Fermi holes dynamic, charge

For the nonuniform electron gas at a metal surface, the Slater potential has an erroneous asymptotic behavior both in the classically forbidden region as well as in the metal bulk. In the vacuum region, the Slater potential has the analytical [10] asymptotic structure [35,51] V r) = — Xs(p)/x, with the coefficient otsiP) defined by Eq. (103). In the metal bulk this potential approaches [35] a value of ( — 1) in units of (3kp/27r) instead of the correct Kohn-Sham value of ( — 2/3). Further, in contrast to finite systems, the Slater potential V (r) and the work W,(r) are not equivalent [31, 35, 51] asymptotically in the classically forbidden region. This is because, for asymptotic positions of the electron in the vacuum, the Fermi hole continues to spread within the crystal and thus remains a dynamic charge distribution [34]. 

Recall that the concept of Fermi quasilevels, suggested by Shockley (1950), can be introduced as follows. Under steady state photogeneration of charge carriers, a dynamic equilibrium arises in a semiconductor between generation and recombination of electron-hole pairs. As a result, certain steady state (but not equilibrium ) concentration values nj and p are established. The quasiequilibrium concentrations ng and pg are defined by the relations ng = n0 + A and Po = Po + Ap> and since photogeneration of carriers occurs in pairs, we have An = Ap = A. Let the following inequalities be satisfied ... 

---