Can Intraband Transitions Produce Holes in the Conduction Band of Metals?

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Discussion Overview

The discussion revolves around the concept of intraband transitions in metals and whether such transitions can produce holes in the conduction band. Participants explore theoretical implications, distinctions between metals and semiconductors, and the behavior of electrons and holes in these contexts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions if intraband transitions of electrons in the conduction band can create holes, suggesting a conceptual link to the behavior of electrons at points k and -k.
  • Another participant argues that the hole concept is typically associated with the valence band, stating that in metals, the conduction band is filled with free electrons, and thus, holes do not exist.
  • A different viewpoint suggests that if an electron at point k moves to another state, it could create a hole at k, challenging the notion that holes cannot exist in the conduction band.
  • One participant explains that the electron states in a metal's conduction band have delocalized wave functions, which allows for conduction without transitioning to another band, contrasting this with semiconductors.
  • Another participant asserts that while intraband transitions can produce holes, these holes behave differently from those in semiconductors, noting their negative effective mass and positive charge, which affects their movement in an applied field.
  • This participant also mentions the relevance of these holes in the context of superconductors.

Areas of Agreement / Disagreement

Participants express differing views on the existence and behavior of holes in the conduction band of metals, with no consensus reached on the validity of the hole concept in this context.

Contextual Notes

Participants reference the behavior of electrons and holes in both metals and semiconductors, highlighting distinctions in their conduction mechanisms and the implications of intraband transitions. The discussion includes assumptions about the nature of electron states and the definitions of holes.

hokhani
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Could intraband transition (in metals) of an electron in the conduction band produce a hole there?
 
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The hole concept is related to a missing electron in the valence band. The valence band of a metal is completely filled and the electrons in the conduction band are FREE to begin with.

Therefore, there is no such thing as a hole in metals.
 
Ok, but as far as I know, the hole at the point k is a concept which is contributed to the electron at the point -k. Until the electron at k is not removed, its effect is neutralized by the electron at -k but if it is removed, the electron at -k participates in conduction which its conduction is attributed to the hole at k. This situation could happen in the conduction band as if we have one electron at k and another at -k and if the electron at k moves to any different state, why we wouldn't have the hole at k?
 
because an electron state in a metal conduction band has a de-localized wave function. It can contribute to conduction without having to transition to another band as in a semiconductor. Of course, it is more interesting to ask what happens when an electron is removed as in photoelectric effect.. do you see a creation of a hole? No.. because the valance band is completely filled and
 
hokhani said:
Could intraband transition (in metals) of an electron in the conduction band produce a hole there?

Yes, but the hole, like the excited electron, will quickly relax and be scattered to the vicinity of the Fermi surface. They behave differently than holes in the valence band in so far as their effective mass is negative. As their charge is also positive (that of the electron being negative), they will move in an applied field in the same direction as the electrons, so there won't be a charge separation as in a semi-conductor.

These kind of holes are also important in the formation of superconductors.
 

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