I guess this link might be helpful to you.

http://www.sciencedirect.com/science/article/pii/S0749603614001554

The in-homogeneity in a material (due to metal -semiconductor mixing) creates uneven conductivity, in turn, availability of free electron/hole are not uniform. As the barrier is creates due to recombination of free electron-hole, results in in-homogeneity in barrier

The barrier inhomogeneity results mainly from the Gaussian distribution of the surface/interface defect density (trap density) over the area of the Schottky contact. The ideal Schottky barrier height is reduced by the potential drop over the interfacial layer between the semiconductor and the metal; this potential drop results from the charged traps. Trap charge density non-uniformity leads to interfacial potential drop non-uniformity, which ultimately results in the barrier height non-uniformity. The semiconductor/interfacial-layer interface is not equipotential; this is why the interface potential varies over the barrier area. The interfacial traps may result from the bonding defects and/or interfacial strain and/or chemical impurities. 

the barrier inhomogeneity basically judge by the variation of ideality  factor from unity and variation of the barrier height with respect to temperature, the cause of  this non uniformity is well describe by the Sir Samaras Kar, for further discussion you can go through following paper, Pd Schottky Contacts on Sol–Gel Derived ZnO Thin Films With Nearly Ideal Richardson Constant, Electron Device Letters, IEEE  (Volume:35 ,  Issue: 7 ) 

Hi Macho

Inhomogeneities in the metal-semiconductor (MS) are normally originating from immature/premature crystal growth and the I-V-T characteristics of Schottky contacts are affected by the barrier height inhomogeneities (BHI). The BHI can alter both Schottky barrier height (SBH) and Richardson contact.

During formation an MS potential barrier, defects are established on the epitaxy interfaces mostly in form of unstrained defects like a sharp tooth. The growth of those sharp teeth (due to the fabrication process) will localize an enhancement in the electric field and so in the carrier emission in SBH. That is why BHI are existed.

Cheers