The splitting of electron states in Ge/Si nanosystem with germanium quantum dots

Optical Absorption on Electron Quantum-Confined States of Perovskite Quantum Dots

“…In Formula (3), the states | 〉 and | 〉 electron are described by the electron wave functions and of an infinitely deep spherical potential well. Let us write explicitly the electron wave functions and for the states (where ) [ 33 , 34 , 35 ]. To simplify notation, let: ; ; , then: where are the spherical Bessel functions and are the polar angle defining the position of electron radius vector.…”

Theory of spatially indirect excitons in nanosystems containing double semiconductors quantum dots

“…[17]), electrons e( 1) and e( 2) with effective masses (1) were localized over the spherical surfaces of QD(A) and QD(B) in potential wells caused by Coulomb attraction (x) (6) electrons and holes (where x is the electron distance from the surface of the QD).An exciton quasimolecule with an increase in the distance D between the surfaces of the QD (condition (3) is satisfied), so that , decayed into two SIEs [17]. Such SIEs appeared when the photon with the energy smaller than the width of the bandgap = 1.17 eV) of the silicon matrix was absorbed by the nanosystem [15][16][17][18][19].With an increase in the QD radius a (so that a ≥ 22.2 nm), SIE withenergy (a) turned into 2D SIE with energy (a) = = 2 [15,16]. In this case, is the binding energy of the 2D SIE and = 2.6 nm.In refs.…”

“…In this case, is the binding energy of the 2D SIE and = 2.6 nm.In refs. [15,16] and [18,19], the energy of the SIE state (a)was measured from the bottom of the conduction band of the silicon matrix ( = ). The potential barrier ))…”

“…(2) (a). In [18,19], using the semiclassical approximation, an expression was obtained that describes the splitting Δ (a, D) = ( (1) (a) (2) (a)) of the SIE level =  …”

“…In the Ge/Si heterostructure, at distances D between the QD surfaces exceeding the splitting of electron states localized over spherical interfaces (QD is a silicon matrix) occurred.This splitting of electron states was caused by the tunneling of electrons through a potential barrier separating the double QDs. In this case, a band of localized electronic states appeared in the band gap of the silicon matrix [18,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The mini-review considers the appearance of in the Ge/Si heterostructure SIEs and exciton quasimolecules depending on the distance D between the surfaces of germanium QDs.It was shown that the binding energy of the singlet ground state of an exciton quasimolecule took on a gigantic value, exceeding the binding energy of a biexciton in a silicon single crystal by almost two orders of magnitude.It was found that, as a result of the splitting of electron levels in the chain of germanium QDs, a band of localized electron states appeared.…”