Is the photoelectric effect possible for semiconductors?
Given that Jaques Pankove's excellent book on 'Optical Processes in Semiconductors' devotes chapter 13 to 'Photoelectric Emission', you can rest assured that the photoelectric effect is alive and well in semiconductors.  While somewhat more complex than emission from simple metals, there is no need for two-photon processes. The 'tricky' part is that you have to look at where the electron states are, and then how much energy is needed to take it out of the semiconductor.

The work function is the energy difference from the Fermi energy to the vacuum level.  There may not be any states at the Fermi energy though.

The electron affinity is the energy difference from the bottom of the conduction band to the vacuum level.

One has to take the band structure into account, since direct and indirect transitions will likely have different energies required. 
Also, surface band bending may make interpretation of experimental results more difficult. Again, perusing Pankove may prove useful.