The authors of [ 10 ] assumed that this shift was caused by quantum confinement of the energy spectra of the electron and the hole localized near the spherical surface of the QD. In this case, the following problem remained open: the quantum confinement of the state of which electron and hole the hole moving in the QD volume and the electron localized at the outer spherical QD-dielectric matrix interface or the electron and hole localized in the QD volume caused such a shift in the luminescence spectrum peak?

The use of semiconductor nanosystems as the active region of nanolasers is prevented by the low binding energy of the QD exciton [ 8 , 9 , 13 ]. Therefore, studies directed at the search for nanostructures in which a significant increase in the binding energy of QD excitons can be observed are of importance.

Currently, the theory of exciton states in quasi- zero- dimensional semiconductor nanosystems has not been adequately studied. In particular, no theory exists for an exciton with a spatially separated electron and hole in quasi- zero- dimensional nanosystems. Therefore, in this study, we developed the theory of an exciton formed from a spatially separated electron and hole the hole is in the semiconductor QD volume and the electron is localized at the outer spherical surface of the QD-dielectric matrix interface [ 20 - 22 ].

It was shown that the short wavelength shift of the peak of the low temperature luminescence spectrum of samples containing zinc selenide QDs, observed under the experimental conditions of [ 10 ], was caused by quantum confinement of the ground state energy of the exciton with a spatially separated electron and hole.

The effect of significantly increasing the binding energy of an exciton with a spatially separated electron and hole in a nanosystem containing zinc selenide QDs, compared with the binding energy of an exciton in a zinc selenide single crystal by a factor of 4. It was noted [ 10 , 19 ] that at such a QD content in the samples, the interaction between charge carriers localized above the QD surfaces must be taken into account.

Therefore, in [ 23 , 24 ], we develop the theory of excitonic quasimolecules biexcitons formed from spatially separated electrons and holes in a nanosystem, which consists of ZnSe QDs synthesized in a borosilicate glass matrix. Let us consider the simple model of a quasi-zero-dimensional system, i. Let us assume that the QD valence band is parabolic.

## Excitons in Low-Dimensional Semiconductors : Theory Numerical Methods Applications - suiremolod.tk

Let us also assume that there is an infinitely high potential barrier at the spherical QD-dielectric matrix interface; therefore, the hole h cannot leave the QD volume and the electron e cannot penetrate into the QD volume in the model under study [ 20 - 22 ]. The fact that all characteristic dimensions of the problem are significantly larger than the interatomic distances a 0 ,. In this case, the exciton with the spatially separated electron and hole the hole moves within the semiconductor material and the electron lies in the borosilicate glass matrix becomes two-dimensional [ 20 - 22 ].

In the first approximation, this contribution can be disregarded.

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In this case, only the electron-hole Coulomb interaction energy 11 remains in the potential energy of the Hamiltonian 10 [ 20 - 22 ]. The Bohr radius of such a two-dimensional exciton is described by the following formula:. To determine the ground-state energy of an exciton with a spatially separated electron and hole in a nanosystem containing QDs of the radius a , we applied the variational method. When choosing the variational exciton wave function, we used an approach similar to that developed in [ 14 ].

Let us write the variational radial wave function of the exciton ground-state 1 s electron state and 1 s hole state in the nanosystem under study in the following form [ 20 - 22 ]:. Here, the coefficient A is determined from the condition of normalization of the exciton wave function 16 :. This leads to the variational exciton wave function 16 containing the Wannier-Mott two-dimensional exciton wave eigenfunction [ 33 , 34 ]. The optical properties of such nanosystems are primarily controlled by the energy spectra of electrons and holes localized near the spherical surface of individual QDs synthesized in the borosilicate glass matrix.

In this case, the problem of the quantum confinement of which electron and hole states the hole moving within the QD volume and the electron localized at the outer spherical QD-dielectric matrix interface or the electron and hole localized in the QD volume caused such a shift of the luminescence-spectrum peak remained open. The QD radius a 1 may be slightly overestimated, since the variational calculation of the exciton ground-state energy can yield slightly overestimated energies [ 33 , 34 ]. In this case, the hole moves within the QD volume and the electron is localized at the outer spherical QD-dielectric matrix interface.

Since the average energies of the interaction of the hole with its image and the average energies of the interaction of the electron with its image deliver contributions that take opposing signs to expression 21 , they significantly compensate for each other.