Quantum dots confining potential

In fact, quantum dots provide an attractive opportunity to develop optical switches, modulators, and other nonlinear optical devices. This occurs because quantum confinement enhances nonlinear absorption and nonlinear refractive index. Quantum dots can be used for optical switches and logic gates which work faster than 15 terabits per second. Another important application is the quantum dot, in which the tunable band gap of quantum dots makes the laser wavelength changeable. Also, lasers with quantum dots have potential for very low-threshold current density, which is currently required to stimulate the laser or create output power from the device. 

In order to explain the band structure for the small confinement regime the nature of the potential energy function in the Hamiltonian has been examined in the internal space. Since, for quasi-one-dimensional quantum dots, the electrons can only move along the z coordinate, their x and y dependence is neglected in the analysis. The internal space is defined by a unitary transformation from the independent electron coordinates (z, Z2, , zn) into the correlated electron coordinates (za, zp,...). The coordinate za represents the totally symmetric center-of-mass coordinate za = 7=(zi + Z2 + + zn), and the remaining correlated electron coordinates zp,..., zn represent the internal degrees of freedom of the N electrons [20,21]. In the case of two electrons the correlated coordinates are defined by... 

The Hamiltonian (1) for quasi-one-dimensional two-electron quantum dots is simplified by neglecting the x and y degrees of freedom and by approximating the confining Gaussian potential by a harmonic-oscillator potential with >z... 

In order to analyze the origin of this difference between the energy spectra of quasi one- and two-dimensional quantum dots in the small confinement regime, the internal space for two electrons is considered as in the quasi-one-dimensional cases. Using a harmonic approximation to the Gaussian confining potential, and neglecting the dependence on the z coordinate, the Hamiltonian of Equation (1) for two electrons takes the form... 

The energy spectrum of two electrons confined in a quasi-fwo-dimensional Gaussian potential has also been studied for the same set of the strengths of confinement as the corresponding quasi-one-dimensional cases, and are compared to them. The energy spectrum of the quasi-two-dimensional quantum dot is qualitatively different from that of the quasi-one-dimensional quantum dot in the small confinement regime. The origin of the differences is due to the difference in the structure of the internal space. 

The size-dependent properties of nanoparticles differ greatly from the corresponding bulk materials. An example is the size quantization phenomenon commonly observed in II-VI and III-V inorganic semiconductor nanocrystals.6 During the intermediate transition towards that of the bulk metal (usually between 2 and 20 nm), localization of electrons and holes in a confined volume causes an increase in its effective optical band gap as the size of the nanoparticle decreases, observed as a blue shift in its optical spectrum. Bms predicted that there should also be a dependence on the redox potential for these same classes of quantum dots.7 Bard and coworkers showed this experimentally and have reported on the direct observation between the... 

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. 

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