Equilibrium alloy properties by direct simulation: Oscillatory segregation at the Si-Ge(100) 2 x 1 surface

Composition-dependent chemical ordering predicted in Pt-Ag nanoalloys

Pt-Ag nanoalloys display an astonishing chemical organization depending on their size and composition. Reversed size-dependent stabilization of ordered nanophases [J. Pirart et al., Nat. Commun., 2019, 10, 1982-1989] has recently been shown around equiconcentration. We extend this study by a theoretical investigation on the whole range of compositions showing a significant composition-dependent chemical ordering in Pt-Ag nanoalloys. At a low silver content, the surface exhibits a strong Ag segregation coupled to a (2 × 1) superstructure on the (100) facets. By increasing the silver concentration, the system displays an L1₁ ordered phase in the core, interrupted in a narrow range of concentrations by a concentric multishell structure characterized by an alternation of Ag-pure/Pt-pure concentric layers starting from the surface shell to the core. Although the L1₁ ordered phase has been observed experimentally, the concentric multishell structure is lacking due to the difficulty of the experimental characterization.

Stress effect on segregation and ordering in Pt-Ag nanoalloys

We performed a theoretical study of the chemical ordering and surface segregation of Pt-Ag nanoalloys in the range of size from 976 to 9879 atoms (3.12 to 6.76 nm). We used an original many-body potential able to stabilize the L1₁ordered phase at equiconcentration leading to a strong silver surface segregation. Based on a recent experimental study where nanoparticles up to 2.5 nm have been characterized by high transmission electron microscopy with the L1₁ordered phase in the core and a silver surface shell, we predict in our model via Monte Carlo simulations that the lower energy configuration is more complicated with a three-shell alternance of Ag/Pt/Ag from the surface surrounding the L1₁ordered phase in the core. The stress analysis demonstrates that this structure softens the local stress distribution inside the nanoparticle which contributes to reduce the internal energy.

Capacity retention behavior and morphology evolution of SixGe1-x nanoparticles as lithium-ion battery anode

Engineering silicon into nanostructures has been a well-adopted strategy to improve the cyclic performance of silicon as a lithium-ion battery anode. Here, we show that the electrode performance can be further improved by alloying silicon with germanium. We have evaluated the electrode performance of SixGe1-x nanoparticles (NPs) with different compositions. Experimentally, SixGe1-x NPs with compositions approaching Si50Ge50 are found to have better cyclic retention than both Si-rich and Ge-rich NPs. During the charge/discharge process, NP merging and Si-Ge homogenization are observed. In addition, a distinct morphology difference is observed after 100 cycles, which is believed to be responsible for the different capacity retention behavior. The present study on SixGe1-x alloy NPs sheds light on the development of Si-based electrode materials for stable operation in lithium-ion batteries (e.g., through a comprehensive design of material structure and chemical composition). The investigation of composition-dependent morphology evolution in the delithiated Li-SiGe ternary alloy also significantly broadens our understanding of dealloying in complex systems, and it is complementary to the well-established understanding of dealloying behavior in binary systems (e.g., Au-Ag alloys).

Crossover among structural motifs in Pd–Au nanoalloys

The crossovers among the most abundant structural motifs (icosahedra, decahedra and truncated octahedra) of Pd–Au nanoalloys are determined theoretically in a size range between 2 and 7 nm and for three compositions equivalent to Pd₃Au, PdAu and PdAu₃.

Lattice thermal conductivity of Si(1-x)Ge(x) nanocomposites

We calculate the lattice thermal conductivity in model Si(1-x)Ge(x) nanocomposites by molecular dynamics in a transient thermal conduction regime. Our simulations provide evidence that thermal transport depends only marginally on stoichiometry in the range 0.2≤x≤0.8, while it is deeply affected by the granulometry. In particular, we show that Si(1-x)Ge(x) nanocomposites have lattice thermal conductivity below the corresponding bulk alloy with the same stoichiometry. The main role in affecting thermal conduction is provided by grain boundaries, which largely affect vibrational modes with a long mean-free path.

Theoretical studies of the passivants' effect on the Si(x)Ge(1-x) nanowires: composition profiles, diameter, shape, and electronic properties

Theoretically, we have performed a systematic investigation on the passivants' effect on the geometrical and electronic properties of Si(x)Ge(1-x) nanowires. First-principles calculations revealed that, in the nanowires passivated by fluorine (F)∕chlorine (Cl)∕hydrogen (H) atoms, Si atoms preferred to segregate towards the surface due to the stronger Si-X bonds than that of Ge-X bonds (X = F, Cl, H). The energy barriers of X atoms' desorption is higher than that of the Si∕Ge atoms' exchanging, inducing a feasible and strong surface segregation of Si atoms at proper temperature. Considering the Si∕Ge interactions and mixing entropy, the composition profiles of Si∕Ge distributions are obtained by minimizing the Gibbs free energy, which indicates the outmost layer of surface should be mostly occupied by Si. With total Si surface segregation, the diameter and shape of most stable Si(x)Ge(1-x) nanowires are found to be determined by the composition x and the passivants' chemical potential. In addition, charge distribution of near-gap levels can be modulated through the surface passivants. Our finding provides a practical avenue to tune the electronic properties of Si(x)Ge(1-x) nanowires, by modulating the morphologies of nanowires with the composition control of Si∕Ge and the chemical potential of passivants.

Lattice thermal conductivity of semiconducting bulk materials: atomistic simulations

This paper presents a theoretical investigation of the microscopic mechanisms responsible for heat transport in bulk Si, Ge and SiGe alloys, with the goal of providing insight into design rules for efficient Si-based nanostructured thermoelectric semiconductors. We carried out a detailed atomistic study of the thermal conductivity, using molecular dynamics and the Boltzmann transport equation. We investigated in detail the effects of the physical approximations underlying each approach, as well as the effect of the numerical approximations involved in the implementation of the two different methods. Our findings permitted us to understand and reconcile apparently conflicting results reported in the literature.

Ordering mechanisms in epitaxial SiGe nanoislands

We investigate and elucidate the surprising observation of atomically ordered domains in dome-shaped SiGe nanoislands. We show, through atomistic Monte Carlo simulations, that this ordering is a surface-related phenomenon, and that is driven by surface equilibrium rather than by surface kinetics. The ordering depends on facet orientation. The main source of ordering is the {15 3 23} facet, while the {105} and {113} facets contribute less. Subsurface ordered configurations self-organize under this facet and are frozen-in and buried during island growth, giving rise to the ordered domains. Ordering mechanisms based on constrained surface kinetics, requiring step-mediated segregation at the island facets, are shown to be much less likely.

Suppression of intermixing in strain-relaxed epitaxial layers

Misfit strain plays a crucial role in semiconductor heteroepitaxy, driving alloy intermixing or the introduction of dislocations. Here we predict a strong coupling between these two modes of strain relaxation, with unexpected consequences. Specifically, strain relaxation by dislocations can suppress intermixing between the heterolayer and the substrate. Monte Carlo simulations and continuum modeling show that the suppression, though not absolute, can be surprisingly large, even at high temperatures. The effect is strongest for a large misfit (e.g., InAs on GaAs) or for thin substrates (e.g., Ge on silicon on insulator).

Nanoscale pit formation at 2D Ge layers on Si: influence of energy and entropy

The structural stability of two-dimensional (2D) SiGe nanostructures is studied by scanning tunneling microscopy. The formation of pits with a diameter of 2-30 nm in one atomic layer thick Ge stripes is observed. The unanticipated pit formation occurs due to an energetically driven motion of the Ge atoms out of the Ge stripe towards the Si terminated step edge followed by an entropy driven GeSi intermixing at the step edge. Using conditions where the pits coalesce results in the formation of freestanding 8 nm wide GeSi wires on Si(111).

Thermodynamic theory of epitaxial alloys: first-principles mixed-basis cluster expansion of (In, Ga)N alloy film

Epitaxial growth of semiconductor alloys onto a fixed substrate has become the method of choice to make high quality crystals. In the coherent epitaxial growth, the lattice mismatch between the alloy film and the substrate induces a particular form of strain, adding a strain energy term into the free energy of the alloy system. Such epitaxial strain energy can alter the thermodynamics of the alloy, leading to a different phase diagram and different atomic microstructures. In this paper, we present a general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions. With a finite number of first-principles calculation inputs, our method can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves. Epitaxial (In, Ga)N zinc-blende alloy grown on GaN(001) substrate is taken as an example to demonstrate the details of the method. Two (210) superlattice structures, (InN)(2)/(GaN)(2) (at x = 0.50) and (InN)(4)/(GaN)(1) (at x = 0.80), are identified as the ground state structures, in contrast to the phase-separation behavior of the bulk alloy.

Evolution of thermodynamic potentials in closed and open nanocrystalline systems: Ge-Si:Si(001) islands

An open (closed) system, in which matter is (not) exchanged through surface diffusion, was realized via growth kinetics. Epitaxially grown Si-Ge:Si (001) islands were annealed in different environments affecting the diffusivity of Si adatoms selectively. The evolution of the driving forces for intermixing while approaching the equilibrium was inferred from Synchrotron x-ray measurements of composition and strain. For the open system, intermixing due to the Si inflow from the wetting layer (reservoir) caused a decrease in the Ge content, leading to a lowering of the elastic energy and an increase in the mixing entropy. In contrast, for the closed system, while keeping the average Ge composition constant, atom rearrangement within the islands led to an increase in both elastic and entropic contributions. The Gibbs free energy decreased in both cases, despite the different evolution paths for the composition profiles.

Strain-minimizing tetrahedral networks of semiconductor alloys

The atomic size mismatch between different binary semiconductors has been long known to limit their mutual solubility, leading instead to phase separation into incoherent phases, forming inhomogeneous mixtures that severely limit technological applications that rely on carrier transport. We show here that this atomic size mismatch can lead, under coherent conditions, to the formation of a homogeneous alloy with characteristic (201) two-monolayer ordering. This occurs because such specific layer arrangement corresponds to a unique strain-minimizing network in tetrahedral systems.

Thermodynamics of coherently-strained GexSi1-x nanocrystals on Si(001): alloy composition and island formation

We determined the enthalpic and entropic contributions to the thermodynamics of coherently strained nanocrystals grown via deposition of pure Ge on Si(001) surfaces at 600 and 700 degrees C by analyzing their composition profile and local strain. We found that the free energy associated with the entropy of mixing, which drives GexSi1-x alloy formation, was significantly larger than the relaxation enthalpy that produces the islands. Thus, entropy plays a significant role in the evolution of the size and shape of the islands during growth through the strong thermodynamic drive to form an alloy.

Probing the structure and energetics of dislocation cores in SiGe alloys through Monte Carlo simulations

We present a methodology for the investigation of dislocation energetics in segregated alloys based on Monte Carlo simulations which equilibrate the topology and composition of the dislocation core and its surroundings. An environment-dependent partitioning of the system total energy into atomic contributions allows us to link the atomistic picture to continuum elasticity theory. The method is applied to extract core energies and radii of 60 degrees glide dislocations in segregated SiGe alloys which are inaccessible by other methods.

Atomistics of Ge deposition on Si(100) by atomic layer epitaxy

Chlorine termination of mixed Ge/Si(100) surfaces substantially enhances the contrast between Ge and Si sites in scanning tunneling microscopy observations. This finding enables a detailed investigation of the spatial distribution of Ge atoms deposited on Si(100) by atomic layer epitaxy. The results are corroborated by photoemission measurements aided by an unusually large chemical shift between Cl adsorbed on Si and Ge. Adsorbate-substrate atomic exchange during growth is shown to be important. The resulting interface is thus graded, but characterized by a very short length scale of about one monolayer.

Growth model for atomic ordering: the case for quadruple-period ordering in GaAsSb alloys

Quadruple-period ordering in GaAsSb alloys is studied both theoretically and experimentally. A growth model is proposed to account for the observed three-dimensional (3D) ordered structure. The model is qualitatively different from the widely accepted surface reconstruction and dimerization-induced ordering models that strictly speaking explain only the in-plane 2D patterns. Here, we show that the already ordered substrate will affect the reconstruction of the growth front with respect to the substrate to ensure a correct stacking of the individual 2D ordered layers into the observed 3D lattice.

Thermodynamics of C incorporation on Si(100) from ab initio calculations

We study the thermodynamics of C incorporation on Si(100), a system where strain and chemical effects are both important. Our analysis is based on first-principles atomistic calculations to obtain the important lowest-energy structures, and a classical effective Hamiltonian which is employed to represent the long-range strain effects and incorporate the thermodynamic aspects. We determine the equilibrium phase diagram in temperature and C chemical potential, which allows us to predict the mesoscopic structure of the system that should be observed under experimentally relevant conditions.

Diffusion of Ge below the Si(100) surface: theory and experiment

We have studied diffusion of Ge into subsurface layers of Si(100). Auger electron diffraction measurements show Ge in the fourth layer after submonolayer growth at temperatures as low as 500 degrees C. Density functional theory predictions of equilibrium Ge subsurface distributions are consistent with the measurements. We identify a surprisingly low energy pathway resulting from low interstitial formation energy in the third and fourth layers. Doping significantly affects the formation energy, suggesting that n-type doping may lead to sharper Si/Ge interfaces.

(110) HREM of interfacial structures in semiconductor hetero-structures

We have established a (110) cross-sectional high-resolution transmission electron microscopy (HREM) method to observe atomic structures of semiconductor hetero-interfaces. We show theoretically that the semiconductors in a hetero-structure exhibit strong contrast for an EM specimen thickness near their extinction distances, allowing atomic-scale observations of the interfacial structures between them. Furthermore, to obtain a clear HREM image, an EM specimen preparation technique is developed in which chemical etching is used to remove ion milling artifacts. This HREM method allows edge-on imaging of interfaces formed along the (110) direction; observations of atomic steps at AlAs/GaAs interfaces and a chemically ordered structure at Si/Ge interfaces are demonstrated.