Pit-patterned Si Research Articles

Monte Carlo Simulation of Heteroepitaxial Growth of Ge on Pit-patterned Si(100) Substrate and Parallelization of Calculations

Methods and algorithms of Monte Carlo simulation of heteroepitaxial growth of Ge on Si are considered. The computational complexity analysis of simulation program blocks is carried out. Parallelization of time-consuming cycles using directives of the open standard OpenMP is proposed. The Monte Carlo simulation of heteroepitaxial growth of Ge on pitpatterned Si substrate was carried out. The position of Ge nanoislands is determined by the competition between the nucleation process of three-dimensional islands due to the accumulation of elastic strain in the growing layer and the process of diffusion of Ge atoms into the pits serving as a drain.

Groups of Ge nanoislands grown outside pits on pit-patterned Si substrates

Ordered arrays of Ge quantum dot groups (QDs) were grown on pit-patterned silicon-on-insulator (SOI) substrates with deep pits, prepared by electron beam lithography (EBL) and plasma-chemical etching (PCE). Experiments were carried out for the square and hexagonal pit lattices with the lattice period varied. The QDs were found to be sited at the periphery of pits. It was demonstrated that for both pit lattice types the number of QDs per pit can be controlled by varying the period of the pit lattice. The Monte Carlo (MC) simulations of QDs growth on pit-patterned Si substrates were carried out, using the model, which takes strain into account. The island patterning depending on the inter-pit distance is interpreted as the result of competition between stress-driven QD nucleation and Ge migration downward into the pits, which serve as the sinks for Ge atoms.

Self-Organization of Ge(Si) Nanoisland Groups on Pit-Patterned Si(100) Substrates

Space-arranged arrays of pits on Si(001) substrates were prepared using electron-beam lithography and plasma chemical etching. The positions of pits were arrange to the square and hexagonal lattices with a varying spacing. It was shown that the location of three-dimensional (3D) Ge nanoislands subsequently grown on the pit-patterned Si substrates depends on spacing for the both lattice types. In the case of the small spacing Ge nanoislands are located mainly inside the pits, while for the larger inter-pit distance the groups of Ge nanoislands at the pit periphery is also observed. This effect is interpreted in terms of critical volume for the 3D island nucleation which is achieved at the pit periphery with the increase of Ge amount deposited per pit. The effect of nanoisland growth, first inside the pits, then at their periphery was reproduced by Monte Carlo simulations of Ge growth on the pit-patterned Si substrates.

Orientational competition in quantum dot growth in Si-Ge heteroepitaxy on pit-patterned Si(001) substrates.

Towards precisely controlled nanostructure growth, patterned substrates are used as templates to direct heteroepitaxial self-assembly. This affects the size, shape and ordering of nanostructures, which are formed as a consequence of the mismatch in strain. In the well-studied case of Si-Ge heteroepitaxy on Si, the lattice mismatch leads to spontaneous formation of quantum dots. On patterned substrates, the competition between the length scale of the pattern and the intrinsic quantum dot size leads to rich behavior, where the localization of dots can be modified with respect to the features of the patterns. We show by continuum modeling that, in cubic elastic materials such as silicon and germanium, there is also a competition between the pattern orientation and the elastically soft directions of the film, which affects the precise location of quantum dots on the surface. When the pattern is between the elastically soft directions, the quantum dots can form purely in the narrow region directly between two neighboring pits, referred to as the saddle region. On the other hand, when the pattern is along the elastically soft directions, the quantum dots prefer to form in the region at the centre of four pits, referred to as the crown region. This resolves a discrepancy between theory and experiments and gives another dimension to control quantum dot formation in strained nanocrystalline systems.

Modeling of quantum dot and nanoring pattern formation on pit-patterned semiconductor substrates

We develop a properly parameterized, three-dimensional continuum-scale kinetic model for monitoring the surface morphological evolution of coherently strained heteroepitaxial thin films that captures the morphological response of epitaxially grown Ge thin films on pit-patterned Si{100} substrates. The model accounts for curvature-driven atomic diffusion on the film surface, biaxial lattice misfit strain in the film, and the wetting potential between the film and the substrate. Self-consistent dynamical simulations based on our model show formation of complex nanostructures on the epitaxial film surface, including nanorings at the rims of pits, a single quantum dot at the center of a pit, as well as multiple quantum dots inside pits with rectangular openings, consistent with experimentally observed nanostructures. Our simulation results reproduce the variation in the formed nanostructural features observed experimentally by properly varying the key experimental parameters, namely, the pit size and the pit geometry. Our study sets the stage for designing systematic experimental protocols toward precise control of complex nanoring and quantum dot patterns forming on surfaces of epitaxially grown coherently strained semiconductor thin films.

Nucleation sites of Ge nanoislands grown on pit-patterned Si substrate prepared by electron-beam lithography

Regular pit-patterned Si(001) substrates were prepared by electron-beam lithography followed by plasma chemical etching. The geometry of the pits was controlled by varying the etching conditions and the electron-beam exposure duration. It was shown that the location of three-dimensional (3D) Ge nanoislands subsequently grown on the pit-patterned Si substrates depends on the shape of the pit bottom. In the case of pits having a sharp bottom, 3D Ge islands nucleate inside the pits. For pits with a wide flat bottom, the 3D Ge island nucleation takes place at the pit periphery. This effect is attributed to the strain relaxation depending not only on the initial pit shape, but also on its evolution during the Ge wetting layer deposition. It was shown by Monte Carlo simulations that in the case of a pit with a pointed bottom, the relaxation is most effective inside the pit, while for a pit with a wide bottom, the most relaxed area migrates during Ge deposition from the pit bottom to its edges, where 3D Ge islands nucleate.

Elastic strain relaxation of GeSi nanoislands grown on pit-patterned Si(001) substrates

In this paper, we systematically investigate the elastic strain relaxation of GeSi nanoislands grown on pit-patterned Si(001) substrate using finite element method. The multi-faceted GeSi nanoislands, including domes, barns and cupolas, inside square pit are modeled based on experimental observations. The impacts of aspect ratio, pit angle and pit filling level are analyzed, based on which a fitting expression is obtained to give a complete description of the strain relaxation. The pit angles corresponding to the best strain relaxation and to the critical point for better relaxation in pit are determined at filling levels (range from 0 to 1) and aspect ratios (range from 0.2 to 0.4). It can be seen that beyond a specific aspect ratio, the relaxation keeps worse than the case of same nanoisland grown on flat substrate, regardless of the pit angle and pit filling level. Moreover, based on the strain energy balance criterion, the conditions to ensure that nanoislands grown inside pit are demonstrated as well.

Photoluminescence investigation of strictly ordered Ge dots grown on pit-patterned Si substrates

We investigate the optical properties of ordered Ge quantum dots (QDs) by means of micro-photoluminescence spectroscopy (PL). These were grown on pit-patterned Si(001) substrates with a wide range of pit-periods and thus inter QD-distances (425–3400 nm). By exploiting almost arbitrary inter-QD distances achievable in this way we are able to choose the number of QDs that contribute to the PL emission in a range between 70 and less than three QDs. This well-defined system allows us to clarify, by PL-investigation, several points which are important for the understanding of the formation and optical properties of ordered QDs. We directly trace and quantify the amount of Ge transferred from the surrounding wetting layer (WL) to the QDs in the pits. Moreover, by exploiting different pit-shapes, we reveal the role of strain-induced activation energy barriers that have to be overcome for charge carriers generated outside the dots. These need to diffuse between the energy minimum of the WL in and between the pits, and the one in the QDs. In addition, we demonstrate that the WL in the pits is already severely intermixed with Si before upright QDs nucleate, which further enhances intermixing of ordered QDs as compared to QDs grown on planar substrates. Furthermore, we quantitatively determine the amount of Ge transferred by surface diffusion through the border region between planar and patterned substrate. This is important for the growth of ordered islands on patterned fields of finite size. We highlight that the Ge WL-facets in the pits act as PL emission centres, similar to upright QDs.

Pure, single crystal Ge nanodots formed using a sandwich structure via pulsed UV excimer laser annealing

In this paper, a sandwich structure comprising a SiO2 capping layer, amorphous Germanium (a-Ge) nanodots (NDs), and a pit-patterned Silicon (Si) substrate is developed, which is then annealed by utilizing a pulsed ultraviolet excimer laser in order to fabricate an array of pure, single crystal Ge NDs at room temperature. A wide bandgap SiO2 capping layer is used as a transparent thermally isolated layer to prevent thermal loss and Si–Ge intermixing. The two-dimensional pit-patterned Si substrate is designed to confine the absorbed laser energy, reduce the melting point, and block the surface migration of the Ge. After optimizing the laser radiation parameters such that the laser energy density is 200 mJ cm−2, the laser annealing period is 10 s, and the number of laser shots is 10, pure, single crystal Ge NDs that have both a regular arrangement and a uniform size distribution are obtained in the pits of the Si substrates. The Raman spectrum shows a highly symmetric Ge transversal optical peak with a full width at half maximum of 4.2 cm−1 at 300.7 cm−1, which is close to that of the original Ge wafer. In addition, the high-resolution transmission electron microscopy image for the Ge NDs and the corresponding selected area electron diffraction pattern shows a clear single crystalline structure without any impurities.

Simulating the nucleation and growth of Ge quantum dots on Si using high-efficiency algorithms

Original approaches are presented for elucidating a microscopic mechanism of surface atomic diffusion and simulating the heteroepitaxial nanostructure growth on substrates with a complex relief. Using the molecular dynamics method, the energy surface of a pit-patterned Si substrate is mapped out and the conditions for the nucleation of more than one Ge island in a pit are established. A Monte Carlo model is developed that reproduces the Ge growth on Si with regard to elastic effects in a heterosystem. By the example of this Monte Carlo model, it is demonstrated how to reduce the calculation time by optimizing the description of the crystal lattice state in computer cache memory and by using parallel algorithms for working on a computer cluster.

Effect of surface Si redistribution on the alignment of Ge dots grown on pit-patterned Si(001) substrates

Thermally activated redistribution of Si surface atoms is found to be a crucial factor for the growth of aligned Ge dots on pit-patterned Si(001) substrates. A phenomenon of Si accumulation around the edge of pits significantly alters the substrate surface morphology. As the pit spacing is reduced to below 100 nm, a convex morphology developed between adjacent pits causes a chemical potential distribution that drives the Ge dots into the pits. In addition, the pits of an etching depth greater than 60 nm will evolve into truncated inverted pyramids with sharp base corners that provide deep potential wells for the confinement of Ge dots. Perfectly aligned Ge dots are obtained on pit-patterned Si substrates with this range of pit spacing and etching depth. We also find that the initial geometric shape of the pits does not affect the spatial arrangement of Ge dots.

Electronic structures of GeSi nanoislands grown on pit-patterned Si(001) substrate

Patterning pit on Si(001) substrate prior to Ge deposition is an important approach to achieve GeSi nanoislands with high ordering and size uniformity. In present work, the electronic structures of realistic uncapped pyramid, dome, barn and cupola nanoislands grown in {105} pits are systematically investigated by solving Schrodinger equation for heavy-hole, which resorts to inhomogeneous strain distribution and nonlinear composition-dependent band parameters. Uniform, partitioned and equilibrium composition profile (CP) in nanoisland and inverted pyramid structure are simulated separately. We demonstrate the huge impact of composition profile on localization of heavy-hole: wave function of ground state is confined near pit facets for uniform CP, at bottom of nanoisland for partitioned CP and at top of nanoisland for equilibrium CP. Moreover, such localization is gradually compromised by the size effect as pit filling ratio or pit size decreases. The results pave the fundamental guideline of designing nanoislands on pit-patterned substrates for desired applications.

Formation of germanium nanoislands on pit-patterned silicon substrates by means of the molecular dynamics method

The molecular dynamics method is used to study the formation of Ge nanoislands on pit-patterned Si(100) substrates. For substrates with overlapping pits and pits in the shape of truncated inverted pyramids, the energy surface is calculated. On the basis of its analysis, the mechanism of nuclear surface diffusion on the pit-patterned surface is described. The specific energy of Ge/Si heterostructures with different morphology of nanoislands in pits is calculated. It is shown that the configuration with multiple nanoislands in a pit can be thermodynamically favorable.

Dislocation engineering in SiGe on periodic and aperiodic Si(001) templates studied by fast scanning X-ray nanodiffraction

Fast-scanning X-ray nanodiffraction microscopy is used to directly visualize the misfit dislocation network in a SiGe film deposited on a pit-patterned Si substrate at the beginning of plastic relaxation. X-ray real-space diffracted intensity maps are compared to topographic atomic force microscopy images, in which crosshatch lines can be seen. The change in intensity distribution as a function of the incidence angle shows localized variations in strain within the SiGe film. These variations, which reflect the order imposed by the substrate pattern, are attributed to the presence of both bunches of misfit dislocations and defect-free regions.

Recipes for the fabrication of strictly ordered Ge islands on pit-patterned Si(001) substrates

We identify the most important parameters for the growth of ordered SiGe islands on pit-patterned Si(001) substrates. From a multi-dimensional parameter space we link individual contributions to isolate their influence on ordered island growth. This includes the influences of: the pit size, pit depth and pit period on the Si buffer layer and subsequent Ge growth; the pit sidewall inclination on Ge island growth; the amount of Ge on island morphologies as well as the influences of the pit-size homogeneity, the pit period, the Ge growth temperature and rate on island formation. We highlight that the initial pit shape and pit size in combination with the growth conditions of the Si buffer layer should be adjusted to provide suitable preconditions for the growth of Ge islands with the desired size, composition and nucleation position. Furthermore, we demonstrate that the wetting layer between pits can play the role of a stabilizer that inhibits shape transformations of ordered islands. Thus, dislocation formation within islands can be delayed, uniform arrays of one island type can be fabricated and secondary island nucleation between pits can be impeded. These findings allow us to fabricate perfectly ordered and homogeneous Ge islands on one and the same sample, even if the pit period is varied from a few hundred nanometres to several micrometres.

Closely spaced SiGe barns as stressor structures for strain-enhancement in silicon

We present tensile and compressive strains realized within the same Si capping layer on an array of SiGe islands grown on pit-patterned (001) Si substrates. The strain distributions are obtained from synchrotron X-ray diffraction studies in combination with three-dimensional finite element calculations and simulations of the diffracted intensities. For barn-shaped islands grown at 720 °C with average Ge contents of 30%, the Si cap layer is misfit- and threading-dislocation free and exhibits compressive strains as high as 0.8% in positions between the islands and tensile strains of up to 1% on top of the islands.

Factors influencing epitaxial growth of three-dimensional Ge quantum dot crystals on pit-patterned Si substrate

We investigated the molecular beam epitaxy growth of three-dimensional (3D) Ge quantum dot crystals (QDCs) on periodically pit-patterned Si substrates. A series of factors influencing the growth of QDCs were investigated in detail and the optimized growth conditions were found. The growth of the Si buffer layer and the first quantum dot (QD) layer play a key role in the growth of QDCs. The pit facet inclination angle decreased with increasing buffer layer thickness, and its optimized value was found to be around 21°, ensuring that all the QDs in the first layer nucleate within the pits. A large Ge deposition amount in the first QD layer favors strain build-up by QDs, size uniformity of QDs and hence periodicity of the strain distribution; a thin Si spacer layer favors strain correlation along the growth direction; both effects contribute to the vertical ordering of the QDCs. Results obtained by atomic force microscopy and cross-sectional transmission electron microscopy showed that 3D ordering was achieved in the Ge QDCs with the highest ever areal dot density of 1.2 × 1010 cm−2, and that the lateral and the vertical interdot spacing were ∼10 and ∼2.5 nm, respectively.

Anomalous Smoothing Preceding Island Formation During Growth on Patterned Substrates

We show that on suitably pit-patterned Si(001), deposition of just a few atomic layers of Ge can trigger a far larger flow of Si into the pits. This surprising effect results in anomalous smoothing of the substrate preceding island formation in the pits. We show that the effect naturally arises in continuum simulations of growth, and we identify its physical origin in the composition dependence of the surface diffusivity. Our interpretation suggests that anomalous smoothing is likely to also occur in other technologically relevant heteroepitaxial systems.

Thermally induced morphology evolution of pit-patterned Si substrate and its effect onnucleation properties of Ge dots

We demonstrate the effect of the pre-growth heat treatment process on the nucleationproperties of Ge dots grown on pit-patterned Si(001) substrates. The prefabricated 200 nmdiameter pits inherently evolve into truncated inverted pyramids (TIPs) with⟨110⟩ base edgesand a 7°–9° sidewall slope during heat treatment; this morphology transformation is robust against variationsin shape and orientation of the pit patterns. Uniform Ge dots with an areal density of4 × 109 cm − 2 were obtained on the Si substrates having TIPs. Each TIP containsfour aligned Ge dots locating symmetrically with respect to ⟨110⟩. These dots exhibit an elliptical dome shape with major axis oriented along⟨100⟩. The nucleation position, shape and spatial orientation of these Ge dots coincide with thecalculated surface chemical potential distribution of the TIP.

A Combined <I>In Situ</I> Grazing Incidence Small Angle X-Ray Scattering and Grazing Incidence X-Ray Diffraction Study of the Growth of Ge Islands on Pit-Patterned Si(001) Substrates

The growth of Ge islands on a pit-patterned Si(001) template is investigated in situ, combining grazing incidence diffraction, multiple wavelength anomalous diffraction, and small angle scattering. This allows monitoring in situ the detailed structural and morphological evolutions of the pits, of the wetting-layer and of the nucleated islands on the pit-patterned Si(001) substrate. It is shown that after Si regrowth, the Si substrate displays {107} and {1 1 11} facets. During the very first stages of Ge growth, the preliminary facets of the Si substrate are energetically unfavourable, and the pit facets break up into a rather complex pattern of {10n} and {11m} facets with n > 7 and m > 11. At 5 and 6 ML, intensity rods from {105} and {113}-type facets appear in the GISAXS images revealing the formation of pyramids and domes, respectively. The degree of ordering, the shape, strain and composition of the islands are characterized during the growth process to provide a detailed evolution of their structure and morphology.