The contact and thermionic phenomena.
§1 A work function
electrons do not leave spontaneously metal in appreciable quantity
this results from the fact that metal represents for them a potential
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 Ep0.
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 Ep0; for an electron which is on a Fermi level energy is sufficientEp –Emax=Ep –EF. 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 = Ep – EF
(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 Ep0 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.
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
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
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.
a quantum theory it is proved that the interior contact potential
difference arises because of various concentrations of electrons in
Δφ" depends on temperature Т of contact of metals (since EF depends on temperature), and is at the cause of thermoelectric phenomenas. As a rule
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.