Erratum: Low Frequency Raman Scattering from Acoustic Phonons Confined in ZnO Nanoparticles [Phys. Rev. Lett. 97, 085502 (2006)]

摘要

Our recent Letter contained a few errors. (i) The eigenvalue equations for the spheroidal modes of the homogenous elastic body [Eq. (3) of our Letter] should read as follows: 2{η~2+(l-1)(l+2)[ηj_(l+1)(η)/j_l(η)-(l+1)]}ξj_(l+1)(ξ)/j_l(ξ)-η~4/2+(l-1)(2l+1)η~2+[η~2-2l(l-1)(l+2)]ηj_(l+1)(η)/j_l(η)=0 for (l＞0) and tan(ξ)(1-η~2/4)-ξ=0 for(l=0). (ii) The theoretical Raman mode frequencies were calculated using Eqs. (7), (8) which were not derived from Eq. (4) as was erroneously written in the Letter. These equations were reported by Tanaka et al. [1] and are essentially the same for ZnO as for CdS since the ratio of the longitudinal and the transverse sound velocities in CdS is the same as that in ZnO. [The longitudinal and the transverse sound velocities for ZnO are 6365 m/s (v_l) and 2735 m/s (v_t), respectively, and the ratio (v_l/v_t) is 2.32 [2] and for CdS this ratio is 2.28 due to v_l being 4247 m/s and v_t = 1859 m/s [1].]