Quadrupole Susceptibility and Elastic Softening due to a Vacancy in Silicon Crystal

Abstract

We investigate the electronic states around a single vacancy in silicon crystal by using the Green's function approach. The triply degenerate vacancy states within the band gap are found to be extended over a large distance ∼ 20Å from the vacancy site and contribute to the reciprocal temperature dependence of the quadrupole susceptibility resulting in the elastic softening at low temperture. The Curie constant of the quadrupole susceptibility for the trigonal mode (Oyz, Ozx, Oxy) is largely enhanced as compared to that for the tetragonal mode (O 0 2 , O 2 2 ). The obtained results are consistent with the recent ultrasonic experiments in silicon crystal down to 20 mK. We also calculate the dipole and octupole susceptibilities and find that the octupole susceptibilities are extremely enhannced for a specific mode.

Relativistic tight-binding approximation method for materials immersed in a uniform magnetic field: Application to crystalline silicon

“…Such phenomenon, which is observed in low-temperature ultrasonic measurements, attracts much attention because the density of the vacancies in silicon wafers can be estimated from the behavior of the elastic softening [1]. Several authors have studied this phenomenon theoretically by using a kind of model that includes adjustable or phenomenological parameters in the Hamiltonian [2][3][4][5][6][7]. It is pointed out that the spin-orbit interaction, which is one of the relativistic effects, plays an important role as well as the Zeeman effect [2][3][4][5][6][7].…”

“…Several authors have studied this phenomenon theoretically by using a kind of model that includes adjustable or phenomenological parameters in the Hamiltonian [2][3][4][5][6][7]. It is pointed out that the spin-orbit interaction, which is one of the relativistic effects, plays an important role as well as the Zeeman effect [2][3][4][5][6][7]. In these works, an unusual (negative) value is used for the spin-orbit coupling constant in order to explain the above phenomenon, however, the validity of this approach is open to challenge [7].…”

“…In these works, an unusual (negative) value is used for the spin-orbit coupling constant in order to explain the above phenomenon, however, the validity of this approach is open to challenge [7]. If a calculation method of relativistic energy bands for materials immersed in a uniform magnetic field is developed, then it will become a reliable method not only to check the validity of the arguments based on the model Hamiltonian [2][3][4][5][6], but also to investigate the above phenomenon more directly. In other words, as the first step toward clarifying the above phenomenon in a first-principles way, we need a calculation method that can describe the effects of both magnetic field and relativity.…”

Surface acoustic wave diagnosis of vacancy orbital with electric quadrupoles in silicon

“…[16,17] The theoretical analysis of the vacancy orbital in silicon gives enhanced electric quadrupoles due to an extended radius, which is consistent with the large quadrupole-strain interaction determined by the ultrasonic experiments. [18,19] The deformation energy of 14 eV for the vacancy orbital due to the dangling bonds may be comparable to deformation potential about 15 eV for the electron band due to the host valence bonding in silicon. [20,21] …”

Relativistic tight-binding approximation method for materials immersed in the magnetic field

“…It is also reported that the elastic softening is suppressed by an external magnetic field in the boron-doped silicon [1]. Several papers concerning such phenomena have been published so far, and it is pointed out that the spin-orbit interaction plays an important role on them as well as the Zeeman effect [2][3][4][5].…”