On the theory of the binding energy of exciton quasimolecules in germanium/silicon double quantum dots

A theory of exciton quasimolecules (formed from spatially separated electrons and holes) in a nanosystem consisting of double quantum dots (QDs) of germanium synthesized in a silicon matrix is presented. It is shown that the binding energy of the singlet ground state of the quasimolecule of an exciton is considerably larger than the binding energy of biexciton in a silicon single crystal by almost two orders of magnitude. It is shown that the exciton quasimolecule formation is of the threshold character and possible in a nanosystem, where D is the distance between the surfaces of QD that satisfies the following condition: (where and are some critical distances). Using the variational method, we obtain the binding energy of the exciton quasimolecule singlet ground state of the system as a function of the distance between the surfaces of QD D, and the QD radius a. It is shown that the convergence of two QDs up to a certain critical value of the distance between the surfaces of QD DC leads to the effective overlapping of the electron wave functions and the appearance of exchange interactions. As a result, the exciton quasimolecules can be formed from the QDs. It is shown that the existence of such a critical distance DC arises from the quantum size effects. Dimensional quantization of electrons and holes motion leads to the following fact: as the distance between the surfaces of the QD DC decreases, the decrease in the energies of interaction of the electrons and holes entering into the Hamiltonian of the exciton quasimolecule cannot compensate for the increase in the kinetic energy of the electrons and holes. At larger values of the distance between the surfaces of the QD D, , the exciton quasimolecule breaks down into two excitons (consisting of spatially separated electrons and holes), localized over the QD surfaces. The fact that the energy of the ground state of singlet excitonic quasimolecule is in the infrared range of the spectrum, presumably, allows us to use a quasimolecule for the development of new elements of silicon infrared nanooptoelectronics.