Dielectric Anisotropy of the $\mathrm{GaP}/\mathrm{Si}(001)$ Interface from First-Principles Theory

First-principles calculations of the dielectric anisotropy of the $\mathrm{GaP}/\mathrm{Si}(001)$ interface are compared to the anisotropy extracted from reflectance measurements on GaP thin films on Si(001) [O. Supplie et al., Phys. Rev. B 86, 035308 (2012)]. Optical excitations from two states localized in several Si layers adjacent to the interface result in the observed anisotropy of the interface. The calculations show excellent agreement with experiment only for a gapped interface with a P layer in contact with Si and show that a combination of theory and experiment can reveal localized electronic states and the atomic structure at buried interfaces.

Figure 1

Atomic structures of slabs with $(2\times 2)\mathrm{H}$ surface terminations used for the IDA calculations. Left: GaP layer terminated in a $\mathrm{P}/\mathrm{Si}$ interface with ${\mathrm{Ga}}_{\mathrm{Si}}$ substitution in the first Si layer. The net charges in Ga-P or Si bilayers are shown in the panels on the right of the slabs. The filter functions used to extract contributions to the dielectric function from specific layers are shown on the left of the slabs for Si bilayers adjacent to the GaP thin film and for bilayers on both sides of the interface. Right: GaP layer terminated in a $\mathrm{Ga}/\mathrm{Si}$ interface with ${\mathrm{P}}_{\mathrm{Si}}$ substitution in the first Si layer. The small spheres are H atoms, the medium sized red spheres are P atoms, the large green spheres are Ga atoms, and the medium sized gray spheres are Si atoms.

Figure 2

Atom projected band structure of the $\mathrm{P}/\mathrm{Si}$ interface with Ga compensation (upper panel). The atom layers onto which bands are projected correspond to the four layers marked on the left of Fig. 1. P layer, red squares; mixed $\mathrm{Ga}/\mathrm{Si}$ layer, green circles; second Si layer, blue upward triangles; third Si layer, black downward triangles. Bulk band projections for GaP and Si are shown as dark and light shading, respectively. The GaP bulk valence band maximum is the reference energy. Modulus squared of interface localized states at $\overline{\mathrm{\Gamma }}$ and ${\overline{J}}^{\prime }$ points of the Brillouin zone (lower panel).

Figure 3

Upper panel: interface dielectric functions of gapped $\mathrm{P}/\mathrm{Si}$ and $\mathrm{Ga}/\mathrm{Si}$ interfaces with the incident radiation electric vector aligned parallel or perpendicular to the P dimer bond (solid and dotted curves, respectively). Lower panel: the IDA calculated for gapped $\mathrm{P}/\mathrm{Si}$ and $\mathrm{Ga}/\mathrm{Si}$ interfaces using filter functions of width three $\mathrm{Si}+\text{three GaP bilayers}$ (solid curves), three Si bilayers (dashed curve), and experiment redrawn from Ref. [5].