Theoretical study of stress impact on formation enthalpy and thermal equilibrium concentration of impurities and dopants in Si single crystal

Abstract

In Si-based VLSI manufacturing processes, complicated plane stress is applied near the (001) surface of Si wafers as device feature sizes further shrink. For this technical trend, the control of impurities including contamination metals and light elements as well as dopants becomes more and more important to improve device performance. In this study, density functional study calculations were performed to evaluate the dependence of the formation energy (Ef), volume change (ΔVol), and formation enthalpy (Hf) of impurities and dopants on isotropic or plane stress up to 2 GPa. Thirteen metal atoms (Ti, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo, Ru, Hf, Ta, and W), which are concerned in LSI processes, 4 light elements (H, C, N, and O), which exist normally in CZ-Si wafers, and 3 dopants (B, P, and As), which are generally used for Si, were considered. It was found that the dominant factor in the change of Hf was the ΔVol. On the basis of calculated results, we classified impurities and dopants according to the stress that increases the thermal equilibrium concentration (Ceq) in Si crystal. Furthermore, the stress dependence of the Hf of impurities and dopants in Si was formulated. The results obtained in the present work should be a useful database for controlling the behavior of impurities and dopants in stressed Si crystal.