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ne of the most exciting areas of chemical research is inorganic nanomaterials—metals, semiconductors, or insulators made with dimensions on a scale of 1–100 nm. The Journal of the American Chemical Society, Nature, and Science frequently have a paper or two describing some of the latest advances in making and measuring properties of nanomaterials. The National Nanotechnology Initiative (www.nano.gov), started by former President Clinton, promoted the formation of nanoscience and nanotechnology research groups across the country. Chemists, physicists, engineers, and biologists are collaborating to study these materials and to harness their properties for many different applications. Why are these materials so exciting? The size range of nanomaterials coincides with some fundamental length scales in physics. The mean free path of an electron in a metal at room temperature, for example, is ~10–100 nm (1). The Bohr radius of photoexcited electron–hole pairs in semiconductors is ~1–10 nm (2). The 1- to 100-nm dimension is the range over which molecules assemble into viruses; in solids, chemical bonds give way to electronic bands (Figure 1). There is still a great deal of fundamental physics and chemistry to discover in nanomaterials, but now applications are being explored. This article will give an overview of these exciting materials and describe their potential, especially in optical detection schemes.
What’s a quantum dot?
Catherine J. Murphy University of South Carolina
A quantum dot is a semiconductor particle that has all three dimensions confined to the 1- to 10-nm-length scale. The literature also refers to them as zero-dimensional (0-D) materials, semiconductor nanoparticles, or nanocrystallites. (Confinement in two dimensions produces 1-D quantum wires, and confinement in one dimension produces 2-D quantum wells.) To understand why a semiconductor particle of this size would be interesting from a quantum mechanical point of view, consider what happens in a material when an electron is promoted to the conduction band from the valence band (Figure 2). Left behind in the valence band is a “hole”, which can be thought of as a particle with its own charge (+1) and effective mass. The electron and hole are considered “bound” to each other via Coulombic attraction, and this quasiparticle is then known as an “exciton”. The exci-
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ton can be considered a hydrogenlike system, and a Bohr approximation of the atom can be used to calculate the spatial separation of the electron–hole pair of the exciton by r = h2/πmre2
(1)
where r is the radius of the sphere (defined by the 3-D separation of the electron–hole pair), is the dielectric constant of the semiconductor, mr is the reduced mass of the electron–hole pair, h is Planck’s constant, and e is the charge on the electron. For many semiconductors, the masses of the electron and hole have been determined by ion cyclotron resonance and are generally in the range 0.1–3 me (me is the mass of the electron). For typical semiconductor dielectric constants, the calculation suggests that the electron–hole pair spatial separation is ~1–10 nm for most semiconductors (2). The electronic structure of these quantum dots, then, becomes intermediate between localized bonds and delocalized bands (Figure 1). Because the physical dimensions of a quantum dot can be smaller than the exciton diameter, the quantum dot is a good example of the “particle-in-a-box” calculations of undergraduate physical chemistry. In those calculations, the energies of the particle in the box depend on the size of the box. In the quantum dot, the bandgap energy becomes size-dependent (2–7 ), which becomes obvious when simple absorption spectra of quantum dot solutions are taken (Figure 3). The bandgap energy of the semiconductor from such spectra is generally taken as the absorption energy onset. As the particle size decreases, the absorption onset shifts to higher energy (blue shifts), indicating an increase in bandgap energy (3–9). According to an early effective mass model calculation by Brus (8), estimating particle size from such data can be done as Eg(quantum dot) = Eg(bulk) + (h 2/8R2)(1/me + 1/mh) – 1.8e2/4π0R
σ∗ p
(2)
Conduction band
Energy
Bandgap sp3 Valence band s
σ
Atomic orbitals Hybrid orbitals Molecular orbitals Density of states
FIGURE 1. Silicon as a prototype semiconductor. Comparison of the electronic structure of the atomic orbitals in a silicon atom (left) to that of a silicon cluster molecule (middle) and to that of bulk silicon (right). Atomic orbitals in the atom give rise to bonding and antibonding molecular orbitals in the cluster molecule, which give rise to the filled valence band and (mostly) empty conduction band in the bulk semiconductor. (Adapted with permission from Ref. 2.)
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in which Eg is the bandgap energy of a quantum dot or bulk solid, R is the quantum dot radius, me is the effective mass of the electron in the solid, m h is the effective mass of the hole in the solid, is the dielectric constant of the solid, and 0 is the permittivity of a vacuum. The middle term on the right-hand side of the equation is a particle-in-a-box-like term for the exciton, and the third term represents the electron–hole pair Coulombic attraction, which is mediated by the solid. Implicit in this equation is the assumption that the quantum dots are spherical and that the effective masses of the charge carriers and the dielectric constant of the solid are constant as a function of size. The Brus model maps Eg and size well for larger quantum dots, but its predictions do not match experimental data well for very small particle sizes. Other calculations have been performed that better match experimentally determined bandgap energies and quantum dot sizes for smaller particle sizes (9). The above calculations usually are done for materials in the “strong confinement” limit, that is, the physical dimensions of the semiconductor nanoparticle are substantially smaller than the excitonic Bohr radius. It is also possible for a material to be in “weak confinement”, in which case the particle size is somewhat larger than the excitonic Bohr radius. Another predicted property of quantum dots is that the oscillator strength of the lowest-energy transition becomes size-dependent (2). In the weak confinement case, the oscillator strength of the excitonic transition in a quantum dot appears to be proportional to the dot volume (2). In the strong-confinement case, the oscillator strength is nearly size-independent (2, 8).
How to make them Inorganic semiconductors include the Group 14 (old Group IV) elements silicon and germanium; compounds such as GaN, GaP, GaAs, InP, and InAs (collectively the III–V materials); and ZnO, ZnS, ZnSe, CdS, CdSe, and CdTe (II–VI materials). Periodic properties of the electronic properties of semiconductors are observable; as one goes down the periodic table, the bandgap energy of the solid decreases (10). Solid solutions of many of these semiconductors can be made, and the bandgap of the resulting solid solutions is intermediate between the two end-members; thus GaP has a room-temperature bandgap of 2.3 eV ( onset ~540 nm), GaAs has a room-temperature bandgap of 1.4 eV ( onset ~890 nm), and GaPx As1–x has a bandgap energy that depends nearly linearly on x (10). Quantum dots are not yet commercially available, thus a great deal of work (literally hundreds of papers on CdS and CdSe alone) has gone into their synthesis and characterization. Quantum dots can be made as colloidal solutions or grown on solid substrates. In the colloidal approach, precursors of the material are reacted in the presence of a stabilizing agent that will restrict the growth of the particle and keep it within the quantum confinement limits estimated by Equation 1. Examples are abundant for the II–VI quantum dots; aqueous Cd(II) salts can be mixed with anionic or Lewis basic polymers such as sodium polyphosphate or polyamines (11–13), and the subsequent addition of a sulfide source produces CdS nanoparticles that are in the 1- to 10-nm-size range. Size tuning is possible by controlling relative concentrations and rates of addition.
Optical properties of quantum dots Quantum dots have bandgap energies, and hence onsets of light absorption, which vary as a function of size, as described
Conduction band e– Trap
Energy
The most popular route to synthesizing CdSe quantum dots is organometallic (14): Dimethylcadmium is reacted with a selenium reagent in the presence of a phosphine oxide surfactant at high temperature. Careful control of reaction conditions produces CdSe quantum dots that are quite homogeneous in size (
