Medical, Pharma, Engineering, Science, Technology and Business

**Sergey I Pokutnyi ^{*}**

Chuіko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17 General Naumov Str. Kyiv UA 03164, Ukraine

- *Corresponding Author:
- Sergey I Pokutnyi

Chuіko Institute of Surface Chemistry

National Academy of Sciences of Ukraine

17 General Naumov Str. Kyiv UA 03164, Ukraine

**Tel:**380442396666

**E-mail:**[email protected] (or) [email protected]

**Received Date:** September 02, 2016;** Accepted Date:** September 14, 2016;** Published Date:** September 20, 2016

**Citation:** Pokutnyi SI (2016) Excitonic Quasimolecules in Nano Systems of Semiconductor and Dielectric Quantum Dots. Mod Chem appl 4:188. doi: 10.4172/2329-6798.1000188

**Copyright:** © 2016 Pokutnyi SI. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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A review devoted to the theory of excitonic quasimolecules (Biexcitons) (formed of spatially separated electrons and holes) in a nanosystems that consists of semiconductor and dielectric **quantum** dots synthesized in a dielectric matrix. It is shown that exciton quasimolecules formation is of the threshold character and possible in nanosystems, in with the spacing between the quantum dots surfaces is larger than a certain critical spacing. It was found that the **binding** energy of singlet ground state of exciton quasimolecules, consisting of two semiconductor quantum dots is a significant large values, larger than the binding energy of the biexciton in a semiconductor single crystal almost two orders of magnitude.

Spatially separated electron and holes; Quantum dots; Binding energy; Coulomb and exchange interaction

The idea of superatom was fruitful for the development of nanophysics [1-3] Superatom (quasiatomic nanoheterostructures) consists of a **spherical** quantum dot (QD) with radius a, the volume of that contains the semiconductor (or dielectric) material. QD is surrounded by dielectric (semiconductor) matrix [2,3]. A hole is localized in the volume of QD, and the **electron** is localized over a spherical interface (QD-matrix). In this nanosystem the lowest electronic level is in matrix, and the lowest hole level is within volume of QD. A large shift of the valence band (700 meV) generates the localization of holes in the volume of QD. A significant shift of the conduction band (about 400 meV) is a potential barrier for electrons [4] (**Figure 1**). The electrons moving in the matrix and do not penetrate in the volume of QD [2-4]. The energy of the Coulomb interaction of electron with hole and the energy of the polarization interaction of electron with interface (QDmatrix) form a potential well, in which the electron is localized over the surface of quantum dot. The certain orbitals, localized surrounding quantum dot correspond to electrons in superatom [2,3]. During investigation of the optical characteristics of nanosystems with CdS, ZnSe, Al_{2}O_{3} and Ge quantum dots in experimental papers [4-8] it was found that the electron can be localized above the surface of the QD while the hole here moves in the volume of the QD. In Ref. [4-8] the appearance of super atoms located in dielectric matrices as cores containing CdS, ZnSe, Al_{2}O_{3} and Ge quantum dots was apparently established experimentally for the first time. A substantial increase in the bond energy of the ground state of an electron in a super atom in comparison with the bond energy of an exciton in CdS, ZnSe and Al_{2}O_{3} and single crystals was detected in Ref. [2-10].

**Figure 1:** Band diagram of the QD - matrix nano hetero structure. In the nano hetero structure, the QD is a potential well for a hole and a barrier for an electron. The energies E_{c(1)}, E_{v(1)}, E_{c(2)} and E_{v(2)}, correspond to the positions of the bottom of the conduction band and the top of the valence band of the matrix and QD, respectively.

In Ref. [5-8] the optical characteristics of samples of borosilicate glasses doped with CdS, ZnSe and Al_{2}O_{3} at concentrations between x ≈ 0.003% to 1% were investigated. The average radii Ä of CdS and ZnSe QDs were in the range of Ä ≈ 2.0 - 20 nm. When there were large concentrations of CdS quantum dots in the samples (from x ≈ 0.6% to x ≈ 1%) a maximum, interpreted by the appearance of bonded QD states, was detected in the low-temperature absorption **spectra**. In order to explain the optical characteristics of such nanosystems we proposed a model of a quasimolecules representing two ZnSe and CdS QDs that form an exciton quasimolecule as a result of the interaction of electrons and holes [3,11-14].

It was noted Ref. [4-6] that, at such a QD content in the samples, one must take into account the interaction between charge carriers localized above the QD surfaces. Therefore, in Ref. [11-14], we develop the theory of a exciton quasimolecule (or biexciton) (formed from spatially separated electrons and holes) in a nanosystems that consists of ZnSe and CdS QDs synthesized in a borosilicate glassy matrix. Using the variational method, we obtain the total **energy** and the binding energy of the exciton quasimolecule (or biexciton) singlet ground state in such system as functions of the spacing between the QD surfaces and of the QD radius. We show that the biexciton formation is of the threshold character and possible in a nanosystems, in which the spacing between the QD surfaces exceeds a certain critical spacing. It is established that the spectral shift of the low-temperature luminescence peak [6] in such a nanosystem is due to quantum confinement of the energy of the biexciton ground state.

The convergence of two (or more) QDs up to a certain critical value Dc between surfaces of QD lead to overlapping of electron orbitals of superatoms and the emergence of exchange interactions [3,11-14]. In this case the overlap integral of the electron wave functions takes a significant value. As a result, the conditions for the formation of quasimolecules from QDs can be created [3,11-14]. One can also assume that the above conditions of formation of quasimolecules can be provided by external physical fields. This assumption is evidenced by results of Ref. [15,16] in which the occurrence of the effective interaction between QDs at considerable distances under conditions of electromagnetic field was observed experimentally. In Ref. [17] energies of the ground state of “vertical” and “horizontal” located pair of interacting QDs (“molecules” from two QDs) were determined as a function of the steepness of the confining potential and the **magnetic** field strength. The quantum part of nanocomputer, which was implemented on a pair of QDs (“molecules” from two QDs) with charge states is n qubits [18]. The first smoothly working quantum computer has been on QDs with two electron orbital states as qubits, described by a pseudospin 1/2. As a single cell was taken a couple of asymmetric pair QDs with different sizes and significantly different own energy. The electron, injected into the heterostructure from the channel occupied the lower level. That is, it was located in a QD with larger size. The review deals with the theory of excitonic quasimolecules (biexcitons) (formed of spatially separated electrons and holes) in a nanosystems that consists of semiconductor quantum dots synthesized in a borosilicate glass matrix. It is shown that exciton quasimolecule formation is of the threshold character and possible in nanosystem, in with the spacing between the quantum dots surfaces is larger than a certain critical spacing. It was found that the binding energy of singlet ground state of exciton quasimolecule, consisting of two semiconductor quantum dots is a significant large values, larger than the binding energy of the biexciton in a semiconductor single crystal almost two orders of magnitude.

Consider the model of nanosystems [3,11-14], containing of two superatom. In this model superatoms consist from spherical semiconductor QDs, A and B, synthesized in a matrix of borosilicate glass with dielectric constant ε_{1} . Let the QD radii be a, the spacing between the spherical QD centers be L, and the spacing between the spherical QD surfaces be D. Each QD is formed from a semiconductor material with dielectric constant ε_{2} For simplicity and without loss of generality, we assume that holes h(A) and h(B) with effective masses mh are localized in centers of QD (A) and QD(B) and electrons e(1) and e(2) with effective masses *m ^{(1)}_{e}* are localized near the spherical surfaces of QD(A) and QD(B), respectively (r

**Figure 2:** Schematic representation of a nano system consisting of two spherical QDs, QD(A) and QD(B) of radii a. The holes* h(A)* and *h(B)* are located in the QD(A) and QD(B) centers, and the electrons *e(1)* and *e(2)* are localized near the QD(A) and QD(B) surfaces r_{A(1)} is the distance of the electron *e(1)* from the QD(A) center; r_{B(2)} is the distance of the electron *e(2)* from the QD(B) center; r_{A(2)} is the distance of the electron *e(2)* from the QD(A) center; r_{B(1)} is the distance of the electron *e(1)* from the QD(B) center; r_{12} is the spacing between the electrons *e(1)* and *e(2)*; L is the spacing between the QD centers; D is the spacing between the QD surfaces; *e’(1)*, *e’(2)* and *h’(A)*, *h’(B)* are the image charges of the electrons and holes.

In such a model of the nanosystem we will study the possible formation of an exciton quasimolecule from spatially confined electrons and holes. The holes are located at the centers of QD(A) and QD(B), while the electrons are localized close to the spherical surfaces of QD(A) and QD(B). In terms of the adiabatic approximation and also in the effective mass approximation we write the Hamiltonian of such a quasimolecule in the following form [3-11].

(1)

Here and are the Hamiltonians of the superatoms. The hole h(A) is at the center of QD(A) while the electron Ðµ(1) is localized above the **surface** of QD(A); the hole h(B) is located at the center of QD(B) while the electron e(2) is localized above the surface of QD(B) respectively. The Hamiltonian of the superatom will therefore take the following form [3-11]

(2)

In (2), the first term is the kinetic energy operator of the exciton; the energy of Coulomb interaction V_{e(1)h(A)} between the electron e(1) and the hole h(A) is described by the formula [2]:

(3)

the potentials

(4)

(5)

describe the motion of quasiparticles in the nanosystem in the model of an infinitely deep potential well; and E_{g} is the band gap in the semiconductor with the permittivity ε_{2} . In [2] in the context of the modified effective mass method [19] the theory of an exciton formed from an electron and a hole spatially separated from the electron was developed (the hole was in motion within the QD and the electron was localized on the outer side of the spherical QD–matrix interface). In [2], the energy of the polarization interaction of the electron and hole with the spherical interface with the relative permittivity (ε=(ε_{2} /ε_{1})<<1), U(r_{A(1)},r_{h(A)}, a), is represented as the algebraic sum of the energies of interaction of the hole h(A) and the electron Ðµ(1) with their own (V_{h(A)h’(A)} V_{e(1)e’ (1)} and foreign V_{e(1)h(A)} V_{h(1)e’} ) images:

(7)

(8)

(9)

(10)

Here r_{h(A)} is the distance of the hole from the QD(Ð) center.

In the quasimolecule Hamiltonian (1), is the Hamiltonian of an exciton formed from an electron and a hole spaced from the electron (the hole h(B) is located in the QD (B) center and the electron e(2) is localized above the QD(B) surface). The Hamiltonian has a form similar to that of the Hamiltonian in (2):

(11)

The terms entering into the Hamiltonian (11) are expressed by formulas similar to the corresponding formulas in the Hamiltonian (2). Let us write the expression for the Hamiltonian [3-11]

(12)

Here, V_{AB(D,a)} is the energy of the interaction of charge carries (the electrons e(1) and e(2) and the holes h(A) and h(B)) with polarization fields induced by these charge carries at the QD(Ð) and QD(Ð) surfaces:

V_{e(1)h(B)} is the energy of interaction of the electron e(1) with the hole h(B); and V_{e(2)h(A)} is the energy of inter- action of the electron e(2) with the hole h(A). The last- mentioned energies are described by the expressions:

(14)

(15)

The energy of Coulomb interaction between the electrons e (1) and e(2), V_{e(1)e(2)}(r12) is determined by the formula:

(16)

and the energy of interaction between the holes h(A) and h(B) is described by the expression:

(17)

According to Ref. [2], the major contribution to the energy of the ground state of the exciton (formed by an electron and a hole spatially separated from the electron) is made by the average energy of the Coulomb interaction between the electron and hole (or) on the basis of the Coulomb – shaped variational wave functions

(18)

Here, is the variational parameter is the reduced exciton effective mass, m_{0} is the electron mass in vacuum) and the normalization constant is

(19)

where is the dimensionless QD radius,

is the Bohr radius of a two-dimensional (2D) exciton localized above the planar interface between a semiconductor with the permittivity ε_{2} and a matrix with the permittivity ε_{1} (the hole is in motion within the semiconductor, whereas the electron is in the matrix), e is the electron charge μ_{0}=m_{e}^{(1)}m_{h})/m_{e}(1)+m_{h}) is the reduced 2D- exciton effective mass.

The above-mentioned feature allows us to retain only the energies of the Coulomb interaction between the electron and hole V_{e(1)h(A)} (r_{A (1)} , (3) and V_{e(2)h(B)} (r_{B (2)} , determined by a formula similar to (3), correspondingly, in the Hamiltonians (2) and [14] and to retain only the energy of the interaction between the holes h(A) and h(B) V_{h(A)h(B)} (D,a) [17] in the interaction energy V_{AB}(D,a) [13]. At the same time, the energy V_{AB}(D,a) is determined by the formula (17):

(20)

With the above assumptions, the superatom Hamiltonians (2) and (11) take the form:

(21)

(22)

In this case, the quasimolecule Hamiltonian involves the superatom Hamiltonians (21) and (22) as well as the Hamiltonian (15), in which (12), in which the interaction energy V_{AB}(D,a) is determined by formula (20).

On the assumption that the spins of electrons e (1) and e (2) are antiparallel we write the normalized wave function of the singlet ground state of the exciton quasimolecule in the form of a linear combination of wave functions and [11-14]

(23)

Considering that electrons e(1) and e(2) move independently of each other we represent wave functions and (23) as the product of one-electron variational wave functions and and alsoand respectively [3,11-14]

(24)

(25)

We represent the one-electron wave functions r_{A(1)} and ( r_{B(2)} that describe, correspondingly, the electron e(1) localized above the QD(A) surface and the electron e(2) localized above the QD(B) surface and the wave functions that describe, correspondingly, the electron e(2) localized above the QD(A) surface and the electron e(1) localized above the QD(B) surface as variational Coulomb-shaped wave functions [11]

(26)

(27)

(28)

(29)

Because of the identity of the electrons, the wave function ( r_{A(2)},r_{B(1)} (25) is equivalent to the wave function In (23), the overlapping integral S (D,a) is determined by the formula

(30)

where is the volume element of the electron e(1).

In the first approximation, the energy of the exciton quasimolecule singlet ground state is defined by the average value of the Hamiltonian on the basis of states described by the zero-approximation wave functions [11]

(31)

With the explicit form of the wave functions (23) – (29), the energy **functional** of the exciton quasimolecule singlet ground state takes the form

(32)

Here, is the energy functional of the exciton ground state (for the exciton formed from an electron and a hole spatially separated from the electron):

(33)

The second term in (32) is a functional E_{B}(D,a) the binding energy of singlet ground state of excitonic quasimolecule. In the functional determined by formula (32), is determined by the expression (here

(34)

The functional (34) can be represented as the algebraic sum of the functionals of the average energies of Coulomb interaction [11].

In the functional described by (32), is determined by the formula

(35)

The functional (35) can be represented as the algebraic sum of the functionals of the average energies of the exchange interaction [11].

In the case it spins of e(1) and e(2) electrons are parallel than similarly to the theory of the chemical bond of hydrogen molecule [20] the excitonic quasimolecule, consisting of two QDs is not formed [14]. Therefore, we did not consider this case.

Within the framework of the variational method at a first approximation the total energy of ground singlet state of excitonic quasimolecule is determined by average value of the Hamiltonian Ä¤(1) for states, which are described by wave functions of the zero approximation [14]:

(36)

Where E_{B}(D,a) is the binding energy of singlet ground state of excitonic quasimolecule and the binding energy of E_{ex}(a) of ground state of electron in superatom, found in Ref. [2-9]. The wave function ψs r_{A(1)}, r_{A(2)}), r_{B(1)}, r_{B(2)} [21] contains wave functions. The results of a numerical variational calculation of the binding energy E_{B}(D, a) of ground singlet state of excitonic quasimolecule, containing two CdS QDs with average radii of ε_{2} =9.3, effective hole mass in QD (m_{h}/m_{0} is 5)), grown in a matrix of borosilicate glass ε_{1} =2 the electron effective mass in the matrix (m_{e}^{(1)}/m_{0}) is 0.537)), which was investigated in experimental work [5,6] are shown in **Tables 1** and **2** [14].

Dnm |
||||
---|---|---|---|---|

4 | -320 | 1.8 | 0 | -640 |

4 | -320 | 2.2 | -27 | -667 |

4 | -320 | 2.6 | -28.1 | -668.1 |

4 | -320 | 3 | -27.8 | -667.8 |

4 | -320 | 4 | -23.2 | -663.2 |

4 | -320 | 6 | -9.5 | -649.5 |

4 | -320 | 8.4 | 0 | -640 |

**Table 1:** Dependence of the binding energy and also the total energy of the singlet ground state of the excitonic quasimolecule, consisting of two CdS QDs with average radii 4nmon the distance D between the surfaces of the QD. In this case the binding energies of an electron in a superatoms are

nm | mev | D nm |
meV |
meV |
---|---|---|---|---|

4.4 | -344 | 1.6 | 0 | -688 |

4.4 | -344 | 2.2 | -29.4 | -717.4 |

4.4 | -344 | 2.48 | -32.8 | -720.8 |

4.4 | -344 | 2.6 | -31.9 | -719.9 |

4.4 | -344 | 3 | -28.9 | -716.9 |

4.4 | -344 | 4 | -24.4 | -712.4 |

4.4 | -344 | 6 | -13.2 | -701.2 |

4.4 | -344 | 8 | -3.4 | -691.4 |

4.4 | -344 | 9.8 | 0 | -688 |

**Table 2:** Dependence of the binding energy and also the total energy of the singlet ground state of the excitonic quasimolecule, consisting of two CdS QDs with average radii on the distance D between the surfaces of the QD. In this case the binding energies of an electron in a superatoms are

In Ref. [5,6], we studied the optical properties of the samples of borosilicate glass, doped with CdS with concentrations from x≈0,003% to 1%. The average **radius** of CdS QDs was ranged At concentrations CdS QD in the order of x≈0,6% to x≈1% the peak, which is (E-E_{g}) ≈ -712meV was found in the absorption spectra of the samples at a temperature of 4 K (where E_{g} is width band gap of CdS QD) [6]. The variational method, used for estimation of the binding energy E_{B}(D,a) of ground singlet state of excitonic quasimolecule will be valid if the binding energy E_{B}(D,a) of quasimolecule is small, compared with the binding energy Eex(a) of the ground state of superatom [11-14].

(37)

Binding energies E_{B}(D,a) of ground singlet state of excitonic quasimolecule, containing two CdS QDs with average radii of =4nm and =4.4nm have a minimum for a **distance** and meV for a distance and correspond to critical temperatures

Tc(1) ≈ 326 K and Tc(2) ≈ 380 K) (**Tables 1** and **2**) [14]. Binding energies of the ground state of electron of superatoms are and [9]. In this case energies of singlet ground state (4) of the excitonic quasimolecule are (**Tables 1** and **2**). From a comparison of the total energy of quasimolecule with a maximum (E-E _{g}) ≈ -712 meV we get the value of the distance D3≈4.0nm between QDs [14]. Criterion [11] of the applicability of used variational estimation of the binding energy E_{B} (D, a) of the quasi-molecule is implemented

With increasing of QDs radius a the binding energy E_{ex}(a) of the ground state of electron in a superatom increases [2-9]. The average size of the state of electron in the superatom decreases. Therefore the distance, for which the square of the overlapping integral S(D, a) of the one-electron wave functions takes on a maximum value. Also it decreases with increasing of QD radius a, and so the distance between surfaces of QD D_{2} is less than D_{1}. As a result, with increasing of QD radius a also the maximum value of the binding energy of singlet ground state of excitonic quasimolecule E_{B}(D,a) increases (i.e .E_{B} (2) more E_{B} (1). In this case, criterion [11] of the applicability of used variational estimation of the binding energy E_{B}(D,a) of the quasimolecule is implemented [14].

Thus, proposed model of excitonic quasimolecule [14] let us to explain the optical properties of nanosystems, consisting of CdS QDs, grown in a borosilicate glass matrix [5,6] in particular, the appearance of a peak (E-E_{g}) ≈ -712meV in the absorption spectra of the samples at 4 K. It should be noted that the binding energy E_{ex}(a) of the ground state of an electron in superatom [2,9] can be applicable only for values of binding energy E_{ex}(a) for which the inequality

(38)

is correctly, where ∇V is the depth of the potential well for electron and hole in a QD. In the experimental work [5] it found that for CdS QDs with radii of a ≤ 20 nm ∇V = 2.5 eV. This condition (38) makes it possible to consider the motion of electron and hole in the superatom, using QD model as an infinitely deep potential well [2-9] (**Figure 1**). In the Hamiltonian (1) of quasimolecule members, causing fluctuations of QD in quasimolecule were not considered. The obtained quasimolecule binding energies (**Tables 1** and **2**) are significantly higher than typical energy of QD fluctuations. Therefore, it is not adjusting for QD in this quasimolecule model is warranted.

From **Tables 1** and **2**, it is following that the excitonic quasimolecule, consisting of two QD occurs, starting from the distance between surfaces of for QD with a radius of and for QD with a radius of Ä_{2}=4.4nm [14]. The formation of such quasimolecule is threshold character. It is possible only for nanosystems, containing QD with average radii of Ä_{1} and Ä_{2} in which the distance D between surfaces of QDs exceeds some critical distance D_{c}^{(1)}. The existence of such critical distance D_{c}^{(1)}. is associated with dimensional quantum effect, for which a decreasing of distance D between surfaces of QDs led to decrease in the interaction energies of electrons and holes in the Hamiltonian (1) of quasimolecule can not compensate the increase in the kinetic energy of electrons. With the increase in the distance D between surfaces of QDs, starting from values for QD with a radius of Ä_{2} =4.4nm and for QD with a radius of Ä_{2} =4.4nm the excitonic quasimolecule splits into two superatoms.

Thus, the excitonic quasimolecule of nanosystem may occur when the condition is realized (**Tables 1** and **2**) [14]. In addition, quasimolecule can exist only at temperatures below a certain critical temperature Tc_{(1)} ≈ 326 K and Tc_{(2)} ≈ 380 K) Biexcitons arose in CdS single-crystal with a binding energy E _{b} ≈ 0.59 mev [11].

The binding energies and of excitonic quasimolecule are significant exceeding E_{B} almost two orders of magnitude. Apparently the latter fact opens the possibility of observing such excitonic quasimolecules at room temperature. The energy of the exchange interaction between electrons and holes main contributes to the binding energy of excitonic quasi-molecule, which is significantly greater than that for energy of the Coulomb interaction between electrons and holes (i.e., their ratio ≤ 0,11). The estimations of the binding energy E_{B}(D,a) of the singlet ground state of quasi-molecule are variational and may give low values of the binding energy E_{B}(D,a) and

The binding energies of the exciton quasimolecule consisting of two CdS QDs acquires an anomalously high value that exceeds the bond energy EB of the biexciton in CdS by almost two orders of magnitude. Such an effect opens up the possibility of using the exciton quasimolecules as active medium in nanolasers emitting in the infrared region and operating on exciton transitions at room temperatures in the elementary base of quantum nanocomputers [17,18,21]. The presented results demonstrate the fundamental possibility of creating novel quasi atomic nanosystems in the form of exciton quasimolecules, including natural systems with new physical characteristics [3,11- 14]. On their basis it is possible to construct new nanosystems or quasicrystals in which control of the symmetry and **lattice** constant will make it possible to realize unique physical effects and phenomena and to create new principles in materials behavior.

- Ashoori RC(1996) Electrons in artificial atoms.Nature 379: 413-415.
- Pokutnyi SI (2013) On an exciton with a spatially separated electron and hole in quasi-zero-dimensional semiconductor nanosystems.Semiconductors4
**7**:791-798. - Pokutnyi SI (2014) Theory ofexcitons and excitonic quasimolecules formed from spatially separated electrons and holes in quasi-zero-dimensional nanosytems.Optics 1:10-21.
- Yakimov AI, Dvurechensky AV (2001) Effects of electron-electron interaction in the optical properties of dense arrays of quantum dots Ge/Si.JETP 119: 574-589.
- Grabovskis V, Dzenis Y, Ekimov A (1989) Photo ionization of semiconductor microcrystals in glass.Sov PhysSolid State.31: 272-275.
- Bondar N (2010) Photoluminescence quantum and surface states of excitons in ZnSe and CdSnano clusters.Journal ofLuminescence 130: 1-7.
- Ovchinnikov OV, Smirnov MS, Shatskikh TS (2014) Spectroscopic investigation of colloidal CdS quantum dots methylene blue hybrid associates.J Nanopart Res 16:2286-2292.
- Dzyuba VP, Kulchin YN, Milichko VA(2013) Quantum size states of a particle inside the nanospheres AdvancedMaterial ResearchA 677:42-48.
- Pokutnyi SI(2013) Binding energy of the exciton with a spatially separated electron and hole in quasi-zero-dimensional semiconductor nanosystems.Technical Physics Letters 39: 233-235.
- Pokutnyi SI, Kulchin YN, Dzyuba VP (2015) Binding energy of excitons formed from spatially separated electrons and holes in insulating quantum dots.Semiconductors 49:1311-1315
- Pokutnyi SI (2013) Biexcitons formed from spatially separated electrons and holes in quasizero dimensionalsemiconductor nanosystems Semiconductors 47: 1626-1635.
- Pokutnyi SI, Salejda W (2015) Theory ofexcitons and excitonic quasimolecules formed from spatially separated electrons and holes in quasi-zero-dimensional nanostructures. pp: 10-21
- Pokutnyi SI, Kulchin YN, Dzyuba VP (2016) Excitonic quasimolecules in quasi-zero-dimensional nanogeterostructures. Theory Pacific Science ReviewA 17:11-13.
- Pokutnyi SI(2016) Quantum chemical analysis of system consisting of two CdS quantum dots.Theoretical and Experimental Chemistry52:27-32.
- Lalumiure K, Sanders B, VanLoo F (2013)Input - output theory for waveguide QED with an ensemble of inhomogeneous atoms.Phys Rev A 88: 43806-43811.
- VanLoo F, Fedorov A, Lalumiure K (2013) Photon-mediated interactions between distant artificial atoms.Science 342: 1494-1496.
- Lozovik YE (2014) Electronic and collective properties of topological insulators.Advanc Phys Scienc 57: 653-658.
- Valiev K (2005) Quantum computers and quantum computing.Advanc Phys Scienc48: 1-22.
- Pokutnyi SI (2007) Exciton states in semiconductor quantum dots in the framework of the modified effective mass method. Semiconductors 41: 1323-1328.
- Schiff L (1955) Quantum Mechanics. McGraw-Hill Book Company Inc., New York, Toronto, London.
- Pokutnyi SI, Ovchinnikov OV, Kondratenko TS (2016)Absorption of light by colloidal semiconductor quantum dots.J Nanophotonics10: 033506-1-033506-9.

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**Analytical Chemistry**

August 29-30, 2018 Toronto, Canada - International Conference on
**Pharmaceutical Chemistry**

Oct 31- Nov 01, 2018 San Francisco, USA

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Peer Reviewed Journals

International Conferences
2018-19