  Quantum efficiencies of surface (SPE) and volume (VPE) photo-emissions from
metal nanoparticles are calculated by quantum mechanical perturbation theory
and compared with each other. Along with discontinuities in the potential
barrier and dielectric function, the discontinuity in electron effective mass
on the metal-environment interface is taken into account. General formulas for
quantum efficiencies of SPE and VPE are derived. An example of spherical gold
particles with rectangular potential barrier on the interface is considered,
analytical formulas for quantum efficiencies of SPE and VPE on the red border
of photoemission are derived. It is found that the efficiency of SPE is less
decreased with the reduction of the electron effective mass than the efficiency
of VPE, so SPE is more efficient that VPE for small particles and large
discontinuity in effective mass. Nanoparticle size, when SPE is more efficient
than VPE, is found to be tens of nm or less.
