Fermi dirac distribution at T->0

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SUMMARY

The Fermi-Dirac distribution describes the statistical distribution of particles over energy states in a system of non-interacting fermions. At absolute zero temperature (T=0), the Fermi energy is definitively equal to the chemical potential for free electrons in metals. This relationship holds true and is a fundamental concept in solid-state physics, clarifying that the equality does not apply at temperatures above absolute zero.

PREREQUISITES
  • Understanding of Fermi-Dirac statistics
  • Knowledge of chemical potential in thermodynamics
  • Familiarity with the concept of Fermi energy
  • Basic principles of solid-state physics
NEXT STEPS
  • Study the implications of Fermi energy in semiconductor physics
  • Explore the differences between Fermi-Dirac and Bose-Einstein distributions
  • Investigate the behavior of electrons in metals at various temperatures
  • Learn about the role of chemical potential in phase transitions
USEFUL FOR

Students and professionals in physics, particularly those focusing on solid-state physics, materials science, and thermodynamics, will benefit from this discussion.

ch3m
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Studying the free electron model I found the fermi dirac distribution and the book told me that when T->0 we have that the fermi energy is equal to the chemical potential... why?
 
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Er... are you sure you read it right? For metals (free electrons), at T=0, the Fermi energy is equal to the chemical potential, not at T>0.

Zz.
 
ZapperZ said:
Er... are you sure you read it right? For metals (free electrons), at T=0, the Fermi energy is equal to the chemical potential, not at T>0.

Zz.

with the arrow i mean the limit T=0
 

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