Relationship Between Work Function, Vacuum Electric Potential, and Fermi Level (voltage)
If we remove an electron from a solid, to a state of zero total energy, then the thermodynamic work required is given by -EF, where EF is the Fermi level (electrochemical potential) in that system. The work function is however defined by placing the electron into the vacuum nearby the surface, where there is an electrostatic potential ϕ; at this point, the electron's total energy is not zero but instead Evac=-eϕ. Thus, the work function W is defined by
In other words, it is the sum of the work required to completely remove the electron (-EF), and the work required to place it back just outside the surface (-eϕ).
The work function is in fact a property of the surface material, and EF is fixed by the electrode that is attached to the material. Practically, this means that the material's work function acts to determine the value of ϕ (rather than the other way around). We can define the electrode's internal voltage V as V = -EF/e, giving
In other words, if we use a battery to apply a voltage V to an electrode, then the actual ϕ produced in the vacuum will vary depending on the work function. W depends on what material the electrode is made from. The reason for this dependence of W on material can be attributed to a variety of effects (binding energy, surface dipoles, etc.), discussed below.
Read more about this topic: Critical Absorption Energy
Famous quotes containing the words level, relationship, electric, vacuum and/or work:
“The man who loves other countries as much as his own stands on a level with the man who loves other women as much as he loves his own wife.”
—Theodore Roosevelt (1858–1919)
“Some [adolescent] girls are depressed because they have lost their warm, open relationship with their parents. They have loved and been loved by people whom they now must betray to fit into peer culture. Furthermore, they are discouraged by peers from expressing sadness at the loss of family relationships—even to say they are sad is to admit weakness and dependency.”
—Mary Pipher (20th century)
“Persons grouped around a fire or candle for warmth or light are less able to pursue independent thoughts, or even tasks, than people supplied with electric light. In the same way, the social and educational patterns latent in automation are those of self- employment and artistic autonomy.”
—Marshall McLuhan (1911–1980)
“When a daughter tries suicide
and the chimney falls down like a drunk
and the dog chews her tail off
and the kitchen blows up its shiny kettle
and the vacuum cleaner swallows its bag
and the toilet washes itself in tears ...”
—Anne Sexton (1928–1974)
“I have done a great deal of work, as much as a man, but did not get so much pay. I used to work in the field and bind grain, keeping up with the cradler; but men doing no more, got twice as much pay.... We do as much, we eat as much, we want as much.”
—Sojourner Truth (1797–1883)