Work function: Difference between revisions

Revision as of 13:56, 21 December 2020

Revision as of 14:01, 26 December 2020

Line 18:

;[[Thermionic emission]]: In thermionic [[electron gun]]s, the work function and temperature of the [[hot cathode]] are critical parameters in determining the amount of current that can be emitted. [[Tungsten]], the common choice for vacuum tube filaments, can survive to high temperatures but its emission is somewhat limited due to its relatively high work function (approximately 4.5 eV). By coating the tungsten with a substance of lower work function (e.g., [[thorium]] or [[barium oxide]]), the emission can be greatly increased. This prolongs the lifetime of the filament by allowing operation at lower temperatures (for more information, see [[hot cathode]]).

;[[Band bending]] models in solid-state electronics: The behavior of a solid-state device is strongly dependent on the size of various [[Schottky barrier]]s and [[heterojunction|band offset]]s in the junctions of differing materials, such as metals, semiconductors, and insulators. Some commonly used heuristic approaches to predict the band alignment between materials, such as [[Anderson's rule]] and the [[Schottky-Mott rule]], are based on the thought experiment of two materials coming together in vacuum, such that the surfaces charge up and adjust their work functions to become equal just before contact. In reality these work function heuristics are inaccurate due to their neglect of numerous microscopic effects. However, they provide a convenient estimate until the true value can be determined by experiment.<ref>[[Herbert Kroemer]], "[https://www.nobelprize.org/nobel_prizes/physics/laureates/2000/kroemer-lecture.html Quasi-Electric Fields and Band Offsets: Teaching Electrons New Tricks]" Nobel lecture</ref><ref>{{cite web|url=http://academic.brooklyn.cuny.edu/physics/tung/Schottky/systematics.htm|title=Barrier Height Correlations and Systematics|website=academic.brooklyn.cuny.edu|accessdateaccess-date=11 April 2018}}</ref>

;Equilibrium electric fields in vacuum chambers: Variation in work function between different surfaces causes a non-uniform electrostatic potential in the vacuum. Even on an ostensibly uniform surface, variations in {{math|''W''}} known as patch potentials are always present due to microscopic inhomogeneities. Patch potentials have disrupted sensitive apparatus that rely on a perfectly uniform vacuum, such as [[Casimir force]] experiments<ref>{{Cite journal | doi = 10.1103/PhysRevA.85.012504| title = Modeling electrostatic patch effects in Casimir force measurements| journal = Physical Review A| volume = 85| issue = 1| pages = 012504| year = 2012| last1 = Behunin | first1 = R. O.| last2 = Intravaia | first2 = F.| last3 = Dalvit | first3 = D. A. R.| last4 = Neto | first4 = P. A. M. | last5 = Reynaud | first5 = S.|arxiv = 1108.1761 |bibcode = 2012PhRvA..85a2504B | s2cid = 119248753}}</ref> and the [[Gravity Probe B]] experiment.<ref>{{Cite journal | doi = 10.1103/Physics.4.43| title = Finally, results from Gravity Probe B| journal = Physics| volume = 4| issue = 43| pages = 43| year = 2011| last1 = Will | first1 = C. M. |arxiv = 1106.1198 |bibcode = 2011PhyOJ...4...43W | s2cid = 119237335}}</ref> Critical apparatus may have surfaces covered with molybdenum, which shows low variations in work function between different crystal faces.<ref name="venables">{{cite web|url=http://venables.asu.edu/qmms/PROJ/metal1a.html|title=Metal surfaces 1a|website=venables.asu.edu|accessdateaccess-date=11 April 2018}}</ref>

;[[Contact electrification]]: If two conducting surfaces are moved relative to each other, and there is potential difference in the space between them, then an electric current will be driven. This is because the [[surface charge]] on a conductor depends on the magnitude of the electric field, which in turn depends on the distance between the surfaces. The externally observed electrical effects are largest when the conductors are separated by the smallest distance without touching (once brought into contact, the charge will instead flow internally through the junction between the conductors). Since two conductors in equilibrium can have a built-in potential difference due to work function differences, this means that bringing dissimilar conductors into contact, or pulling them apart, will drive electric currents. These contact currents can damage sensitive microelectronic circuitry and occur even when the conductors would be grounded in the absence of motion.<ref>{{Cite journal | last1 = Thomas Iii | first1 = S. W. | last2 = Vella | first2 = S. J. | last3 = Dickey | first3 = M. D. | last4 = Kaufman | first4 = G. K. | last5 = Whitesides | first5 = G. M. | title = Controlling the Kinetics of Contact Electrification with Patterned Surfaces | doi = 10.1021/ja902862b | journal = Journal of the American Chemical Society | volume = 131 | issue = 25 | pages = 8746–8747 | year = 2009 | pmid = 19499916| citeseerx = 10.1.1.670.4392 }}</ref>

Line 79:

Photoelectric measurements require a great deal of care, as an incorrectly designed experimental geometry can result in an erroneous measurement of work function.<ref name="pitfalls"/> This may be responsible for the large variation in work function values in scientific literature.

Moreover, the minimum energy can be misleading in materials where there are no actual electron states at the Fermi level that are available for excitation. For example, in a semiconductor the minimum photon energy would actually correspond to the [[valence band]] edge rather than work function.<ref>{{cite web|url=http://www.virginia.edu/ep/SurfaceScience/PEE.html|title=Photoelectron Emission|website=www.virginia.edu|accessdateaccess-date=11 April 2018}}</ref>

Of course, the photoelectric effect may be used in the retarding mode, as with the thermionic apparatus described above. In the retarding case, the dark collector's work function is measured instead.

Line 278:

In a [[semiconductor]], the work function is sensitive to the [[doping (semiconductor)|doping level]] at the surface of the semiconductor. Since the doping near the surface can also be [[field effect (semiconductor)|controlled by electric fields]], the work function of a semiconductor is also sensitive to the electric field in the vacuum.

The reason for the dependence is that, typically, the vacuum level and the conduction band edge retain a fixed spacing independent of doping. This spacing is called the [[electron affinity]] (note that this has a different meaning than the electron affinity of chemistry); in silicon for example the electron affinity is 4.05 eV.<ref>{{cite web|url=http://www.virginiasemi.com/pdf/generalpropertiessi62002.pdf|title=The General Properties of Si, Ge, SiGe, SiO2 and Si3N4 |author=Virginia Semiconductor|date=June 2002|accessdateaccess-date=6 Jan 2019}}</ref> If the electron affinity ''E''_EA and the surface's band-referenced Fermi level ''E''_F-''E''_C are known, then the work function is given by

:<math> W = E_{\rm EA} + E_{\rm C} - E_{\rm F}</math>

where ''E''_C is taken at the surface.

From this one might expect that by doping the bulk of the semiconductor, the work function can be tuned. In reality, however, the energies of the bands near the surface are often pinned to the Fermi level, due to the influence of [[surface state]]s.<ref>{{cite web|url=http://academic.brooklyn.cuny.edu/physics/tung/Schottky/surface.htm|title=Semiconductor Free Surfaces|website=academic.brooklyn.cuny.edu|accessdateaccess-date=11 April 2018}}</ref> If there is a large density of surface states, then the work function of the semiconductor will show a very weak dependence on doping or electric field.<ref>{{Cite journal | last1 = Bardeen | first1 = J. | title = Surface States and Rectification at a Metal Semi-Conductor Contact | doi = 10.1103/PhysRev.71.717 | journal = Physical Review | volume = 71 | issue = 10 | pages = 717–727 | year = 1947 |bibcode = 1947PhRv...71..717B }}</ref>

=== Theoretical models of metal work functions ===