Formation of Vacancies and Divacancies in Plane-Stressed Silicon

Abstract

The effect of compressive and tensile plane-stress loading on formation energies and electronic properties of vacancies and divacancies in silicon are studied by first-principles approach for in-plane strains up to 0.7%. It is demonstrated that contributions to defect formation energies from the elastic lattice relaxation and from the band structure modification respond to stress in a different manner, leading to noticeable different behaviour of formation energies for different charges states. The most stable vacancy charge states at different Fermi level are shown to be sensitive to strain magnitude and sign. This results in the strain-induced shifts and even disappearance of some of thermal ionization levels of vacancies and divacancies in the band gap.

Ab Initio Analysis of Point Defects in Plane-Stressed Si or Ge Crystals

“…In order to simulate the strain effect, the supercell was strained equally along the [100] and [010] directions, while [001] direction was allowed to relax so as to minimize the energy of the system (2). In other words, we simulate a Si or Ge crystal in the plane-stressed loading mode (2). Figures 4(a), and (b) show the dependence of the normal strain along the [001] direction and of the cell volume of Si or Ge crystals on in-plane strain.…”

“…Note that all values in the right-hand side of eqs. [1] or [2] should be taken for the calculation cells in the same strain state (2).…”

“…Very high stresses can arise in the Si layer due to the lattice mismatch between Si and SiGe. When the Si layer is sufficiently thin and the stress in the normal direction is sufficiently relaxed, the stress state in the Si layer can be treated as plane-stress (2).…”

“…On the other hand, information on the point defect properties in plane-stressed Si is scarce. Recently, Nicolaysen et al studied the formation of vacancies and divacancies in plane-stressed Si (2). They showed that E f of vacancies and divacancies decreases under compressive in-plane strain.…”

“…Table II summarizes the calculated results of Poisson's ratio of Si and Ge crystals and compares them with the experimental results. The Poisson's ratio of [1][2][3][4][5][6][7][8][9][10] direction in [110] tensile strain was not determined due to the scattered values of small lattice strain. It was found that the calculated Poisson's ratio of Si or Ge crystals are in good agreement with experimental results in [100] and [110] tensile deformation.…”