Strong QuadrupoleStrain Interaction of Vacancy Orbital in BoronDoped Czochralski Silicon
Strong QuadrupoleStrain Interaction of Vacancy Orbital in BoronDoped Czochralski Silicon
Okabe, K.; Akatsu, M.; Baba, S.; Mitsumoto, K.; Nemoto, Y.; YamadaKaneta, H.; Goto, T.; Saito, H.; Kashima, K.; Saito, Y.
Abstract
We have carried out ultrasonic measurements of a borondoped silicon ingot grown by the Czochralski method in order to determine the quadrupolestrain interaction constant of a vacancy orbital. The lowtemperature 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 lowtemperature 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_{Γ5} = (2.8±0.2)×10^{5} K for the quadrupolestrain interaction H_{QS} = g_{Γ5}O_{zx}ε_{zx} of the vacancy orbital. The huge deformation energy of 1.6×10^{5} K per vacancy with the Γ_{8} ground state for unit strain ε_{zx} = 1 verified the strong electron–lattice interaction of the vacancy orbital. Employing the onetoone correspondence between the softening of ΔC_{44}/C_{44} = 1.0×10^{4} down to 30 mK and the vacancy concentration of N = 1.5 ×10^{13} cm^{3}, we can determine the vacancy concentration by lowtemperature ultrasonic measurements. The present work surely puts forward a novel semiconductor technology based on lowtemperature ultrasonic measurements for evaluating vacancy concentration in silicon wafers.
Keywords: vacancy; borondoped silicon wafer; ultrasound; quadrupole; softening
Involved research facilities
 High Magnetic Field Laboratory (HLD)

Journal of the Physical Society of Japan 82(2013)12, 124604
DOI: 10.7566/JPSJ.82.124604
ISSN: 00319015
Cited 9 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ19599