Urbach energy

, with dimensions of energy, used to quantify energetic disorder in the band edges of a semiconductor.

It is often used to describe electron transport in structurally disordered semiconductors such as hydrogenated amorphous silicon.

[1] In the simplest description of a semiconductor, a single parameter is used to quantify the onset of optical absorption: the band gap,

[2] However, the density of states in 3 dimensional semiconductors increases further from the band gap (this is not generally true in lower dimensional semiconductors however).

The Urbach Energy quantifies the steepness of the onset of absorption near the band edge, and hence the broadness of the density of states.

A sharper onset of absorption represents a lower Urbach Energy.

While an exponential dependence of absorbance had been observed previously in photographic materials,[3] it was Franz Urbach that evaluated this property systematically in crystals.

He used silver bromide for his study while working at the Kodak Company in 1953.

[5][6] Absorption as a function of energy can be described by the following equation:[1][7]

are fitting parameters with dimensions of inverse length and energy, respectively, and

[1] The Urbach Energy has been shown to increase with dangling bond density in hydrogenated amorphous silicon[9] and has been shown to be strongly correlated with the slope of band tails evaluated using transistor measurements.

, in semiconductors governed by multiple trapping and release.

To evaluate the Urbach Energy, the absorption coefficient needs to be measured over several orders of magnitude.

For this reason, high precision techniques such as the constant photocurrent method (CPM)[11] or photothermal deflection spectroscopy are used.