Formation of Ge nanoripples on vicinal Si (1110): from Stranski-Krastanow seeds to a perfectly faceted wetting layer

Observation of negative surface and interface energies of quantum dots

Surface energy is a fundamental property of materials and is particularly important in describing nanomaterials where atoms or molecules at the surface constitute a large fraction of the material. Traditionally, surface energy is considered to be a positive quantity, where atoms or molecules at the surface are less thermodynamically stable than their counterparts in the interior of the material because they have fewer bonds or interactions at the surface. Using calorimetric methods, we show that the surface energy is negative in some prototypical colloidal semiconductor nanocrystals, or quantum dots with organic ligand coatings. This implies that the surface atoms are more thermodynamically stable than those on the interior due to the strong bonds between these atoms and surfactant molecules, or ligands, that coat their surface. In addition, we extend this work to core/shell indium phosphide/zinc sulfide nanocrystals and show that the interfacial energy between these materials is highly thermodynamically favorable in spite of their large lattice mismatch. This work challenges many of the assumptions that have guided thinking about colloidal nanomaterial thermodynamics, investigates the fundamental stability of many technologically relevant colloidal nanomaterials, and paves the way for future experimental and theoretical work on nanocrystal thermodynamics.

Design and synthesis of multigrain nanocrystals via geometric misfit strain

The impact of topological defects associated with grain boundaries (GB defects) on the electrical, optical, magnetic, mechanical and chemical properties of nanocrystalline materials^1,2 is well known. However, elucidating this influence experimentally is difficult because grains typically exhibit a large range of sizes, shapes and random relative orientations^3-5. Here we demonstrate that precise control of the heteroepitaxy of colloidal polyhedral nanocrystals enables ordered grain growth and can thereby produce material samples with uniform GB defects. We illustrate our approach with a multigrain nanocrystal comprising a Co₃O₄ nanocube core that carries a Mn₃O₄ shell on each facet. The individual shells are symmetry-related interconnected grains⁶, and the large geometric misfit between adjacent tetragonal Mn₃O₄ grains results in tilt boundaries at the sharp edges of the Co₃O₄ nanocube core that join via disclinations. We identify four design principles that govern the production of these highly ordered multigrain nanostructures. First, the shape of the substrate nanocrystal must guide the crystallographic orientation of the overgrowth phase⁷. Second, the size of the substrate must be smaller than the characteristic distance between the dislocations. Third, the incompatible symmetry between the overgrowth phase and the substrate increases the geometric misfit strain between the grains. Fourth, for GB formation under near-equilibrium conditions, the surface energy of the shell needs to be balanced by the increasing elastic energy through ligand passivation^8-10. With these principles, we can produce a range of multigrain nanocrystals containing distinct GB defects.

Formation of Self-Connected Si0.8Ge0.2 Lateral Nanowires and Pyramids on Rib-Patterned Si(1 1 10) Substrate

In this work, Si_0.8Ge_0.2 is deposited onto the rib-patterned Si (1 1 10) template oriented in the [1 -1 0] direction. Atomic force microscopy (AFM) reveals that the rib sidewalls reshape into pyramid-covered (0 0 1) and smooth {1 1 3} facets, respectively, while the {1 0 5} facets-bounded lateral SiGe nanowires dominate the rib top along the [5 5 -1] direction. At both the rib shoulder sites and the pyramid vacancy sites, self-connecting occurs between the meeting nanowire and pyramids to form elongated huts, which are driven by the minimization of the total energy density according to the finite-element simulations results. These results suggest a convenient solution to form lateral SiGe nanowires covering multi-faceted surfaces on the patterned template.

Theoretical Investigation of Biaxially Tensile-Strained Germanium Nanowires

We theoretically investigate highly tensile-strained Ge nanowires laterally on GaSb. Finite element method has been used to simulate the residual elastic strain in the Ge nanowire. The total energy increment including strain energy, surface energy, and edge energy before and after Ge deposition is calculated in different situations. The result indicates that the Ge nanowire on GaSb is apt to grow along 〈100〉 rather than 〈110〉 in the two situations and prefers to be exposed by {105} facets when deposited a small amount of Ge but to be exposed by {110} when the amount of Ge exceeds a critical value. Furthermore, the conduction band minima in Γ-valley at any position in both situations exhibits lower values than those in L-valley, leading to direct bandgap transition in Ge nanowire. For the valence band, the light hole band maxima at Γ-point is higher than the heavy hole band maxima at any position and even higher than the conduction band minima for the hydrostatic strain more than ∼5.0%, leading to a negative bandgap. In addition, both electron and hole mobility can be enhanced by owing to the decrease of the effective mass under highly tensile strain. The results suggest that biaxially tensile-strained Ge nanowires hold promising properties in device applications.

Towards promising modification of GeSi nanostructures via self-assembly on miscut Si(001) substrates

Self-assembled GeSi nanostructures on miscut Si(001) substrates are studied systematically with regard to the miscut angle and azimuth, the amount of Ge and the growth temperature. The comprehensive dependence of the spatial arrangement, which can exhibit one- and two-dimensional (1D and 2D) ordering, as well as the shape and density, of GeSi nanostructures on the miscut angle is observed. The orientation and side-walls of the 1D ordered in-plane GeSi nanowires on miscut Si(001) substrates are intimately associated with the miscut azimuth towards the 〈110〉 or 〈010〉 directions. Furthermore, the unique evolution of the GeSi nanostructures with the amount of Ge and the growth temperature on miscut Si (001) substrates towards the 〈010〉 direction is discovered. Such promising features of self-assembled GeSi nanostructures on miscut Si (001) substrates are explained in terms of the thermodynamics and growth kinetics, which are both affected significantly by the substrate vicinality. These results demonstrate that the miscut substrates offer a promising degree of freedom for the feasible modification of self-assembled nanostructures.

Generalized Muller-Kern formula for equilibrium thickness of a wetting layer with respect to the dependence of the surface energy of island facets on the thickness of the 2D layer

Experimental results indicate a particular importance of such a value as the equilibrium thickness of the wetting layer during epitaxial growth according to the Stranski-Krastanow mechanism in systems with a lattice mismatch. In this paper the change in free energy during the transition of atoms from the wetting layer to the island in such systems is considered. Recent experimental results also show that the surface energy of the island's facets depends upon the thickness of the deposited material. So, in this paper the equilibrium thickness of the wetting layer, at which transition from 2D to 3D growth becomes energetically favorable, is calculated with the assumption that the specific energy of the island's facets depends upon the wetting layer thickness. In this approximation a new generalized Muller-Kern formula is obtained. As an illustration of the proposed method, an example of a numerical calculation according to the new formula for the material system of germanium on a silicon (001) surface is given. The result for the found equilibrium thickness of the wetting layer is rather unexpected since it differs from the value obtained in the bounds of the traditional Muller-Kern model.

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.

Unique features of laterally aligned GeSi nanowires self-assembled on the vicinal Si (001) surface misoriented toward the [100] direction

We demonstrate laterally aligned and catalyst-free GeSi nanowires (NWs) via self-assembly of Ge on miscut Si (001) substrates toward the [100] direction by an angle θ (θ < 11°). The NWs are bordered by (001) and (105) facets, which are thermodynamically stable. By tuning the miscut angle θ, the NW height can be easily modulated with a nearly constant width. The thickness of the wetting layer beneath the NWs also shows a peculiar behavior with a minimum at around 6°. An analytical model, considering the variation of both the surface energy and the strain energy of the epilayer on vicinal surfaces with the miscut angle and layer thickness, shows good overall agreement with the experimental results. It discloses that both the surface energy and stain energy of the epilayer on vicinal surfaces can be considerably affected in the same trend by the surface steps. Our results not only shed new light on the growth mechanism during heteroepitaxial growth, but also pave a prominent way to fabricate and meanwhile modulate laterally aligned and dislocation-free NWs.

Evolution of epitaxial semiconductor nanodots and nanowires from supersaturated wetting layers

In this tutorial we review recent progress in the design and growth of epitaxial semiconductor nanostructures in lattice-mismatched material systems. We focus on the Ge on Si model system after pointing out the similarities to III-V and other growth systems qualitatively as well as quantitatively. During material deposition, the first layers of the epitaxial film wet the surface before the formation of strain-driven three-dimensional nanostructures. In particular, we stress that the supersaturation of the wetting layer (WL), whose relevance is often neglected, plays a key role in determining the nucleation and growth of nanodots (NDs), nanodot-molecules and nanowires (NWs). At elevated growth temperatures the Ge reservoir in the planar, supersaturated WL is abruptly consumed and generates NDs with highly homogeneous sizes - a process mainly driven by elastic energy minimization. Furthermore, the careful control of the supersaturated Ge layer allows us to obtain perfectly site-controlled, ordered NDs or ND-molecules on pit-patterned substrates for a broad range of pit-periods. At low growth temperatures subtle interplays between surface energies of dominant crystal facets in the system drive the material transfer from the supersaturated WL into the elongating NWs growing horizontally, dislocation- and catalyst-free on the substrate surface. Due to the similarities in the formation of nanostructures in different epitaxial semiconductor systems we expect that the observation of the novel growth phenomena described in this Tutorial Review for Ge/Si should be relevant for other lattice-mismatched heterostructure systems, too.

SOWOS: an open-source program for the three-dimensional Wulff construction

A Fortran90 program for the determination of the Wulff construction, starting solely from the directions of the bounding facets (defined by the user), is presented.SOWOSstands for solid of Wulff open source, and the program is distributed freely with no charge to the user, being readily available to the community for immediate use. Its simple algorithm (which will be explained) allows the determination of complex solids with hundreds of facets in just seconds on any machine, requiring only a small amount of memory. It is able to determine even the smallest facets and shortest edges and to distinguish almost adjacent vertices. The output files give a complete range of information about the structure: the coordinates of the vertices and the facets common to them, the extension of the facets and bounding vertices, and the length of the edges and extreme vertices. These details enable the reconstruction of the shape in any other (commercial) software for further processing. Visualization is straightforwardviathe free programgnuplot. A feature for the creation of cubic crystal atomistic models of the resultant solids is included. The program may be a useful tool for crystallography, nanostructures and any other field where crystal facets are involved.

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.

Monolithic growth of ultrathin Ge nanowires on Si(001)

Self-assembled Ge wires with a height of only 3 unit cells and a length of up to 2 micrometers were grown on Si(001) by means of a catalyst-free method based on molecular beam epitaxy. The wires grow horizontally along either the [100] or the [010] direction. On atomically flat surfaces, they exhibit a highly uniform, triangular cross section. A simple thermodynamic model accounts for the existence of a preferential base width for longitudinal expansion, in quantitative agreement with the experimental findings. Despite the absence of intentional doping, the first transistor-type devices made from single wires show low-resistive electrical contacts and single-hole transport at sub-Kelvin temperatures. In view of their exceptionally small and self-defined cross section, these Ge wires hold promise for the realization of hole systems with exotic properties and provide a new development route for silicon-based nanoelectronics.

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.