Recoil effects of photoelectrons in a solid

High-energy-resolution $\mathrm{C}1s$ photoelectron spectra of graphite were measured at excitation energies of 340, 870, 5950, and $7940\mathrm{eV}$ using synchrotron radiation. On increasing the excitation energy, i.e., increasing kinetic energy of the photoelectron, the bulk origin $\mathrm{C}1s$ peak position shifts to higher binding energies. This systematic shift is due to the kinetic-energy loss of the high-energy photoelectron by kicking the atom and is clear evidence of the recoil effect in photoelectron emission. It is also observed that the asymmetric broadening increases for the higher-energy photoelectrons. All these recoil effects can be quantified in the same manner as the Mössbauer effect for $\gamma$-ray emission from nuclei embedded in crystals.

Figure 1

(Color online) (a) Photon energy dependence of $\mathrm{C}1s$ core-level spectra of graphite. The soft x ray ($h\nu =340$ and $870\mathrm{eV}$) and hard x ray ($h\nu =5950$ and $7940\mathrm{eV}$) are measured at the emission angles of 90° and 85° relative to the sample surface. (b) Theoretically obtained spectra taking into account the recoil effect in a Debye model with $\hslash {\omega }_{b,D}=75\mathrm{meV}$.

Figure 2

(Color online) (a) $\mathrm{C}1s$ core-level spectra of graphite measured at the photon energy of $7940\mathrm{eV}$ at the emission angles of 85° (normal) and 30° (grazing) relative to the sample surface. (b) Theoretically obtained spectra with the Debye energies $\hslash {\omega }_{b,D}=75\mathrm{meV}$ and $\hslash {\omega }_{s,D}=150\mathrm{meV}$ for the bending and the stretching mode, respectively.