(a) In Chapter 5, we did not calculate any interaction Hamiltonian terms that would couple a photon directly to a phonon. However, a second-order process is possible in which an electronic transition to a virtual state occurs by dipole photon interaction, and then the electron returns to its original state by a phonon emission, leading effectively to the creation of a phonon by a photon.

The semiconductor Cu₂0 has O_h symmetry (Tables 6.7 and 6.8), electron bands with symmetries Γ^±₆ , Γ^±₇ , and Γ^±₈, and optical phonons with symmetries Γ⁻₂, Γ⁻₃ ,Γ⁺₄ , and Γ⁺₅ (all at zone center). For which optical phonons is this process allowed, at zone center?

(b) In Section 7.8, we will introduce Raman scattering, in which a photon scatters from a crystal, leaving behind a phonon and continuing on its way with its energy and momentum shifted by the loss of the phonon. One type is resonant Raman scattering, a third-order process with three multiplied matrix elements,

are electronic states. (We will also return to this in Chapter 8.) Find the optical phonons for which this process is allowed in Cu₂O at zone center, and show that they do not also participate in the absorption process of part (a). This is generally true, that phonons active in infrared absorption are not active for Raman scattering, and vice versa.

Transcribed Image Text:

(i Hdipole n) (n Hphon (m) (m Hdipole i), where i), m), and [n)