Luminescence in Low-dimensional Nanostructures

Luminescence in Low-dimensional NanostructuresNANO AU RSYLuminescence in Low-dimensional Nanostructures Quantum exertion Effect, Surface EffectWhenever the carrier localization, at least in atomic number 53 spatial direction, becomes comparable or little than the de Broglie wavelength of carriers, quantum mechanical pieceuate occur. In this limit the optical and electronic properties of the material change as a conk out of the step to the fore and the system is called a nanostructure. As the coat is decrease the electronic bows argon sliped toward higher strength and the oscillator strength is voiceless into a couple of(prenominal) transitions. Nanostructures argon classified by the number of dimensions in which the carriers are confined or, alternatively, free to move. In case of lying-in in and wizard spatial direction, the nanostructure is named a quantum rise (QW). The carrier motion is arctic in one dimension but electrons and holes idler still freely move over the other 2 directions. Therefore the QW is a quasi(prenominal) two-dimensional (2D) system. A structure which provides carrier lying-in in two directions, allowing the motion along the remaining dimension, is called quantum wire (QWR) and it is a quasi 1D system. In the case of trade union movement in all three spatial coordinates, the nanostructure is denominated quantum dust (QD). QDs are 0D systems since the carrier motion is completely frozen. The physics of the quantum size exercise relies on the Heisenberg uncertainty principle between the spatial position and kinetic impulsion of a quantum mote. It is not possible to measure both the pulse and position of a particle to an arbitrary precision. The product of the standard deviance in space and momentum satisfies the uncertainty relation-x.-p /2 (1.26)This equation means that the smaller is the carrier localization in the nanostructure, the big is the spread in the momentum p, or, better said for semiconductor de vice systems, in the crystal momentum k. The dynamism may still be well defined, but the momentum is not well defined. In bulk systems, for states virtually the edge of conduction and valence dance stripes, the dependence of the energy on the wavevector k is quadratic,Where m* is the carrier effective mass. Following this equation, the spread in the momentum k gives minimum kinetics energy to the localized particle. This is in blood with the classical physics, where the lowest energy state in whatever capability corresponds to no kinetic energy. The uncertainty principle of quantum mechanics imposes a haughty zero-point energy, which is approximately inversely proportional to the square toes of the nanostructure size. Therefore, the energy of theground state of electrons and holes in semiconductor nanostructures not only depends on the materials but in addition on the dimension of the task region.Nanostructured materials with a size mountain range of 1-100 nm start out b een the focus of recent scientific research because of their important optical properties, quantum size effects, electrical properties, chemical properties, etc. The low-dimensional materials have proveed a wide range of optical properties that depend sensitively on both size and shape, and are of both fundamental and technological interest. The ability to control the shapes and size of nanocrystals affords an hazard to further test theories of quantum labor and yields materials with desirable optical characteristics from the point of estimate of application. The exciting emerging important application of low-dimensional nanocrystals is in light-emitting diodes (LEDs) and Displays.Recently, there has been ofttimes recent interest in low dimensional systems such as quantum well (two dimensional system), quantum wire (one dimensional system) and quantum dot (zero dimensional system). optical properties of low-dimensional systems are substantially different from those of three-d imensional (3D) systems. The most remarkable fitting comes from different distributions of energy levels and densities of states originating from the spatial working class of electrons and holes. The simplest model for two dimensional (2D) systems is that of a particle in a box with an continuously plentiful well potential, as shown in visualise 1.6. The wave functions and energy levels in the well are known from basic quantum mechanics and are draw byn(z)=(2/Lz)1/2 cos ( nz/Lz ) (1.28 )n = 1,2,3,. (1.29) anatomy 1.6 A particle in a box made of infinitely tall potential barriersIn semiconductor quantum wells (two dimensional (2D) systems such as layered materials and quantum wells), both electrons and holes are confined in the selfsame(prenominal) wells. The energy levels for electrons and holes are described by 1.8(1.30) (1.31) Where and are the effective stack of electron and hole, respectivelyIf electric dipole transitions are allowed from the valence band to the conduct ion band, the optical transition occurs from the state described by nh , kx , and ky to the state described by ne, kx and ky . Therefore, the optical transition takes place at energy(1.32)Where is the reduced mass tending(p) by -1 =The joint density of states 3D for the 3D for an allowed and direct transition in semiconductors is(1.33)The joint densities of states for 2D, 1D and 0D systems are(1.34)(1.35) (1.36)Where is a step function and is a delta function. The sum of quantum confinement energies of electrons and holes are be by El , Em and En where El , Em and En refer to the three directions of spatial confinementObviously the physics of the nanostructures powerfully depends on their dimensionality (Figure 1.7). In a semiconductor structure a granted energy usually corresponds to a large number different electronic states resulting from the carrier motion. In a bulk material where the motion shag occur in three different directions the density of states increases propor tionally to the square root of the energy. In quantum wells the motion in the plane gives a staircase commonwealth, where each step is associated with a newstate in the confining potential. In quantum wires a continuum of states is still present, but strong resonances appear in the DOS associated with the states in the confining potential. Finally in quantum dots only discrete energy states are allowed and the DOS is therefore a comb of delta functions. The possibility to condense the DOS in a reduced energy range is passing important for a large variety of fundamental topics and device applications. It is at the base of the quantum Hall effect in quantum well (QW), of the quantization of the conductance in quantum wire (QWR), and of the single electron tunnelling in QDs. In the case of lasers the nominal head of a continuum DOS leads to losses associated with the population of states that do not post to the laser action. Conversely, the concent balancen of the DOS produces a r eduction of the threshold circulating(prenominal) and enhances the thermal stability of the device ope proportionalityn. Clearly this property is optimized in QD structures. delinquent to the three-dimensional carrier confinement and the resulting discrete energy spectrum, semiconductor QDs can be regarded as artificial atoms.Figure1. 7 Density of states of three-dimensional ( 3D ) bulk semiconductors, a two dimensional ( 2D ) quantum well, a one dimensional ( 1D ) quantum wire, and zero dimensional ( 0D ) quantum dots.The most striking property of nanoscale semiconductor materials is the massive change in optical properties as a function of size due to quantum confinement. This is most readily manifest as a blue-shift in the absorption spectra with the go down of the particle size. The blue-shift in the absorption spectra with decrease of particle size in semiconductor nanoparticles is due to the spatial confinement of electrons, holes, and excitons increases the kinetic energy of these particles. Simultaneously, the same spatial confinement increases the Coulomb interaction between electrons and holes. The exciton Bohr roentgen is a useful parameter in quantifying the quantum confinement effects in nanometer size semiconductor particles. The exciton Bohr radius is given by 1.8(1. 37)and an inequality holds. Here and are defined asand (1.38 )Where is the reduced mass given by are the effective masses of electron and hole, respectively. And also is the dielectric constant, is the Planck constant.As the particle size is reduced to get down to the exciton Bohr radius, there are drastic changes in the electronic structure and material properties. These changes include shifts of the energy levels to higher energy, the development of discrete features in the spectra (Figure 1.8).Figure 1.8 A schematic models for the energy structures of bulk solids, nanoparticles and isolated molecules.The quantum confinement effect can be classified into three categorie s the weak confinement, the in preconditionediate confinement and the strong confinement regimes, depending on the relative size of the radius of particles R compared to an electron , a hole , and an exciton Bohr radius , respectively. In strong confinement (R , ), the individual motion of electrons and holes is quantized and the Coulomb int eraction energy is much smaller than the quantized kinetic energy. The ground state energy is 1.8(1.39)Where the second terminus is the kinetic energy of electrons and holes, the third term is the Coulomb energy, and the last term is the correlation energy. In intermediate confinement ( ), the electron motion is quantized, age the hole is bound to the electron by their Coulombic attraction. In weak confinement ( ), the center-of-mass motion of exciton is quantized. The ground state energy is written as (1.40 )Where is the translational mass of the excitonFigure 1.9 Size dependence of band gap for CdS nanoparticles.In strong confinement, ther e is appearance of an increase of the energy gap (blue shift of the absorption edge), which is roughly proportional to the inverse of the square of the particle radius or diameter. For example, it can be detect from Figure 1.9 that the strong confinement is exhibited by CdS particles with diameter less than 6 nm (R 3 nm), and this is lucid with the strong confinement effect for particles with The luminescence dynamics in low-dimensional nanostructures also deals with the interaction of light with the material. The interaction of light depends strongly on the surface properties of the materials. As the size of the particle approaches a few nm, both surface area to garishness ratio and surface to bulk atom ratio dramatically increases. The basic relationship between the surface area to brashness ratio or surface atoms to bulk atoms and the diameter of nanoparticles can be seen in Figure 1.10.Figure 1.10 Surface area to volume ratio and percentage of surface atoms (%) as a functi on of particle size.It is observed that the percentage of surface atoms in corner and edge vs. Particle sizes parade dramatic increase when the size is decreased below a few nm, whereas percentage of face atoms decreases. For particles of 1 nm, more than 70% atoms are at corners or edges. This aspect is important because light interaction with material highly dependent on the atomic scale surface morphology. As in nanoparticles, a large percentage of the atoms are on or cuddle the surface, therefore, surface states near the band gap can mix with internal levels to a substantial degree, and these effects may also influence the place of the energy levels. Thus in many cases it is the surface of the particles rather than the particle size that determines the optical properties. Optical excitation of semiconductor nanoparticles often leads to both band edge and deep trap luminescence. The size dependence of the excitonic or band edge emission has been studied extensively. The absenc e of excitonic or band edge emission has attributed to the large non-radiative decay rate of the free electrons confine in these deeptraps of surface states. As the particle size becomes smaller, the surface to volume ratio and hence the number of surface states increases rapidly, reducing the excitonic emission. The semiconductor nanoparticles exhibit broad and Stokes-shifted luminescence arising from the deep traps of surface states 1.25 1.27.