Theoretical Studies on the Effect of Confinement on Quantum Dots Using the Brus Equation (original) (raw)
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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.
2017
Quantum confinement effect in semiconductor quantum dots (QD’s) of Indium Phosphate and Lead Sulphide has been studied within the framework of Brus Equation, using the particle-in-a-box model. The two nanocrystals used exhibit a size dependence phenomenon as predicted by the model used. The results indicate that ground state confinement energy is inversely proportional to the dot size. As such, when the radius of the dot increases, its confinement energy decreases without getting to zero. i.e., the lowest possible energy for the quantum dot sample is never zero. This phenomenon has made the nano-particles considered more relevant even in today’s world of technology.
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.
Confinement Effects and Emission Spectra of − Quantum Dots Nanostructure
Communication in Sciences, 7(3):164-173 , 2021
Quantum confinements in − spherical semiconductor quantum dots (QDs) has been theoretically studied using the Particle in a box Model based on the effective mass approximation and quantum confinement effects. The valence band degeneracy in Г point of the Brillouin zone and the effective mass anisotropy are also taken into account. The emission intensity spectrum was also investigatedtoo understand the effect of alloy composition(x) on the spectrum. The results show that the ground state confinement energy is largely dependent on radius of the dot and alloy composition(x). Thus, as dot radius decreases, the confinement energy increases. Hence, confinement energies could be tuned by changing the radius of QDs and the GaNcompositions, which play a fundamental role in the optical and electronic properties of QDs of all the transitions in the degenerate bands. Also, the theoretically calculated emission intensity spectrum shifted towards higher energy region (lower wavelengths) by mere increasing the alloy compositions (x) of the semiconductor quantum Dot active region − .
The influence of shape and potential barrier on confinement energy levels in quantum dots
Journal of Applied Physics, 2010
The influence of the shape of silicon quantum dots embedded in an amorphous silica matrix on the quantum confinement energy levels, as well as that of the Si/ SiO 2 potential barrier, are studied. The energy levels are computed using both the infinite and finite rectangular quantum well models for spherical quantum dots and the infinite rectangular quantum well for prolate spheroidal quantum dots. The results are compared with each other and also with the experimental activation energies obtained from the temperature dependence of the dark current. These activation energies are identified with the differences between the quantum confinement energies, subject to the selection rules. The finite rectangular quantum well model takes into account the experimental value of the finite potential barrier and the matrix-to-dot electron mass ratio. The energy levels are smaller than those for the infinite rectangular quantum well case; they decrease when the potential barrier decreases and the mass ratio increases. Different aspects of the models are discussed. All the errors are less than about 4%. The spheroidal shape lifts the degeneracy on the magnetic quantum number. The energy levels can decrease or increase with eccentricity as a consequence of the different quantum confinement effects along the major and minor axes. The supplementary information on the magnetic quantum number is beneficial for optical applications.
The size effects on the energy gap of CdSe, ZnS and GaAs quantum dots have been studied using particle in a box model. The obtained model enabled a computation of dot energy gaps over large size ranges in order to investigate the size dependent effects. With decreasing size, the following effects were observed: the energy gap became size dependent and increased with the decreasing size and discrete energy levels were observed at band-edges of both the conduction band and valence band. It was found that emission and absorption spectra corresponding to the energy gap of the quantum dots were consistent with quantum confinement principles in a potential well. Thus, energy gap is inversely proportional to the square of the dot radius(size). Among the three quantum dots considered, CdSe quantum dot exhibited an exceptional optical properties, such as size-tunable photo-luminescence that spanned the entire visible spectrum, and therefore could be used for optical display applications.
Confinement Effects and Tunability of Quantum Dots within Strong Confinement Regime
In this age of miniaturization and nanotechnology, nano sized zero dimensional particles called quantum dots are finding wide range applications. The reasons behind their growing popularity are their controllable electrical and optical properties. This control is achieved by tuning their bandgaps by changing their shape and size. But quantum effects are most prominent only within strong confinement regime. That is, the radius of the quantum dots are much less than the exciton Bohr radius of the bulk material of which the quantum dots are made. In this paper, we have studied the confinement effects on Indium Gallium Nitride, Gallium Arsenide and Cadmium Selenide quantum dots under strong confinement. We have calculated the possible range of tunable bandgap for each of them. We also calculated the range of wavelengths that can be captured by each of these quantum dots and compared them.
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.
Experimental Observation of Quantum Confinement in the Conduction Band of CdSe Quantum Dots
Physical Review Letters, 2007
X-ray absorption spectroscopy has been used to characterize the evolution in the conduction band (CB) density of states of CdSe quantum dots (QDs) as a function of particle size. We have unambiguously witnessed the CdSe QD CB minimum (CBM) shift to higher energy with decreasing particle size, consistent with quantum confinement effects, and have directly compared our results with recent theoretical calculations. At the smallest particle size, evidence for a pinning of the CBM is presented. Our observations can be explained by considering a size-dependent change in the angular-momentumresolved states at the CBM.
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.