In Chapter 5 we saw that the energy levels E _b( ) in a periodic solid can labeled in terms of , with the number of branches b equal to the number of basis functions per unit cell. Strictly speaking, this requires us to assume periodic boundary conditions in all directions so that the periodicity is preserved everywhere even at the ends. Real solids usually have ends where periodicity is lost, but this is commonly ignored as a surface effect that has no influence on bulk properties. The finite size of actual solids normally leads to no observable effects, but as we scale down the size of device structures, the discreteness of energy levels becomes comparable to the thermal energy k _B T leading to experimentally observable effects. Our objective in this chapter is to describe the concept of subbands which is very useful in describing such size quantization effects. In Section 6.1 we will describe the effect of size quantization on the E( ) relation using specific examples. We will then look at its effect on experimentally observable quantities, like the density of states (DOS), D( E) in Section 6.2 and the number of subbands or modes, M( E). In Section 6.3 we will see that the maximum conductance of a wire is proportional to the number of modes around the Fermi energy ( E = ), the maximum conductance per mode being equal to the fundamental constant G