The quantitative application of Fermi-Dirac functions to two- and three-dimensional systems

Abstract

Expressions for the various physical parameters of the ideal Fermi-Dirac gas in two dimensions are derived and compared to the corresponding threedimensional expressions. These derivations show that the Fermi-Dirac functions most applicable to the two-dimensional problem are Fo(*7), FI(.7), and F~o(*7). Analogous to the work of McDougall and Stoner in three dimensions, these functions and parameters derived from them are tabulated over the range of the argument, -4 <_ '7 <-20. The physical applications of the tabulated 2D and 3D functions to 3He monolayer and bulk liquid 3He nuclear magnetic susceptibilities, respectively, are considered. Calculational procedures of fitting data to theoretical parameters and criteria for judging the quality of fit of data to both two-and three-dimensional Fermi-Dirac values are discussed.

The work function of the crystal faces of metals

“…These electrons reside on the surface forming a twodimensional electron gas and are prevented from leaving the surface by image forces in the surface atoms and are assumed non-interacting due to the presence of the surface counter-ions. The zero order, zero temperature formula for the Fermi energy EF of a simple noninteracting 2-D electron gas is given by [4,5], 2 19 2.398 10 4…”