Negative differential conductivity (NDC) is a nonlinear electrical phenomenon.
If J is not a monotonic function

Monotonic function

In mathematics, a monotonic function is a function that preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory....

 of E at some values of E, the conductivity will be negative:
and negative differential conductivity is experienced; that is, in some electric field, as the current density increases, the electric field strength is decreased. In practice, one observes that the voltage drop across the "device under test" decreases when the current is increased.

Negative differential conductivity has been observed experimentally in some semiconductors (tunnel diode

Tunnel diode

A tunnel diode or Esaki diode is a type of semiconductor diode which is capable of very fast operation, well into the microwave frequency region, by using quantum mechanical effects....

s, thyristor

Thyristor

A thyristor is a solid-state semiconductor device with four layers of alternating N and P-type material. They act as bistable switches, conducting when their gate receives a current trigger, and continue to conduct while they are forward biased .Some sources define silicon controlled rectifiers and...

s, and like structures). As well, non-equibrium plasma

Plasma (physics)

In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

 shows this behaviour. Even a simple gas-filled tube from a fluorescent lamp

Fluorescent lamp

A fluorescent lamp or fluorescent tube is a gas-discharge lamp that uses electricity to excite mercury vapor. The excited mercury atoms produce short-wave ultraviolet light that then causes a phosphor to fluoresce, producing visible light. A fluorescent lamp converts electrical power into useful...

 does.

The physical mechanisms that result in such effect are different, but they can be understood generally under processes such as impact ionisation.

Types

Different shapes of the J versus E function exist, which according to the shape, S, N, and Z-type materials can be categorised. In the S-type or S-shaped negative differential conductivity (SNDC) in a range of electric field, the current density is a multi-valued function of the electric field but the electric field is a single-valued function

Single-valued function

A single-valued function is an emphatic term for a mathematical function in the usual sense. That is, each element of the function's domain maps to a single, well-defined element of its range. This contrasts with a general binary relation, which can be viewed as being a multi-valued function...

 of current density and can be calculated withouth ambiguity from the value of the current density. A current filaments— an inhomogeneity in the current density distribution lateral to the direction of the current flow (orthogonal to the current density vector)—is common in devices showing current-type negative differential conductivity, especially of S-types. A Thyristor

Thyristor

A thyristor is a solid-state semiconductor device with four layers of alternating N and P-type material. They act as bistable switches, conducting when their gate receives a current trigger, and continue to conduct while they are forward biased .Some sources define silicon controlled rectifiers and...

is a good example of an SNDC device.