Geometry and quantum delocalization of interstitial oxygen in silicon

The problem of the geometry of interstitial oxygen in silicon is settled by proper consideration of the quantum delocalization of the oxygen atom around the bond-center position. The calculated infrared absorption spectrum accounts for the 517 and 1136 cm$^{-1}$ bands in their position, character, and isotope shifts. The asymmetric lineshape of the 517 cm$^{-1}$ peak is also well reproduced. A new, non-infrared-active, symmetric-stretching mode is found at 596 cm$^{-1}$. First-principles calculations are presented supporting the nontrivial quantum delocalization of the oxygen atom.Comment: uuencoded, compressed postscript file for the whole. 4 pages (figures included), accepted in PR

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

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 $\sim20 {\rm \AA}$ 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 ($O_{yz},O_{zx},O_{xy}$) is largely enhanced as compared to that for the tetragonal mode ($O_{2}^{0},O_{2}^{2}$). 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.Comment: 6 pages, with 5 figure

Low-Temperature Softening Due to Vacancy Orbital with Γ₈ Quartet Ground State in Boron-Doped Floating Zone Silicon

We have carried out low-temperature ultrasonic measurements using shear-mode ultrasound to clarify the quantum state of a vacancy orbital in boron-doped silicon grown by the floating zone (FZ) method. The elastic constants (C-11 - C-12)/2 and C-44 of the transverse mode exhibit considerable softening below 2 and 5 K down to the base temperature of 30 mK, respectively. The elastic constant C-44 measured by the three ultrasonic modes (k(x), u(y)), (k(z), u(x)), and (k(x), u(z)) shows the different magnetic field dependences among the configurations under applied magnetic fields along the z-axis. The elastic softening and the magnetic field dependence of the elastic constants are accounted for by the quadrupole susceptibility based on the energy level scheme of the vacancy orbital with a Gamma(8) quartet ground state and Gamma(7) doublet excited state located at an energy of 1 K. The difference in C-44 between the two ultrasonic modes (k(z), u(x)) and (k(x), u(z)) at fields along the z-axis indicates that the Gamma(8) quartet ground state is slightly split by local strain in the silicon sample. The quantum state of the vacancy orbital is expected to be sensitive to strain because of the extremely large quadrupole-strain coupling energy of g(Gamma) approximate to 10(5) K due to the extensively spreading orbital radius of r approximate to 1 nm. The differences in variation of the low-temperature softening and magnetic field dependence among eight samples cut out from different locations of the present boron-doped FZ silicon ingot evidence the inhomogeneous distribution of the vacancy concentration

Strong Quadrupole-Strain Interaction of Vacancy Orbital in Boron-Doped Czochralski Silicon

We have carried out ultrasonic measurements of a boron-doped silicon ingot grown by the Czochralski method in order to determine the quadrupole-strain interaction constant of a vacancy orbital. The low-temperature softening of the elastic constant C-44 shows a remarkable variation depending on positions of the ingot, which reflects the distribution of vacancy concentration N in the ingot. An infrared laser scattering tomograph was employed to measure the density and size of voids in the silicon wafers by determining the vacancy concentration N-cons consumed in void formation. Using a combination of laser scattering tomography and low-temperature softening, we have found a sum rule in which the initially created vacancy concentration N-total corresponds to the sum of the residual vacancy concentration N and the consumed vacancy concentration N-cons as N-total N + N-cons. Taking account of the sum rule, we deduce the interaction constant g(Gamma 5) = (2.8 +/- 0.2) x 10(5) K for the quadrupole-strain interaction H-QS = -g(Gamma 5)O(zx)epsilon(zx) of the vacancy orbital. The huge deformation energy of 1.6 x 10(5) K per vacancy with the Gamma(8) ground state for unit strain epsilon(zx) = 1 verified the strong electron-lattice interaction of the vacancy orbital. Employing the one-to-one correspondence between the softening of Delta C-44/C-44 = 1.0 x 10(-4) down to 30 mK and the vacancy concentration of N = 1.5 x 10(13) cm(-3), we can determine the vacancy concentration by low-temperature ultrasonic measurements. The present work surely puts forward a novel semiconductor technology based on low-temperature ultrasonic measurements for evaluating vacancy concentration in silicon wafers