Cd, Te and C atoms we have shown the projected density of states (PDOS) of the 2WNT–C₆₀ hybrid systems in the same figure. From the figure it is clear that the major contribution of the VBT in the 2WNT–C₆₀ system comes from the p orbitals of the Te atoms of the nanotube while the p orbitals of the C atoms of the fullerene have major contributions to the CBM. Fig. 6 represents the projected density of states of 2WNT (red), 3WNT (green), 4WNT (violet) and C₆₀ (blue shaded) in the NT–C₆₀ hybrid systems. In these hybrid nanosystems, all the CdTe nanotubes have a similar inner tube radius but have a different wall thickness. From the figure it is clear that these hybrid nanostructures show the type II band alignments. The position of the CBM of the hybrid nanostructures is fixed however the position of the VBT of the hybrid nanostructures is changed due to the upward movement of the VBT of the nanotube with the increase in the wall thickness. Hence the band gap of these nanocomposites decreases with the increase in the wall thickness. Fig. 6 reveals one interesting feature that the difference between the CBM of the NT and the LUMO of the C₆₀ decreases with the increasing thickness of the NTs. On the basis of the Marcus theory of electron transfer, where the energy difference between the donor and the acceptor is the driving force,^69,70 we could expect a faster electron transfer rate for thin-walled CdTe NT as compared to thick-walled NTs when they are coupled with the C₆₀. However, it should be mentioned that faster electron transfer rates with thin-walled NTs do not necessarily mean that these systems will show better photovoltaic efficiencies since these depend on other factors such as the rate of the hole transfer and the rate of the recombination of charge carriers. In a very recent article, Bang et al. demonstrated that the rate of the hole transfer and the rate of the recombination of charge carriers are more important than the rate of the electron injection in dictating the photovoltaic efficiencies in the CdSe QD–C₆₀ system.⁵³ In Fig. 7, we represent the total density of states of the NT–C₆₀ hybrid systems with the increasing number of C₆₀–thiol moieties, where the size and thickness of the nanotube are same. The figure reveals that the density of states (DOS) increased at the position of the LUMO of C₆₀ with the increasing number of C₆₀–thiol moieties but all other features of the DOS remain unchanged. This characteristic feature has a great impact on the photovoltaics.⁵³ As the density of states at the position of the LUMO of C₆₀ increases with the increasing concentration of C₆₀–thiol, the lifetime of the excited electrons of the CdTe nanotube becomes shorter and this results in a faster deactivation of the charge-separated states of CdTe NTs via electron transfer from CdTe NT to the thiolated C₆₀. Hence we can maximize the light harvesting efficiency of these nanohybrids with the increasing number of C₆₀–thiol moieties. Our theoretical prediction agrees well with the experimental observation of Bang et al.⁵³ in which the authors observed increased photovoltaic efficiencies with the increasing concentrations of fullerene in similar CdSeQD–fullerene nanocomposite systems.

Fig. 5 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.

Fig. 6 The projected local density of states of 2WNT, 3WNT, 4WNT and C₆₀ in the NT–C₆₀ 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.

Fig. 7 The total density of states 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.

Fig. 8a and b represent the spatial distribution of the charge densities of the CdTe 2WNT–C₆₀ nanohybrid at the Γ point. The distribution of the VBT charge density (in Fig. 8a) of the hybrid systems is localized on the CdTe nanotube only, and is largely dispersed perpendicular to the growth direction, which is similar to the pure CdTe nanotube (shown earlier). However the LUMO charge density distribution (Fig. 8b) of the hybrid systems is localized on the C₆₀ only. A detailed analysis of the charge densities at the VBT and CBM reveal that the VBT has major contributions from the Te p orbitals and also little contribution from the Cd p orbitals while the CBM has all contribution from the C p orbitals which is also evident from Fig. 5. Thus, the VBT of the 2WNT–C₆₀ hybrid systems which has the characteristic feature of the CdTe nanotube and the CBM of the 2WNT–C₆₀ hybrid systems which has the characteristic feature of C₆₀, construct type II hetero-junctions. The charge separation of the electrons and holes at the interface between the CdTe nanotubes (behaving as the electron donor) and C₆₀ (behaving as the electron acceptor) occurs, leading therefore to the localization of the electrons in the C₆₀ region and holes in the CdTe region. This spatial separation of the charge carriers to different regions of the nanohybrids results in type-II band alignments, which is a highly desirable property for nanotube sensitized solar cells.⁷⁶ To understand how the coupling of C₆₀ with the CdTe nanotubes affects the electronic properties, we calculated the charge density difference of the 2WNT–C₆₀ hybrid system. The charge density difference is defined as the difference between the total charge density and the atomic charge density. In Fig. 8c, the positive value of the charge density difference is shown. The thiolated C₆₀ part of the hybrid system gains more electrons as it is coupled to the CdTe nanotube. This difference describes the effect of electron migration upon the coupling between the CdTe NT and thiolated C₆₀. So, the figure suggests a substantial charge transfer from CdTe to C₆₀ in 2WNT–C₆₀ donor–acceptor materials. This charge transfer from CdTe NT to fullerene is consistent with the various experimental observations in recent times.^66–68 Thus, Guldi et al.⁶⁶ have shown that there is a considerable decrease in the intensity of the CdTe nanoparticles in fullerene–CdTe nanoparticle composites as compared to isolated CdTe nanoparticles. Brown et al.⁶⁷ and Song et al.⁶⁸ also in their studies on CdSe–C₆₀ composites observed a strong emission quenching. This quenching of emission is evidently due to the charge transfer from the nanoparticles to the fullerenes.

Fig. 8 Isosurface plots of the charge density (squared wave functions) of the (a) valence band top (VBT) and (b) conduction band minimum (CBM) for the 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 the charge density. The isosurface value used for (a) and (b) was 0.0002 e Å⁻³ and for (c) 0.01 e Å⁻³.

In the continuous search for suitable systems useful in photovoltaics, electron donor–acceptor arrays are particularly promising. Now, we have used a series of fullerenes e.g. C₆₀, C₆₈, C₇₀, C₇₆, C₈₀ and C₈₄ to construct different types of donor–acceptor CdTe nanotube–fullerene nanohybrids. To obtain the details of the understanding of the electronic structure of these hybrid systems, we have calculated the band structures and density of states of these nanohybrids and which are shown in Fig. 9. There are few flat bands incorporated into the band gap region of the CdTe nanotube. These bands represent the molecular orbitals of the fullerenes, which is very much clear from the projected density of states. The hybrid systems (a) 2WNT–C₆₀ and (f) 2WNT–C₈₄ have no flat bands below the Fermi levels but all other hybrid systems have flat bands above and below the Fermi levels. Therefore the VBT of the 2WNT–C₆₀ and 2WNT–C₈₄ hybrid systems have the characteristic feature of the CdTe nanotube and the CBM of the 2WNT–C₆₀ and 2WNT–C₈₄ hybrid systems have the characteristic feature of the fullerenes. But both the VBT and CBM of the (b) 2WNT–C₆₈, (c) 2WNT–C₇₀, (d) 2WNT–C₇₆ and (e) 2WNT–C₈₀ hybrid systems have the characteristic feature of the fullerenes. The idea of “band gap engineering” which uses the modification of the relative position of the electronic energy levels of the semiconductor materials to produce new electronic gaps across the hybrid nanostructures, has a great impact on the characteristic properties of the final device, such as the polarization offset of the photodiodes or the open-circuit voltage in excitonic solar cells. Fig. 10 shows the positions of the VBT and CBM of the clean CdTe NT and NT–fullerene hybrid systems along with the HOMO and LUMO of the fullerenes. The figure reveals very interesting features. The band gap of the 2WNT–C₆₀ and 2WNT–C₈₄ hybrid systems form a staggered alignment (type II), so that the position of the VBT remains close to the VBT of the CdTe but the position of the CBM remains close to the LUMO of the C₆₀ and C₈₄, respectively. However, the band gaps of the other hybrid systems have been guided by the corresponding fullerenes. This specific configuration is characterized by a straddling band alignment, where at the hetero-junction of the two materials both the HOMO and LUMO of the fullerene are localized within the energy gap of the CdTe nanotube, forming the type I nanohybrids. The band gaps of the hybrid systems 2WNT–C₆₀, 2WNT–C₆₈, 2WNT–C₇₀, 2WNT–C₇₆, 2WNT–C₈₀ and 2WNT–C₈₄ are 1.51, 0.62, 1.17, 1.01, 0.18 and 1.03 eV respectively, and are very low compared to the clean CdTe nanotube (2.65 eV). So, depending on the nature of the fullerenes in the NT–fullerene hybrid system, the electronic structures are quite different. From the position of the VBT and CBM, we conclude that the hybrid systems 2WNT–C₆₀ and 2WNT–C₈₄ represent type II and others are type I nanocomposites. We would like to mention here that as density-functional theory is a one electron theory, the band gap and the band energy alignment obtained from this have to be handled with care. However, we feel that the inherent error in the method will affect both the VBT and CBM in a more or less similar way and so the qualitative trend we found will still be valid and is often very useful in predicting material properties.

Fig. 9 The left panel of (a), (b), (c), (d), (e) and (f) represent the electronic band structures of the 2WNT–C₆₀, 2WNT–C₆₈, 2WNT–C₇₀, 2WNT–C₇₆, 2WNT–C₈₀ and 2WNT–C₈₄ nanohybrids, respectively. The right panel of (a), (b), (c), (d), (e) and (f) represent the density of states (DOS) of the 2WNT–C₆₀, 2WNT–C₆₈, 2WNT–C₇₀, 2WNT–C₇₆, 2WNT–C₈₀ and 2WNT–C₈₄ nanohybrids, respectively. The blue shaded area in the DOS reflects the projected local density of states of the CdTe NT of the 2WNT–C_n (n = 60, 68, 70, 76, 80 and 84) hybrid systems and the red peaks are the projected local density of states of C_n–thiol (n = 60, 68, 70, 76, 80 and 84) of the 2WNT–C_n (n = 60, 68, 70, 76, 80 and 84) 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.

Fig. 10 The valence band top (HOMO for molecule) (red) and conduction band minimum (LUMO for molecule) (blue) energy alignment for the considered 2WNT–C_n (n = 60, 68, 70, 76, 80 and 84) hybrid systems (bold) and C_n–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).

4 Conclusion

In conclusion, we report here the structural and electronic properties of the (101̄0) faceted CdTe nanotubes with hexagonal cross-sections. The formation energies of the CdTe nanotubes are studied as a function of both the size and surface atom ratio to understand the possibility of their formation and are compared with (101̄0) faceted CdTe nanowires. The atomic relaxations of the surface of the (101̄0) CdTe nanotubes are also compared with the corresponding (101̄0) CdTe surface. Despite having structural distortions on the surfaces, the faceted nanowires and nanotubes are energetically favorable since they preserve the bulk wurtzite structure. The nanowires with a larger diameter and thick-walled nanotubes are most favorable thermodynamically. The possibility of band gap engineering is explored either by varying the size or wall thickness of the nanotubes. Surface effects have a larger influence on the band gaps of the CdTe (101̄0) faceted nanotubes than the size effect. We found that the band gap of the CdTe nanotubes decreases slightly with the increase of the radius of the tube when they have the same surface atom ratios. On the other hand the band gaps efficiently decreases with the decrease of the surface atom ratio of the nanotubes despite their similar diameters. A detailed analysis of the charge densities at the VBT and CBM suggests that the VBT has major contributions from the Te p orbitals and also little contribution from the Cd p orbitals while the major contribution to the CBM originates from the Te d orbitals with little contribution from the Cd p orbitals. The interactions between the p states of the VBT in the CdTe nanotubes result in the dispersion of the VBT, while the interaction between the d and p states of the CBM in the CdTe nanotubes result in the dispersion of the CBM, thus, the valence and conduction bands shifted to higher and lower energies, respectively, with the increase of the wall-thickness of the nanotubes.

We have also modified the band gap of the CdTe nanotubes by the fabrication of fullerenes onto the nanotube surface via covalent linking through an organic thiol chain. The density of states (DOS) of the CdTe nanotube–fullerene hybrid nanostructures is considerably modified as compared to the clean CdTe nanotube. The most pronounced feature is that a new peak appears above the Fermi level for the C₆₀–thiol derivative which is attributed to the LUMO of the C₆₀–thiol moieties and originates from the p orbitals of the C atoms. The hybrid systems 2WNT–C₆₀, 3WNT–C₆₀ and 4WNT–C₆₀ construct type II band alignments, and there is a charge separation of the electrons and holes at the interface between the CdTe NT (donor) and C₆₀ (acceptor). The charge density difference describes the effect of the electron migration upon the coupling with thiolated C₆₀ and shows that a substantial charge transfer occurred from CdTe to C₆₀ in 2WNT–C₆₀. From the band alignment we conclude that there is faster electron injection in the thin-walled CdTe NTs as compared to a thick-walled one when coupled to the electron acceptor C₆₀. Furthermore, we can also increase the light harvesting efficiency of these nanohybrids by increasing the concentration of the C₆₀–thiol moieties. Finally, we have used various types of fullerenes e.g. C₆₀, C₆₈, C₇₀, C₇₆, C₈₀ and C₈₄ to construct different types of donor–acceptor nanohybrids. We can conclude from the position of the VBT and CBM, that the hybrid systems 2WNT–C₆₀ and 2WNT–C₈₄ represent type II and others are type I nanohybrids. So, depending on the nature of the fullerenes in the hybrid systems, the electronic structures are quite different and may be utilized in multifarious photovoltaic applications. To the best of our knowledge, this represents the first systematic theoretical study on the electronic structure of CdTe (101̄0) faceted nanotubes and CdTe nanotube–fullerene nanocomposites. We do hope that our study will stimulate the experimentalist for further exploration of these nanomaterials in designing nanotube sensitized solar cells.

Acknowledgements

The financial supports from CSIR, New Delhi [01(2744)/13/EMR-II], DST, Govt. of India [SR/NM/NS-49/2007] through research grants are gratefully acknowledged. The first two authors are grateful to CSIR, New Delhi for the award of Senior Research Fellowships (SRF).

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