Interface and confined optical phonons in wurtzite nanocrystals

We derive within the dielectric-continuum model an integral equation that defines interface and confined polar optical-phonon modes in nanocrystals with a wurtzite crystal structure. It is demonstrated theoretically that, while the frequency of confined polar optical phonons in zinc-blende nanocrystals is equal to that of the bulk crystal phonons, the confined polar optical phonons in wurtzite nanocrystals have a discrete spectrum of frequencies different from those of the bulk crystal. The calculated frequencies of confined polar optical phonons in wurtzite ZnO nanocrystals are found to be in an excellent agreement with the experimental resonant Raman-scattering spectra of spherical ZnO quantum dots.

Figure 1

Spectrum of several polar optical-phonon modes in spherical wurtzite ZnO nanocrystals as a function of the optical dielectric constant of the exterior medium. Note that the scale of frequencies is different for confined LO, interface, and confined TO phonons. Large black dots show the experimental points from Ref. 8.

Figure 2

(Color online) Cross sections of the phonon potentials of several polar optical-phonon modes in spherical wurtzite ZnO nanocrystals $({\epsilon }_D=1)$. Black circles indicate the boundary of the nanocrystal. The $z$ axis is directed vertically. In the color version, blue and red colors denote positive and negative values of the phonon potential, respectively.