In the system's ground state, states with energy less than the Fermi Level are occupied, and states above the Fermi Level are not occupied. The energy required to liberate an electron in the Fermi Level is the work function. However, usually the Fermi Energy is referenced to energy zero: that of the lowest energy electron free of the metal. In that case the Fermi Energy would have a negative value i. The thermionic work function depends on the orientation of the crystal and will tend to be smaller for metals with an open lattice, larger for metals in which the atoms are closely packed.
The range is about 1. It is somewhat higher on dense crystal faces than open ones. The magnitude of the work function is usually about a half of the ionization energy of a free atom of the metal. For example, caesium has ionization energy 3. 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.
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.
Then, the correct formula for work function is:. In electronics the work function is important for design of the metal - semiconductor junction in Schottky diodes and for design of vacuum tubes. Many techniques have been developed based on different physical effects to measure the electronic work function of a sample. One may distinguish between two groups of experimental methods for work function measurements: absolute and relative.
Methods of the first group employ electron emission from the sample induced by photon absorption photoemission , by high temperature thermionic emission , due to an electric field field emission , or using electron tunnelling.
All relative methods make use of the contact potential difference between the sample and a reference electrode. Experimentally, either an anode current of a diode is used or the displacement current between the sample and reference, created by an artificial change in the capacitance between the two, is measured the Kelvin Probe method, Kelvin probe force microscope. Photoelectron emission spectroscopy PES is the general term for spectroscopic techniques based on the outer photoelectric effect.
In the case of Ultraviolet Photoelectron Spectroscopy UPS , the surface of a solid sample is irradiated with ultraviolet UV light and the kinetic energy of the emitted electrons is analysed.
Due to limitations of the escape depth of electrons in solids UPS is very surface sensitive, as the information depth is in the range of 2 — 20 monolayers nm. The resulting spectrum reflects the electronic structure of the sample providing information on the density of states, the occupation of states, and the work function. Time Traveler for work function The first known use of work function was in See more words from the same year.
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