Vacancy diffusion in silicon: analysis of transition state theory

Abstract

Transition state theory TST is the most widely used formalism for theoretical calculations of di usion coe cients of defects in solids. In this work, we test its validity for the case of vacancy di usion in silicon. The di usion coe cient directly obtained from molecular-dynamics simulations with a classical Stillinger-Weber potential is compared with TST predictions. Our results con rm the validity of TST for this system. Di usion coe cient calculations for defects in solids are almost exclusively done in the framework of transition state theory TST 1 . Within this formalism, the defect jump rate , is written as , = e ,Em=kT ; 1 where the migration energy E m is determined by the energy di erence between two absolutely static atomic con gurations: The ground state and the saddle-point, i.e.,2 The saddle-point is the con guration of maximum energy along the adiabatic reaction pathway. The prefactor can be seen as an e ective "jump-attempt" frequency, and it is given within TST bywhere the products in the numerator and denominator are over all normal mode frequencies of the ground state and saddle-point, respectively.In this work, we test the validity of TST predictions for the speci c case of vacancy di usion in silicon. Vacancy in silicon has been and still is 2 one of the most studied point defects in semiconductor physics, partly due to its role in mediating impurity di usion. Our calculations are based on a classical Stillinger-Weber 3 SW interatomic potential. This potential is chosen mainly for its simplicity but, as shown below, it provides a reasonable agreement with more sophisticated methods for many calculated properties.The system is modeled by a supercell with periodic boundary conditions and we start out by searching for its ground state. A vacancy is initially formed by removing one of the silicon atoms in the supercell, without relaxing the remaining atoms. This unrelaxed conguration is found to be a metastable state for the SW potential. The true ground state is associated with a 0.56 A i n ward relaxation of the vacancy rst neighbors, and it is shown in Fig. 1 a or Fig. 1 c . Our result using a classical potential is in reasonable agreement with recent ab initio calculations 4 which indicate an inward relaxation of 0.4 A. The saddle-point con guration can be guessed from symmetry arguments and is known as split-vacancy. The resulting migration pathway is then indicated in Fig. 1, which shows the initial, saddle and nal con gurations. In this pathway, one of the vacancy neighbors moves to an intermediate position midway its initial location and the vacancy position.The formation energies for the vacancy and splitvacancy calculated for a 64-site cell thus containing 63 silicon atoms are shown in Table 1 , along with the

Resonant Rutherford backscattering spectrometry for carbon diffusion in silicon

“…Carbon is bound to vacancies and the binding energy of C with vacancy is 0.19 eV [21]. Due to the vacancy flux drags carbon atoms to surface and hence the activation energy of C in this case should be similar to the vacancy migration energy in silicon which is $0.44 eV [10,11]. The measured activation energy of C migration in our experiment is 0.434 eV which is close to the activation energy of vacancy diffusion in silicon indicating a vacancy drag mechanism for C diffusion in irradiation condition.…”

“…In the case of ion implantation technique, in addition to those mechanisms the implantation induced defects (like vacancy, interstitials) are also participate in diffusion process. Especially, vacancies play a major role for impurity diffusion in silicon [11]. To our knowledge, not many studies have been conducted to study the C diffusion in Si under irradiation condition which assumes importance in the context of SiC synthesis by ion implantation and use of high concentration of C to reduce TED.…”