Why is the Fermi level a constant in thermal equilibrium?(adsbygoogle = window.adsbygoogle || []).push({});

just like PN diode (P=material 1 ; N=material 2)

the fermi levels are the same (Ef1=Ef2) in thermal equilibrium

i confused that

why there is no energy transfer

so that can judge each energy E will obey

rate from 1 to 2 ~ N1(E)f1(E)*N2(E)[1-f2(E)] ...(*)

rate from 2 to 1 ~ N2(E)f2(E)*N1(E)[1-f1(E)] ...(**)

does the electron hop from 1(Ea) to 2(Eb)

and another electron fell from 2(Ec) to 1(Ed)?

where Eb-Ea=Ec-Ed (←the energy differences are still the same, obey energy conservation)

so it is possible for electron to hop from material1's Ea to material2's Eb

it wont just transfer in the same energy

Why the book say "each energy" will obey eqs.(*) & (**)?

I think it should be

integral E1 and E2 {N1(E1)f1(E1)*N2(E2)[1-f2(E2)]}dE1 dE2 = integral {N2(E1)f2(E1)*N1(E2)[1-f1(E2)]}dE1 dE2

(it's possible to hop anywhere, just obey "rate from 1 to 2=rate from 2 to 1")

but i calculated it

i cant derive that Ef1=Ef2?

Is anything wrong?@@

Thanks for helping!!:shy:

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why is the Fermi level a constant in thermal equilibrium?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Fermi level constant |
---|

A Conductivity and Integration over Fermi-Sphere? |

I Valence band and Fermi level difference? |

I Why can't there be a 2-level laser with Non-Optical Pumping |

I Fermi-Dirac distribution, when does it break? |

**Physics Forums | Science Articles, Homework Help, Discussion**