The contact and thermionic phenomena.

§1 A work function

Conduction electrons do not leave spontaneously metal in appreciable quantity this results from the fact that metal represents for them a potential hill.

To leave metal it is possible only to those electrons which energy appears sufficient for overcoming of the potential hill which is available on a surface which arises for following parents: casual removal of an electron from an outside stratum of positively ionised atoms of a lattice (from a metal surface) leads to occurrence in that place which was left by an electron, a redundant plus charge. The Coulomb interaction with this charge forces an electron which velocity is not so great, to return back. Thus separate electrons all time leaves a metal surface, leave from it on some interatomic distances and then turn back. As a result metal has appeared the surrounded thin cloud of electrons. This cloud forms a double electrical stratum together with an outside stratum of ions. The forces operating on an electron in such stratum, are guided in metal. The operation made against these forces while translating of an electron from metal outside, goes on magnification of potential energy of an electron of E_p0.

For removal metal limits different electrons need to be informed different energy. To an electron which is at the lowermost level of a conduction band, it is necessary to inform energy of E_p0; for an electron which is on a Fermi level energy is sufficientE_p –E_max=E_p –E_F. The least energy which is necessary for informing an electron to remove it from a solid body or a fluid in vacuum, is termed as a work function:

ej = E_p – E_F

(At Т = 0 both at valid "T and for semiconductors).

The Fermi level depends on temperature:

Besides, with temperature change depth of a potential hill of E_p0 changes. ⇒ The Work function ej depends  on temperature.

            The work function depends also on cleanliness of a surface and presence oxide films on a metal surface.

§2 Contact of two metals on a band theory.

Contact potential difference (c.р.d.).

            If two different metals to lead to touch between them there will be a potential difference termed with a contact potential difference. The Italian physicist A.Volta (1745-1827) has established that if metals to give Al, Zn, Sn, Pb, Sb, Bi, Hg, Fe, Cu, Ag, Au, Pt, Pd contact in the specified sequence everyone previous at touch with one of the following will be charged plusly. This series term as a series Volta. The contact difference j for the various metals makes from the tenth to whole volt.

            Two laws Volta:

• The contact potential difference depends only on a chemical compound and temperature of adjoining metals.
• The contact potential difference of consistently pairing various conductors which are at identical temperature does not depend on a chemical compound of the intermediate conductors and is equal to a contact potential difference, arises at immediate contact of extreme conductors.

            To explain occurrence of a contact potential difference (c.p.d.) it is possible by means of the theory. To view contact of two metals to various work functions А₁ and А₂, i.e. with various standings of a Fermi level. If А₁ < А₂ the Fermi level settles down in metal 1 above, than in metal 2.⇒, at contact of metals electrons from higher levels of metal 1 will transfer to lower levels of metal 2 that will lead to that metal 1 will have the plus charge, and metal 2 - subzero. Simultaneously there is the relative bias of energy levels: in metal 1 all levels are biased downwards (since electrons leave it), in metal 2 - upwards. This process will occur until between adjoining metals balance will not be established, i.e. Fermi levels will not be levelled yet.

            Since for adjoining metals Fermi levels coincide, and work functions А₁ and А₂ do not change, (they are constants of metals and do not depend on that, there is a metal in contact or not), potential energy of electrons in the points lying out of metals in immediate proximity to their surface (in points A and B on fig.) will be various. ⇒ Between p. A and B the potential difference which is equal is established

Δφ'=

The potential difference caused by distinction of work functions of contact metals, is termed as an exterior contact potential difference.

If Fermi levels of two contact metals are not identical, between interior points of metals the intrinsic-contact potential difference is observed.

Δφ"=

In a quantum theory it is proved that the interior contact potential difference arises because of various concentrations of electrons in contact metals.

            Δφ" depends on temperature Т of contact of metals (since E_F depends on temperature), and is at the cause of thermoelectric phenomenas. As a rule

Δφ"<<Δφ '

The intrinsic-contact potential difference arises in the double electron sheath formed in near contact of field, as termed the contact stratum. The thickness of a contact stratum of ~ 10^-10 m, i.e. is comparable with interstitial-site in distances in a crystalline lattice. Number of the electrons diffusing through a crystalline stratum from ~2% total number of electrons, being on a metal surface. Conductivity of metals at their contact does not change also a crystalline stratum spends an electric current.