Tilt Grain Boundaries In Silicon Research Articles

Structures and energies of Σ3 asymmetric tilt grain boundaries in silicon

We optimize 23 silicon Σ3 asymmetric tilt grain boundaries (ATGBs) using Stillinger Weber (SW), Tersoff and the optimized Modified Embedded Atom Method (MEAM) potentials. It is demonstrated that conventional GB optimization via rigid body translations in combination with atom deletions is totally incapable of driving an as-constructed flat Si grain boundary (GB) to its equilibrated state since it may inevitably cause lattice distortions in GB. But it can be easily achieved by initially introducing some pre-designed steps into as-constructed flat GB model. These steps are composed of coherent twin boundary (CTB) and symmetric incoherent twin boundary (SITB) facets. By doing so, energies of all 23 ATGBs are greatly reduced. Meanwhile, some ATGBs may have degenerate states with different structures but same energies. This work not only facilitates the structural characterization of Si Σ3 ATGBs, but may provide new insights into microstructure design in polycrystalline silicon.

Thermal conductivity and its relation to atomic structure for symmetrical tilt grain boundaries in silicon

We perform a systematic study of thermal resistance/conductance of tilt grain boundaries (GBs) in Si using classical molecular dynamics. The GBs studied are naturally divided into three groups according to the structural units forming the GB core. We find that, within each group, the GB thermal conductivity strongly correlates with the excess GB energy. All three groups predict nearly the same GB conductivity extrapolated to the high-energy limit. This limiting value is close to the thermal conductivity of amorphous Si, suggesting similar heat transport mechanisms. While the lattice thermal conductivity decreases with temperature, the GB conductivity slightly increases. However, at high temperatures it turns over and starts decreasing if the GB structure undergoes a premelting transformation. Analysis of vibrational spectra of GBs resolved along different directions sheds light on the mechanisms of their thermal resistance. The existence of alternating tensile and compressive atomic environments in the GB core gives rise to localized vibrational modes, frequency gaps creating acoustic mismatch with lattice phonons, and anharmonic vibrations of loosely-bound atoms residing in open atomic environments.

Incommensurate grain boundary in silicon and the silver-ratio sequence

A scheme is proposed to solve the structure of incommensurate interfaces, starting from high-resolution images of electron microscopy, supplemented by adapted simulation techniques and complemented by theoretical tools. Direct silicon bonding is a way to produce artificial interfaces, in particular incommensurate ones. We focus on a technology-driven tilt grain boundary in silicon. While the Fibonacci sequence, linked to the golden ratio, is a prototype of the quasicrystalline structures, a silver-ratio sequence allows us to analyze this incommensurate interface. The four-fold coordination of the Si atoms is kept at the interface.

Slip of shuffle screw dislocations through tilt grain boundaries in silicon

In this paper, molecular dynamics (MD) simulations of the interaction between tilt grain boundaries (GBs) and a shuffle screw dislocation in silicon are performed. Results show that dislocations transmit into the neighboring grain for all GBs in silicon. For Σ3,Σ9 and Σ19 GBs, when a dislocation interacts with a heptagon site, it transmits the GB directly. In contrast, when interacting with a pentagon site, it first cross slips to a plane on the heptagon site and then transmits the GB. The energy barrier is also quantified using the climbing image nudged elastic band (CINEB) method. Results show that Σ3 GB provides a barrier for dislocation at the same level of the Peierls barrier. For both Σ9 and Σ19 GBs, the barrier from the heptagon sites is much larger than the pentagon sites. Since the energy barrier for crossing all the GBs at the heptagon sites is only slightly larger than the Peierls barrier, perfect screw dislocations cannot pile up against these GBs. Furthermore, the critical shear stress averaged over the whole sample for the transmission through the Σ9 and Σ19 GBs is almost twice on heptagon site for initially equilibrium dislocation comparing with dislocations moving at a constant velocity.

Complex Nanotwin Substructure of an Asymmetric Σ9 Tilt Grain Boundary in a Silicon Polycrystal.

Grain boundaries in materials have substantial influences on device properties, for instance on mechanical stability or electronic minority carrier lifetime in multicrystalline silicon solar cells. This applies especially to asymmetric, less ordered or faceted interface portions. Here, we present the complex atomic interface structure of an asymmetric Σ9 tilt grain boundary in silicon, observed by high resolution scanning transmission electron microscopy (HR-STEM) and explained by atomistic modeling and computer simulation. Structural optimization of interface models for the asymmetric Σ9 and related symmetrical Σ9 and Σ3 tilt grain boundaries, by means of molecular-statics simulations with empirical silicon potentials in combination with first-principles calculations, results in a faceted asymmetric interface structure, whose grain-boundary energy is so low that it is likely to exist. The simulated local atomic structures match the observed HR-STEM images very well.

Ab initio and atomistic simulation of local structure and defect segregation on the tilt grain boundaries in silicon

This paper reports the results of atomistic and ab initio simulation of several different tilt grain boundaries in silicon. The boundary structures obtained with genetic algorithm turned out to have no coordination defects, i.e., all silicon atoms restored their tetrahedral coordination during the structure optimisation. That concerns previously known symmetric Σ5 (130), Σ3 (211), and Σ29 (520) boundaries and previously unknown asymmetric Σ9 (2¯55)/(2¯11), Σ3 (2¯55)/(211), and Σ13 (790)/(3 11 0) structures. An extensive study has been performed on defect segregation on the boundaries, including neutral vacancy and carbon, phosphorus, and boron impurities. A clear correlation has been revealed between the segregation energy of the defect and local geometry of the boundary site where the defect is segregated. The authors propose a simple purely geometric model for evaluating approximate segregation energies of the listed defects.

A molecular dynamics study of tilt grain boundary resistance to slip and heat transfer in nanocrystalline silicon

We present a molecular dynamics study of grain boundary (GB) resistance to dislocation-mediated slip transfer and phonon-mediated heat transfer in nanocrystalline silicon bicrystal. Three most stable ⟨110⟩ tilt GBs in silicon are investigated. Under mechanical loading, the nucleation and growth of hexagonal-shaped shuffle dislocation loops are reproduced. The resistances of different GBs to slip transfer are quantified through their constitutive responses. Results show that the Σ3 coherent twin boundary (CTB) in silicon exhibits significantly higher resistance to dislocation motion than the Σ9 GB in glide symmetry and the Σ19 GB in mirror symmetry. The distinct GB strengths are explained by the atomistic details of the dislocation-GB interaction. Under thermal loading, based on a thermostat-induced heat pulse model, the resistances of the GBs to transient heat conduction in ballistic-diffusive regime are characterized. In contrast to the trend found in the dislocation-GB interaction in bicrystal models with different GBs, the resistances of the same three GBs to heat transfer are strikingly different. The strongest dislocation barrier Σ3 CTB is almost transparent to heat conduction, while the dislocation-permeable Σ9 and Σ19 GBs exhibit larger resistance to heat transfer. In addition, simulation results suggest that the GB thermal resistance not only depends on the GB energy but also on the detailed atomic structure along the GBs.

Energy of the Two Variants 11A and 11B in Silicon and Germanium by the Semi-Empirical Tight-Binding Method

A semi-empirical tight-binding model was used to study the total energy of Σ = 11 tilt grain boundaries in silicon and germanium. At low temperature the structures A in silicon and B in germanium were found to be more stable in agreement with the experimental results.

Relative Stability of Two Structures of the Σ=11<011> Tilt Grain Boundary in Silicon and Germanium by the Tight-Binding Method

The Σ = 11 tilt grain boundary is known to exhibit two atomic structures A and B. Moreover, at low temperature, the A structure has been observed is silicon and the B structure in germanium. The classical empirical potentials are unable to describe this unexpected difference between two elements which are very close in many other respects. Wilder and Teichler used an empirical bond charge model to account for these phenomena. In the present paper, the semi-empirical tight-binding method is used with a relaxation method that also leads to results in agreement with observations.

Potential energy of two structures of Σ = 11〈0 1 1〉 tilt grain boundary in silicon and germanium with empirical potentials and tight-binding methods

Two atomic structures A and B of the Σ = 11〈0 1 1〉 grain boundary were observed in silicon and germanium. We have performed a complete study of the stability of these two grain boundaries using some empirical potentials and also the semiempirical, tight-binding (TB) method. The TB method has confirmed the experimental observations at low temperatures. The A structure is more stable in silicon whereas for germanium the B structure is obtained. The empirical potentials, such as those of Keating (1966), Baraff et al. (1980) and of Stillinger and Weber (1985), give the A structure as the most stable for both germanium and silicon. The non-ability of these empirical potentials to make a difference between germanium and silicon and the advantage of TB method are discussed.

Potential Energy Calculation of two Structures of the Σ=11 <011> Tilt Grain Boundary in Silicon and Germanium

ABSTRACTAvailable experimental data concerning two possible atomic structures (A and B) of the Σ=11 <011> tilt grain boundary in silicon and germanium are analyzed. Previous empirical calculations concerning low and high temperature stability of these structures are summarized and criticized. New calculations using the semi-empirical tight-binding method (SETBM) are presented for low temperature stability. The tight-binding parameters of Mercer and Chou give results in agreement with experimental observations by high resolution electron microscopy.

Free Energy of the Σ = 11 (332) Tilt Grain Boundary in Silicon

Free Energy of the Σ = 11 (332) Tilt Grain Boundary in Silicon

Energy Calculation of the Σ = 9<001> Tilt Grain Boundary in Silicon Using Keating Potential and Tight-Binding Model

Energy Calculation of the Σ = 9<001> Tilt Grain Boundary in Silicon Using Keating Potential and Tight-Binding Model

Structure and precipitation on a Σ = 13 tilt grain boundary in silicon

The structure of a Σ=13 (510), [001] pure tilt grain boundary in a Czochralski-grown silicon bicrystal was characterized by high-resolution electron microscopy. The observed boundary exhibited a coincident site lattice periodicity but had an aperiodic interface dislocation core structure. Discrete impurity precipitate particles were observed at the boundary. High-spatial-resolution electron-energy-loss-spectroscopy analysis showed them to be oxide particles of the form SiO x , with 0< x<1. The role of oxygen as an intrinsic impurity in the bicrystal on the structure of the boundary and on the oxide precipitation at the boundary is briefly discussed.

Analysis of pure tilt grain boundary in silicon by Fresnel fringe technique

One of the main emphases of research on interfaces is to characterize them both structurally and chemically. The atomic structure of interfaces and the existence of thin interfacial glassy phases are being investigated mainly by HREM imaging methods. In addition, a few other methods including dark field diffuse imaging and Fresnel Fringe techniques have been developed to identify the interfacial films and quantify their width. Fresnel fringe profiles from the interface images have been used to deduce the mean inner potential of thin interfacial films. In our research the Fresnel fringe contrast behavior of a tilt grain boundary in silicon whose structure and chemistry were previously characterized by HREM and high spatial resolution AEM was analyzed by comparing the experimental Fresnel fringe profiles with computer simulations of these images.

Calculated structures for [001] symmetrical tilt grain boundaries in silicon

The structures of [001] tilt boundaries in silicon have been systematically investigated by computer modeling, using the harmonic Keating potential to describe the interatomic forces. The full angular range of symmetrical tilt boundaries can be described in terms of linear combinations of characteristic groupings of atoms. More than one stable relaxed structure has been found for most grain boundaries. In all cases the relaxed bicrystal consists of localized groups of pure edge or 45° dislocation cores embedded in a tetrahedrally coordinated, stable structure.

Σ =13 tilt grain boundary in silicon bicrystal

The structure of grain boundaries (GBs) in metals, semiconductors and ceramics is of considerable interest because of their influence on physical properties. Progress in understanding the structure of grain boundaries at the atomic level has been made by high resolution electron microscopy (HREM) . In the present study, a Σ=13, (510) &lt;001&gt;-tilt grain boundary in silicon was characterized by HREM in conjunction with digital image processing and computer image simulation techniques.The bicrystals were grown from the melt by the Czochralski method, using preoriented seeds. Specimens for TEM observations were cut from the bicrystals perpendicular to the common rotation axis of pure tilt grain boundary, and were mechanically dimpled and then ion-milled to electron transparency. The degree of misorientation between the common &lt;001&gt; axis of the bicrystal was measured by CBED in a Philips EM 400ST/FEG: it was found to be less than 1 mrad. HREM was performed at 200 kV in an ISI-002B and at 400 kv in a JEM-4000EX.

Theoretical calculations of the structure and energy of the .SIGMA.=5 tilt grain boundary in silicon.

The structure and energy of the ∑=5 (130) symmetrical tilt grain boundary in Si were calculated theoretically. The valence force fields, the bond orbital model, and the semiempirical tight-binding method with the use of the supercell technique were used and the computed results were compared with each other. All the computations have shown that the structural model by Bacmann et al. is more energetically favored than that by Hornstra and that the optimum rigid-body translation of the former model is characterized by a translation of about 1/8a0 along the direction. These results are in good agreement with the experimental observation of a germanium bicrystal. However, there are diferences in the absolute values of calculated boundary energies. The energy values obtained by the valence force potentials with the parameters fitted to the elastic constants and by the bond orbital model are overestimated, although the energy values by the valence force potential with the parameters fitted to the finite wave vector modes of lattice distortions are comparable with those by the semiempirical tight-binding method.

Structures and Energies of Symmetrical 〈001〉 Tilt Grain Boundaries in Silicon

AbstractThe energies and atomic structures of a series of symmetrical 〈001〉 tilt grain boundaries in silicon are calculated using the tight‐binding type electronic theory (the bond orbital model). There exists a continuity of boundary structures in the ranges 0° ≦ θ &lt; 53.13° and 53.13° ≦ 90°. The type of boundary structures changes at the Σ = 5(130) boundary (θ = 53.13°); for this boundary, the model by Bacmann et al. is shown to be more energetically favorable. At the Σ = 5(120) (θ = 36.87°) and Σ = 5(130) (θ = 53.13°) boundaries, there exist comparatively deep cusps in the energy against θ curve. The discrepancy between the present results in silicon and the experimental observations in germanium for the Σ = 25(170) and Σ = 41(190) boundaries is discussed.

Reconstructed Structures of Symmetrical 〈011〉 Tilt Grain Boundaries in Silicon

AbstractThe energies of reconstructed structures of symmetrical 〈011〉 tilt grain boundaries with θ &gt; 70.53° in silicon are calculated using the tight‐binding type electronic theory (bond orbital model). The energies of the most stable reconstructed boundary structures are in the same range or a little larger than those with θ ≦ 70.53°. These reconstructed structures are more stable than those with dangling bonds. There exists the continuity of boundary structure in the range 70.53° ≦ θ ≦ 148.41° (Σ = 27). Shallow cusps in the energy against θ curve can be found at special boundaries of type Σ = 3 (θ = 109.47°), Σ = 11 (θ = 129.52°), and Σ = 27 (θ = 148.41°), all of which are composed of one kind of original patterns. For θ &gt; 148.41°, boundary structures are composed of an array of a0[100] edge dislocations.