Derive density of states of low dimensional crystals and understand the unique characteristics the low dimensional structures present and identify all possible electron configurations under the given constraints and deduce Fermi-Dirac probability function from them. The derivation should consist of four parts:(1) unit volume in k-space,(2) The total k-space volume occupied by the energy range from 0 to E, and(3) Calculation of the density of states by differentiating the total k-space volume with respect to E and then divide by unit k-space volume. Must also multiply by 2 for spin degeneracy.(4) Can the learner identify all possible electron configurations under the given constraints and deduce Fermi-Dirac probability function from them?