I`m studying solid state physics and I have a question about this. I know that the Fermi energy is the energy which can be defined at $0K$.
In $k$ space electrons occupy each k state from zero at 0K so, if we draw picture in $k$ space it should be left side of attached picture.
In this, Fermi level is located at $K_F$ and Fermi energy is summation of all of $k$ state.
When we apply electric field, electron can get additional energy $-eV$, so sphere is larger than before and has a hole which radius is $-eV.$ In this, right side of the attached picture, Fermi energy and Fermi energy are shifted. Is it right?