Exciton Of Single Electron Hole Coupled Under Electric And Magnetic Field Pdf

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In physics , chemistry , and electronic engineering , an electron hole often simply called a hole is the lack of an electron at a position where one could exist in an atom or atomic lattice. Holes are not actually particles , but rather quasiparticles ; they are different from the positron , which is the antiparticle of the electron. See also Dirac sea.

Correlated electron-hole transitions in bulk GaAs and GaAs- Ga,Al As quantum wells: effects of applied electric and in-plane magnetic fields. Duque I ; L. Oliveira II ; M. Physics, Univ. The effects of crossed electric and magnetic fields on the electronic and exciton properties in semiconductor heterostructures have been investigated within the effective-mass and parabolic band approximations for both bulk GaAs and GaAs-Ga 1- x Al x As quantum wells.

Coupling effects on photoluminescence of exciton states in asymmetric quantum dot molecules

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. The ground state energy and the binding energy of the exciton are obtained as a function of the quantum dot size, confinement strength and the magnetic field and compared with those available in the literature.

The variation of the exciton size and the oscillator strength of the exciton are also studied as a function of the size of the quantum dot. This can open up the possibility of having quantum dot lasers using excitonic states. With the advent of modern sophisticated fabrication methods such as molecular beam epitaxy, nano-lithography and etching techniques, the study of low-dimensional systems has undergone a renaissance.

It is now possible to realize ultra-small semiconductor structures with quantum confinement of carriers in all the spatial directions. These structures are typically of the order of a few nanometers in size and are commonly referred to as zero-dimensional objects or more technically as quantum dots. Interest in the subject of QDs has continued unabated for the last four decades mainly for two reasons. First and foremost, it has an intrinsic appeal because the natural length scales involved in it are of the order of a few nanometers where the quantum effects can show up in their full glory.

Therefore a QD can be considered to provide a tiny laboratory where the predictions of quantum mechanics can be tested 1. Secondly and perhaps more importantly, the QD systems exhibit very many new physical effects which are very interesting and are also quite different from those of their bulk counterparts.

Furthermore, QD structures can be realized in both two and three dimensions and can also be fabricated in different sizes and shapes. This design flexibility and the novel physical effects make QD structures technologically very promising for applications in micro-electronic devices like quantum dot lasers 2 , single electron transistors 3 and ultrafast quantum computers.

Various elementary excitations are possible in a semiconductor QD. One of the important among them is an exciton which is a bound pair of an electron and a hole. An exciton can be created by shining light on a semiconducting material. Quantum confinement can dramatically change the optical properties of a QD that depend on excitonic processes. The explanation is simple. It is well-known that the confinement per se enhances the energy of a particle in general.

For an exciton, however, it increases the Coulomb attraction between the electron and the hole and thus lowers the energy. The interplay between these two contrasting effects can give rise to some interesting excitonic effects. Furthermore, the increase in the proximity between the electron and the hole due to confinement enhances the probability of radiative recombination. Therefore, one has to understand the precise effects of all these processes and also the ways to control them so that one can tune the different QD parameters to have a desired optical property.

Excitonic effects have been captured through photoluminescence experiments 4. Excitonic effects have also been found to play a central role in optoelectronic devices such as semiconductor QDs-based photovoltaic cells and light emitting diodes 5 , 6 , 7 , 8 , 9 , Their results show that the inclusion of the excitonic effect enhances the third harmonic generation by about hundred percent.

Yuan et al. They have furthermore shown that excitonic effects enhance the optical absorption by a factor of two. To study the properties of a QD theoretically one has to introduce an empirical potential known as the confining potential. The simplest confining potential would of course be an infinitely deep potential well.

Initial experiments 13 , 14 together with the generalized Kohn theorem 15 , 16 , however, suggested that the confining potential in a QD would be more or less parabolic in nature. This observation has made the application of quantum mechanics to a QD system quite straightforward and consequently a large number of investigations exploring several electronic and optical properties of parabolic QDs PQD 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 has piled up in the literature in the last few decades.

Several authors have also explored the properties of excitons in PQDs 25 , 26 , 27 , 28 , Some recent experiments have indicated that the confining potential in a QD is not really harmonic but rather anharmonic and has a finite depth. Recently Adamowski et al. This potential has a central minimum and a finite depth and in the neighborhood of the dot centre would behave like a parabolic potential and would thus approximately satisfy the generalized Kohn theorem.

Furthermore, in contrast to the rectangular potential well, it is continuous at the dot boundary and this makes it easier to handle mathematically. Also the force experienced by the particles within this potential well is nonzero, which is again a desirable feature.

The other advantages with the Gaussian confining potential vis-a-vis a parabolic potential are that the former can describe, in addition to the excitations, the ionization and tunneling processes. Masumoto and Takagahara 31 have shown that for small QDs, the Gaussian potential is indeed a good approximation for the confining potential. The Gaussian potential has already been used by several authors as the model for confinement to study the electronic properties of a QD 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , Although the ground state GS of an exciton a GQD has been investigated by several authors, studies on the excited states of an exciton in a GQD are few and far between.

The excited states of an exciton are important in both infrared spectroscopy and two-photon spectroscopy Xie 47 has considered the exciton problem in a GQD and has studied the ground and the first excited states by using the matrix diagonalization method. It is well known that a magnetic field provides an additional confinement and can be used to tune the confinement in a much better and cleaner way as compared to the other QD parameters which have electrostatic effects.

Gu and Liang 6 have considered the exciton problem in a GQD in the presence of a magnetic field and studied it using the matrix diagonalization method. Obviously this problem does not admit an exact solution and therefore an exact numerical solution is indeed useful. However, many a time numerical solutions fail to provide some of the interesting physics of the system. Furthermore, the wave function used in the numerical diagonalization method does not provide any insight about the state of the system in contrast to a variational method or other analytical methods.

Therefore it is always desirable to develop an approximate analytical method keeping all the key features of the system into account which can give results that compare well with the numerical results. We shall also investigate the correlation between the size and oscillator strength of the exciton and the QD radius.

We shall also obtain all the excited states of the system for a few set of parameters. This might open up the possibility of having excitonic lasers using QDs. More specifically we write H 1 as. The exact analytical evaluation of E r is not possible in general. The exciton oscillator strength is another important quantity of interest. In the envelop-function approximation, the exciton oscillator strength 26 can be written as. The methods discussed above are quite general in nature and can be applied to any quantum dot.

But, for the sake of concreteness, we apply them to a GaAs QD. One can see from the figure that as the potential depth increases, the distribution decreases. The distribution of the hole is little larger than that of the electron.

We also find that, as the magnetic field increases, the distribution decreases not shown here. We furthermore find that while the parabolic model underestimates the electron distribution, it overestimates the hole distribution not shown here. Distribution of electron and hole of an exciton in a GaAs QD for two values of the potential depth V 0.

In Fig. In all the three cases as R decreases, the exciton energy monotonically increases and this increase becomes very rapid below a certain critical value of R. The reason is understandable. As R decreases, the uncertainty in the exciton momentum increases leading to an increase in the kinetic energy of the exciton. Thus as R decreases, GSE increases in general. As B increases, GSE also increases which is again on the expected line.

Also the nature of confinement becomes unimportant when the QD size becomes large. First, as we have already alluded to in the introduction, it provides an analytical expression for the energy which is always preferable. Secondly, it allows us to calculate the wave functions of the system analytically and can thus provide a much better understanding of the physics of the system.

Thirdly, once the wave functions are obtained, one can calculate average values of several dynamical variables. Finally, since this method provides the entire energy spectrum, one can also calculate all the important thermodynamic quantities. It may be noted that since the confining potential is negative for all finite values of the electron and hole coordinates, one would expect that bound state of an exciton should correspond to a negative energy value.

However for this bound state to be stable it is necessary that the BE energy as defined earlier should be positive. We see that as the QD size decreases, BE increases and the rate of increase is larger for smaller dots. This is understandable because with a decrease in the dot size, the spatial overlap between an electron and a hole increases leading to a stronger coulomb binding.

As suggested by Fig. As expected, BE increases with increasing magnetic field. The figure shows that as R increases, the size of the exciton also increases.

However, the exciton size seems to saturate as R increases beyond some critical value which may be identified as the bulk limit.

We have plotted the exciton size vs. As the magnetic field increases, the size of an exciton decreases. This is a direct consequence of the localizing property of the magnetic field. As expected, the exciton size decreases with increasing magnetic field. Also the exciton size decreases as the potential becomes deeper. According to Fig. Thus one can conclude that as the size of the exciton increases, the binding energy decreases.

We have also studied the variation of the exciton oscillator strength f ex as a function of R and results are shown in Fig. One can see that as R decreases, f ex also decreases. This happens because as R decreases, the exciton energy increases and hence f ex decreases. Again the explanation is simple. The application of the magnetic field leads to an additional confinement, which induces an enhancement in the exciton energy and hence the oscillator strength decreases in the presence of a magnetic field.

From Eqs 20 and 21 we can calculate the energy of all the excited states.

Electron hole

E-mail: bhaskar. Two-dimensional 2D group-VI transition metal dichalcogenide TMD semiconductors, such as MoS 2 , MoSe 2 , WS 2 and others manifest strong light matter coupling and exhibit direct band gaps which lie in the visible and infrared spectral regimes. These properties make them potentially interesting candidates for applications in optics and optoelectronics. The excitons found in these materials are tightly bound and dominate the optical response, even at room temperatures. Large binding energies and unique exciton fine structure make these materials an ideal platform to study exciton behaviors in two-dimensional systems.

Electronic structure is obtained by finite element calculations, and Coulomb effects are included using a perturbative approach. According to our simulated spectra, bright excited states may become optically accessible at low temperatures in hybridization regimes where intermixing with the ground state is achieved. Our results show effective magnetic control on the energy, polarization and intensity of emitted light, and suggest these coupled nanostructures as relevant candidates for implementation of quantum optoelectronic devices. The development of novel devices for spintronics and quantum information processing e. Confined excitons offer the possibility of using laser for initialization, readout, and coherent manipulation of spins.

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. The ground state energy and the binding energy of the exciton are obtained as a function of the quantum dot size, confinement strength and the magnetic field and compared with those available in the literature. The variation of the exciton size and the oscillator strength of the exciton are also studied as a function of the size of the quantum dot.

Coherence and Optical Emission from Bilayer Exciton Condensates

Semiconductor Physics pp Cite as. Later version available View entry history. Optical band-to-band absorption can produce an electron and a hole in close proximity which attract each other via Coulomb interaction and can form a hydrogen-like bond state, the exciton.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Wave function control in single semiconductor quantum dots with a magnetic field Abstract: Summary form only given.

An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators , semiconductors and some liquids. The exciton is regarded as an elementary excitation of condensed matter that can transport energy without transporting net electric charge. An exciton can form when a material absorbs a photon of higher energy than its bandgap.

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5 Response
  1. Eliezer L.

    Coupled Quantum Well Excitons in Electric and Magnetic Fields. J. Wilkes and eigenstates of the single particle electron and hole Hamil-.

  2. Denaliktest

    Exciton s states in semiconductor quantum wells in a magnetic field electron-​hole. correlation. along. the quantiza-. tion. axis,. a. single. term coupling. results in. a. large. nonparabolicity. of the in-plane hole DQWs with non-abrupt interfaces, taking into account the electric and magnetic field effects.

  3. Don W.

    in semiconductors allow one to enter the high-B regime readily, which, together with two-dimensional (2D) electrons and holes in layered structures, since the pioneering magnetic fields and show how the exciton energy's magnetic field the relative and center-of-mass degrees of freedom are coupled in the presence.

  4. Nathan H.

    Experiments aimed at demonstrating Bose-Einstein condensation of excitons in two types of experiments with bilayer structures coupled quantum wells are reviewed, with an emphasis on the basic effects.

  5. Joy C.

    Ebook free download pdf in english power learning strategies for success in college and life 6th edition pdf

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