If by 'effective k points' you are meaning the special points, then they are determined by the shape / symmetry of the underlying lattice, or the cell defining the fundamental period of the function under consideration. These special points are in the first Brillouin zone (1BZ) of the reciprocal space corresponding to the underlying Bravais lattice. Suppose you have a simple cubic lattice with the lattice constant a. The 1BZ corresponding to this lattice is a cube of sides 2π/a × 2π/a × 2π/a. Now if you choose a cubic supercell consisting of 8 original cubic cells (primitive cells), then the associated 1BZ is a cube of sides π/a × π/a × π/a. The special points in this 1BZ are obtained from those of the original special points by dividing the length of each original special point by 2. 

Incidentally, since the size of the 1BZ scales inversely with the size of the corresponding unit cell in the direct space (see above), if the sizes of the matrices to be dealt with numerically pose no technical problems (that is if one can allocate sufficiently large fast physical memory on one's computer), one can artificially perform calculations over large supercells, thereby dealing with an accordingly smaller 1BZs. In the ideal case of working with an infinitely large supercell, the underlying 1BZ reduces to a single point, namely k = 0, so that integration (or summation) over the 1BZ is no longer an issue (recall that if f(x) has period L, nL, with n an integer,  is also its period).

Dear Dr. Farid,

Thanks a lot for your answer.

I actually want to know about the k conservation rule in the auger recombination or impact ionization process. For example, for the impact ionization, we need to have k1+k2+G0 = k3+k4 where k1,k2 are initial wavevector and k3,k4 is final wavevector. Now for bulk Si, I have fcc primitive cell and from that I need to check the conservation as far I understand. Then if we want to include any defect for simulation, we have to create super cell. My question is, which k point should I use for conservation check in calculation with defects? For defects do we need to unfold the k to primitive brillouin zone.

If I understand correctly you mentioned about the underlying crystal. So in that case I think I have to use the supercell k vector for conservation check in defected semiconductor auger rate calculation. And it is due to the fact that I don't have any more translational symmetry and supercell is basically the primitive cell for semiconductor with defect. Is that right?

Thanks a lot.

Best,

Raihan