Give an expression (an integral) for the total number of electrons in the conduction band of a bulk three-dimensional semiconductor and then in the first subband of a quantum well of width L in terms of the density of states and the Fermi function (assume box eigenstates in the confined direction). If at T = 0 K we dope the first subband in the conduction band and we fill all the states in the first subband, how many electrons do we need per unit area?