Exchange energy for electrons in two dimensions: Effects of finite temperature and finite thickness

The effects of finite temperature and finite thickness on the exchange energy for a two-dimensional system of electrons such as those confined in quantum wells are evaluated and expressed as a parametrized correction factor [1+(π²/16)τ²ln{τ}-0.874τ²+1.786τ³]-0.109{κ}+0.0076κ² for 00.4 and 05.5. Here {τ}=kBT/(²{K}F²$/2${m}*) is the ratio of thermal energy to the Fermi energy and κ={K}F$L, ${K}F$ and L being the two-dimensional Fermi wave number and the thickness, respectively. The absolute value of the (negative) exchange energy is decreased by these effects.