In this chapter, the qualitative understanding of the electronic band structure of semiconductors and of the way the bands are occupied by charge carriers (electrons and holes), developed in Chaps. 2 and 3 , is extended to the counting of electronic states and examining the occupancy of band states in equilibrium at a given temperature. Periodic boundary conditions are defined to calculate first the density of states of three-dimensional semiconductors and then the equivalent in low-dimensional structures including quantum wells, quantum wires, and quantum dots. The chapter concludes with the introduction of the Fermi-Dirac distribution to quantify the occupation probability of states with a given energy at temperature T and the introduction of carrier distributions to distinguish between intrinsic (undoped), n-type, and p-type semiconductors.