Pathway for the strain-driven two-dimensional to three-dimensional transition during growth of Ge on Si(001)

Kinetic Monte Carlo simulations of self-organization of Ge islands on Si(001)

The self-organization of germanium islands on a silicon(001) substrate is studied using lattice-based kinetic Monte Carlo simulations. These islands form spontaneously via the Stranski-Krastanov mode during growth. The interplay of deposition flux and competing surface diffusion leads to a size and shape distribution of islands that varies with temperature and coverage. For the simulation parameters chosen, a kinetic regime of irreversible growth is observed at 500 K, and this changes to quasi-equilibrium growth at 600 K. At 550 K, we see that the surface roughness increases abruptly from a low value and crosses the roughness curve at 600 K. This behavior is explained on the basis of a change in the island formation mechanism. At 500 K, the island formation involves a nucleation barrier; whereas at 600 K this barrier is almost nonexistent. At an intermediate temperature, the stochastic effects due to the incoming flux initially slow down island growth, but the subsequent island nucleation rapidly increases the roughness. These results illustrate how island self-assembly is affected by mechanistic in addition to kinetic and energetic effects. Our results are discussed in the context of experiments on a Si-Ge system and show how the kMC models can be used to understand the processes in heteroepitaxial growth.

Atomically resolved 3D structural reconstruction of small quantum dots

Semiconducting quantum dots (QDs) have potential applications in light-emitting diodes, single-photon sources and quantum computing due to shape-dependent (opto) electronic properties. Atomic resolution 3D-structure determination is important in understanding growth kinetics and improving device performance. 3D-reconstruction of large QDs was reported using characterization techniques like atomic force microscopy, atom probe tomography and tilt series electron tomography, but, still, atomic resolution tomography of QDs, especially those sized below 10 nm, is a challenge. Inline-3D-holography is an emerging and promising technique to perform atomic resolution tomography at low electron doses. In the present study, atomically resolved 3D structures of QDs were reconstructed using inline-3D-holography, implemented on InN QDs (<10 nm) grown on a Si substrate. The residual amorphous glue distorts the exit surface geometry; hence an error correction method was proposed. This is the first experimental evidence of pre-pyramid shaped 3D structure of QDs sized below 10 nm that supports theoretical predictions.

Capillary-driven elastic attraction between quantum dots

We present a novel self-assembly route to align SiGe quantum dots. By a combination of theoretical analyses and experimental investigation, we show that epitaxial SiGe quantum dots can cluster in ordered closely packed assemblies, revealing an attractive phenomenon. We compute nucleation energy barriers, accounting for elastic effects between quantum dots through both elastic energy and strain-dependent surface energy. If the former is mostly repulsive, we show that the decrease in the surface energy close to an existing island reduces the nucleation barrier. It subsequently increases the probability of nucleation close to an existing island, and turns out to be equivalent to an effective attraction between dots. We show by Monte-Carlo simulations that this effect describes well the experimental results, revealing a new mechanism ruling self-organisation of quantum dots. Such a generic process could be observed in various heterogeneous systems and could pave the way for a wide range of applications.

Theoretical study on nanostructural modifications of the Si(111) surface

Modified Si(111) surface with designed nanostructural modifications including grown pits, nanobars and nanoislands as well as deposited hill-, diamond- and cage-like nanoclusters were studied using density-functional theory (DFT) calculations. The thermal stabilities, electronic structures and optical properties of these various nanostructural modifications of the Si(111) surface were calculated and discussed. The results indicate that the optical absorption of the modified Si(111) surface can be enhanced by these surface modifications especially when depositing diamond-like nanoclusters on the surface.

Evidence for Kinetic Limitations as a Controlling Factor of Ge Pyramid Formation: a Study of Structural Features of Ge/Si(001) Wetting Layer Formed by Ge Deposition at Room Temperature Followed by Annealing at 600 °C

The article presents an experimental study of an issue of whether the formation of arrays of Ge quantum dots on the Si(001) surface is an equilibrium process or it is kinetically controlled. We deposited Ge on Si(001) at the room temperature and explored crystallization of the disordered Ge film as a result of annealing at 600 °C. The experiment has demonstrated that the Ge/Si(001) film formed in the conditions of an isolated system consists of the standard patched wetting layer and large droplike clusters of Ge rather than of huts or domes which appear when a film is grown in a flux of Ge atoms arriving on its surface. We conclude that the growth of the pyramids appearing at temperatures greater than 600 °C is controlled by kinetics rather than thermodynamic equilibrium whereas the wetting layer is an equilibrium structure.

PACS

Primary 68.37.Ef; 68.55.Ac; 68.65.Hb; 81.07.Ta; 81.16.Dn.

Heteroepitaxy of Ge on singular and vicinal Si surfaces: elastic field symmetry and nanostructure growth

Starting with the basic definition, a short description of a few relevant physical quantities playing a role in the growth process of heteroepitaxial strained systems, is provided. As such, the paper is not meant to be a comprehensive survey but to present a connection between the Stranski-Krastanov mechanism of nanostructure formation and the basic principles of nucleation and growth. The elastic field is described in the context of continuum elasticity theory, using either analytical models or numerical simulations. The results are compared with selected experimental results obtained on GeSi nanostructures. In particular, by tuning the value of quantities such as vicinality, substrate orientation and symmetry of the diffusion field, we elucidate how anisotropic elastic interactions determine shape, size, lateral distribution and composition of quantum dots.

Modification of Stranski-Krastanov growth on the surface of nanowires

The heteroepitaxial growth of strained islands on a planar substrate offers an attractive route to the fabrication of quantum dots (QDs). To obtain more functions and superior properties, recent efforts have focused on using nanowires (NWs) as substrates to produce attractive structures that combine QDs with NWs. As the lateral size of an NW is large, it is possible that islands are formed on the side walls of the NW. However, no islands exist, and the lateral surface is rather smooth in thin, core-shell NWs. The existing theoretical models on the growth on planar and patterned substrates are not appropriate for the growth transition on the surface with nanoscale curvature. We thus urgently need to understand the basic physics involved in the strain-induced growth on the surface with nanoscale curvature. Here, we established a theoretical model to study the strain-induced growth on the surface, which showed that the Stranski-Krastanov (SK) mode can change to the Frank-van der Merwe (FM) mode due to the limit of the surface to the island's lateral growth. Using the model to investigate the heterostructured core/shell nanowires (NWs), we found, in addition to the SK mode on thick NWs and the FM mode on thin NWs, that there is a multiplex mode on medium NWs which includes the initial layer growth, the intermediate islands' growth and the final layer growth again. The established theoretical model not only explained some puzzling experimental results but also provided useful information to design and control the epitaxial growth on the surface with nanoscale curvature.

Strain relief and shape oscillations in site-controlled coherent SiGe islands

Strain engineering and the crystalline quality of semiconductor nanostructures are important issues for electronic and optoelectronic devices. We report on defect-free SiGe island arrays resulting from Ge coverages of up to 38 monolayers grown on prepatterned Si(001) substrates. This represents a significant expansion of the parameter space known for the growth of perfect island arrays. A cyclic development of the Ge content and island shape was observed while increasing the Ge coverage. Synchrotron-based x-ray diffraction experiments and finite element method calculations allow us to study the strain behavior of such islands in great detail. In contrast to the oscillatory changes of island shape and average Ge content, the overall strain behavior of these islands exhibits a clear monotonic trend of progressive strain relaxation with increasing Ge coverage.

Addition of Mn to Ge quantum dot surfaces--interaction with the Ge QD {105} facet and the Ge(001) wetting layer

The interaction of Mn with Ge quantum dots (QD), which are bounded by {105} facets, and the strained Ge wetting layer (WL), terminated by a (001) surface, is investigated with scanning tunneling microscopy (STM). These surfaces constitute the growth surfaces in the growth of Mn-doped QDs. Mn is deposited on the Ge QD and WL surface in sub-monolayer concentrations, and subsequently annealed up to a temperature of 400 ° C. The changes in bonding and surface topography are measured with STM during the annealing process. Mn forms flat islands on the Ge{105} facet, whose shape and position are guided by the rebonded step reconstruction of the facet. Voltage-dependent STM images reflect the Mn-island interaction with the empty and filled states of the Ge{105} reconstruction. Scanning tunneling spectra (STS) of the Ge{105} facet and as-deposited Mn-islands show a bandgap of 0.8 eV, and the Mn-island spectra are characterized by an additional empty state at about 1.4 eV. A statistical analysis of Mn-island shape and position on the QD yields a slight preference for edge positions, whereas the QD strain field does not impact Mn-island position. However, the formation of ultra-small Mn-clusters dominates on the Ge(001) WL, which is in contrast to Mn interaction with unstrained Ge(001) surfaces. Annealing to T < 160 °C leaves the Mn-clusters on the WL unchanged, while the Mn-islands on the Ge{105} facet undergo first a ripening process, followed by a volume gain which can be attributed to the onset of intermixing with Ge. This development is supported by the statistical analysis of island volume, size and size distribution. Increasing the annealing temperature to 220° and finally 375 ° C leads to a rapid increase in the Mn-surface diffusion, as evidenced by the formation of larger, nanometer size clusters, which are identified as germanide Mn5Ge3 from a mass balance analysis. This reaction is accompanied by the disappearance of the original Mn-surface structures and de-wetting of Mn is complete. This study unravels the details of Mn-Ge interactions, and demonstrates the role of surface diffusion as a determinant in the growth of Mn-doped Ge materials. Surface doping of Ge-nanostructures at lower temperatures could provide a pathway to control magnetism in the Mn-Ge system.

Nucleation of size calibrated three-dimensional nanodots in atomistic model of strained epitaxy: a Monte Carlo study

We introduce a simple model of strained epitaxy to study the growth of coherent several-monolayers-high nanoislands at low coverage. The size mismatch between the substrate (which is assumed to be rigid and passive) and the growing overlayer is modelled by the hard-sphere interaction between the adatoms. In the case of positive misfit the sphere diameter is larger than the substrate lattice parameter. Elastic interactions are described within the harmonic approximation to the substrate potential in the vicinity of the deposition sites. With additional attractive interaction between the nearest neighbour atoms the model exhibited the growth of miniature nanoislands of several morphologies with their kinetics similar to those found in real quantum dot (QD) systems. The 3D QDs exhibited narrow distributions of their heights, diameters and volumes in qualitative agreement with experimental observations.

Morphological evolution of Ge/Si(001) quantum dot rings formed at the rim of wet-etched pits

We demonstrate the formation of Ge quantum dots in ring-like arrangements around predefined {111}-faceted pits in the Si(001) substrate. We report on the complex morphological evolution of the single quantum dots contributing to the rings by means of atomic force microscopy and demonstrate that by careful adjustment of the epitaxial growth parameters, such rings containing densely squeezed islands can be grown with large spatial distances of up to 5 μm without additional nucleation of randomly distributed quantum dots between the rings.

One-dimensional to three-dimensional ripple-to-dome transition for SiGe on vicinal Si (1 1 10)

SiGe heteroepitaxy on vicinal Si (1 1 10) is studied as a model system for one-dimensional (1D) to three-dimensional growth mode transitions. By in situ scanning tunneling microscopy it is shown that the 1D-3D transition proceeds smoothly from perfectly facetted 1D nanoripples to coarsened superripples, tadpoles, asymmetric domes, and barns without involving coalescence or agglomeration. By extension of the studies to a wide range of SiGe compositions, a 1D-3D growth phase diagram is obtained. Total energy calculations reveal that the observed critical transition volumes are fully consistent with thermodynamic driven strain relaxation.

Layer-by-layer nucleation mechanism for quantum dot formation in strained heteroepitaxy

We study the spontaneous formation of quantum dots in the form of three-dimensional (3D) islands on facetted surfaces in heteroepitaxy. Island development from fast kinetic Monte Carlo (KMC) simulations at low deposition rates is found to follow a layer-by-layer nucleation pathway characterized by energetics driven continuous lateral expansion interrupted by a sequence of independent two-dimensional (2D) upper-layer nucleation events. The process involves only unstable 2D upper-layer nuclei but no unstable 3D nucleus. We have calculated analytically the elastic strain energy of an island in the form of an axisymmetric stepped mound using a small-slope approximation. The total free energy of a system with a 3D island and an adatom bath is obtained. Our theory explains island formation via a free energy driven layer-by-layer nucleation mechanism. Upper-layer nucleation energy barrier, nucleation time, critical radius, and island step spacings are estimated. The relevance of entropic step-step repulsion is discussed. Our theory satisfactorily explains the 3D KMC simulations and may describe the initial evolution of islands in the form of stepped mounds observed in experiments.

Kinetic Monte Carlo simulation of faceted islands in heteroepitaxy using a multistate lattice model

A solid-on-solid model is generalized to study the formation of Ge pyramid islands bounded by (105) facets on Si(100) substrates in two dimensions. Each atomic column is not only characterized by the local surface height but also by two deformation state variables dictating the local surface tilt and vertical extension. These local deformations phenomenologically model surface reconstructions in (105) facets and enable the formation of islands which better resemble faceted pyramids. We apply the model to study a kinetic limited growth regime. Transitions from stepped mounds into faceted islands under deposition conditions are demonstrated. It is shown that a significantly reduced growth rate after faceting leads to a continuous nucleation of new islands until overcrowding occurs. The island size distribution is now dominated by fluctuations in the initial island size during faceting and the increased diversity in the ages of the islands. This multistate model may find applications in kinetic simulations of other nanostructures or nanoclusters involving arbitrary high-index surfaces.

Shaping Ge islands on Si(001) surfaces with misorientation angle

A complete description of Ge growth on vicinal Si(001) surfaces in the angular miscut range 0 degrees -8 degrees is presented. The key role of substrate vicinality is clarified from the very early stages of Ge deposition up to the nucleation of 3D islands. By a systematic scanning tunneling microscopy investigation we are able to explain the competition between step-flow growth and 2D nucleation and the progressive elongation of the 3D islands along the miscut direction [110]. Using finite element calculations, we find a strict correlation between the morphological evolution and the energetic factors which govern the {105} faceting at atomic scale.

Efficient first-principles simulation of noncontact atomic force microscopy for structural analysis

We propose an efficient scheme to simulate noncontact atomic force microscopy images by using first-principles self-consistent potential from the sample as input without explicit modeling of the atomic force microscopy tip. Our method is applied to various types of semiconductor surfaces including Si(111)-(7x7), TiO2(110)-(1x1), Ag/Si(111)-(sqrt[3]xsqrt[3])R30 degrees, and Ge/Si(105)-(1x2) surfaces. We obtain good agreement with experimental results and previous theoretical studies, and our method can aid in identifying different structural models for surface reconstruction.

Is the elongation of Ge huts in the low-temperature regime governed by kinetics?

Contrary to pyramids and domes, elongated huts on a Si(001) substrate are commonly considered as kinetically limited structures. In this work, however, based on detailed scanning tunneling microscopy observations of Ge huts growing on Si(001) at temperatures below 550 degrees C and finite element analysis, the possibility of an equilibrium-driven elongation is raised, where hut-preceding pits are thought to lift the energetic degeneracy of {105} facets and cause elongation along energetically preferred directions.

Dendrochronology of strain-relaxed islands

We report on the observation and study of tree-ring structures below dislocated SiGe islands (superdomes) grown on Si(001) substrates. Analogous to the study of tree rings (dendrochronology), these footprints enable us to gain unambiguous information on the growth and evolution of superdomes and their neighboring islands. The temperature dependence of the critical volume for dislocation introduction is measured and related to the composition of the islands. We show clearly that island coalescence is the dominant pathway towards dislocation nucleation at low temperatures, while at higher temperatures anomalous coarsening is effective and leads to the formation of a depletion region around superdomes.

Orientation dependence of strained-Ge surface energies near (001): role of dimer-vacancy lines and their interactions with steps

Recent experiments and calculations have highlighted the important role of surface-energy (gamma) anisotropy in governing island formation in the Ge/Si(001) system. To further elucidate the factors determining this anisotropy, we perform atomistic and continuum calculations of the orientation dependence of gamma for strained-Ge surfaces near (001), accounting for the presence of dimer-vacancy lines (DVLs). The net effect of DVLs is found to be a substantial reduction in the magnitude of the slope of gamma vs orientation angle, relative to the highly negative value derived for non-DVL, dimer-reconstructed, strained-Ge(001) surfaces. The present results thus point to an important role of DVLs in stabilizing the (001) surface orientation of a strained-Ge wetting layer.

Bombardment-induced tunable superlattices in the growth of Au-Ni films

Highly ordered superlattices are typically created through the sequential deposition of two different materials. Here, we report our experimental observation of spontaneous formation of superlattices in coevaporation of Au and Ni under energetic ion bombardment. The superlattice periodicities are on the order of a few nanometers and can be adjusted through the energy and flux of ion beams. Such a self-organization process is a consequence of the bombardment-induced segregation and uphill diffusion within the advancing nanoscale subsurface zone in the film growth. Our observations suggest that ion beams can be employed to make tunable natural superlattices in the deposition of phase-separated systems with strong bombardment-induced segregation.

Island, pit, and groove formation in strained heteroepitaxy

We study the morphological evolution of strained heteroepitaxial films using a kinetic Monte Carlo method in three dimensions. The elastic part of the problem uses a Green's function method. Isolated islands are observed under deposition conditions for deposition rates slow compared with intrinsic surface roughening rates. They are hemispherical and truncated conical for high and low temperature cases, respectively. Annealing of films at high temperature leads to the formation of closely packed islands as in instability theory. At low temperature, pits form via a multistep layer-by-layer nucleation mechanism in contrast to the conventional single-step nucleation process. They subsequently develop into grooves, which are energetically more favorable.

Effect of strain on the appearance of subcritical nuclei of ge nanohuts on Si(001)

Real-time scanning tunneling microscopy observations of nucleation and heteroepitaxial growth of Ge nanocrystals (from germane) on Si(001) indicate that in the absence of Si-Ge intermixing the formation of full hut cluster islands is preceded by the nucleation of "subcritical" nuclei consisting of two adjacent truncated tetrahedral pyramids, which, upon unification, form a tiny square-based pyramidal "critical nucleus" It is suggested that such a precursor aids in surpassing the nucleation barrier and that the recently reported gradual faceting of prepyramids is characteristic of only Ge(Si) alloys.

Kinetic evolution and equilibrium morphology of strained islands

Self-assembled SiGe islands grown on Si(001) leave behind characteristic "footprints" that reveal that small islands shrink, losing material to nearby larger islands. The critical size, dividing shrinking from growing islands, corresponds to the pyramid-to-dome shape transition, consistent with "anomalous coarsening" While shrinking, {105}-faceted pyramids transform into truncated pyramids and ultimately into unfaceted mounds. The similarity to behavior during island growth indicates that island shape and facet formation are thermodynamically determined.

Role of strain-dependent surface energies in Ge/Si(100) island formation

Formation energies for Ge/Si(100) pyramidal islands are computed combining continuum calculations of strain energy with first-principles-computed strain-dependent surface energies. The strain dependence of surface energy is critically impacted by the presence of strain-induced changes in the Ge {100} surface reconstruction. The appreciable strain dependencies of rebonded-step {105} and dimer-vacancy-line-reconstructed {100} surface energies are estimated to give rise to a significant reduction in the surface contribution to island formation energies.

Towards quantitative understanding of formation and stability of Ge hut islands on Si(001)

We analyze Ge hut island formation on Si(001), using first-principles calculations of energies, stresses, and their strain dependence of Ge/Si(105) and Ge/Si(001) surfaces combined with continuum modeling. We give a quantitative assessment on strain stabilization of Ge(105) facets, estimate the critical size for hut nucleation or formation, and evaluate the magnitude of surface stress discontinuity at the island's edge and its effect on island stability.

Directed self-assembly of Ge nanostructures on very high index, highly anisotropic Si(hkl) surfaces

Families of very high-index planes, such as those which bifurcate spontaneously to form a hill-and-valley structure composed of opposing facets, provide natural templates for the directed growth of position-controlled self-organized nanostructures with shapes determined by the facet width ratio R. For example, deposition of a few ML of Ge on Si(173 100 373), corresponding to R(113/517) = 1.7, results in a field of 40-nm-wide Ge nanowires along [72 187] with a uniform period of 60 nm.

Initial surface roughening in Ge/Si(001) heteroepitaxy driven by step-vacancy line interaction

The initial surface roughening during Ge epitaxy on Si(001) is shown to arise from an effective repulsion between S(A) surface steps and dimer vacancy lines (VLs). This step-VL interaction gradually inactivates a substantial fraction of adatom attachment sites at the growth front, causing a rapid increase in the rate of two-dimensional island nucleation. The mutual repulsion hinders the crossing of S(A) surface steps over VLs in the second layer, thus organizing the developing surface roughness into a periodic array of anisotropic 2D terraces. Isolated (105) facets forming at specific sites on this ordered template mediate the assembly of first 3D Ge islands.

Self-organized superlattice formation during crystal growth from continuous beam fluxes

Alloy superlattice structures consisting of alternating Si-rich and C-rich layers form spontaneously during gas-source molecular beam epitaxy of Si(1-y)C(y) on Si(001) from constant Si2H6 and CH3SiH3 precursor fluxes at T(s)=725-750 degrees C. The self-organized patterning is due to a complex interaction among competing surface reactions. During growth of the initial Si-rich layer, strain-driven C segregation to the subsurface results in charge transfer from surface Si atom dangling bonds to C backbonds. This decreases the Si2H6 sticking probability, and, hence, the instantaneous deposition rate, thereby enhancing C segregation. The Si-rich layer continues until a critical C coverage is reached allowing nucleation of a C-rich layer which grows until the excess subsurface C is depleted. The process then repeats with periods tunable through the choice of T(s) and y(avg).

Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study

We study the morphological evolution of strained heteroepitaxial films using kinetic Monte Carlo simulations in two dimensions. A novel Green's function approach, analogous to boundary integral methods, is used to calculate elastic energies efficiently. We observe island formation at low lattice misfit and high temperature that is consistent with the Asaro-Tiller-Grinfeld instability theory. At high misfit and low temperature, islands or pits form according to the nucleation theory of Tersoff and LeGoues.

Barrierless formation and faceting of SiGe islands on Si(001)

The initial stages of the formation of SiGe islands on Si(001) pose a long-standing puzzle. We show that the behavior can be consistently explained by one simple assumption-that for strained SiGe, (001) is a stable orientation but not a facet orientation. Calculations of energy and morphology reproduce the key features of "prepyramid" and "pyramid" islands, and explain the initial formation and subsequent shape transition. Scanning tunneling microscopy measurements confirm the key assumptions and predictions of the model.

Critical role of the surface reconstruction in the thermodynamic stability of (105) Ge pyramids on Si(001)

We show by molecular dynamics simulations on a scale comparable to experimental dimensions that a peculiar surface reconstruction of the (105) facets is responsible for the stability of Ge pyramids on Si(001). This finding is confirmed by ab initio total energy calculations for competing surface reconstructions and a very satisfactory comparison of the corresponding charge density maps to scanning tunneling microscopy measurements of the facets, both for filled and empty states.

Origin of the stability of Ge(105) on si: a new structure model and surface strain relaxation

The structure of Ge(105)-(1 x 2) grown on Si(105) is examined by scanning tunneling microscopy (STM) and first-principles calculations. The morphology evolution with an increasing amount of Ge deposited documents the existence of a tensile surface strain in Si(105) and its relaxation with increasing coverage of Ge. A detailed analysis of high-resolution STM images and first-principles calculations produce a new stable model for the Ge(105)-(1 x 2) structure formed on the Si(105) surface that includes the existence of surface strain. It corrects the model developed from early observations of the facets of "hut" clusters grown on Si(001).

Reversible shape evolution of Ge islands on Si(001)

The evolution of strained Ge/Si(001) islands during exposure to a Si flux was investigated by scanning tunneling microscopy. Dome islands display appreciable shape changes at Si coverages as low as 0.5 monolayer. With increasing coverage, they transform into [105]-faceted pyramids, and eventually into stepped mounds with steps parallel to the <110> directions. These morphological changes are induced by alloying and represent a complete reversal of those previously observed during Ge island growth. The results are interpreted with a simple model in which the equilibrium shape of an island mainly depends on its volume and composition.

Minute SiGe quantum dots on Si(001) by a kinetic 3D island mode

We investigated the initial growth stages of Si(x)Ge(1-x)/Si(001) by real time stress measurements and in situ scanning tunneling microscopy at deposition temperatures, where intermixing effects are still minute (< or =900 K). Whereas Ge/Si(001) is a well known Stranski-Krastanow system, the growth of SiGe alloy films switches to a 3D island mode at Si content above 20%. The obtained islands are small (a few nanometers), are uniform in shape, and exhibit a narrow size distribution, making them promising candidates for future quantum dot devices.