Photoelectric Emission from Silicon

Abstract

Effects of band structure on photoelectric yields from silicon have been determined from the interpretation of measurements which were made on surfaces oriented perpendicular to (111), (110), and (100). It was established that the yield spectrum for properly polished and annealed silicon is the same as that for cleaved and annealed silicon; low-energy electron diffraction patterns were obtained for all surfaces. Photoelectric thresholds obtained for (111), (110), and (100) silicon were 4.60, 4.73, and 5.11 eV, respectively. Improved experimental procedures show that yields well above threshold vary more rapidly with photon energy than those previously observed. Crystallographic differences in yields near threshold are ascribed to two sources: (1) the ionization energy $\xi$, which represents surface-barrier energy, and (2) the additional energy $E_A$ required to emit electrons with crystal momentum (k) at an angle $\theta$ to the surface normal, beyond that for k at $\theta =0\mathrm{}$. It is shown that for transitions near the center of the Brillouin zone (BZ), $E_A$ can be quite small (∼0.15 eV); hence, electrons at large $\theta$ can be emitted for $h\nu -h{\nu }_0$ only a few tenths of an eV, where $h{\nu }_0$ is the threshold photon energy. For $(h\nu -h{\nu }_0)>\mathrm{}1.0\mathrm{}$ eV, electrons are emitted for all $\theta$, i.e., for all excitation within the inner half of the BZ. A quantitative estimate of crystallographic yield dependence gives good agreement for the assumption, suggested by the band structure, of transitions near threshold peaked for k along $〈111〉$. These considerations lead to a more accurate interpretation of $Y$ versus ($h\nu -h{\nu }_0$), which depends on the position in the BZ of the operant optical transition. Such effects must be considered in analyzing all photoemission experiments, including both yield and energy distribution measurements.