Let us consider the following question.

What are the correct responses to this question? It depends.

In this question, the expected answer is probably C. This is what I call a simple-minded answer.

This is an OK answer. It is not an incorrect answer, but it is just a simple-minded answer, based on a simple-minded definition of a hole (which this on-line activity is limited to). It is like when we have a collection of electrons in a metal such as Na or Al, we call them a collection of holes. Or, when we have 6 electrons in the 3d shell of Fe$^{2+}$ ions, we can call them 4 holes instead, as it takes 10 electrons to fill the 3d shell. This is a sometimes-useful general view.

In this view, as the hole is just the absence of the electron, it may not be viewed as fundamental. Also, microscopically, hole is not really free (and neither is electron). Therefore, A and B are not good choices.

OK, but what if we go beyond this simple minded view? Let us take a sophisticated point of view, which I advertised in this course. This is a better view. In such a view, all of A,B,C can be answers.

Recall that the more useful meaning of holes in a semiconductor is the absence of electrons on top of the valence band, which is almost full. This is generally what we mean by holes in a semiconductor, and it is for a good reason. In such a case, a hole gains a fundamental nature, since the effective mass becomes positive only in the language of a hole. Such a hole is fundamentally distinguishable from an electron. The signs of the Hall coefficient ($R_H$) and thermopower are examples which can clearly distinguish between an electron and a hole. In this view, a hole is fundamentally distinguishable from an electron by experiment. So, A is a good choice (see more discussion in the last two paragraphs below).

As regards the choice of B, this is also a good choice in this sophisticated point of view. Let us ask this question. When we talk of an electron or a hole in a semiconductor, what mass do we associate with it? The most sensible answer is the effective mass! Then, an electron or a hole in a semiconductor is quite a different particle from a bare electron or a bare hole that we may normally conjure up. And, such an electron or a hole moves completely independent of atoms, since the effect of the bare-electron—atom or bare-hole—atom interaction is already included in the effective mass!

[Optional reading from this point on.] Note that in this sophisticated view, we can easily understand why the positron is viewed as a fundamental particle. Also, you might note that even if we generally consider a bare electron (an electron in vacuum) as a free electron, the modern view (QED) is that an electron in vacuum is itself a result of complex interactions of bare electrons (or barer electrons so to speak) and photons. The theory shows that the mass of the barer electron gets renormalized to an effective mass, which we simply call the electron mass (0.511 MeV)! That is, an electron in vacuum carries the effective mass of the QED theory. Also, the magnetic moment of the electron is such an effective quantity too, which Feynman's QED theory famously produced with high accuracy and has been a very important quantity to confirm the theory.

The formal name of this sophisticated point of view is the renormalization group theory, a quite fundamental subject in all of physics. For this reason, the effective mass is also called the renormalized mass.