Hole states in Ge∕Si quantum-dot molecules produced by strain-driven self-assembly

Abstract

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.

Optical study of strained double Ge/Si quantum dot layers

“…In the range hν < 1.0 eV, we observed two bands ascribed to transitions related to the Ge QDs. In a previous study on the samples used in this work, cross-section transmission electron microscopy revealed the presence of QDs in each Ge layer [6]. The assignment of the optical transitions is supported by numerical calculations [5].…”

Sb-mediated Ge quantum dots in Ti–oxide–Si diode: negative differential capacitance

“…At the same time, if the QDs are small enough, they can confine down to single electrons in individual QDs, which makes them promising candidates for Si-compatible spin-based quantum information processing [2]. There have also been suggestions that they might serve as building blocks for quantum information processing, due to entanglement of confined electrons, holes or excitons, in case the QDs are coupled [3]. …”

Increased conductance of individual self-assembled GeSi quantum dots by inter-dot coupling studied by conductive atomic force microscopy

“…As the efficiency of single-layer QDs is relatively low, vertically aligned multilayer QDs are often adopted for practical applications [ 3 - 6 ]. By repeating dot layers separated by spacer layers with a few nanometers in thickness, a more homogeneous size distribution could be achieved, simultaneously with novel physical properties induced by coupling [ 7 , 8 ]. The coupling effects between the vertically aligned QDs have been investigated by various macroscopic techniques such as photoluminescence (PL) and admittance spectroscopies [ 6 , 8 - 13 ], which are found to be strongly dependent on the thickness of the spacer layer.…”

“…By repeating dot layers separated by spacer layers with a few nanometers in thickness, a more homogeneous size distribution could be achieved, simultaneously with novel physical properties induced by coupling [ 7 , 8 ]. The coupling effects between the vertically aligned QDs have been investigated by various macroscopic techniques such as photoluminescence (PL) and admittance spectroscopies [ 6 , 8 - 13 ], which are found to be strongly dependent on the thickness of the spacer layer. On the other hand, both high-density QDs and QD molecules have attracted a lot of interests for their potential applications [ 3 , 14 ], where the lateral couplings between adjacent QDs significantly modify the QDs’ properties.…”