Validity analysis of Sommerfeld expansion in solving Fermi level of two-dimensional electron gas
Sommerfeld expansion is an important method in solid-state physics for discussing the properties of free electron gases.Two-dimensional electron gases,a special case of metallic free electron gases,have recently attracted widespread attention from researchers.Fermi level of two-dimensional electron gases was calculated using both rigorous numerical solutions and Sommerfeld expansion approximations,and a comparison between the two methods was made.The analysis found that if the temperature of the gas is low,the error caused by the Sommerfeld expansion approximation is small,thus elucidating the effectiveness and usage conditions of the Sommerfeld expansion method.This work will be helpful for students to deepen their understanding of relevant knowledge in solid-state physics.
Sommerfeld expansiontwo-dimensional electron gasFermi level
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