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.
Dear Dmitry Lev
The Ef means the highest energy occupied by electrons in a electron system. It is determined by the electron density. When an electric field is applied in x-direction, the Fermi ball will shift with the distance P0 in momentum space along x-axis (or Px-axis), just as shown in your figure. But this does not mean the change of the Fermi surface. If it is a free electron system, this Fermi ball will move along x-axis and never stop. In this case the Ef will certainly change. But in the system you considered, the ball stopped at P0. So this is not a free electron system, this system must be bounded by some potential field. In this potential field, the dashed circle in your figure is only the kinetic energy, but total energy. In other words, the dashed circle is not a really Fermi ball. The total energy includes the kinetic energy and potential energy. And the total energy level is filled by the electrons from lowest to Ef. The lowest energy does not change in the applied electric field, so doesn’t the Ef.
Dear Yun,
Thank you for your answer. This is the case described for the metals. In free electron systems.. you mean when the electrons totally free to move without any potential fields like gases or plasma?
This is the case when the valence electrons have translation energy and they move between the ion lattice. Can you consider it as free electrons?
In this case the Fermi energy is like the maximum translation energy of electron or maximum kinetic energy.
Tell me when it will change either the ball will increase or decrease?
take a look at the attached file.
Dear Lev
1. Electrons in metals are roaming electrons, they can not be seen as free electrons. So the Ef is not a ball. Ef forms a complicated shape, let’s name it as S1. When applying an electric field, the Fermi surface will change from S1 to S2. S2 is a closed surface, in which the state density will also change. In consequently, the ability of containing electrons will change inside S2. So the Ef will change.
2. From the energy band picture, let’s assume the electric field is an infinitesimal disturbance. The applied electric field will lead the electron transition. Some electrons occupying the –Px stats will transit to +Px states with higher energy, so the Fermi energy will increase. If the electric field is not the infinitesimal disturbance, the energy bands will change, so the Ef will also change.
Dear Lev
1, the electrons moving in crystal or metal is not free electrons, they are itinerant electrons, because they are influenced by lattice potential.
2, in this case, the fermi energy is the highest occupied energy, which is not the maximum energy in zone. Just as water in a bottle, the water face corresponds to the Fermi energy,
3, in crystal or metal, the Fermi surface is a complicated closed surface, instead of a ball. If the external field is strong enough, the Fermi surface will change. there is a metaphor, if the earth was not a ball but a cube and covered by water, the sea surface would not be a ball. And the sea surface would change caused by the influence of moon, just as tide.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics
- Quantum Mechanics