On the relation between Fermi energy of low-dimensional electron gas and temperature

In the course of exploring new type materials, it is found that many experimental phenomena of metal materials can not be interpreted by the relation of 3D electron gas's Fermi energy and temperature. However, these phenomena show low dimensional characteristics apparently. In this paper,the relation of low dimensional electron gas's Fermi energy and temperature is studied. The obtained result makes it clear that the change in the low dimensional electron gas's Fermi energy with temperature is different from that in 3D electron gas's Fermi energy on the low temperature condition. It is interesting that the regularity of the change in one dimensional electron gas's Fermi energy with temperature is just opposite to that of 3D electron gas's Fermi energy.