2D-3D Transition Research Articles

Electron microscopy investigation of the defect configuration in CdSe/ZnSe quantum dot structures

Abstract In this study we report the dependence of the defect configuration observed in CdSe/ZnSe quantum dot structures on the ZnSe cap layer thickness by transmission electron microscopy (TEM) and reflection high-energy electron diffraction (RHEED). The samples were grown by molecular-beam epitaxy at 350°C. The nominal thickness of the CdSe layers was approximately 3 monolayers and the cap layer thickness was varied in the range from 3 to 60 nm. In all samples, RHEED showed a transition from the two-dimensional (2D) to the three-dimensional (3D) growth mode during the CdSe deposition. By TEM we found pairs of stacking faults (SFs) lying on one of the two pairs of lattice planes given by {(111)-(1 11)} and {(111)-(111)}. The SFs are bound by Shockley partial dislocations. Both of the SFs forming one pair originate from the same stair-rod dislocation with Burgers vector b = ⅙{110} lying at the CdSe-ZnSe interface inside a Cd-rich region (island). Measuring the atomic displacements in the vicinity of the SFs, we obtained that all SFs have an intrinsic nature. At the line of contact of two SFs that belong to different pairs, we observed stair-rod dislocations with b = ⅓{100} which are inclined to the interface. The length of all dislocation lines and the sizes of the SFs increase with increasing ZnSe cap layer thickness. We find that the 2D-3D transition observed by RHEED is most probably caused by defect formation, which is discussed with respect to the relaxation of strain in the CdSe layer.

Nucleation and ripening of seeded InAs/GaAs quantum dots

We have investigated the nucleation and ripening of pairs of InAs/GaAs quantum dot layers separated by thin (2–20 nm) GaAs spacer layers. Reflection high energy electron diffraction (RHEED) measurements show that the 2D–3D transition in the second layer can occur for less than 1 monolayer deposition of InAs. Immediately after the islanding transition in the second layer chevrons were observed with included angles as low as 20° and this angle was seen to increase continuously to 45±2° as more material was deposited. Atomic force microscopy showed the dot density in both layers to be the same. It is proposed that surface morphology can radically alter processes that determine the nucleation and ripening of the 3D islands.

Modified Stranski-Krastanov Growth in Stacked Layers of Self-Assembled Cubic GaN/AlN Quantum Dots

In a stacked structure of cubic GaN/AlN islands grown in a Stranski-Krastanov mode, the critical thickness for the GaN islanding (2D-3D transition) decreases by a factor of up to 10 between the initial dot layer and the third one. This variation of the critical thickness is strongly dependent on the AlN spacer thickness. Moreover, we observe systematically a change of the quantum dot strain state and an increase of island size, depending on the GaN island layer number.

Modified Stranski-Krastanov Growth in Stacked Layers of Self-Assembled Cubic GaN/AlN Quantum Dots

In a stacked structure of cubic GaN/AlN islands grown in a Stranski-Krastanov mode, the critical thickness for the GaN islanding (2D-3D transition) decreases by a factor of up to 10 between the initial dot layer and the third one. This variation of the critical thickness is strongly dependent on the AlN spacer thickness. Moreover, we observe systematically a change of the quantum dot strain state and an increase of island size, depending on the GaN island layer number.

RHEED investigation of the formation process of InAs quantum dots on (1 0 0) InAlAs/InP for application to photonic devices in the 1.55 μm range

Self-assembled InAs quantum dots (QDs) on In 0.52Al 0.48As lattice matched to (1 0 0) InP substrates were grown by solid-source molecular beam epitaxy. We present in situ reflection high-energy electron diffraction studies of the initial growth processes and strain relaxation behaviors of the InAs QDs. The growth process of an InAs layer at the initial stage is clearly divided into two-dimensional (2D) growth and QD formation. It was found that the critical thickness for the 2D–3D transition is about two monolayers. The photoluminescence peak energies from the QDs were found to depend strongly on the InAs coverage, and the emission wavelength can be controlled over the 1.3–1.55 μm range.

Rate equation approach to film growth

Recent progress of the rate equation method in the field of film growth, covers the modeling of island density behavior in the whole range of surface coverages and the stress-driven 2D–3D transition in island morphology, as it occurs in the Stranski–Krastanov growth mechanism. In the former case, rate coefficients are evaluated both on the basis of stochastic approaches which also allow one to deal with spatial correlation effects among nuclei and exploiting computer simulations. In the latter case, rate coefficients for adatom capture and for 2D–3D island transition are computed, respectively, by solving the diffusion equation and exploiting the quasi equilibrium approximation.

MOVPE strain layers – growth and application

The critical thickness, characteristic for the lattice-mismatch parameter, plays a key role in the growth of strain layers. The driving force for the 2D–3D transition can be minimized by slowing the relaxation of misfit strain. As a result – the relatively smooth layer is deposited at lower temperature for the optimal growth rate. The quality of the InGaAs- and AlAs-strained layers deposited on InP substrate have been examined by the XRD, AFM and SIMS methods. Atomic force microscopy allows to observe 3D growth mode even for very thin layers. Relatively strong relaxation effects are recognized by surface roughness. Two-dimensional diffraction measurement is a much more sensitive tool for the estimation of relaxation degree. The observations results were applied in the heterostructure barrier varactor (HBV) diode. In order to minimize the conduction current through HBV two materials with different design of the barriers were studied: one heterostructure with three homogeneous lattice matched barriers consisting of 20 nm Al 0.48In 0.52As and another one with strained step-like barriers consisting of 5 nm Al 0.48In 0.52As, 3 nm AlAs and 5 nm Al 0.48In 0.52As. We found that the use of strained step-like barriers results in a much lower conduction current. For current density ⩽0.1 μA/μm 2, the maximum voltage was about 10 V per barrier, which is to our knowledge more than for any reported HBV material.

Investigation of the low field irreversibility line in Bi 2Sr 2CaCu 2O 8+ x epitaxial thin films

The irreversibility line in Bi 2Sr 2CaCu 2O 8+ x epitaxial thin films in low applied magnetic fields (5 < H < 10 4 G) has been studied by means of AC susceptibility. The temperature, frequency, AC and DC magnetic field dependence of the peak of the absorptive component of the susceptibility allow us to deduce the field, temperature and current functional dependences of the activation energy U( H,T,J). A U( H) ∼ H −0.5 dependence, typical of dislocation-mediated thermally activated flux motion, is found in the magnetic field range 10 3 ≤ H ≤ 10 4 G whereas a transition to a higher pinning energy appears below 2 * 10 2 G, which may be interpreted as a result of a 2D–3D transition in the vortex system.

Structural evolution of ZnO/sapphire(001) heteroepitaxy studied by real time synchrotron x-ray scattering

The structural evolution during heteroepitaxial growth of ZnO/sapphire(001) by radio-frequency magnetron sputtering has been studied using real-time synchrotron x-ray scattering. The two-dimensional (2D) ZnO(002) layers grown in the initial stage are highly strained and well aligned to the substrate having a mosaic distribution of 0.01° full width at half maximum (FWHM), in sharp contrast to the reported transition 2D layers grown by molecular-beam epitaxy. With increasing film thickness, the lattice strain is relieved and the poorly aligned (1.25° FWHM) three-dimensional (3D) islands are nucleated on the 2D layers. We attribute the 2D–3D transition to the release of the strain energy stored in the film due to the film/substrate lattice mismatch.

Nucleation of superconductivity in a mesoscopic loop of finite width

The normal/superconducting phase boundary T c has been calculated for mesoscopic loops as a function of an applied perpendicular magnetic field H. While for thin-wire loops and filled disks, the T c( H) curves are well known, the intermediate case, namely, mesoscopic loops of finite wire width, have been studied much less. The linearized first Ginzburg–Landau (GL) equation is solved with the proper normal/vacuum boundary conditions both at the internal and at the external loops radii. For thin-wire loops, the T c( H) oscillations are perfectly periodic, and the T c( H) background is parabolic (this is the usual Little–Parks effect). For loops of thicker wire width, there is a crossover magnetic field above which T c( H) becomes quasi-linear, with the period identical to the T c( H) of a filled disk (i.e., pseudoperiodic oscillations). This dimensional transition is similar to the 2D–3D transition for thin films in a parallel field, where vortices start penetrating the material as soon as the film thickness exceeds the temperature-dependent coherence length by a factor 1.8. For the presently studied loops, the crossover point is controlled by a similar condition. In the high-field ‘3D’ regime, a giant vortex state establishes, where only a surface superconducting sheath near the sample's outer radius is present.

Quantum dots formed by ultrathin insertions in wide-gap matrices

We report on experimental and theoretical studies on a new type of quantum-dot (QD) structures obtained using ultrathin, i.e. below the critical thickness for 2D–3D transition, strained narrow gap insertions in wide bandgap matrices. We concentrate on submonolayer (SML) or slightly above 1 ML CdSe insertions in a wide-gap II–VI matrices and give the first results on ultrathin InGaN insertions in a GaN matrix. A discussion on detailed comparison of our original results with the results of other authors is presented. The formation of dense arrays (up to 1012 cm−2) of nanoscale two-dimensional (2D) islands is revealed in processed high-resolution transmission electron microscopy images. In the case of stacked sheets of SML insertions, the islands in the neighboring sheets are formed predominantly in correlated or anticorrelated way for thinner and thicker spacer layers, respectively. Different polarization of photoluminescence (PL) emission recorded in edge geometry for vertically-uncoupled and coupled QDs confirms the QD nature of excitons. By monitoring of sharp lines due to single QDs using cathodoluminescence the 3D confinement is manifested. We demonstrate significant squeezing of the QD exciton wavefunction in the lateral direction using magneto-optical experiments. We point to complete suppression of lateral motion of excitons bound to islands in case of wide-gap (ZnMgSSe) matrices, as follows from PL excitation studies. A resonant (0-phonon) lasing is observed in ultrathin CdSe insertions and proves the lifting of the k-selection rule for QD excitons. We show that lack of exciton screening in QDs up to high excitation densities enables strong resonant modulation of the refractive index in stacked ultrathin insertions and allows realization of resonant (excitonic) waveguiding and lasing. This enables the realization of a new type of heterostructure laser operating without external optical confinement by layers having lower average refractive indices. Ultrahigh QD excitonic gain in dense arrays of stacked QDs allows a new type of surface-emitting laser.

Formation and dissolution of InAs quantum dots on GaAs

In situ reflection high energy electron diffraction (RHEED) has been used to study the time evolution during self-assembled molecular beam epitaxy (MBE) growth of InAs quantum dots on GaAs. Using a special data acquisition technique, two characteristic time constants are determined very precisely: the time t c up to the first appearance of InAs dots and the time t f it takes to complete the 2D–3D transition of all islands. Surprisingly, we find that t c increases with temperature which disagrees with a thermally activated process. In contrast to this, t f behaves Arrhenius-like and an activation energy of E f≃0.39 eV is determined. Furthermore, the sum t c+ t f does not depend significantly on temperature and corresponds to an InAs coverage of ≃2.0 monolayers. A second focus of this paper is the study of dissolution of InAs dots after interruption of the As flux. From the experiments, an activation energy of 3.2 eV for desorption of In located on top of the wetting layer is determined, whereas direct desorption from the wetting layer corresponds to an activation energy of 3.4 eV.

Two-dimensional electron gas scattering mechanisms in AlGaN/GaN heterostructures

ABSTRACTWe present the results of the experimental and theoretical studies of the low field mobility of two-dimensional electrons in the homoepitaxial AlGaN/GaN heterostructures and in the AlGaN/GaN heterostructures grown on SiC. We show that, at cryogenic temperatures, the temperature dependence of the mobility is primarily determined by the deformation potential scattering and that most of other important scattering mechanisms are temperature independent. We show also that two-dimensional (2D) and three-dimensional (3D) mobility models yield very close results. The analysis of the mobility dependence on the electron sheet density ns shows two possible explanations of the non monotonic mobility versus carrier density dependence: i) the alloy/interface scattering and ii) transfer of the 2D electrons into 3D states in GaN. We present experimental data suggesting that for high 2D gas densities in the investigated structure grown on SiC the 2D-3D transition should take place and might be responsible for the mobility decrease at high electron sheet densities.

Island shape instabilities and surfactant-like effects in the growth of InGaAs/GaAs quantum dots

InGaAs/GaAs island formation during vapor phase epitaxy showed diverging behaviors when varying group V partial pressures (PP). Differences include changes in critical thicknesses for the onset of the Stranski–Krastanow (S–K) transformation, surface coverages, ratios between coherent and incoherent islands, and dissimilar morphologies upon annealing. These results show that slightly different values for the 2D–3D transition can also be obtained in InGaAs/GaAs depending on AsH 3 PP. Photoluminescence spectroscopy of capped islands showed that the wetting layer thickness does not change beyond the onset of the S–K transformation for conditions producing stable islands. Annealing experiments done at high AsH 3 PP show Ostwald ripening, but we also observe that small, high density, lens-shaped islands are unaffected by prolonged annealing and do not ripen when an ‘optimum’ low AsH 3 PP is used during the island growth and in-situ annealing. The later experiments show that small lens shaped islands can be found in equilibrium if InGaAs surface energies are minimized. These findings lead to the conclusion that AsH 3 can raise surface energies acting as an impurity-free ‘morphactant’ in InGaAs growth.

Growth and Optical Characterization of InGaN Quantum Dots Resulting from a 2D–3D Transition

The growth of InGaN on GaN by plasma-assisted molecular beam epitaxy is studied using reflection high energy electron diffraction. We find that InGaN follows a layer-by-layer growth mode for low In contents and a Stranski-Krastanov growth mode for In concentrations above a critical value. Using this 2D–3D transition, nanometric islands are grown. These islands are characterized by atomic force microscopy. Their size is found to be small enough to expect strong confinement effects. Photoluminescence experiments show strong blue light emission at room temperature. The temperature dependence of dots' luminescence is compared to that of a quantum well and a bulk sample.

Growth and Optical Characterization of InGaN Quantum Dots Resulting from a 2D–3D Transition

Growth and Optical Characterization of InGaN Quantum Dots Resulting from a 2D–3D Transition

Dimensional crossover in a mesoscopic superconducting loop of finite width

Superconducting structures with a size of the order of the superconducting coherence length $\ensuremath{\xi}(T)$ have a critical temperature ${T}_{c},$ oscillating as a function of the applied perpendicular magnetic field H (or flux $\ensuremath{\Phi}).$ For a thin-wire superconducting loop, the oscillations in ${T}_{c}$ are perfectly periodic with H (this is the well-known Little-Parks effect), while for a singly connected superconducting disk the oscillations are pseudoperiodic, i.e., the magnetic period decreases as H grows. In the present paper, we study the intermediate case: a loop made of thick wires. By increasing the size of the opening in the middle, the disklike behavior of ${T}_{c}(H)$ with a quasilinear background [characteristic of three-dimensional (3D) behavior] is shown to evolve into a parabolic ${T}_{c}(H)$ background (2D), superimposed with perfectly periodic oscillations. The calculations are performed using the linearized Ginzburg-Landau theory, with the proper normal/vacuum boundary conditions at both the internal and external interfaces. Above a certain crossover magnetic flux $\ensuremath{\Phi},$ ${T}_{c}(\ensuremath{\Phi})$ of the loops becomes quasilinear, and the flux period matches with the case of the filled disk. This dimensional transition is similar to the 2D-3D transition for thin films in a parallel magnetic field, where vortices enter the material as soon as the film thickness $t&gt;1.8\ensuremath{\xi}(T).$ For the loops studied here, the crossover point appears for $w\ensuremath{\approx}1.8\ensuremath{\xi}(T)$ as well, with w the width of the wires forming the loop. In the 3D regime, a ``giant vortex state'' is established, where superconductivity is concentrated near the sample's outer interface. The vortex is then localized inside the loop's opening.

Surface morphology evolutions during the first stages of epitaxial growth of Si on Ge(0 0 1): a RHEED study

Solid source molecular beam heteroepitaxial growth of thin Si films on Ge(0 0 1)-2×1 pseudo-substrates has been investigated over a large range of substrate temperatures (from room temperature to 400°C) and Si deposition rate (from 1.5 to 25 Å/min) using reflection high-energy electron diffraction (RHEED). Due to the lower surface free energy of Ge with respect to Si, a Volmer–Weber growth mode is expected at equilibrium conditions. Nevertheless, at low temperature, RHEED patterns, in-plane lattice parameter measurements ( a ‖) and specular beam intensity oscillations reveal prolonged two-dimensional growth imposed by kinetic limitations for this tensile strained system. Actually, the critical thicknesses for which island formation takes place can be significantly increased by lowering the surface diffusion length of the Si adatoms, by either temperature decrease or deposition rate increase. These thicknesses are determined by the passage from streaky to spotty patterns and the onset of concomitant a ‖ decreases. This indicates varying and delayed 2D–3D transitions with respect to the equilibrium criterion. Such variations are not observed for the Stranski–Krastanov mode of the inverse compressive Ge/Si interface, whose critical thicknesses are only weakly dependent on the kinetic conditions. These differentiated morphology stabilities as a function of the strain sign are discussed in terms of strain dependent adatom diffusivities.

Size and shape modification of self assembled InAs quantum dots and stacked layers by in-situ etching

We present investigations of the structural and optical properties of in-situ etched, self assembled InAs islands using AsBr3 within a molecular beam epitaxy system. This procedure allows reshaping and downsizing of quantum dots with atomic layer precision. The critical thickness of a second InAs layer on top of a thin GaAs layer covering a first InAs dot layer was investigated by RHEED using the 2D–3D transition due to the Stranski–Krastanov growth mode. In-situ etching of the GaAs spacer layer results in an array of small dips on the surface due to enhanced etching at locally strained areas. The dips influence the nucleation of the second dot layer.

Thickness dependent Curie temperatures of ferromagnetic Heisenberg films

We develop a procedure for calculating the magnetic properties of a ferromagnetic Heisenberg film with single-ion anisotropy which is valid for arbitrary spin and film thickness. Applied to s.c.(100) and f.c.c.(100) films with spin S= 7 2 the theory yields the layer dependent magnetizations and Curie temperatures of films of various thicknesses making it possible to investigate magnetic properties of films at the interesting 2D–3D transition.