Space-charge spectroscopy has been used to study the hole energy spectrum of an array of Ge quantum dots ͑QD's͒ coherently embedded in a Si matrix and subjected to a ruby laser ͑ = 694 nm͒ nanosecond irradiation ex situ. The laser energy density in a single pulse was near the melting threshold of the Si surface. The number of laser pulses was varied from 1 to 10, and the duration of each pulse was 80 ns. From the capacitance-voltage characteristics, temperature-and frequency-dependent admittance measurements, the energies of holes confined in Ge QD's were determined. The pulsed laser annealing was found to result in a deepening of the hole energy level relative to the bulk Si valence band edge and in a decrease of the hole energy dispersion. After the treatment with ten laser pulses, the spread of the hole energies due to varying sizes of the QD's within the ensemble was reduced by a factor of about 2. The obtained results give evidence for a substantial reduction of the QD's size dispersion and for a narrowing distribution of the hole energy levels stimulated by nanosecond laser irradiation. A possible explanation of the improved uniformity of QD's sizes involves dissolving small size Ge QD's in a Si matrix by pulsed laser melting of the Ge nanoclusters and their subsequent intermixing with surrounding solid Si.

Space-charge spectroscopy was employed to study hole emission from the confined states in vertically self-aligned double Ge quantum dots separated by a Si barrier. From the temperature- and frequency-dependent measurements, the hole binding energy was determined as a function of the separation between the dots, tSi. Increasing of the ground state hole energy due to formation of a bonding molecular orbital was found to be as large as ∼50meV at tSi=1.5nm. For a dot layer separation exceeding 3nm, the hole binding energy in double-dot molecule becomes smaller than the ionization energy of the single Ge dot, contrasting with a simplified quantum-mechanical molecular model. To analyze the experiment the electronic structure of two vertically coupled pyramidal Ge quantum dots embedded in Si was investigated by a nearest neighbor tight-binding single-particle Hamiltonian with the sp3 basis. The elastic strain due to the lattice mismatch between Ge and Si was included into the problem. The three-dimensional spatial strain distribution was found in terms of atomic positions using a valence-force-field theory with a Keating interatomic potential. It was demonstrated that formation of single-particle hole states in self-organized molecules is governed by the interplay among two effects. The first is the quantum-mechanical coupling between the individual states of two dots constituting the molecule. The second one originates from asymmetry of the strain field distribution within the top and bottom dots due to the lack of inversion symmetry with respect to the medium plane between the dots. Analysis of the biaxial strain distribution showed that anomalous decreasing of the hole binding energy below the value of the single dot with increasing interdot separation is caused by the partial strain relaxation upon dot stacking accompanied by the strain-induced reduction of the hole confinement potential. We found that the molecule-type hole state delocalized fairly over the two dots is formed only at tSi<3.3nm and at tSi>3.8nm. For the intermediate distances (3.3nm⩽tSi⩽3.8nm), the hole becomes confined mostly inside the bottom, most strained Ge dot. The overall agreement between theory and experiment turns out to be quite good, indicating the crucial role played by strain fields in electronic coupling of self-assembled quantum-dot molecules.

We study the ground state of a hole confined in two vertically coupled GeSi/Si quantum dots as a function of the interdot distance and dot composition within the sp(3) tight-binding approach. Both quantum-mechanical tunneling and inhomogeneous strain distribution are included. For pure Ge dots, the strain is found to have two effects on the hole binding energy: (i) reduction of the binding energy below the value of the single dot with increasing dot separation and (ii) molecular bond breaking for intermediate interdot distances and posterior bond restoration at larger distance. Both effects are smeared upon Ge-Si intermixing.