Isotopic Effect on the Lattice Constant of Silicon A Quantum Monte Carlo Simulation

Path-integral Monte Carlo simulations in the isothermal-isobaric ensemble have been carried out to study the dependence of the lattice parameter of silicon upon the isotopic mass. This computational method allows a quantitative and nonperturbative study of such anharmonic effect. Atomic nuclei were treated as quantum particles interacting via a Stillinger-Weber-type potential. At 300 K, the isotopic effect leads to a decrease of 0.8 and 1.6 x 10 -4 A in the lattice parameter of isotopically pure crystals of 29 Si and 30 Si, respectively, as compared to the crystal with natural isotopic composition. At low temperatures (T 50 K), this isotopic effect is 50% larger than at room temperature. Results of the quantum simulations are compared with those derived from classical Monte Carlo simulations (infinite-mass limit) and with results of quasiharmonic approximations.