Theoretical Study of Impact of Internal and External Stresses on Thermal Equilibrium Concentrations of Intrinsic Point Defects in Doped Si Crystals

Abstract

Intrinsic point defects (vacancy V and self-interstitial I) play an important role in a wide variety of processes in Si crystals. During large-diameter crystal growth, the thermal stress, which is the compressive internal stress, of around several tens of MPa is originated in Si crystals. In the LSI (Large Scale Integration) using Si substrate, external stress of around GPa order is applied to the channel region between source and drain in the MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) to enhance the carrier mobilities. These internal and external stresses affect V and I; thus, changing the thermal equilibrium concentrations (Ceq) of V and I in Si. To explain and engineer the intrinsic point defect behavior in Si crystals, such as in the growing Si crystals and in the channel region of Si wafers, the impact of internal or external stress on the Ceq of V (I) should be theoretically obtained in doped Si crystals. In this study, we calculated the formation energy (Ef) and relaxation volume (ΔVol) of V (I) from the 1st to 5th sites around dopant (B, C, Sn, P, and Sb) atoms in isotropically stressed Si by using density functional theory (DFT) to determine the formation enthalpy (Hf) of V and I. The impact of isotropic internal stress (σin) or isotropic external stress (σex) on the Ceq values of V (I) in doped Si was obtained using the Hf at each site around a dopant atom. The following important information was obtained from the Ceq of V (I) in doped Si crystals. (1) The Ef and ΔVol of V (I) around the dopant atoms change depending on the site position and dopant type, (2) Ef of V (I) and ΔVol of I around the dopant atoms are hardly affected by the stresses, while ΔVol of V around the dopant atoms changes due to the stresses, (3) B and C atoms make the Si crystal more I-rich, while Sn, P, and Sb atoms make the Si crystal more V-rich, and (4) the compressive σin makes the doped Si crystal more V-rich, and its impact depends on the type of dopant, while the σex has an opposite impact except for C. The data summarizing the impact of stress in doped Si are useful as the more precisely control of the point defect behavior is required in more advanced Si crystals.