Two band model for a semiconductor quantum dot (original) (raw)
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Semiconductor quantum dots: Theory and phenomenology
Bulletin of Materials Science, 1999
Research in semiconductor quantum dots (q-dots) has burgeoned in the past decade. The size (R) of these q-dots ranges from 1 to 100 nm. Based on the theoretical calculations, we propose energy and length scales which help in clarifying the physics of this mcsoscopic system. Some of these length scales are: the Bohr exciton radius (a*), the carrier de Broglie and diffusion length (~'D and ID) , the polaron radius (ap), and the reduction factor modulating the optical matrix element (M). R <a a is an individual particle confinement regime, whereas the larger ones are exciton confinement regime wherein Coulomb interaction play an important role. Similarly a size-dependent dielectric constant ~(R) should be used for R <ap <a n. An examination of M reveals that an indirect gap material q-dot behaves as a direct gap material in the limit of very small dot size. We have carried out effective mass theory (EMT) calculations to estimate the charge density on the surface of the quantum dot. We present tight binding (TB) calculation to show that the energy upshift scales as 1/R x, where x is less than 2 and the exponent depends on the orientation of the crystallite.
Simulation of quantum dots (QDs) in the confinement regime
International Journal of Applied Science and Engineering Research, 2012
The ground state confinement energy and its associated wavelength as a function of radius for three different semiconductor quantum dots (QDs) were calculated using the Brus equation. The experimental observation of the size dependence on the band gap energy is in good agreement with the theoretical models for the semiconductor nanocrystals considered. The confinement of electrons in semiconductor quantum dots increases dramatically with decrease in its size (radius) and shows exponential dependence on wavelength of light emitted.
ELECTRONIC STATES OF QUANTUM DOTS
The self-assembled quantum dots are grown on wetting layers and frequently in an array-like-assembly of many similar but not exactly equal dots. Nevertheless, most simulations disregard these structural conditions and restrict themself to simulating of a pure single quantum dot. Moreover, many simulations settle for the linear model with constant instead of the rational eective mass. In this work we argue that the nonlinear model is necessary to correctly capture the interesting part of the spectrum. We advocate the eective one electronic band Hamiltonian with the energy and position dependent eective mass approximation and a finite height hard-wall 3D confinement potential for computation of the energy levels of the electrons in the conduction band. Within this model we investigate the geometrical eects mentioned above on the electronic structure of a pyramidal InAs quantum dot embedded in a GaAs matrix. We find that the presence of a wetting layer may aect the electronic structure...
Numerical study of 2-D quantum dots
We present a numerical study of the chemical potential and of the capacitance in a model quantum dot. Our model includes the electron-electron interaction and exchange and correlation effects within the framework of density functional theory. Our results exhibit the typical features observed in experiments, such as the increase in the capacitance for increasing number of electrons and the presence of irregularities in the succession of the chemical potential values vs. the electron number.
Quantum confinement induced shift in energy band edges and band gap of a spherical quantum dot
Physica B: Condensed Matter
We have proposed and validated an ansatz as effective potential for confining electron/hole within spherical quantum dot in order to understand quantum confinement and its consequences associated with energy states and band gap of Spherical Quantum Dot. Within effective mass approximation formalism, considering an ansatz incorporating a conjoined harmonic oscillator and coulomb interaction as the effective potential for confining an electron or a hole within a spherical quantum dot and by employing appropriate boundary conditions we have calculated the shifts in energy of minimum of conduction band(CBM) and maximum of valence band(VBM) with respect to size of spherical quantum dot. We have also determined the quantum confinement induced shift in band gap energy of spherical quantum dot. In order to verify our theoretical predictions as well as to validate our ansatz, we have performed phenomenological analysis in comparison with available experimental results for quantum dots made of CdSe and observe a very good agreement in this regard. Our experimentally consistent theoretical results also help in mapping the probability density of electron and hole inside spherical quantum dot. The consistency of our results with available experimental data signifies the capability as well as applicability of the ansatz for the effective confining potential to have reasonable information in the study of real nano-structured spherical systems.
The confinement energy of quantum dots
One of the most significant research interests in the field of electronics is that on quantum dot, because such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules. Confinement energy is a very important property of quantum dot. In this study, quantum confinement energy of a quantum dot is concluded to be h2/8md2 (d being the diameter of the confinement) and not h2/8ma2 (a being the radius of the confinement), as reported in the available literature. This is in the light of a recent study [1]. This finding should have a significant impact in the understanding of the physics of quantum dot and its technological application.
2018
We have proposed and validated an ansatz as effective potential for confining electron/hole within spherical quantum dot in order to understand quantum confinement and its consequences associated with energy states and band gap of Spherical Quantum Dot. Within effective mass approximation formalism, considering an ansatz incorporating a conjoined harmonic oscillator and coulomb interaction as the effective potential for confining an electron or a hole within a spherical quantum dot and by employing appropriate boundary conditions we have calculated the shifts in energy of minimum of conduction band(CBM) and maximum of valence band(VBM) with respect to size of spherical quantum dot. We have also determined the quantum confinement induced shift in band gap energy of spherical quantum dot. In order to verify our theoretical predictions as well as to validate our ansatz, we have performed phenomenological analysis in comparison with available experimental results for quantum dots made o...
Calculation of the energy levels in quantum dots
Solid State Communications, 1994
We present a detailed effective mass calculation of the energy levels in InAs quantum dots embedded in GaAs. We compare the results of a separable approximate treatment with a more complete numerical approach. A satisfying agreement is found with the available experimental data. Even for dot diameters of the order of 3Onm, we find large distances between consecutive energy levels, which should play an important role in the energy relaxation rates.
The effect of band offsets in quantum dots
Solar Energy Materials and Solar Cells, 2016
The insertion of quantum dots in a host material produces band offsets which are greatly dependent on the field of strains brought about by this insertion. Based on the Empiric KP Hamiltonian model, the energy spectrum of the quantum dot/host system is easily calculated and a relationship between the conduction and valence band offsets is determined by the energy at which the lowest peak of the subbandgap quantum efficiency of an intermediate band solar cell is situated; therefore knowledge of the valence band offset leads to knowledge of both offsets. The calculated sub-bandgap quantum efficiency due to the quantum dot is rather insensitive to the value of the valence band offset. However, the calculated quantum efficiency of the wetting layer, modeled as a quantum well, is sensitive to the valence band offset and a fitting with the measured value is possible resulting in a determination of both offsets in the finished solar cell with its final field of strains. The method is applied to an intermediate-band solar cell prototype made with InAs quantum dots in GaAs.
Electronic energy spectrum and the concept of capacitance in quantum dots
Physical Review B, 1993
The chemical potential and the capacitance of a model quantum dot have been computed, including contributions of exchange and correlation in the limit of 0 K temperature. The Schrodinger equation has been solved self-consistently, taking into account the electron-electron Coulomb interaction and many-body effects within the framework of density-functional theory. We have also studied the eKect of conducting backgates and of nearby electrodes using the method of images. Depending on the size of the dot, we derive a prevalence of either the quantization energy or the electrostatic energy: there is a smooth transition from predominant quantum eKects for small dots to classical capacitance behavior for large dots. Our simulation reproduces characteristic eKects that have been experimentally observed, such as the capacitance increase for increasing electron numbers and irregularities in the chemical potential values when randomly distributed charged impurities are present.