Quantum confinement Three-dimensional

Pelton, M., Vuckovic, J., Solomon, G.S., Scherer, A., and Yamamoto, Y., 2002, Three-dimensionally confined modes in micropost microcavities quality factors and Purcell factors,/LEE J. Quantum. Electron. 38(2) 170-177. 

There are two very broad, general conclusions resulting from the above review. The first is that MoS2-type nanoparticles are very different than other types of semiconductor nanoparticles. Nanoparticles of several different types of semiconductors, such as CdSe, CdS, and InP, have been extensively studied. Experimental and theoretical studies have elucidated much of their spectroscopy, photophysics, and dynamics. The results reviewed above are, in many places, in sharp contrast with those obtained on other types of quantum dots. This does not come as a surprise. The properties of the bulk semiconductor are reflected in those of the nanoparticle, and properties of layered semiconductors are vastly different from those of semiconductors having three-dimensional crystal structures. Although the electronic and spectroscopic properties of nanoparticles are strongly influenced by quantum confinement effects, the differences in the semiconductors cause there to be few generalizations about semiconductor quantum dots that can be made. 

The interest in semiconductor QD s as NLO materials has resulted from the recent theoretical predictions of strong optical nonlinearities for materials having three dimensional quantum confinement (QC) of electrons (e) and holes (h) (2,29,20). QC whether in one, two or three dimensions increases the stability of the exciton compared to the bulk semiconductor and as a result, the exciton resonances remain well resolved at room temperature. The physics framework in which the optical nonlinearities of QD s are couched involves the third order term of the electrical susceptibility (called X )) for semiconductor nanocrystallites (these particles will be referred to as nanocrystallites because of the perfect uniformity in size and shape that distinguishes them from other clusters where these characteriestics may vary, but these crystallites are definitely of molecular size and character and a cluster description is the most appropriate) exhibiting QC in all three dimensions. (Second order nonlinearites are not considered here since they are generally small in the systems under consideration.)... 

Quantum confinement can act in three spatial directions, thus one has zero-dimensional, one-dimensional, and two-dimensional confined systems. 

Quantum dots represent three-dimensional confinement in semiconductor materials. The optical spectroscopy of lanthanides-doped III-V semiconductor QDs has been observed to be very different from the bulk or thick film. For example, carrier confinement in QDs can strongly enhance the radiative quantum efficiency of the lanthanide emission, which thus makes lanthanide-doped III-V semiconductor QDs very promising candidates for full-color LEDs. It is notoriously difficult to dope lanthanide into III-V semiconductor nanocrystals by wet chemical synthesis methods. To date, most of these samples were prepared either by MBE, ion implantation or magnetron co-sputtering. 

If a metal particle, independent of the element, is reduced in one, two, or in all three dimensions to such an extent that the mobility of the electrons is decisively restricted, one speaks of size quantization because the electrons no longer follow the laws of classical physics based on the statistics of an inflnite assembly of atoms in three dimensions, but rather obey quantum mechanical mles as they are used to describe atoms or molecules. Figure 1 illustrates the formal transition from 3D to a OD state, represented by a so-called quantum dot with three-dimensional quantum confinement. ... 

The wavefunctions for three-dimensional confinement have three quantum numbers (n, I, m) plus spin. The selection rules for dipole-allowed absorption and emission were given above for interband transitions. For intraband transitions between the ladder of electron or hole states, the selection rules for the simplest case of non-interacting electrons and holes are An 0 AL = 0, + 1 Am = 0, + 1. 

Charge carriers in semiconductors can be confined in one spatial dimension (ID), two spatial dimensions (2D), or three spatial dimensions (3D). These regimes are termed quantum films, quantum wires, and quantum dots as illustrated in Fig. 9.1. Quantum films are commonly referred to as single quantum wells, multiple quantum wells or superlattices, depending on the specific number, thickness, and configuration of the thin films. These structures are produced by molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) [2j. The three-dimensional quantum dots are usually produced through the synthesis of small colloidal particles. 

To calculate the effective transition dipole moment we need to know the wave-function of the exciton. In a quantum dot it depends on two interactions (i) the electron and hole confinement potential, which we shall assume to be infinite for r > Ri and zero for r < f i and (ii) the electron and hole Coulomb attraction. For these interactions we have to consider the following characteristic lengths f i - the radius of the quantum dot, and ag - the Bohr radius of an exciton in a macroscopic three-dimensional semiconductor. The problem of solving the two-particle Schrodinger equation for an arbitrary ratio of these lengths is quite difficult but the situation simplifies substantially in two important limiting cases. 

One subject that attracted much attention is the nonlinear optical properties of these semiconductor nanoclusters [17], The primary objective is to find materials with exceptional nonlinear optical response for possible applications such as optical switching and frequency conversion elements. When semiconductors such as GaAs are confined in two dimensions as ultrathin films (commonly referred to as multiple quantum well structures), their optical nonlinearities are enhanced and novel prototype devices can be built [18], The enhancement is attributed mostly to the presence of a sharp exciton absorption band at room temperature due to the quantum confinement effect. Naturally, this raises the expectation on three-dimensionally confined semiconductor nanoclusters. The nonlinearity of interest here is the resonant nonlinearity, which means that light is absorbed by the sample and the magnitude of the nonlinearity is determined by the excited state... 

---