To answer your question one must briefly describe idea of introducing holes to description of semiconductors.
Holes are introduced, because (typically) in semiconductors we have two energy ranges in which presence of electrons is allowed, which are significantly separated (relative to kT). Moreover Fermi level on typical case is between these allowed energy ranges (between valence and conduction bands).
Such configuration causes almost total occupation on valence band, and emptying of conduction band. Therefore we decide treat valence and conduction band separately. In case of conduction band description using single-electron states is very natural. However in case of valence band we have almost all single electron states occupied. Therefore (because electrons are indistinguishable) instead of describing which states are occupied, we describe which states are not occupied. It is like if we had a box almost-full with water. Instead of observing how water moves around the box we decide to observe how bubbles of air move around the box (see figure).
However in case of conductors we do not have clearly separated highly-occupied and lowly occupied states, therefore system cannot be naturally separated into two subsystems. Back to analogy with box. In semiconductor we have two separated boxes, one above the other, one almost full, and another almost empty. In conductors we have only one box, half-full of water. Moreover water surface is not smooth, but rather recalls raging foam. Introducing both droplets and bubbles in the surface region would than only add new object do description instead of simplifying problem.
It does not mean that introducing holes into description of conductors (materials without band-gap) is impossible. It is just not as convenient as in semiconductors. Example of case when it is done, despite zero band-gap, is graphene. Very often states below Dirac point are called hole states and those above - electron states. In this situation it quite natural, for example when describing excitation of carriers with light - because electron are always excited from hole states (below Dirac point) to electron states (above Dirac point), and electron-hole pair is generated.
To answer your question one must briefly describe idea of introducing holes to description of semiconductors.
Holes are introduced, because (typically) in semiconductors we have two energy ranges in which presence of electrons is allowed, which are significantly separated (relative to kT). Moreover Fermi level on typical case is between these allowed energy ranges (between valence and conduction bands).
Such configuration causes almost total occupation on valence band, and emptying of conduction band. Therefore we decide treat valence and conduction band separately. In case of conduction band description using single-electron states is very natural. However in case of valence band we have almost all single electron states occupied. Therefore (because electrons are indistinguishable) instead of describing which states are occupied, we describe which states are not occupied. It is like if we had a box almost-full with water. Instead of observing how water moves around the box we decide to observe how bubbles of air move around the box (see figure).
However in case of conductors we do not have clearly separated highly-occupied and lowly occupied states, therefore system cannot be naturally separated into two subsystems. Back to analogy with box. In semiconductor we have two separated boxes, one above the other, one almost full, and another almost empty. In conductors we have only one box, half-full of water. Moreover water surface is not smooth, but rather recalls raging foam. Introducing both droplets and bubbles in the surface region would than only add new object do description instead of simplifying problem.
It does not mean that introducing holes into description of conductors (materials without band-gap) is impossible. It is just not as convenient as in semiconductors. Example of case when it is done, despite zero band-gap, is graphene. Very often states below Dirac point are called hole states and those above - electron states. In this situation it quite natural, for example when describing excitation of carriers with light - because electron are always excited from hole states (below Dirac point) to electron states (above Dirac point), and electron-hole pair is generated.
Simply, metal with (dominantly) hole conduction has positive Hall coefficient.
Example is Berilium (in some directions) or some of high-temperature superconductors.
Hi arpit.. Holes do exist in conductors.. infact holes are the only ones in conductors that carry current! electrons are minority charge carriers. only some nA of current is carried by electrons! Holes play a vital role in carrying electrons! though we say that, free electrons are the main reason for carrying electricity. it is infact holes which are otherwise termed as free electrons or valence electrons that carry electricity! Holes not only exist in conductors , but also in semi conductors and also in insulators! In insulators it is entirely zero ! That is the main reason we dont talk about holes in insulators! In conductors the valence band and conduction band overlap! Hence we cannot see holes. Hence we talk about these free electrons!
There is no such thing like "hole". It is just the absence of electrons.
When electron move from its place, it leaves behind a vacant space, we call this vacant space as holes.
Regards,
Nitish
@Nitish: The absence of an electron acts very much differently than an electron itself, therefore the concept of a hole is useful. For once, the mobillity of electrons is different than that of "absence of electrons" (holes), in Si much higher, but in organic semiconductors much lower - due to the trapping nature. Hole is, in fact, the accepted term for the absence of an electron, hence electron/hole pairs, etc...
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