In semiconductor physics, what is the difference between steady state and equilibrium. How analysis of devices varies in these processes?

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    $\begingroup$ "Steady state" in general means the system may be dynamic but the derivatives are zero. For example, a fire burning inside a box reaches steady state when the energy dissipated to the exterior matches the rate of energy generated by the fire. This is not at equilibrium because energy is being dissipated. $\endgroup$ Commented Mar 17, 2014 at 20:08

1 Answer 1


"Equilibrium" means thermal equilibrium. The solid has one well defined temperature, and a constant Fermi energy. The Fermi energy is an energy value against which energy levels are compared to determine how fully occupied (or not) an energy level is. Generally when the Fermi level is constant throughout a solid electrons diffuse equally in all directions.

"Steady state" means that the properties of the system do not change with time. Non-equilibrium states can be steady states if there is a source of energy to maintain the non-equilibrium condition. Without the source of energy, the system would quickly settle into an equilibrium state.

A p-n junction (electrical diode) with no voltage applied is in an equilibrium state. The same diode with a voltage applied across it is in a non-equilibrium, but steady, state. The applied voltage raises the Fermi energy on one side of the junction relative to the other, and that difference in Fermi energy is maintained by the voltage (energy) source. Electrons diffuse preferentially in one direction. The properties of the system do not change with time, but the state is non-equilibrium.

The analysis of these states is more or less the same in both cases. Solid state physics, statistical mechanics, and transport theory all apply to both cases. The conditions under which the analysis is performed changes, though. For example, in a biased p-n junction one has to set the condition that the Fermi energy changes at the junction.

  • $\begingroup$ If the system has a well defined temperature can it be in both in steady state and equilibrium? Assuming the heat flux is zero every where in the system does this implies that is in thermal equilibrium or steady state (or both)? $\endgroup$ Commented May 7, 2020 at 13:08
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    $\begingroup$ @AntoniosSarikas Yes. And the distinctions are not perfectly cut and dry. If you have boundary conditions that take energy for example. And something else putting energy in. Or if you have a control volume in a pipe with constant flow. Some people believe “has achieved steady state” or even “has settled down to steady state”, is a sensible statement (like me). Other do not. Usually they are thinking of an isolated system and a case where boundaries can or cant be open and think it generalizes. $\endgroup$
    – Al Brown
    Commented Aug 29, 2021 at 5:09

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