Fermi energy Ef changes with applied electric field?

• A
Hi people,

I dont understand why when we apply the electric field to the metal Ef remains the same. Ef as translation energy of electrons remains the same but we accelerate the electrons with applied electric field so the translation energy increases too? In other hand according the formula for Ef(m*,N/L^3), where m* is the effective mass depends only on material, N/L^3-number of electrons in unit volume-depends on material too. So it turns out that the Ef actually depends only on properties of the metal.

Please take a look at the attached picture.

Thank you.

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Is this an electrostatic situation?

I dont understand why when we apply the electric field to the metal Ef remains the same. Ef as translation energy of electrons remains the same but we accelerate the electrons with applied electric field so the translation energy increases too? In other hand according the formula for Ef(m*,N/L^3), where m* is the effective mass depends only on material, N/L^3-number of electrons in unit volume-depends on material too. So it turns out that the Ef actually depends only on properties of the metal.
I think there is a relationship of applied E-field and charge density - rate of change of E can be related to charge density-
for a good discussion pl. see
<http://www-inst.eecs.berkeley.edu/~ee143/sp06/lectures/Semiconductor_tutorial_2.pdf> [Broken]

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I think there is a relationship of applied E-field and charge density - rate of change of E can be related to charge density-
for a good discussion pl. see
<http://www-inst.eecs.berkeley.edu/~ee143/sp06/lectures/Semiconductor_tutorial_2.pdf> [Broken]