where Z F [ = z S d F 2 ] is the effective supply for state F, and is defined by this equation. Strictly, the lower limit of the integral should be − K F, where K F is the Fermi energy ; but if d F is very much less than K F (which is always the case for a metal) then no significant contribution to the integral comes from energies below K F, and it can formally be extended to –∞.