Diamond Cubic Si Research Articles

High thermoelectric performance in metastable phase of silicon: A first-principles study

In this work, both thermal and electrical transport properties of diamond-cubic Si (Si-I) and metastable R8 phases of Si (Si-XII) are comparatively studied by using first-principles calculations combined with the Boltzmann transport theory. The metastable Si-XII shows one magnitude lower lattice thermal conductivity than stable Si-I from 300 to 500 K, attributed from the stronger phonon scattering in three-phonon scattering processes of Si-XII. For electronic transport properties, although Si-XII with smaller bandgap (0.22 eV) shows a lower Seebeck coefficient, the electrical conductivities of anisotropic n-type Si-XII show considerable values along the x axis due to the small effective masses of electrons along this direction. The peaks of the thermoelectric figure of merit (ZT) in n-type Si-XII are higher than that of p-type ones along the same direction. Owing to the lower lattice thermal conductivity and optimistic electrical conductivity, Si-XII exhibits larger optimal ZT compared with Si-I in both p- and n-type doping. For n-type Si-XII, the optimal ZT values at 300, 400, and 500 K can reach 0.24, 0.43, and 0.63 along the x axis at carrier concentrations of 2.6×1019, 4.1×1019, and 4.8×1019 cm−3, respectively. The reported results elucidate that the metastable Si could be integrated to the thermoelectric power generator.

Phase stability and the interface structure of a nanoscale Si crystallite in Al-based alloys.

An atomic-scale understanding of the role of strain on the microstructural properties of nanoscale precipitates will be helpful to explore the precipitation behavior as well as the structure-property relationships in crystalline multi-phase systems. Nanoscale Si precipitates are formed in Al-based alloys prepared by selective laser melting. The phase structure and the nature of heterointerface have been characterized using advanced electron microscopy. The nanocrystalline Si mainly contains two polymorphs, diamond-cubic Si (DC-Si) and 4H hexagonal Si (4H-Si). Heteroepitaxy occurs at the DC-Si(111)/Al(100) and 4H-Si(0001)/Al(100) interfaces in terms of a coincidence-site lattice model. The nanocrystalline Si undertakes tensile strain superposed by the matrix through heterointerfaces, facilitating the formation of 4H-Si in the nanoscale crystallite, which provides a strategy for designing Si polymorphic materials by strain engineering.

Modeling and simulation of phase transformation and crack formation during scribing of mono-crystalline silicon

This paper presents a simple two-parameter constitutive model to describe the material deformation behavior during scribing of mono-crystalline silicon (Si) – a process characterized by phase transformation and crack formation. The effect of phase transformation and volume densification of diamond-cubic Si (Si-I) to metallic Si (β-Si) during the loading stage is described by a modified Drucker-Prager yield surface. During the unloading stage, β-Si is completely transformed to amorphous Si (a-Si) due to the high unloading rate. The volume expansion accompanying the amorphization is described by a newly defined yield surface. The initiation and propagation of cracks are modeled using the extended finite element method (XFEM). The two constitutive model parameters, namely the cohesion parameter d and the initial yield stress ps, are calibrated using data from nano-indentation tests. The model is shown to be capable of predicting the load-displacement curve during nano-indentation of Si, including the elbow feature experimentally observed during the unloading stage. The material model is then used in a finite element model of scribing of mono-Si, and shown to successfully predict the residual depth of the scribed groove as well as the crack formation observed at the ductile-brittle transition point.

The atomistic representation of first strain-gradient elastic tensors

We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy–Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.

Thermal evolution of the metastable r8 and bc8 polymorphs of silicon

The kinetics of two metastable polymorphs of silicon under thermal annealing was investigated. These phases with body-centered cubic bc8 and rhombohedral r8 structures can be formed upon pressure release from metallic silicon. In this study, these metastable polymorphs were formed by two different methods, via point loading and in a diamond anvil cell (DAC). Upon thermal annealing different transition pathways were detected. In the point loading case, the previously reported Si-XIII formed and was confirmed as a new phase with an as-yet-unidentified structure. In the DAC case, bc8-Si transformed to the hexagonal-diamond structure at elevated pressure, consistent with previous studies at ambient pressure. In contrast, r8-Si transformed directly to diamond-cubic Si at a temperature of . These data were used to construct diagrams of the metastability regimes of the polymorphs formed in a DAC and may prove useful for potential technological applications of these metastable polymorphs.

Precipitation and hardening in Al–Si–Ge

The principal focus of this work is to explain precipitation in Al–1 at.%Si–1at%Ge. The microstructure is characterized using conventional and high resolution transmission electron microscopy, as well as energy dispersive X-ray spectroscopy. The first precipitates to come out of solid solution have a cube–cube orientation relationship with the matrix. High resolution TEM demonstrated that all the precipitates start out, and remain multiply twinned throughout the aging treatment. Any twinned section of the precipitate no longer maintains a low index interface with the matrix, and consequently goes from a crystallographic to a spherical interface with the matrix. This explains the equiaxed shape of the Si–Ge precipitates. There is a variation in the stoichiometry of the precipitates, with the mean composition being Si–44.5 at.%Ge. It is also shown that in Al–Si–Ge it is not possible to achieve satisfactory hardness through conventional heat treatment. This result is explained in terms of sluggish precipitation of the diamond-cubic Si–Ge phase coupled with particle coarsening.

Transferable nonorthogonal tight-binding parameters for silicon.

Nonorthogonal Slater-Koster (``tight-binding'') parameters have been fitted to linear muffin-tin orbital band structures of silicon in the hypothetical sc, fcc, and bcc structures at the density of ordinary diamond-cubic silicon. First- and second-neighbor parameters are used for all three structures. When the eight parameters (${H}_{\mathrm{ss}\ensuremath{\sigma}}$,...,${S}_{\mathrm{pp}\ensuremath{\pi}}$) are plotted as a function of neighbor distance, they describe approximate smooth curves which align well with the values found by Mattheiss and Patel for diamond-cubic Si, even though local coordination is entirely different. This suggests an approximate transferability of tight-binding parameters, at least if the volume is constant and coordination number is four or higher.