Dynamics of electronic relaxation in characteristic x-ray radiation processes in wide-gap insulators: Separation of luminescence from Raman scattering

Abstract

Electronic relaxation dynamics on the separation of luminescence from Raman scatterings are theoretically studied in the x-ray radiation process from a shallow core level to a deep one in a wide-gap insulator. A four-band model composed of dispersionless deep and shallow core bands, and conduction and valence ones, is taken as one of the simplest examples. The Coulomb interactions among the conduction electrons and the valence holes are taken into account by the lowest-order perturbation theory. By these interactions, a conduction electron is scattered together with creation of a valence-hole--conduction-electron pair. Using this model, we calculate a second-order optical process composed of an excitation of an electron from the deep core level to the conduction band by an incident x-ray, and a subsequent transition from a shallow core level to a deep one by radiating another x ray. When the incident x-ray energy is below the absorption edge, the resultant radiation spectra have only one peak due to a Raman scattering. On the other hand, when the incident energy is above the edge, the radiation spectra separate into two peaks: a luminescence peak, and a Raman scattering peaks on the higher-energy side. The luminescence is considered to occur after the following electronic relaxation. The photoexcited electron enters the conduction band by creating a valence-hole--conduction-electron pair through the Coulomb interactions. Afterwards, this pair goes away from the original site, and it results in a dissipation. From this scenario, the calculated x-ray radiation spectra agree with experimental results. We have concluded that the conditions to obtain luminescence is that the conduction- and valence-band-widths are finite, and the lifetime of the deep core hole is long enough. With this scenario, we also qualitatively explain the characteristic x-ray radiation spectra in metals, semiconductors, and atoms. Furthermore, we discuss the spectral shapes in the Auger decay process competitive with the radiation one.