Are holes electrons moving in the same direction of the electric field? Holes are electrons, but with negative mass. That's said, so by applying electric field, electrons (n) move in the opposite direction of the field, while holes (other electrons) move in the same direction. Shouldn't they cancel each other?
We consider holes to be positive charged particles with positive mass, but that's only because they are negative charged particles with negative mass. We can still think of them as "normal" electrons cancelling each other if one's motion opposes another's, right?
 A: There are a few non-intuitive effects that lead to holes.
An entirely filled band does not contribute to current. This is because for every charged particle moving in one direction, there is another moving in the opposite direction that cancels it out. The conduction band is easy because it is nearly empty and we can treat those few electrons that are in it as "normal" electrons with a certain effective mass based on the curvature of the band near the bottom.
Current in a Mostly Filled Band
The valence band on the other hand is nearly completely filled. Mathematically we can model current in a mostly filled band as the current of an entirely filled band, which is equal to zero, minus whatever current would have been contributed by the unfilled states had they been filled.
States at the Top of a Band Have Negative Effective Mass
But holes don't act like electrons. You can tell holes and electrons apart using a Hall measurement, which wouldn't happen if holes were "just" electrons. So there has to be something else going on. Earlier I mentioned effective mass, electrons at the top of a band also have an effective mass driven by the curvature of the band in that region. At the top of a band the effective mass is negative. This applies equally to both filled and unfilled states. An electron at the top of a band has a negative effective mass and also an unfilled state at the top of a band has a negative effective mass. (Note: I didn't call them holes, holes are different)
Empty States Move In the Same Direction as Filled States
Okay, but now as you stated, you might think these should cancel out current with the conduction band electrons. But the final part that I think a lot of people easily miss (at least I did when I was first introduced to this) is how to think about the "unfilled" states. A lot of people like to describe holes using the bubble model, where you have a tube of liquid, the liquid moves one way and the bubble moves the other. This is NOT what happens in semiconductors. In a semiconductor filled and unfilled states move in the SAME direction. Its like a conveyor belt with boxes that are either filled or empty. No matter what is on the belt it moves in the same direction.
Holes
So we have negative effective mass unfilled states that move in the same direction as negative effective mass electrons. Put all of this together and you find that its exactly the same mathematically as positively charged and positive effective mass charge carriers called holes.
A: I would not definitely say holes are electrons with negative mass. Holes are called for the points in atom where there is a lack of electron. One can say that they are due to the absence of electrons. So as electrons have negative charge and move opposite direction as compared to the applied electric field, it's quite straightforward to understand the motion of the holes in a material.
