The work function W for a given surface is defined by the difference  W=-e ϕ-eE where −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and EF is the Fermi level (electrochemical potential of electrons) inside the material.The work function is not a characteristic of a bulk material, but rather a property of the surface of the material (depending on crystal face and contamination.

The surface roughness is accompanied by  surface stresses, which closely follow the surface topography having concentrated at trough (compressive) and  crests (tension) regions.  These stress fluctuations definitely affect the Fermi level as well at the electrostatic potential in the vicinity of surface on the vacuum side, which are used to define the work function similar to the surface contaminates. 

Apart from the above from the other comments, you could also argue that different Ag crystallographic orientations have different work functions and if the surface roughness increases the ratio between these different orientations, present at the surface, might change depending on how oriented the film grows on you substrate. Imagine a perfect surface with only one orientation, if you increase surface roughness, other orientations appear and change the work function.

Based on the theories of flat parallel-plate capacitor and the surface roughness, a numerical model of the relationship of WF and SR was deduced. The numerical model revealed that WFs of the surfaces of the silver samples decreased linearly with Sa. The experimental results demonstrated that WF decreased linearly with SR of silver surface. The numerical model deduced from the software might be used to detect the value of SR or WF after one of them was decided, and could be used to calculate the depth of the groove on the polished surface of the silver samples as well.

Int. J. Electrochem. Sci., 7 (2012) 5204 - 5216

I agree with all authors, but as I understand magnetron sputtering of silver was made on one equipment, and the XPS analysis was carried out on another equipment. Therefore, when you transfer the sample the formation of semiconductor silver oxide with its electronic structure and propertiesis is inevitable. In this case, the work function will be largely determined exactly oxide. We observed the formation of such oxides on the surface of the silver nanoparticles in  colloidal dispersions.

The EWF of a metal is extremely sensitive to the chemical and physical conditions at its surface. Small amounts of contaminants present at a surface can invalidate EWF measurements.To answer your concerns, there are two possibilities of the EWF increase:

1. The EWF increasing is due to progressive inclusion of oxide on metallic

surface. Usually, the work function of a metal oxide is greater than that of the corresponding metal because of the Fermi level change. As the metal is oxidized, it loses its electrons resulting in a decrease of Fermi level. It is worth pointing out that adsorption of atoms or molecules changes the dipole layer and hence the work function: electronegative adsorbates (e.g. O, C, S) increase the work function, electropositive adsorbates (e.g. Na,K, Cs) decrease the work function. Covalent oxygen adsorption on metals involves localized orbital overlap and charge transfer between the adsorbate and surface atoms. The EWF values of  metals are small compared with the energy of ionization of the oxygen (13.618 eV); the oxygen having unoccupied energy levels, the electron transfer is for its benefit. Consequently, the surface is then covered with a negative layer, and the work function increases. In other words, the negative pole of the oxygen molecule points toward the vacuum, so the surface space charge or surface dipole presents an electrostatic field that causes an increase in the work function.

2. The decrease of the EWF with the increase of surface roughness is generally accepted. Nevertheless, we are still lacking sufficient knowledge on the electronic properties of metallic and alloy surfaces to fully understand the behavior of EWF. The mechanism responsible for the effect of surface conditions on EWF is not yet clear or controversial.

These articles might help you:

1. Int. J. Electrochem. Sci., 7(2012) 5204 - 5216

2. Journal of Applied Physics, Volume 111, Issue 12, pp. 123714-123714-6 (2012).

3. Journal of Alloys and Compounds > 2013 > 577 > Complete >1-5

The smoothness increase leads to an increase of the EWF because the atoms become packed more densely on the surface. The influence of surface roughness has been predicted by Smoluchowsky. According to Smoluchowski model, the roughness creates an additionnal dipole in the surface that compensates in part the dipole of the ordered surface. Consequently, the EWF becomes smaller than that for smooth metallic surfaces.

I agree with all authors, and notably Alexander Loskutov. Oxidation of the surface causes an increase of the work function, as i said before, and an increase of the surface roughness, too.  There is no controversy, because the influence of oxidation is dominating. Finally,  oxidation can increase both the work function of the metallic surface and its surface roughness.

You have to use a sensitive method to determine the Work function change, such as UPS, ARPES, EELS. I can see clearly in UPS how much defect surface leads to WF change.

First of all the work function or the specific surface (Helmholtz and/ or Gibbs) free energy is an intrinsic property which may be anisotropic in general should not depend on the morphological features of the surface of crystalline substance. But the effective or appear-ant value of surface free energy, which has the operational definition that involves the limiting value of the ratio of the energy divided by the surface area over which it is evaluated at the limit where measured area goes to zero.!!!. Therefore it is a gross over quantity and it may depend on the surface roughness and it results much higher values. Because, the actual surface area in the microscopic scale is much larger then the macroscopic area (or gross over area) used in the evaluation of that ratio. The roughness amplifies the effective or appear-ant surface free energy which general is anisotropic.

You can follow

Journal of Applied Physics, Volume 111, Issue 12, pp. 123714-123714-6 (2012)