Density-Functional Analysis on Vacancy Orbital and its Elastic Response of Silicon
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1195-B08-11
Density-Functional Analysis on Vacancy Orbital and its Elastic Response of Silicon Takafumi Ogawa1, Kenji Tsuruta2, Hiroshi Iyetomi1, Hiroshi Y. Kaneta1, and Terutaka Goto1 1 Graduate school of science and technology, Niigata University, Niigata 950-2181, Japan. 2 Graduate school of natural science and technology, Okayama University, Okayama 700-8530, Japan.
ABSTRACT Recent experiments on ultrasonic measurements of non-doped and boron-doped silicon indicate that vacancies in crystalline silicon can be detected through the elastic softening at low temperature. This is attributed to enhanced response of electronic quadrupole localized at the vacancies to the elastic strain. In the present work, the electronic quadrupole moment of the vacancy orbital in silicon and their strain susceptibility are evaluated quantitatively by using the density-functional method. We show the orbital of gap state is localized around vacancy but extended over several neighbors. The effect of applied magnetic field on the vacancy orbital and its multipole structures are also investigated. We find that the results obtained from these calculations are consistent with the ultrasonic experiments.
INTRODUCTION Understanding the structural and quantum state of a vacancy in crystalline silicon has been a fundamental issue in semiconductor technology. Unique characters of an isolated vacancy, such as Jahn-Teller effect and Anderson negative-U systems for charged states have been understood via theoretical calculations [1] and electron paramagnetic resonance (EPR) and deep-level transient-spectroscopy (DLTS) experiments [2, 3]. The formation energy of the neutral isolated vacancy has been investigated by recent positron annihilation measurements [4]. Quantitative theoretical calculations have been attempted only recently by ab-initio approaches based on the density-functional theory (DFT) [5, 6]. Despite rapid progresses in DFT methodologies, it is still difficult to obtain conclusive results with respect to formation energies and atomic/electronic structures around a vacancy because of the localized orbital extended over few neighbors which affects large number of neighboring atoms. Recently, Goto et. al. have reported that silicon vacancies can be detected via ultrasonic waves at low temperature [7]. They have measured the elastic softening in non-doped and borondoped silicon grown by a floating zone (FZ) method and concluded that (a) elastic softening appear down to 20 [mK] in non-doped FZ silicon without depending on applied magnetic field up to 16 [T] and (b) elastic softening also appear in boron-doped silicon down to 20 [mK] with suppression in applied magnetic field up to 2 [T], and (c) elastic softening for C44 is larger about ten times than (C11-C12)/2 for both silicon. These observations suggest that the elastic softening is a consequence of an elastic response by the degenerate level associated with a vacancy of nonmagnetic neutral charge state V0 for non-doped silicon and of magnetic positive charge state V+ for boron-dope
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