Recoil effects for valence and core photoelectrons in ${\mathrm{V}}_3$ Si

Hard and soft x-ray photoelectron spectroscopy was performed for core and valence electrons in V${}_3$Si. The recoil effects on the photoelectron emission were observed not only in the case of the Si 2$p$ core level, but also for the valence band, although such effects were not observed for the V 2$p$ and V 3$p$ core levels. The valence-band results are compared with the results of the theoretical model calculation based on the tight-binding cluster approximation and harmonic approximation for lattice vibrations. The Si 2$p$ core-level results interpreted as due to the single nucleus recoil effects are consistent with the interpretation of those of the valence electrons calculated on these approximations. From the $E_{\mathrm{B}}$ dependence of the valence-band recoil shifts, useful information is obtained on the Si 3$p$ partial density of states near the Fermi level.

Figure 1

SXPES and HAXPES spectra of the Si 2$p$ core levels of V${}_3$Si at 20 K. The total resolution is set to 100 meV except for the $h\nu$ $=$ 270-eV spectrum (50 meV).

Figure 2

SXPES at $h\nu$ $=$ 270 eV decomposed into the surface and bulk components.

Figure 3

SXPES and HAXPES spectra of the (a) V 2$p$ and (b) 3$p$ core levels of V${}_3$Si at 20 K.

Figure 4

SXPES and HAXPES spectra of the valence-band Fermi edge of V${}_3$Si at 20 K.

Figure 5

(a) Calculated SXPES and HAXPES spectra of valence band of V${}_3$Si using a (V${}_3$Si)16 cluster. The spectra are so normalized as to give the same height at $E_B$ $=$ 0.4 eV. The $E_B$ dependence of the intensities changes with the excitation photon energies. The spectrum at $h\nu =270$ eV is calculated by considering the 20$\%$ intensity of the 8 occupied surface MOs and 11 occupied bulk MO states in this $E_B$ region, whereas, the spectra at $h\nu$ $=$ 750 and 8180 eV are calculated by considering only the 11 bulk MOs. The parameters employed for the occupied bulk states are summarized in Table . Photoionization cross sections at $h\nu$ $=$ 750 and 8180 eV are summarized in Table . (b) Calculated PDOS of individual atomic orbitals from the 11 MOs with bulk character predicted by DFT cluster calculation for a (SiV${}_3$)${}_{16}$ cluster. In this treatment, Gaussian broadening is taken into account for 11 MO excitations. Only the PDOS of the major four atomic orbitals are shown (namely, Si 3$p$ and V 3$s$, 3$d$, and 4$p$ orbitals) in this figure. (c) Calculated PDOS of individual atomic orbitals in order to get the best fit for the observed spectra at $h\nu =750$ and 8180 eV as shown in (d) for which the energy positions $E_i$ and $|C_{\alpha j}^i{|}^2$ in Eqs. (2) and (3) are treated as fitting parameters. Then, the individual PDOS are different from those obtained by DFT calculation in contrast to the case of (b). In this energy region, seven MOs in the (SiV${}_3$)${}_{16}$ cluster are taken into account while shifting the other four MOs to smaller $E_B$'s. The Gaussian broadening is likewise taken into account. (d) The best-fit results (dotted and dot-dashed lines) for the spectra measured at $h\nu =750$ and 8180 eV based on the PDOS given in (c) are derived from this fitting. The spectrum at $h\nu =270$ eV is strongly influenced by the occupied surface states and is not fitted here within the same scheme.