what is the difference in the work function of photoelectric effect and work function denoted by fermi level?

Question

The work function that is calculated via the photoelectric effect is bound to be a surface phenomenon. When one brings in the energy band picture, then it is claimed that work function is equal to fermi level, and is the energy required to remove an electron from the crystal's influence and bring it to the surface of the crystal. Are the two work functions different in nature? Is the second one more of a bulk phenomenon?

Answer 1

You have several misconceptions. I would suggest that you get two papers, both from Physics Review, and read through them. They are:

E.O. Kane, Theory of Photoelectric Emission from Semiconductors, Physical Review 127(1) 131-141 (1962),

and the companion experimental paper,

G.W. Gobeli and F.G. Allen, Direct and Indirect Excitation Processes in Photoelectric Emission from Silicon, Physical Review 127(1) 141-149 (1962).

I will quote from the Gobeli&Allen abstract:

The spectral dependence of saturation photoelectric emission has been studied for atomically-clean (111) silicon surfaces which were prepared by cleavage in high vacuum. The observed spectra, and their dependence on sample doping, are interpreted as being due to a volume excitation process which is modified by space charge band bending effects. Both direct and indirect optical excitation thresholds are observed, at 5.45 eV and 5.15 eV, respectively, with the latter being equal to the electron affinity, $\chi$, plus the energy gap, $E_g$. The spectral dependence of the direct excitation process is in agreement with the theoretical model developed by Kane, in which there is a complete absence of scattering either in the bulk or at the surface for those excited electrons which are emitted. The indirect process is also in agreement with Kane's theory.

Kane's theory is in the first paper. To quote from the introduction,

The present paper deals primarily with the form of the yield vs energy curve near threshold for a general band structure and for a variety of photoelectron production and scattering mechanisms. These results should be useful in inferring the production mechanism from the yield curve.

So,

1. The work function from the photoelectric effect is not 'bound to be a surface phenomenon', and

2. Good theories of photoelectric emission are readily available.