Nanomaterials are attracting increasing attention due to their novel, tunable and fascinating electronic and optical properties. The following chapter addresses semiconducting materials and the impact of size reduction within the nanometer region. Two main effects related to reduced size of nanomaterials are investigated: the quantum confinement effect and a large volume-to-surface ratio which are explained in more detail.
2.2.1 Regular Quantum Dots
Regular quantum dots (QD) are semiconductor nanocrystals composed of periodic group III-V or II-VI semiconductor materials such as ZnS[41], PbS[42], CdS[43], CdSe[43][44][45], CdTe[43][46] They consist typically of 100–100,000 atoms per QD and have sizes between 2-50 nm depending on the material.[47] They have been studied because of their novel optoelectronic functionalities resulting from their unique size- and shape-dependent properties due to nanoscale size effects.[1][2][45] The size effects find their origin in the quantum confinement and surface effect which are defined below.
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Figure 3: Comparison of electronic energy states and bandgap of different types of semiconductor materials.
Starting with inorganic bulk semiconductors with separated energy bands (left), different sizes of inorganic nanocrystals (quantum dots, middle) and molecular semiconductors with discrete energy levels (right) explain the origin of the nanoscale size effects.
Calculations according the Linear Combination of Atomic Orbitals (LCAO) theory[48] provide more information about the energy band structure in crystalline materials of different sizes.[47][49] In principle, the combination of atomic orbitals leads to the evolution of bonding and anti-bonding molecule orbitals (energy states).[47] The electrons from the individual atoms occupy the bonding molecular orbitals (highest occupied molecular orbital, HOMO). The first unoccupied antibonding orbital is termed the lowest unoccupied molecular orbital (LUMO). The HOMO and LUMO levels are separated by a forbidden energy bandgap Eg where no orbitals exist. For crystalline bulk materials the number of atom increases (~1023 atoms) and the electronic structure changes from a discrete energy level structure to continuous energy bands.[47] The total number of energy levels increases with the number of atoms in the molecule and becomes a continuous energy band. The conduction band is equivalent to the LUMO level and the valence band consists of bonding molecule orbitals (formerly HOMO). For semiconductor materials the energy bands are split into
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two, separated by the bandgap making them different to the parent metal band structure. Nanosized QDs can be considered as large molecules and show the formation of a quantized electronic band structure. [48][49] With the absorption of photons, excitons can be generated which are the bound state of electrons and electron holes driven by electrostatic Coulomb forces.[47][49] The Coulomb forces in semiconductor nanocrystals is much higher compared to bulk material. Due to the size restriction in nanocrystals the spatial extension of the exciton wave function is confined.[45][47][48]
The spatial restriction of the exciton wave function and also the density of electronic states and the bandgap separation Eg.
The degree of the quantum confinement[16][48][49] depends on the nanocrystal shape and is useful for the classification of nanomaterials (Figure 4). Nanoparticles can be synthesized with confinement in all directions (0D). For anisotropic nanocrystals, like quantum rods, wires or tubes, the excitons are confined in only one direction (1D). Nanoplatelets or thin films have the confinement only in their thickness (2D). Due to the ongoing restriction in their dimensions, the density of energy states changes from bulk material (3D) to discrete quantized energy levels for 2-, 1- and 0-dimensional structures.
Figure 4: Schematic illustration of the reduced dimensionality of semiconductor nanocrystals. Bulk semiconductor, quantum well (2D), quantum rod (1D) and quantum dot (0D).
The impact of the quantum confinement effect on the quantum dot properties can be evaluated by the size restriction of the QD and the corresponding Bohr radius rB.[48] One can distinguish between the weak confinement regime and the strong confinement regime depending on the semiconductor nanostructure.[17][48] The confinement phenomena lead to massive changes in the optoelectronic properties of semiconductor nanocrystals and the QD becomes strongly size- and shape-dependent.[1][16][17] By implication, the examination of the light absorbance together with empirical calculations[48][50][51][52] and the photoluminescence/quantum yield detection[17][41][53] give
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information about electronic and optical material properties including the bandgap of semiconducting materials and their elemental composition.[2][17][48]
The second finite size effect is the increased surface-to-volume ratio and important consequences of this are surface-related phenomena.[6][13][45][48][54] The relative proportion of surface atoms in small quantum dots increases with smaller particle sizes, while the total number of atoms gradually decreases. Due to the exceptionally large surface-to-volume ratio, the surface becomes the dominant player in many chemical and physical processes. Surface effects, and particularly surface defects for charge carriers,[48][55] lead to quenching of the radiative recombination of excitons in QDs and to a reduced emission and quantum yield. These so-called surface traps are caused by lattice defects and dangling orbitals. Passivating agents (i.e. ligand molecules) can be used to coat the surface of colloidal nanocrystals to prevent nonradiative recombination of excitons at these traps.[9][18][48][56] The surface modification is very important to lower the surface trap energy and to achieve photostable QDs. Additionally, the organic surfactants are able to control size and shape during preparation but also post preparative ligand exchange[13][18] affect the colloid stability and the electronic/optical properties.
2.2.2 Magic-sized (Nano-)clusters
Over the last few years numerous research groups[4][25][26][52][57][58][59][60] observed the synthesis of II-IV metal chalcogenide nanoparticles yielding some findings concerning the reaction kinetics.
The synthesis of regular quantum dots based on a series of increasing size nanoclusters occurs according the ꞌliving-metal polymer conceptꞌ.[25] In the early stages of the reaction the creation and degradation of discrete nanoclusters could be observed by spectroscopic methods.[4][52][57][60][61][62]
The detection of narrow absorbance peaks during the growth of these products indicate the existence of small nanocluster species.
Magic-sized clusters (MSC) describe clusters of particularly high stability with a core diameter between 0.5 < d < 2 nm.[52][57][61] The MSCs consist of discrete numbers of atoms and show a high monodispersity in size and specific stoichiometry.[57][63] Each cluster size refers to a stable atomic configuration which can be explained by the absence of regular quantum dots and ripening processes.[4][58] A Gaussian fit can be used to characterize the absorbance signals with typical Full Width Half Maximum (FWHM) around 10-30 nm.[60][64]
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Peng et al.[62] were able to synthesize CdSe at 250 °C and to monitor a sequential cluster formation in real-time during the reaction. The particle size 4 ms after the injection was calculated to be 1.75 nm. Kudera et al.[53] observed different families of clusters during the synthesis of CdSe quantum dots by the consumption of more metal precursor. According to these studies, the result indicates that sharp absorption signals of highly stable nanocluster intermediates arise at lower temperatures, whereas at higher temperatures the life-span decreases significantly and the conversion into regular quantum dots could be monitored. The general mechanism describes that relatively mild reaction temperatures slow down the reaction rate and facilitate the study of magic-sized clusters. The formation process depicted in figure 5 involves the appearance of ultra-small cluster peaks in the early growth stages, followed by the diminishing of the cluster peaks and the evolution of new nanocluster sizes (small MSC).[53] A high temperature is favourable for the transformation into regular quantum dots.
Figure 5: Characteristic formation of magic-sized clusters (MSC) during the synthesis of regular quantum dots (QDs). Different families of MSC can be observed within a series of growth steps.One cluster family arises at the expense of smaller cluster sizes.[53]
The stepwise red-shift of individual absorbance peaks from various MSCs underline the sequential series of magic-sized clusters. After recording the UV-vis spectra over many hours, the average size of a family remains constant and grew only in size with sufficient stabilization through organic ligands. Dance et al.[65] synthesized in 1984 the first chalcogenide molecular clusters and claimed that the presence of the ligands lead to stable molecular clusters. During the synthesis of MSCs the (co-)existence of cluster families can be detected which can be assigned to a heterogeneous growth process.[57]
In contrast to this observation, the formation of conventional nanoclusters is termed a homogeneous growth process.[57] The formation of polydisperse ensembles and the gradual shift of the bandgap
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absorbance peak with time during synthesis are characteristic for the formation of ultra-small nanocrystals.[60]
The unique behaviour of MSC is an interplay of the synthetic parameters like the temperature[58][61], the prepared starting material, the monomer concentration[52][60][61] and nature of the ligands (ligand/QD surface chemistry)[58][60], the supersaturation caused by the monomer concentration, the solvent, the affinity of ligands and the ratio of monomers in the system.[57][64] The formation and also the synthesis of stable semiconductor nanoclusters is more challenging compared to metal nanoclusters but all these different approaches gain better access to investigations of early growth stages. The isolation of MSC, their sensitivity to chemical treatments and their insufficient characterization with common methods are the reason that nanoclusters and their resultant properties are only transiently observed.