27 June 2000 -- For the first time, the well known fracture anisotropy of silicon is explained by quantum mechanical bond breaking characteristics. Scientists from the Max Planck Institute for Metals Research (MPI für Metallforschung) in Stuttgart and the Universidad Autonoma de Madrid reported in Physical Review Letters, June 5, 2000, quantum mechanical simulations of the bond breaking process at the tip of a crack in silicon. The macroscopically observable preference for crack propagation in certain crystallographic directions can be linked to the characteristics of the bond breaking process.
Brittle fracture is not only an annoying everyday experience or a safety hazard, but also an important technological process for the shaping of hard materials. Controlling the brittle fracture of flintstone was the crucial step into the stone age and polishing silicon wafers of 300 mm diameter with tolerable height variations of only a few atom spacings is a technological challenge today.
Engineers at the beginning of the last century started to investigate brittle fracture processes and soon realised that the mechanical stress in the solid is concentrated at the crack tip. This stress concentration increases with increasing sharpness of the crack. In a brittle material, the crack tip is atomically sharp and, therefore, the material must sustain fantastically high stresses exceeding the nominal fracture strength of engineering materials. A hundred years ago, it was a puzzle to engineers and scientists how a material can possibly sustain such high stresses until A.A. Griffith (1893-1963) analysed the process on an energetic basis. Griffith showed that the mechanical driving force on the crack must exceed the intrinsic resistance of the material against crack propagation which he identified as the energy to create the two fracture surfaces.
Until today, Griffith's level of understanding is the basis for almost all analysis of brittle fracture processes. Although the simple Griffith picture is very popular, it cannot explain many experimentally observed fracture phenomena. Important questions, like which of the planes of a crystal serves as a cleavage plane and in which direction does the crack want to propagate, cannot satisfactorily be answered. For example, silicon crystals, which are the base material for the entire semiconductor industry, show a very pronounced cleavage anisotropy which could not be explained so far. Cracks in silicon propagate on two types of cleavage planes and clearly prefer one particular direction on both of these planes. On one of the two planes the crack does not even propagate perpendicular to the preferred direction but deviates macroscopically as shown in the figure below.
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Why has it been so difficult to advance our understanding of such fracture processes? The reason is that the fate of a mechanical system under load is determined by the survival of the most vulnerable part, the atomic bond at the crack tip, under the most severe conditions, namely the highly concentrated stresses. The analysis is difficult and many of the tools of solid state physics cannot be applied to fracture studies because cracks form on the atomic scale but extend to macroscopic dimensions; they are irreversible and travel far from equilibrium. However, the enormous increase in computing power in the recent past has now opened new opportunities for such studies.
In the present case, the atoms around the crack tip are first loaded with the stress field of a macroscopic crack. The energy and all the forces on the atoms are then calculated ab initio using density functional theory. These simulations require only the specification of the atomic species and then solve self-consistently for the ground state of the entire electronic system, which of course includes all details of the atomic bonds at the crack tip. Upon increasing the externally applied load one can then monitor the bond breaking process and the relaxations of the surrounding atoms.
The surprising result of the simulations was that the bond breaking at the crack tip proceeds differently for the different crack orientations. While the crack tip bonds smoothly lengthen for the easy propagation direction, the bond length remains almost unchanged for the difficult orientation until the external load reaches a critical value at which the bond abruptly breaks like a snapping elastic spring.
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The discontinuous bond breaking is preceded by a significant load sharing between several bonds at the crack tip, which effectively shields the crack tip bond from the applied load. This leads to a so-called trapping of the crack which stabilises it up to loads far above the Griffith value.
Consequently, the macroscopically observed fracture anisotropy can directly be viewed as a result of the difference in the way the atomic bonds break. This is the first time that macroscopically observable fracture phenomena have directly been simulated with ab initio methods and it demonstrates how far modern computer simulation methods can reach. Nevertheless, it should be emphasised that pure silicon is an almost ideal system for both experiment and theory. Most technically relevant systems are considerably less ideal and will require the treatment of several different atomic species. Although this can be done with the existing simulation tools, computationally it is considerably more demanding. However, the present breakthrough is very encouraging to further proceed towards the simulation of the next more complicated case which is chemical attack and corrosion at the crack tip of the silicon crack.