Elastic constants of defected and amorphous silicon with the environment-dependent interatomic potential

The elastic constants of a wide range of models of defected crystalline and amorphous silicon are calculated, using the environment-dependent interatomic potential (EDIP). The defected crystalline simulation cells contain randomly generated defect distributions. An extensive characterization of point defects is performed, including structure, energy and influence on elastic constants. Three important conclusions are drawn. (1) Defects have independent effects on the elastic constants of silicon up to (at least) a defect concentration of 0.3%. (2) The linear effect of Frenkel pairs on the <110> Young's modulus of silicon is -1653 GPa per defect fraction. (3) 17 different point defect types cause a very similar decrease in the <110> Young's modulus: -(0.28+/-0.05)% when calculated in isolation using a 1728-atom cell. These principles will be very useful for predicting the effect of radiation damage on the elastic modulus of silicon in the typical case in which point-defect concentrations can be estimated, but the exact distribution and species of defects is unknown. We also study amorphous samples generated in quenching the liquid with EDIP, including an ideal structure of perfect fourfold coordination, samples with threefold and fivefold coordinated defects, one with a nanovoid, and one with an amorphous inclusion in a crystalline matrix. In the last case, a useful finding is that the change in the Young's modulus is simply related to the volume fraction of amorphous material, as has also been observed by experiment.