Considering only the T = 0 K case in the Fermi distribution with the relations E = E z + E n , E z = ℏ 2 k 2 z /2m * ( x, ỹ), and dk z = m * ( x, ỹ)/2ℏ 2 E z dE z (the second expression assumes that the effective mass can be closely approximated as a scalar and factored through the spatial derivatives appearing in Schrödinger's equation) gives