Thermal excitation

Boltzmann Equation The fraction of free atoms which are excited thermally, or in other words, the relationship between the ground-state and the excited-state quantum is exclusively represented by the Boltzmann equation given below ... 

The [3 -f 2] cycloaddition of aziridines and dipolarophiles, like dimethyl acetylenedicarboxylate or dimethyl fumarate and maleate, was investigated by Gaebert and Mattay. Via C—C and C—bond cleavage five-membered heterocycles are formed in moderate yields. The different product ratios dependent on the reaction conditions (PET/direct excitation/thermal reaction) gave insights to the reaction details and are summarized in the proposed mechanism (Scheme 52) [84],... 

The energy distribution in the conduction zone extends over several electron volts and is about 5 eV for some metals at absolute zero. Thus, only a small fraction of the electrons in the energy band can be excited above the Fermi level, and only those within an energy range of the order k T can be excited thermally. 

Conversely, doping Ge with As introduces an extra electron that cannot be accommodated in the tetracovalent network (valence band), and this creates a narrow band of occupied donor levels, just below the conduction band in energy. The Fermi level is now located between the donor band and the conduction band, and electrons in the donor band can be readily excited thermally into the conduction band (Fig. 5.5). Thus, a negative or n-type semiconductor is created. Semiconductors can exhibit electrical conductivities in the range 10-3 to 104 S m 1, as compared to 103 to 107 S m 1 for metals. 

The de-excitation path available to conjugated organic molecules is controlled by quantum-mechanical rules which are complex. Some molecules will relax spontaneously, other will not (within a reasonable time) without assistance from another material/mechanism. The presence of Oxygen is a special case. Resonant conjugated molecules with two Oxygen atoms will not fluoresce and there only means of de-excitation is by means of a direct transition that is not allowed because of the presence of the triplet state. The nonresonant conjugates normally de-excite thermally via a two-step process. 

The holes trapped in shallow traps are probably excited thermally into the valence band, so that an equilibrium with free holes is indicated in reaction (7.10). Shallowly trapped holes, h+ms, will therefore have a comparable reactivity to detrapped holes, h+. 

While both types of trapped holes will recombine with the trapped electrons within the first 200 ns after their generation following reaction (7.1), only holes excited thermally from the shallow traps have the chance to migrate to the energetically more favored h+ff(i site (cf. reaction... 

For triatomic molecules, the contribution of hot bands cannot be expressed as a function of energy alone (see (5)) and therefore cannot be expressed in a compact analytic formula like Formula (C.3). However, for rigid triatomic molecules like CO2, NO2, SO2, O3 and N2O, the contribution of hot bands is weak at room temperature (and below) because hco kT for all normal mode frequencies. Note that the width of the contribution to the Abs. XS associated with each excited vibrational level (hot bands) is proportional to the slope of the upper FES along the normal mode of the ground electronic corresponding to each excited (thermally populated) vibrational level. This fact explains why numerical models (e.g. using ground state normal coordinates) are able to calculate the Abs. XS. These calculations are of Frank-Condon type. 

The linear response modulus thus quantifies the small stress fluctuations, which are excited thermally, and relax because of Brownian motion. 

When electrons are excited, thermally or optically to the bottom of the conduction band they behave essentially as free mobile charge carriers. Indeed, we may expand the conduction band energy E lk about the bottom, at k = kc, of the... 

In the present alloys Qpt equals 2kF. Under this condition, the phonon-rotons can easily interact with electrons for T > T0 causing inelastic umklapp scattering of the electrons. Below T0, only elastic umklapp scattering and inelastic scattering with normal phonons occur. Above T0, phonon-rotons can be excited thermally as well as by electron scattering. Electronic transport properties versus temperature may therefore be strongly affected (5.5.4). 

Under strong band-gap excitation, the photo-neutralized ions can de-excite thermally, but in direct-band-gap semiconductors, they can also de-excite efficiently by radiative recombination of the bound electrons with the bound holes. Such photoluminescence (PL) lines are known as donor-acceptor pair (DAP) spectra. In a semiconductor with dielectric constant e, the energy of the photon emitted by a pair whose constituents, with ionization energies Ed and Ea, are both in the ground state and at a distance R is ... 

Like molecules, crystals can also vibrate as a whole. Their vibrations can be excited thermally, and they can display a residual vibrational motion at zero... 

Photothermal models [76-80] Electronic excitations thermalize on a ps timescale, resulting in thermally broken bonds. 

Rosenwasser ei alu have found that NaN, when irradia ed by y-rays at room temperature, develops a band ai 360 m/. This band may also be excited thermally although to a lesser extent. On the other hand, neutron irradiation gives bands at 660 mp and 760 v. However, near the decomposition point, the spectra of NaN3 subjected to any of the irradiation processes are the same. Apparently, many of the bands observed in NaN3 spectra may be connected with the decomposition of the compound. Cohen and Smith36 could excite a band at 275 mu by x-irradiation of Ge-doped synthetic quartz. This band was absent in pure quartz. The colour centre absorption is supposed to be caused by an electric dipole transition. Exhaustive investigations have been carried out on the colour centres in silver halides in connection with photography32. 

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