Forbidden energy gaps

Semiconductors are a class of materials whose conductivity, while highly pure, varies witli temperature as exp (-Ag//cg7), where is tlie size of a forbidden energy gap. The conductivity of semiconductors can be made to vary over orders of magnitude by doping, tlie intentional introduction of appropriate impurities. The range in which tlie conductivity of Si can be made to vary is compared to tliat of typical insulators and metals in figure C2.16.1. 

In an intrinsic semiconductor, tlie conductivity is limited by tlie tlieniial excitation of electrons from a filled valence band (VB) into an empty conduction band (CB), across a forbidden energy gap of widtli E. The process... 

At real values of k this equation has no solution if energy E lies in the forbidden energy gap, i.e. within the range... 

Fig. 19. The scheme of bands explaining the voltage-current curve of a tunnel diode, a. The p-region b, the n-region c, the forbidden energy gap. Arrows show the directions of electron transfer. 0, The case of the zero shift of the Fermi levels 1, 2, tunneling through the forbidden energy gap 3, the position of bands corresponding to the minimum of the voltage current curve for a diode 4, thermal currents.

Most minerals fall into the class of insulator phosphors. The characteristics of the luminescence are usually defined by the electronic structure of an activator ion as modified by the crystal field of the host crystal structure. Although some energy transfer takes place between nearby ions, appearing as the phenomena of co-activation, luminescence poisons, and activator pair interactions, the overall luminescence process is localized in a "luminescent center" which is typically 2 to 3 nm in radius. From a perspective of band theory, luminescent centers behave as localized states within the forbidden energy gap. 

Intrinsic e"/h+ pair generation depends on the width of the forbidden energy gap and therefore takes place at high photon energies. The gain is in general very low (10 6 < G < 10-4) and with similar values for electrons and holes. Moreover, the photoconductivity action spectrum does not generally resemble the absorption spectrum. 

Bond Length Alternation and Forbidden Energy Gap in Conjugated Periodic Polymers... 

The degree of bond length alternation is closely related to the magnitude of the forbidden energy gap, E, which in turn affeqts electrical, optical and other physical properties of the system. Within the one-electron picture (Huckel-model) one can show, that E = 2 I lo where 0 and are... 

Semiconductors are characterized by a forbidden energy gap, Eg, (band-gap) between the valence band (VB) maximum, Evb, and the conduction band (CB) minimum, Ecb- The magnitude of the band-gap is what diiferentiates semiconductors from insulators semiconductors have smaller band-gaps (<4 eV) than do insulators. Semiconductors are termed n-type if the majority charge carriers are electrons in the conduction band and p-type if the majority carriers are holes in the valence band. The Fermi level for most pure or intrinsic semiconductors lies near the middle of the band-gap [12]. The effect of doping is to shift the Fermi level closer to Eqb for n-type semiconductors and closer to vb for p-type semiconductors. For moderate dopant levels near room temperature this can be expressed quantitatively by Fqs. 4 and 5 ... 

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