Excitons and exciton quasimolecules states in nanosystems of semiconductor quantum dots

Abstract

Within the framework of the modified effective mass method, a theory of an exciton quasimolecule (formed from spatially separated electrons and holes) is developed for nanosystems consisting of germanium quantum dots grown in silicon matrices. In an artificial quasi-molecule, the holes are located in the volumes of germanium quantum dots, and the electrons, moving in a silicon matrix, are localized above the spherical surface of germanium quantum dots. The variational method is used to derive the dependences of the total energy, as well as of the binding energy of the ground singlet state of the exciton quasimolecule, on the distance D between the surfaces of the quantum dots, as well as on the radius  of the quantum dot. It is shown that the main contribution into the binding energy of an exciton quasimolecule is made by the energy of the exchange interaction of an electron with holes, which substantially exceeds the contribution that causes the energy of the Coulomb interaction of an electron with holes. It has been found that the appearance of an exciton quasimolecule in a nanosystem has a threshold character, and possibly in a nanosystem where the distance D between the surfaces of quantum dots exceeds the value of a certain critical distance D_c⁽¹⁾. It is shown that an excitonic quasimolecule in a nanosystem can exist only at temperatures below a certain critical temperature T_c. At temperatures below the critical temperature T˂T_c, the exciton quasimolecule splits into two artificial atoms (from space-separated electrons and holes). It has been found that the binding energy of the ground singlet state of an exciton quasimolecule, consisting of two quantum dots of germanium, is an essential quantity that exceeds the binding energy of biexciton in a silicon single crystal by almost two orders of magnitude.