Thermal excitation of electrons

Dark current comes from the thermal excitation of electrons in the detector material - thermally generated electrons can not be distinguished from photoelectrons. 

More precisely, the highest occupied state at Y = 0 K, since at nonzero temperatures thermal excitations of electrons lead to some population of states above the Fermi energy. 

Figure 5.5 Band model of the mechanisms of p-type (left) and n-type semiconduction. Arrows represent thermal excitation of electrons.

The effect of an external electric field is to produce an acceleration of the electrons in the direction of the field, and this causes a shift of the Fermi surface. It is a necessary condition for the movement of electrons in the fc-space that there are allowed empty states at the Fermi surface hence electrical conductivity is dependent on partially filled bands. An insulating crystal is one in which the electron bands are either completely full or completely empty. If the energy gap between a completely filled band and an empty band is small, it is possible that thermal excitation of electrons from the filled to the empty band will result in a conducting crystal. Such substances are usually referred to as intrinsic semiconductors. A much larger class of semiconductors arises from impurities... 

Equations (1.206) and (1.207) describe the ionization of neutral vacancies (Vx, Vm). We assume here that the ionization of V and Vm to Vx and Vm does not take place. In a crystal in thermal equilibrium, electrons and holes will be formed by thermal excitation of electrons from the valence band to the conduction band, and the reverse process is also possible. This process can be expressed by eqn (1.210) as a chemical reaction, (see eqn (1.136)). Such reactions are called creation-annihilation reactions. Equations (1.208) and (1.209) describe the creation-annihilation reactions of neutral vacancies and charged vacancies in a crystal. Equation (1.211) shows the formation reaction of MX from constituent gases. It is to be noted that of these eight equations two are not independent. For example, the equilibrium constants Ks and K x in eqns (1.209) and (1.211) are expressed in terms of the other Ks as... 

Fig. 4.19, The tunnelling luminescence kinetics for the Ej-, Tb3+ pairs in Na20 3Si02-Tb3+ glass. The ultraviolet excitation was at 120 K with further short thermal excitation of electrons above the mobility edge (curve 1) and prolonged heating up to 70 K below the excitation...

It is the Peierl s instability that is believed to be responsible for the fact that most CPs in their neutral state are insulators or, at best, weak semiconductors. Hence, there is enough of an energy separation between the conduction and valence bands that thermal energy alone is insufficient to excite electrons across the band gap. To explain the conductive properties of these polymers, several concepts from band theory and solid state physics have been adopted. For electrical conductivity to occur, an electron must have a vacant place (a hole) to move to and occupy. When bands are completely filled or empty, conduction can not occur. Metals are highly conductive because they possess unfilled bands. Semiconductors possess an energy gap small enough that thermal excitation of electrons from the valence to the conduction bands is sufficient for conductivity however, the band gap in insulators is too large for thermal excitation of an electron accross the band gap. 

Cp.iatvib is the contribution from lattice vibrations, CPtintravaj the contribution from intramolecular vibrations, and CPimag is the magnetic or electronic heat capacity arising from thermal excitation of electrons. 

FIGURE 1.18 Formation of holes in the valence band by thermal excitation of electrons to the conduction band. 

There are other cases of electron motion which must also be considered, as for example, when the oxide is an impurity semiconductor. In that case, any electrons which enter the oxide may be able to migrate through it with relative ease. The question hinges on how easily the electrons can enter and exit from the oxide at the oxide interfaces. One possibility is the thermal excitation of electrons into the oxide from the metal interface, but that in itself may prove to be rate limiting. 

Insulators (e.g. AI2O3) are characterized by large band gaps thermal excitation of electrons is not adequate to permit electrons to assume a state in the conduction band, hence the electrical conductivity of such a material is very low. Conversely, conductive substances, such as metals, have ground state electrons occupying states in the conduction band. Hence, thermal excitation is not required for such a material to be conductive. 

An insulator is characterized by a large band gap between the highest filled band and an even higher empty band. The band gap is sufficiently great to prevent any significant population of the upper band by thermal excitation of electrons from the lower one. The presence of a very intense electric field may be able to supply the required energy, in which case the insulator undergoes dielectric breakdown. Most molecular crystals are insulators, as are covalent crystals such as diamond. 

Structural change resulting from a Peierls distortion can have dramatic effects on the physical properties. Look at the half-filled bands of Figure 6.6. There is no HOMO-LUMO gap. Such a situation depicts a metallic electrical conductor. On the other hand, after Peierls distortion there is a band gap at the Fermi level (Figure 6.10) and the material, depending on the width of the gap, is a semiconductor or an insulator. For a semiconductor, thermal excitation of electrons from the... 

The exponent n, which is known as the hopping index, is actually equal to / d + 1) where d is the dimensionality. Hence, for two-dimensional systems n = /3. Strictly speaking, Eq. 7.12 holds only when the material is near the M-NM transition and at sufficiently low temperatures. At high temperatures, conduction proceeds by thermal excitation of electrons or donors into the conduction band, or injection of holes or acceptors into the valence band. 

Semiconductors are characterized by low carrier densities 10 -10 ° carriers cm and low mobilities, typically 10 to 1.0Vcm -sec. Semicondnctors display an increase in conductivity with increasing temperatnre as the resnlt of thermal excitation of electrons located either at the top of the valence band (intrinsic carriers) or from impnrity sites in the forbidden gap, or from the filling of low lying acceptor levels in the case of p-type materials. In many cases, the temperatnre dependence is of the Ahrrenins form... 

Because the numerator is large (e.g. Cu Ka is 8.04keV) and the denominator small, that is, of the order of electron volts, a large number of electron-hole pairs are produced by each photon. The Si(Li) detectors must be kept at liquid nitrogen temperature at all times in order to minimize thermal excitation of electrons and to prevent lithium thermal diffusion. Either a Dewar vessel or a Peltier thermoelectric device is used in conjunction with the solid state detector. 

A major disadvantage of the Si(Li) counter is that it must be operated at the temperature of liquid nitrogen (77°K = — 196°C) in order to minimize (1) a constant current through the detector, even in the absence of x-rays, due to thermal excitation of electrons in the intrinsic region, and (2) thermal diffusion of lithium, which would destroy the even distribution attained by drifting. Even when not... 

According to band theory, the electrical properties of a solid depend on how the bands are filled. There is no conduction when the bands are filled or empty. If the material has a narrow bandgap, thermal excitations of electrons from the valence band to the conduction band occur, giving rise to conductivity in classical semiconductors. 

For larger values of Eg (e.g., for Si, where Eg = 1.1 eV), the valence band (VB) is almost filled and the conduction band (CB) almost vacant. Conduction becomes possible because of thermal excitation of electrons from the VB into the CB (Figure 18.2.2). This process produces electrons in the CB, which have electrical mobility because they can... 

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

In a defect-free, undoped, semiconductor, there are no energy states within the gap. At r= 0 K, all of the VB states are occupied by electrons and all of the CB states are empty, resulting in zero eonductivity. The thermal excitation of electrons across the gap becomes possible at r> 0 and a net eleetron eoneentration in the CB is established. The electrons excited into the CB leave empty states in the VB. These holes behave like positively eharged electrons. Both the electrons in the CB and holes in the VB participate in the eleetrieal eonductivity. 

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