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According to page-1262 of Fundamentals of Physics by Halliday, Resnick & Walker (10th edition),

Both the electrons in the conduction band and the holes in the valence band serve as charge carriers. The holes do so by permitting a certain freedom of movement to the electrons remaining in the valence band, electrons that, in the absence of holes, would be gridlocked.

So, we can understand that the holes move by means of the "gridlocked" electrons. My guess is, free electrons don't combine with holes as they (free electrons) are in a higher energy state than the "gridlocked" electrons. Consider this, if free electrons had a tendency to combine with holes, why were the free electron-free hole pair created in the first place? The free electron and hole would've combined and would've ceased to exist the moment they were created. Is my logic sound?

So, do free electrons, at any point in transistor physics, combine with holes to become neutral?

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    $\begingroup$ Yes, electrons and holes can recombine. Both generation and recombination are required to have detailed balance. $\endgroup$
    – Jon Custer
    Jun 1, 2021 at 15:45
  • $\begingroup$ Depending on the themperature, the concentration of electrons ans holes changes drastically. Moreover, hole motion is fictitious. It is neutralization of one hole and creating another one at another place. $\endgroup$
    – Vladimir Kalitvianski
    Jun 1, 2021 at 15:48
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    $\begingroup$ @VladimirKalitvianski “Fictitious” is a strong word. The persistent robustness of the quasiparticle picture raises some interesting philosophical questions (which don’t really fit in a comment). $\endgroup$
    – rob ♦
    Jun 1, 2021 at 17:17
  • $\begingroup$ Yes, during the formation of the depletion region, free electrons and holes recombine. $\endgroup$
    – tryingtobeastoic
    Jun 13, 2021 at 6:46

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Yes they do. And as the energy of electron and holes are different the recombination leads to emission of light of various colors depending on the band gap of the material of the diode. After recombination the site where the pair was created becomes neutral but fresh electron -holes pair get created and the process continues.

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  • $\begingroup$ Are fresh electron-pair created due to the energy released by recombination of the electron-hole pair or are they created due to external heat? $\endgroup$
    – tryingtobeastoic
    Jun 1, 2021 at 16:12
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    $\begingroup$ @user545735 Both $\endgroup$
    – Matt
    Jun 1, 2021 at 19:06

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