Work Function and Surface Effect
The work function W of a metal is closely related to its Fermi energy (defined relative to the lowest energy free particle: zero in the above diagram) yet the two quantities are not exactly the same. This is due to the surface effect of a real-world solid: a real-world solid is not infinitely extended with electrons and ions repeatedly filling every primitive cell over all Bravais lattice sites. Neither can one simply take a set of Bravais lattice sites inside the geometrical region V which the solid occupies and then fill undistorted charge distribution basis into all primitive cells of . Indeed, the charge distribution in those cells near the surface will be distorted significantly from that in a cell of an ideal infinite solid, resulting in an effective surface dipole distribution, or, sometimes both a surface dipole distribution and a surface charge distribution.
It can be proven that if we define work function as the minimum energy needed to remove an electron to a point immediately out of the solid, the effect of the surface charge distribution can be neglected, leaving only the surface dipole distribution. Let the potential energy difference across the surface due to effective surface dipole be . And let be the Fermi energy calculated for the finite solid without considering surface distortion effect, when taking the convention that the potential at is zero. Then, the correct formula for work function is:
Where is negative, which means that electrons are bound in the solid.
Read more about this topic: Work Function
Famous quotes containing the words work, function, surface and/or effect:
“I don’t pity any man who does hard work worth doing. I admire him. I pity the creature who does not work, at whichever end of the social scale he may regard himself as being.”
—Theodore Roosevelt (1858–1919)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)
“The surface of the ground in the Maine woods is everywhere spongy and saturated with moisture.”
—Henry David Thoreau (1817–1862)
“I don’t know what effect these men will have upon the enemy, but, by God, they terrify me.”
—Arthur Wellesley, 1st Duke Wellington (1769–1852)