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Wikipedia — Copper(I) oxide says $\ce{Cu2O}$ has semiconducting properties without any explanation. Nolan [1] talks about $\ce{Cu^+}$ vacancies making copper(I) oxide an extrinsic p-type semiconductor, but provides no explanation how these vacancies (I call them “atomic holes”) travel resulting in electrical conductivity.

I understand how silicone doped with boron results in an electron hole so it's a p-type semiconductor. But for $\ce{Cu2O}$ the explanation I found is that one $\ce{Cu+}$ ion is oxidized to $\ce{Cu^2+}$ and to maintain electrical neutrality another $\ce{Cu+}$ ion is removed creating a hole which results in electrical conductivity and a p-type conductor is formed.

However, I don't find this explanation convincing. For $\ce{Si}$ doped with $\ce{B}$ an electron hole was created and I can imagine that hole travelling. But in $\ce{Cu2O}$ the hole is a vacancy as one $\ce{Cu^+}$ leaves the lattice. Such a big “atomic hole” can't appreciably travel for conducting electricity.

So, how is $\ce{Cu2O}$ an extrinsic p-type semiconductor? What is really happening at the atomic level, namely:

  1. What are the holes here responsible for p-type semiconducting?
  2. Is $\ce{Cu2O}$ doped with something, since p-type or n-type semiconductors are usually made by introducing a dopant?

Reference

  1. Nolan, M.; Elliott, S. D. The p-type conduction mechanism in $\ce{Cu2O}$: a first principles study. Phys. Chem. Chem. Phys. 2006, 8 (45), 5350. DOI: 10.1039/b611969g.
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    $\begingroup$ IMHO $\ce{Cu2O}$ as not fully stoichiometric oxide is doped by $\ce{Cu^2+}$, which acts as a hole when the extra positive charge is effectively moving among copper atoms. $\endgroup$
    – Poutnik
    Commented Jun 16, 2021 at 9:19
  • $\begingroup$ @Poutnik (a)So the reason i found(see 'My confusion' in my answer above) is wrong . But that same reason was implied in the research paper (though not clarified). (b)please elaborate what u mean by "which acts as a hole when the extra positive charge is effectively moving among copper atoms"...?(c)Is it just an opinion or you have some sources...just asking...? $\endgroup$ Commented Jun 16, 2021 at 9:36
  • $\begingroup$ I do not claim I am an expert for semiconductors so I can be wrong. // I mean $\ce{Cu^{2+}-Cu^{+}-Cu^{+} -> Cu^{+}-Cu^{2+}-Cu^{+} -> Cu^{+}-Cu^{+}-Cu^{2+}}$ $\endgroup$
    – Poutnik
    Commented Jun 16, 2021 at 9:37
  • $\begingroup$ Ok thanks, but let's wait for some more inputs from other people.... $\endgroup$ Commented Jun 16, 2021 at 9:40
  • $\begingroup$ $\ce{Cu^2+}$ and a $\ce{Cu+}$ vacancy take place of 2 $\ce{Cu+}$ to keep neutrality, but 2+ charge is movable among Cu 1+ charges. $\endgroup$
    – Poutnik
    Commented Jun 16, 2021 at 9:47

3 Answers 3

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Let's start from here

What are the holes here responsible for p-type semiconducting?

and specifically discuss the difference between p-type, n-type and "none-type" semiconductors. Let's first state, that there is no fundamental difference between "normal" semiconductors and "normal" insulators (we shall ignore special cases of Mott insulators and semi-metals here). They are commonly described using band model. We can arrive to idea of a band from two directions: from orbital theory and from free electron model.

When starting from orbital theory, we will note that two or more interacting atomic orbitals produce several molecular orbitals with different energies. When number of the interacting atomic orbitals is finite, we get a discrete spectrum. However, by increasing number of interacting orbitals, we shall see rise of families of collective orbitals. It is possible to have a single family of such orbitals, but more often several such families exist in a solid. In limit of infinite number of interacting orbitals the discrete spectrum within each of those families will transform into continuum.

When starting from free electron model, we recall that an electron is a wave. When we put it into a periodic potential of atomic nuclei, due to quantum mechanics it has no choice but to adopt states where its wavelength is an integer multiple of the period of the atomic cell in any particular direction. This creates families of states that differ by phase of the electron-wave. Depending of the phase, the electron might have different energy.

No matter what model we use to construct band states, a band can be:

  • Completely empty (and NOT contribute to conductivity)
  • Completely filled (still not contributing to conductivity)
  • Filled partially - and contribute to conductivity.

Fundamentally, the important part for conductivity is just that: there must be one or more partially filled band in the solid. If we describe it as "an insulator plus some small amount of electrons on some mostly empty band" we have an n-type semiconductor, and if we describe it as "an insulator minus some small amount of electrons on a mostly full band" we have a p-type semiconductor. Metals have one or more bands that have considerable amount of empty and occupied states, so neither of the two descriptions fit. In theory in all three cases electric current through the solid is a collective movement of electrons. However, also in theory, it is useful to view the current in p-type semiconductor as collective movement of positively charged holes. This IS NOT reflection of reality, but theoretical description convenient in some cases. It is outside of scope of this post, but holes are not the only 'virtual' particle considered in the physics of solids. For example, an electron that is promoted to a conduction band also is a virtual particle in some sense, since when considered as a charge carrier, its properties are different from properties of a free electron - in particular, it might have different effective mass.

In practical terms the most important difference between holes and electrons as charge carriers is their mobility. Electrons move easier. Consequently, in digital electronics FETs with n-type channel are used.

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Now, what would happen if we 'take away' some $\ce{Cu}$ atoms from $\ce{Cu2O}$ ? First and foremost, we shall see new states, associated with the vacancies. Those states do not belong to any band and are localized near their parent vacancies. If we use molecular orbital analogy, $\ce{Cu}$ in $\ce{Cu2O}$ occupies position between oxygen atoms, so it can be described roughly like $[\ce{O:\->Cu^{+}\<-:O}]$. When the copper ion is lost, only the oxygen atoms remain and the electron pairs used to bind the copper atom are no longer shared. Obviously, they are slightly higher in energy than they were. The vacancy, however, is negatively charged (since we removed a cation). Thus, a counter-charge must arise. This charge will appear as an electron lost from the top-most position of the top-most band - a hole. This hole is a positively charged particles, so it shall be attracted to its parent vacancy. In the calculations you referenced this hole manifests as a positive charge on the copper atoms nearest to the copper vacancy, creating an illusion of a delocalised $\ce{Cu^{2+}}$

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The $\ce{Cu^2+}$ ion you call "atomic hole" is responsible for the p-type conductivity. The way to understand is would be a $\ce{Cu+}$ ion with a h+ (hole) associated with it. Conductivity may occur by the hole jumping between neighbouring ions if this association energy can be overcome. Resulting in a temperature-activated hopping process. The hole is moving from copper to copper, not the entire $\ce{Cu^2+}$ ion.

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Is Cu2O doped with something, since p-type or n-type semiconductors are usually made by introducing a dopant?

Cu+ vacancies making copper(I) oxide an extrinsic p-type semiconductor...

The vacancies are the dopants. Without the vacancies, they wouldn't call it "extrinsic".

... , but provides no explanation how these vacancies (I call them “atomic holes”) travel resulting in electrical conductivity.

"Holes" refers to electronic structure rather than vacancies. Electrons' motion, not vacancies' diffusion, is the cause of electrical conductivity. Note that there are other materials, called 'ionic conductors', in which ions and therefore also vacancies carry electrical current. The word 'semiconductor' implies electronic conductivity.

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