Based on the idea that the hardness of covalent crystal is intrinsic and equivalent to the sum of the resistance to the indenter of each bond per unit area, a semiempirical method for the evaluation of hardness of multicomponent crystals is presented. Applied to beta-BC2N crystal, the predicted value of hardness is in good agreement with the experimental value. It is found that bond density or electronic density, bond length, and degree of covalent bonding are three determinative factors for the hardness of a polar covalent crystal. Our method offers the advantage of applicability to a broad class of materials and initializes a link between macroscopic property and electronic structure from first principles calculation.

Hardness of covalent crystals.

Hardness can be defined microscopically as the combined resistance of chemical bonds in a material to indentation. The current review presents three most popular microscopic models based on distinct scaling schemes of this resistance, namely the bond resistance, bond strength, and electronegativity models, with key points during employing these microscopic models addressed. These models can be used to estimate the hardness of known crystals. More importantly, hardness prediction based on the designed crystal structures becomes feasible with these models. Consequently, a straightforward and powerful criterion for novel superhard materials is provided. The current focuses of research on potential superhard materials are also discussed.

Microscopic theory of hardness and design of novel superhard crystals

mentally. In this report, we present in situ TEM observation of the elastic-plastic-fracture processes of a single Si NW recorded at atomic resolution. The study directly shows the strain-induced structural evolution process of Si NWs and its largestrain plasticity (LSP). Our results indicate that the LSP of Si NWs via a brittle-ductile transition originates from a dislocation-initiated amorphization. This behavior is in contrast to the mechanical behavior of bulk Si. Our observation reveals a phenomenon and mechanism of the Si NW mechanics and is fundamentally important for Si-NW-based nanotechnology. The in situ Si NW elastic, elastic-plastic, and plastic deformation investigations were carried out by ultrahigh-resolution TEM (UHRTEM) by axially extending the Si NWs by means of a mechanical force created by a TEM specimen-supporting grid under electron beam irradiation, as reported in detail elsewhere [17,18] (also see the Experimental section and Sup

http://www.nanoscience.gatech.edu/zlwang/paper/2007/07_AM_7.pdf

Low-Temperature In Situ Large-Strain Plasticity of Silicon Nanowires

Semiconductor industry has increasingly resorted to strain as a means of realizing the required node-to-node transistor performance improvements. Straining silicon fundamentally changes the mechanical, electrical (band structure and mobility), and chemical (diffusion and activation) properties. As silicon is strained and subjected to high-temperature thermal processing, it undergoes mechanical deformations that create defects, which may significantly limit yield. Engineers have to manipulate these properties of silicon to balance the performance gains against defect generation. This paper will elucidate the current understanding and ongoing published efforts on all these critical properties in bulk strained silicon. The manifestation of these properties in CMOS transistor performance and designs that successfully harness strain is reviewed in the last section. Current manufacturable strained-silicon technologies are reviewed with particular emphasis on scalability. A detailed case study on recessed silicon germanium transistors illustrates the application of the fundamentals to optimal transistor design.

Fundamentals of silicon material properties for successful exploitation of strain engineering in modern CMOS manufacturing

A new mechanism of work hardening is proposed to explain the athermal hardening in Stage IV of f.c.c. and diamond cubic crystals. The mechanism is related to a cellular dislocation microstructure in which during Stage III, hardening by dislocation accumulation and recovery by various mechanisms occurs primarily in the cell walls. Hardening of the cells is through the build-up of long range misfit stresses that result when the primary dislocation flux cuts trough the geometrically required dislocation density of the cell walls that is associated with the lattice misorientations between cells. Experiments show that these misorientations increase monotonically with increasing strain. There is no recovery in the cells. At the end of Stage III, hardening in the cell walls saturates, but the hardening due to misfit stresses in the cells continues unabated, giving rise to the rate independent hardening of Stage IV. Eventually this hardening is also terminated in Stage V when the misfit stresses inside cells reach a critical level that triggers rate dependent stress relaxation in the cells by secondary glide processes. The new mechanism makes successful predictions for Stage IV processes, including: hardening rate, plastic resistance levels, the gradual increase in hardening rate with plastic resistance, the residual lattice strains on unloading that can be measured with X-ray peak distortions and broadening, and for the Baushinger effect.

A new mechanism of work hardening in the late stages of large strain plastic flow in F.C.C. and diamond cubic crystals

Measurements of the lower yield point in silicon and germanium, covering wide ranges of temperature and strain rate, are presented. The results indicate that Haasen’s model for the beginning of the plastic deformation of semiconductors has to be modified for germanium, while it is confirmed for silicon.

Yield point and dislocation mobility in silicon and germanium

Sophisticated methods have been put forward in the literature to calculate Debye temperatures from the elastic constants C ik . As a simple alternative method for cubic crystals, a relation is often used that correlates Debye temperature and bulk modulus (c 11 + 2c 12 )/3 by a square-root law. It is shown that, with exception of the alkali metals, such a law is only poorly fulfilled for other cubic elements and compounds. If one takes, however, elastic moduli such as [c 44 (c 11 - c 12 ) (c 11 + c 12 + 2c 44 )] 1/3 or {c 44 [(c 11 - c 12 ) c 44 /2] 1/2 (c 11 - c 12 + c 44 )/3} 1/3 instead of the bulk modulus the square-root law is established for various cubic material classes. This procedure eventually allows to easily evaluate hitherto unknown Debye temperatures from the elastic constants with high precision.

The Dependence of the Debye Temperature on the Elastic Constants

In the literature a relation is often used that correlates Debye temperature and bulk modulus by a square‐root law. It was recently shown that, for different cubic crystal structures, such a law is only fulfilled within relatively large error limits. If one takes, however, the average of the elastic constants of the transversal acoustic phonon modes as elastic modulus instead of the bulk modulus, the square‐root law is established with high precision. It is demonstrated that the same procedure may also be applied successfully to materials with hexagonal crystal symmetry such as hexagonal close‐packed metals and semiconducting compounds with the wurtzite structure, and to different structures of the tetragonal system. The adequate moduli are Gh={c44[c44(c11−c12)/2]1/2} 1/2 and Gt=[c44c66(c11−c12)/2]1/3 for materials with hexagonal and tetragonal symmetry, respectively. The difference between the various structures of a crystal system is quantitatively described by the different number of atoms in the cryst...

Debye‐temperature–elastic‐constants relationship for materials with hexagonal and tetragonal symmetry

The stress at the beginning of stage III of the strain-hardening curve has been measured as a function of temperature and strain rate in silicon single crystals. It is shown that the results can be successfully described by two current theories for steady-state creep, which were modified for the purpose of the dynamical test: the expression developed by Barrett and Nix (1965) on the basis of the diffusion-controlled motion of jogged screw dislocations and that of Mohamed and Langdon (1974) which is based on the diffusion-controlled climb of edge dislocations. For high temperatures the experimental results are fitted equally well by both theories while for low temperatures the agreement is better using the expression for the creep rate given by Barrett and Nix (1965). From this the activation energy of self-diffusion has been evaluated to be 3·6 eV; it may be ascribed to a mono-vacancy mechanism.

Dynamical recovery and self-diffusion in silicon

Undoped GaAs single crystals with 〈123〉 orientation are compressed at different strain rates in the temperature range between 730 and 900 °C, using the liquid encapsulation technique to prevent As loss. The resulting stress‐strain curves are characterized by five deformation stages, as is known for other semiconductors. From the lower yield point, at high strain rates, an activation energy of 1.37 eV and a stress exponent of 3.6 are deduced; these parameters nearly agree with those obtained earlier at lower temperatures and under a protective atmosphere of argon. At low strain rates deviations occur, whose origin is discussed. The analysis of the first stage of dynamical recovery (stage III), which shows a uniform behavior over the whole temperature and strain‐rate range, yields an activation energy of 2.3 eV and a stress exponent of 4.2. These values are discussed in terms of a diffusion‐controlled recovery mechanism. The second recovery stage (stage V) probably is governed by cross slip; the cross over ...

Hans Siethoff

Papers

Yield point and dislocation mobility in silicon and germanium

The Dependence of the Debye Temperature on the Elastic Constants

Debye‐temperature–elastic‐constants relationship for materials with hexagonal and tetragonal symmetry

Dynamical recovery and self-diffusion in silicon

Plasticity of undoped GaAs deformed under liquid encapsulation