Chemical Potential - Chemical Potential of Electrons in Solids

Chemical Potential of Electrons in Solids

Electrons in solids have a chemical potential, defined the same way as the chemical potential of a chemical species: The change in free energy when electrons are added or removed from the system. In the case of electrons, the chemical potential is usually expressed in energy per particle rather than energy per mole, and the energy per particle is conventionally given in units of electron-volt (eV).

Chemical potential plays an especially important role in semiconductor physics. For example, n-type silicon has a higher chemical potential of electrons than p-type silicon. Therefore, when p-type and n-type silicon are put into contact–called a p–n junction–electrons will spontaneously flow from the n-type to the p-type. This transfer of charge causes a "built-in" electric field, which is central to how p–n diodes and photovoltaics work.

Chemical potential of electrons in solids is closely related to the concepts of work function, fermi level, electronegativity, and ionization potential. In fact, the chemical potential of an atom is sometimes said to be the negative of the atom's electronegativity. Likewise, the process of chemical potential equalization is sometimes referred to as the process of electronegativity equalization. This connection comes from the Mulliken definition of electronegativity. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e.,

where IP and EA are the ionization potential and electron affinity of the atom, respectively.

As described above, when describing chemical potential, one has to say "relative to what". In the case of electrons in solids, chemical potential is often specified "relative to vacuum", i.e. relative to an electron sitting isolated in empty space.

In practice, the electrochemical potential of electrons is even more important than the chemical potential. The electrochemical potential of electrons in a solid is called the fermi level.