Spin states of holes in Ge/Si nanowire quantum dots

We investigate tunable hole quantum dots defined by surface gating Ge/Si core-shell nanowire heterostructures. In single level Coulomb-blockade transport measurements at low temperatures spin doublets are found, which become sequentially filled by holes. Magnetotransport measurements allow us to extract a g factor g approximately 2 close to the value of a free spin-1/2 particle in the case of the smallest dot. In less confined quantum dots smaller g factor values are observed. This indicates a lifting of the expected strong spin-orbit interaction effects in the valence band for holes confined in small enough quantum dots. By comparing the excitation spectrum with the addition spectrum we tentatively identify a hole exchange interaction strength chi approximately 130 microeV.     

Phonons in Ge/Si superlattices with Ge quantum dots

Ge/Si superlattices containing Ge quantum dots were prepared by molecular beam epitaxy and studied by resonant Raman scattering. It is shown that these structures possess vibrational properties of both two-and zero-dimensional objects. The folded acoustic phonons observed in the low-frequency region of the spectrum (up to 15th order) are typical for planar superlattices. The acoustic phonon lines overlap with a broad emission continuum that is due to the violation of the wave-vector conservation law by the quantum dots. An analysis of the Ge and Ge-Si optical phonons indicates that the Ge quantum dots are pseudoamorphous and that mixing of the Ge and Si atoms is insignificant. The longitudinal optical phonons undergo a low-frequency shift upon increasing laser excitation energy (2.54–2.71 eV) because of the confinement effect in small-sized quantum dots, which dominate resonant Raman scattering.     

Electronic structure of double Ge quantum dots in Si

Theoretical investigations of the electronic structure of elastically stressed double Ge quantum dots in Si performed in the six-band kp approximation with the Bir-Pikus Hamiltonian and with the configuration interaction method are reviewed. The existence of the antibonding ground state of holes has been revealed. It has been found that, when quantum dots approach each other, the exchange energy of two-particle states has a minimum at the point of the intersection of bonding and antibonding levels; the singlet and triplet states at this point are degenerate. For the lowest spin singlet, it has been revealed that Coulomb correlations in the motion of two holes are manifested in the localization of the two-particle wavefunction at opposite quantum dots when the distance between the dots increases. It has been shown that the degree of entanglement of the singlet quantum states reaches 50% in the case of the manifestation of such spatial correlations.     

Luminescence study of Si/Ge quantum dots

We present a photoluminescence (PL) study of Ge quantum dots embedded in Si. Two different types of recombination processes related to the Ge quantum dots are observed in temperature-dependent PL measurements. The Ge dot-related luminescence peak near 0.80 eV is ascribed to the spatially indirect recombination in the type-II band lineup, while a high-energy peak near 0.85 eV has its origin in the spatially direct recombination. A transition from the spatially indirect to the spatially direct recombination is observed as the temperature is increased. The PL dependence of the excitation power shows an upshift of the Ge quantum dot emission energy with increasing excitation power density. The blueshift is ascribed to band bending at the type-II Si/Ge interface at high carrier densities. Comparison is made with results derived from measurements on uncapped samples. For these uncapped samples, no energy shifts due to excitation power or temperatures are observed in contrast to the capped samples.     

Binding of electron states in multilayer strained Ge/Si heterostructures with type-II quantum dots

Mechanical strains in a multilayer Ge/Si(001) heterostructure with vertically aligned Ge nanoclusters (quantum dots) are calculated using an interatomic potential based on the Keating valence-force-field model. It is found that the nonuniform spatial elastic strain distribution in this medium gives rise to a three-dimensional potential well for electrons in the strained Si layers near Ge nanoclusters. The depth of the potential well reaches 100 meV, and its spatial dimensions are determined by the diameter of the Ge nanoclusters. For a structure consisting of four Ge islands 23 nm in diameter arranged one above another, the electron binding energies in this well and the spatial electron density distribution are determined. The ground state has an s-like symmetry and is characterized by an electron binding energy of ～95 and ～60 meV for the elemental composition of Ge in the nanoclusters c = 1 and c = 0.7, respectively. The existence of bound electron states in the conduction band of strained Si must lead to a relaxation of the selection rules that determine the low efficiency of the radiative recombination in indirect-gap semiconductors. This explains the high value of the oscillator strength observed for the interband transitions in multilayer Ge/Si(001) structures with vertical correlation of the arrangement of Ge nanoclusters.     

Folded acoustic phonons in Si/Ge superlattices with Ge quantum dots

The spectra of Raman scattering by folded acoustic phonons in Si/Ge superlattices with pseudomorphic layers of Ge quantum dots (QDs) grown by low-temperature (T = 250°C) molecular beam epitaxy are studied. New features of the folded phonon lines related to the resonant enhancement and unusual intensity ratio of the doublet lines that cannot be explained by the existing theory have been observed. The observed modes are shown to be related to the vibrations localized to the QDs and induced by the folded phonons of the Si spacer layers. The calculations performed in the model of a one-dimensional chain of atoms have allowed the nature of the localization of acoustic phonons attributable to a modification of the phonon spectrum of a thin QD layer to be explained. The observed intensity ratio of the folded phonon doublet lines is caused by asymmetry of the relief of the QD layers.     

Longitudinal conductivity of Ge/Si heterostructures with quantum dots

The conductance along an island layer of Ge quantum dots buried in silicon was investigated. The sizes of the islands varied in the range D ≈ 12−19 nm. It was found that the charge transport is characterized by two activation energies. The first one is associated with the thermal emission of holes from Ge quantum wells into the valence band of Si. The second one is due to the tunneling of holes between islands under Coulomb blockade conditions and is determined by the electrostatic charging energy of a quantum dot. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 423–426 (25 March 1996)     

Excitons in Ge/Si double quantum dots

The spatial structure of excitons and the oscillator strength characterizing the intensity of interband optical transitions in vertically coupled Ge/Si quantum dots have been theoretically studied. It has been found that the probability of the exciton transition under certain conditions (the sizes of the quantum dots, the separation of the dots) can be much larger (up to a factor of 5) than the value for the case of single quantum dots. It is expected that the results will make it possible to approach the creation of efficient light-emitting and photoreceiving devices based on Si and Ge indirect-band semiconductors.     

Resonant Raman scattering of discrete hole states in self-assembled Si/Ge quantum dots

We report the first resonant electronic Raman spectroscopy study of discrete electronic transitions within small p-doped self-assembled Si/Ge quantum dots (QDs). A heavy hole (hh) to light hole (lh) Raman transition with a dispersionless energy of 105 meV and a resonance energy of the hh states to virtually localised electrons at the direct band gap of 2.5 eV are observed. The hh–lh transition energy shifts to lower values with increasing annealing temperature due to significant intermixing of Si and Ge in the QDs. Structural parameters of the small Si/Ge dots have been determined and introduced into 6-band k·p valence band structure calculations. Both the value of the electronic Raman transition of localised holes as well as the resonance energy at the E₀ gap are in excellent agreement with the calculations.     

Hole states in artificial molecules formed by vertically coupled Ge/Si quantum dots

In the tight binding approximation, the spatial configuration of the ground state and the binding energy of a hole in a “diatomic” artificial molecule formed by vertically coupled Ge/Si(001) quantum dots are studied. The inhomogeneous spatial distribution of elastic strain arising in the medium due to the lattice mismatch between Ge and Si is taken into account. The strain is calculated using the valence-force-field model with a Keating interatomic potential. The formation of the hole states is shown to be determined by the competition of two processes: the appearance of a common hole due to the overlapping of “atomic” wavefunctions and the appearance of asymmetry in the potential energy of a hole in the two quantum dots because of the superposition of the elastic strain fields from the vertically aligned Ge nanoclusters. When the thickness of the Si layer separating the Ge dots (t _Si) is greater than 2.3 nm, the binding energy of a hole in the ground state of the two-dot system proves to be lower than the ionization energy of a single quantum dot because of the partial elastic stress relaxation due to the coupling of the quantum dots and due to the decrease in the depth of the potential well for holes. For the values of the parameter t _Si, an intermediate region is revealed, where the covalent molecular bond fails and the hole is localized in one of the two quantum dots, namely, in the dot characterized by the highest strain values.     

Micro-Raman scattering by laser-modified structures with Ge/Si quantum dots

Structures with self-assembled Ge/Si quantum dots grown by molecular-beam epitaxy are exposed to pulsed radiation of a picosecond laser. Changes in the vibrational spectrum of nanostructures under an external action are studied by Raman spectroscopy. An analysis of the Raman spectra measured with a micron spatial resolution along the exposed region indicates a mixing of Ge and Si atoms and a change in the induced mechanical stresses in quantum dots.     

Optical absorption spectra of Si with Ge quantum dots

The results of calculations of optical absorption spectra of silicon containing Ge nanoclusters of spherical shape and different size are reported. The optical transitions from the Ge cluster levels to the silicon bulk energy band states are analyzed.     

Atomic structure of Ge quantum dots on the Si(001) surface

In situ morphological investigation of the “105” faceted Ge islands on the Si(001) surface (hut clusters) have been carried out using an ultra high vacuum instrument integrating a high resolution scanning tunnelling microscope and a molecular beam epitaxy vessel. Both species of hut clusters-pyramids and wedges-were found to have the same structure of the “105” facets which was visualized. Structures of vertexes of the pyramidal clusters and ridges of the wedge-shaped clusters were revealed as well and found to be different. This allowed us to propose a crystallographic model of the “105” facets as well as models of the atomic structure of both species of the hut clusters. An inference is made that transitions between the cluster shapes are impossible.     

Suppression of hole relaxation in small Ge/Si quantum dots

We study the effect of quantum dot size on the mid-infrared photocurrent, photoconductive gain, and hole capture probability in ten-period p-type Ge/Si quantum dot heterostructures. The dot dimensions are varied by changing the Ge coverage during molecular beam epitaxy of Ge/Si(001) system in the Stranski–Krastanov growth mode while keeping the deposition temperature to be the same. A device with smaller dots is found to exhibit a lower capture probability and a higher photoconductive gain and photoresponse. The integrated responsivity in the mid-wave atmospheric window (λ = (3–5) μm) is improved by a factor of about 8 when the average in-plane dot dimension changes from 18 to 11 nm. The decrease in the dot size is expected to reduce the carrier relaxation rate due to phonon bottleneck by providing strong zero-dimensional quantum mechanical confinement.     

Spatial distribution of elastic deformations in Ge/Si structures with quantum dots

A method is developed for calculating the elastic deformation in coherently strained heterostructures on the basis of the valence force field (VFF) model using the Green’s function of the “atomistic” elastic problem. The spatial distribution of the elastic deformations in a Ge/Si system with pyramidal Ge quantum dots buried in a Si matrix is investigated theoretically. The deformation distribution in and around the pyramids is determined. Near quantum dots, the region near the tip of the pyramid is most strongly intensely. Inside quantum dots the region of the vertex is most relaxed, and the most strained section lies on the contour of the pyramid base. Compression occurs in the plane of the pyramid base inside quantum dots, and stretching occurs along the vertical direction. The picture is reversed near quantum dots: stretching occurs in the lateral direction and compression in the vertical direction. It is shown that the local deformations and their spatial distribution are essentially independent (to within the scaling) of the size of the quantum dots for 10–15 nm pyramid bases.     

Ge/Si quantum dots in external electric and magnetic fields

Electric field-induced splitting of the lines of exciton optical transitions into two peaks is observed for Ge/Si structures with quantum dots (QDs). With increasing field, one of the peaks is displaced to higher optical transition energies (blue shift), whereas the other peack is shifted to lower energies (red shift). The results are explained in terms of the formation of electron-hole dipoles of two types differing in the direction of the dipole moment; these dipoles arise due to the localization of one electron at the apex of the Ge pyramid and of the other electron under the base of the pyramid. By using the tight-binding method, the principal values of the g factor for the hole states in Ge/Si quantum dots are determined. It is shown that the g factor is strongly anisotropic, with the anisotropy becoming smaller with decreasing QD size. The physical reason for the dependence of the g factor on quantum-dot size is the fact that the contributions from the states with different angular-momentum projections to the total wave function change with the QD size. Calculations show that, with decreasing QD size, the contribution from heavy-hole states with the angular-momentum projections ±3/2 decreases, while the contributions from light-hole states and from states of the spin-split-off band with the angular-momentum projections ±1/2 increase.     

Photoconductivity of Si/Ge/SiO<Subscript>x</Subscript> and Si/Ge/Si structures with germanium quantum dots

A nonmonotonic dependence of the lateral photoconductivity (PC) on the interband light intensity is observed in Si/Ge/Si and Si/Ge/SiO_x structures with self-organized germanium quantum dots (QDs): in addition to a stepped increase in PC, a stepped decrease in PC is also observed. The effect of temperature and drive field on these features of the PC for both types of structures with a maximum nominal thickness of the Ge layer (N_Ge) is studied. The results obtained are discussed in the context of percolation theory for nonequilibrium carriers localized in different regions of the structure: electrons in the silicon matrix and holes in QDs.     

Zeeman effect for holes in a Ge/Si system with quantum dots

The tight binding approximation is employed to study the Zeeman effect for the hole ground state in a quantum dot. A method is proposed for calculating the g factor for localized states in a quantum dot. This method can be used both for hole states and for electron states. Calculations made for a Ge/Si system with quantum dots show that the g factor of a hole in the ground state is strongly anisotropic. The dependence of the g factor on the size of a germanium island is analyzed and it is shown that anisotropy of the g factor increases with the island size. It is shown that the value of the g factor is mainly determined by the contribution of the state with the angular momentum component J _z =±3/2 along the symmetry axis of the germanium island.     

Negative interband photoconductivity in Ge/Si heterostructures with quantum dots of the second type

It was found that irradiating an array of Ge nanoclusters in n-Si with light that induced interband transitions gave rise to negative photoconductivity. This result was explained by localization of equilibrium electrons at the Si/Ge interface in the potential of the nonequilibrium holes trapped on deep states in Ge islands.