I have been trying to understand the difference between the Work function of a metal and the Local Work Function.
I did some experiments to find the Local Work function of Graphite using an STM and found values ~0.3-0.7 eV. However, the work function of Graphite is ~4eV. Literature values indicate that my experimental results are correct.
Some research leads me to these definitions on a website:
Work Function: The work function corresponds to the minimum energy necessary to extract an electron from the metal
Local Work function: The local work function, which is defined as the energy required to take an electron from the Fermi level to a specified position outside the metal.
I frankly can't see a difference between these two definitions. Admittedly, my concepts in Solid State Physics are shaky. What is the difference between the two work functions? Can someone clarify, without assuming I know too much about Fermi levels.