Why Holes have an effective positive charge? In semiconductor physics, holes or vacancies generated due to absence of electron creates a vacancy there which apparently acts as a particle with effective positive charge.
I can understand that the hole can be seen as moving along the applied external electric field, which is just other electrons drifting motion against the electric field in disguise but I don't see how the hole is supposed to have an effective positive charge.
This method works for calculating total amount of current, but to me this assumption of hole having effective positive charge is like saying a positive charge exists in vacuum without any particle actually there.
During my electrostatics class, I have done problems in which a small spherical part is scooped out of a bigger sphere, uniformly volume charged, in that problem I could think the small sphere separate from the bigger sphere with uniform volume charge density opposite to that of the bigger sphere and then superimpose both of the spheres' electric field, even though in actuality, the smaller sphere is just a  cavity with no charge at all in it. I am thinking the hole effective charge assumption comes from this "trick". Is this true?
 A: "but to me this assumption of hole having effective positive charge is like saying a positive charge exists in vacuum without any particle actually there." - This is actually not that inaccurate. In any material there are many inert positive charges - the nucleons of the atoms that compose the material itself. The net electrons in the material screen these positive charges, and we have that in total the material is not charged (unless we charge is explicitly).
When we want to describe the conductance of the material, or other dynamical properties, we are mostly interested in the electrons, since they are the particles that can move around and are responsible for most of the interesting phenomena. So when we write everything up we usually don't write explicitly the nucleons: doing this will lead to overly cumbersome expressions.
However, their charges are still there! Sitting in the background and mostly inert, and they can (and do) affect the dynamics of the electrons. So, when we remove an electron from somewhere, we note that it leaves some proton less screened, and a net positive charge exists there. It turns out that it is very useful to treat these positive net charges, that are absence of screening electrons, as quasiparticles of themselves, as they move around and respond to electric field etc. These are the holes.
