A quantum dot is a semiconductor which undergoes quantum confinement in all three spatial dimensions. The bohr model can be readily extended to hydrogenlike ions, systems in which a single electron orbits a nucleus of arbitrary atomic number z. It had also been clearly emphasized 35 that commonplace excitonic parameters like bohr radius, exciton binding energy can become imprecise and ambiguous. Theory predicts that at densities well above the mott transition, the system may form an exciton liquid 3, 4. A quantum dot is a semiconductor so small that the size of the crystal is on the same order as the size of the exciton bohr radius. Through electrostatic gating, the exciton charge state can be modi. This results in the increase in the total emission energy the sum of the energy levels in the smaller band gaps in the strong confinement. H h 1 are the confinement energies of electrons and hh and r qw. A large aln barrier thickness provides an increased probability of capturing excitons by er optical centers, leading to a higher excitation e. Optical properties of wurtzite gan and zno quantum dots. Exciton pair is defined as an electron and the hole that it leaves behind when it is excited up to the conduction band. Exciton bohr radius is the average distance between the electron in the conduction band and the hole it leaves behind in the valence band. Multiple exciton generation in nanostructures for advanced. The distance between an electron and a hole in the exciton is known as exciton bohr radius.
The large bohr radius of excitons in comparison to the tube diameter, rules. It is an electrically neutral quasiparticle that exists in. Dependences of the exciton binding energy 1 11 and the coulomb interaction energy 2 12 in the cdse qd on the qd radius a. Hereafter, the discussion is focused on the first type of excitons, the wanniermott excitons. What is meant by bohr exciton radius and what is the role. In connection with the observed e3 excitonic resonance in pbs, we explore the following issues a is the above mentioned classic definition of bohr exciton radius a b precise enough to describe transitions. In this regard, theory suggests that, for this to be the case, the radius of the qd should be less than the bulk exciton bohr radius, calculated as, with. Kane type dispersion relation is used to incorporate such band nonparabolicity. To explain line spectra, neils bohr proposed that the angular momentum of the electrons orbiting the atom is quantized. For this problem, think of an exciton as a hydrogenlike atom, with a negatively charged electron and positively charged hole orbiting each other.
An electron and hole form a hydrogenlike bound state with a bohr radius much larger than the lattice spacing. From the structural point of view, a swnt is a quasi 1d system. As pointed out above, it is important that photovoltaic structures exhibit quantum confinement. The following hamiltonian is used to calculate the exciton states in zno qds. Theory of excitons and excitonic quasimolecules formed. The simple picture of an exciton composed of coupled electrons and holes may fail in the limit of a weakly bound or large exciton bohr radius. Three separate scenarios occur 7 strong confinement. The exciton is regarded as an elementary excitation of condensed matter that can transport energy without transporting net electric charge.
A quantum dot is a semiconductor so small that the size of the crystal is on the same order as the. For the love of physics walter lewin may 16, 2011 duration. Hence, for all practical purposes, the above calculation. Wannier exciton typical of inorganic semiconductors frenkel exciton typical of organic materials binding energy 10mev radius 100a binding energy 1ev radius 10a treat excitons as chargeless particles capable of diffusion, also view them as excited states of the molecule charge transfer ct exciton typical of organic materials. Bohr radius of a particle is defined as yoffe 1993, b m aa m h r 1 where. In analogy to the hydrogen problem the respective orbital wave function for n1 is exp 1 0 1 3 2 a r a x r n s \ with exciton bohr radius 2 2 0 0 4 3 e a x d p shh. This type of exciton is called a wanniermott exciton. Comparisons can be drawn from quantum dots to the particle in a box example from quantum mechanics. Pdf do we need to revisit the bohr exciton radius of hot excitons. Excitons are coupled electronhole pairs via coulomb tt ti attraction. Synthesis and characterization of pbte quantum dots. Effect of chargecarrier screening on the exciton binding.
Photoexcited electron and hole dynamics in semiconductor. The size of a ground state hydrogen atom as calculated by niels bohr using a mix of classical physics and quantum mechanics. The bohr radius a 0 or r bohr is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It has been reported that, when the nanoparticle size is close to the exciton bohr radius, 2.
Semiconductor crystals of size less than double the bohr radius of the excitons experience quantum confinement. When the size of nanomaterial is less than exciton bohr radius the quantum confinement effect is noticed in terms exotic properties such as mechanical, optoelectronic, magnetic, chemical. Do we need to revisit the bohr exciton radius of hot excitons. Roomtemperature lasing action in gan quantum wells in the.
The particle in a box model can be used to model the energy levels, giving energy states dependent on the size of the potential well 2. The coupling between the quasielectron and the quasihole, which form the exciton, may involve both static coulomb and retarded interaction, which should be taken into account for strong electronhole. Diffusionlimited excitonexciton annihilation is sensitive to the dimensionality of the system, resulting in a time dependence of the annihilation rate for low dimensional less than 2 26,27,39,40cases. Exciton and corelevel electron confinement effects in. A quantum dot is a semiconductor so small that the size of the crystal is on the same order as the size of. The excitons in the quantum dot are confined to a distance smaller than the bohr exciton radius, 5. Pdf we report collisional broadening of the e3 excitonic resonances in optical absorption spectra of pbs nanocrystallites of widely varying. Herein, for the first time, the sizedependent excited state optical properties of ag2s qds are systematically investigated by photoluminescence pl, pl excitation ple, and timeresolved pl spectroscopy. The bohr radius is an actual physical constant and has been measured to be about 0. We estimate bohr radius and binding energy of exciton in bulk as well as quantum well for semiconductors with nonparabolic energy band structure. We also computed a very strongly bound and localized exciton in. Democritus the atomic theory of matter has a long history, in some ways all the way back to the ancient greeks democritus ca. These theoretical values obtained 0 from solving the bse agree very well with experimental data.
An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic coulomb force. For d smaller than the exciton bohr radius, the exchange interaction can compensate for the dipole repulsion, and a quantum liquid is formed. In semiconductors, ema works well to describe the motion of electrons and holes. The bohr radius is the radius you get for a free exciton just by considering kinetic energy and the coulomb interaction. Qds are in sharp contrast to molecular systems, whose properties vary discontinuously and require. Excitons types, energy transfer mit opencourseware. Excitons and excitonic bohr radius, energy levels, splitting. The transition is accompanied by the absorption or emission of a single photon.
An exciton pair is defined as an electron and the hole that it leaves behind when it is excited up to the conduction band. Excitons in nanosystems consisting of semiconductor quantum dots. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and some liquids. Excitonexciton annihilation in singlewalled carbon nanotubes.
Some examples of confinementenabled features include a tunable absorption spectrum, bandgap photoluminescence pl, singlettotriplet exciton conversion, and multiple exciton generation, all of which become available when the size of the semiconductor nanoparticle is reduced to or below its corresponding exciton bohr radius. What is the bohr exciton radius for hfo2 nps, can you help. An exciton is a bound electronhole pair in a semiconductor. Controlled synthesis of ag2s quantum dots and experimental. Of course you can reduce the distance between electron and holes by means of confinement as it is done in quantum dots. The exciton binding energies are found to decrease rapidly when the screening length is less than 30az effective exciton. Bandedge exciton in quantum dots of semiconductors with a. Binding energies and oscillator strengths are first increased as the well width is reduced, due to the smaller electronhole. Pdf exciton binding energy in semiconductor quantum dots.
This a b symbolizes the characteristic length scale to observe quantum effects in nanomaterials. It is named after niels bohr, due to its role in the bohr model of an atom. The radius of the quantum dot is less than the bohr radius for both the electron and hole. An exciton bohr radius is the distance in an electronhole pair. Experimentally, we determine the exciton bohr radius of ag2s qds as 2. Bohr radius 3 as long as the electron remains in such a path, it neither gains nor loses energy. From what we can observe, atoms have certain properties and behaviors, which can be summarized as. Derivation of bohrs equations for the oneelectron atom. When the particle size approaches bohr exciton radius, the quantum confinement effect.
371 420 478 939 626 385 851 493 860 1590 53 1119 1595 1518 620 228 1375 485 794 328 751 421 1335 1214 36 476 307 84