Kinetic energy of electrons emitted in Photoelectron Spectroscopy
From Wikipedia (emphasis mine):


  Because the energy of an X-ray with particular wavelength is known
  (for aluminum Kα X-rays, Ephoton = 1486.7 eV), and because the emitted
  electrons' kinetic energies are measured, the electron binding energy
  of each of the emitted electrons can be determined by using an
  equation that is based on the work of Ernest Rutherford (1914):
  
  \begin{equation}
     E_\text{binding} = E_\text{photon} - \left(E_\text{kinetic} + \phi\right)   \end{equation}
  
  where $E_\text{binding}$ is the binding energy (BE) of the electron, $E_\text{photon}$ is
  the energy of the X-ray photons being used, $E_\text{kinetic}$ is the kinetic
  energy of the electron as measured by the instrument and $\phi$ is the
  work function dependent on both the spectrometer &amp; the material. This
  equation is essentially a conservation of energy equation. The work
  function term $\phi$ is an adjustable instrumental correction factor
  that accounts for the few eV of kinetic energy given up by the
  photoelectron as it becomes absorbed by the instrument's detector. It
  is a constant that rarely needs to be adjusted in practice.


So, it is the absorbtion of the photoelectron by the detector of the spectrometer that causes the work function term. The work function of the measured sample should be part of $E_\text{binding}$ as this is the ionisation energy of the electron. However, I think the equation you quote might have it slightly wrong because if $B.E._F$ is the energy difference between the energy level of the electron and the Fermi energy then there is indeed some portion of the work function of the sample missing since $B.E._F$ is not equal to the ionisation energy.