Finally, we want to know the total transition rate Γ Γ ( ω ω ) . Hence we need to sum over all possible initial and final states that can satisfy the energy conservation (i.e. an integral of the Brillouin zone in the k -space), and take into account spin degeneracy, which after calculation results in Γ Γ ( ω ω ) = 4 π π ℏ ℏ ( e A 0 m 0 ) 2 | ε ε ⋅ ⋅ μ μ c v | 2 ρ ρ c v ( ω ω ) where ρ ρ c v ( ω ω ) is the joint valence-conduction density of states (i.e. the density of pair of states; one occupied valence state, one empty conduction state). In 3D, this is ρ ρ c v ( ω ω ) = 2 π π ( 2 m ∗ ∗ ℏ ℏ 2 ) 3 / 2 ℏ ℏ ω ω − − E g , but the joint DOS is different for 2D, 1D, and 0D.