Exciton thermal conductivity

A wide range of condensed matter properties including viscosity, ionic conductivity and mass transport belong to the class of thermally activated processes and are treated in terms of diffusion. Its theory seems to be quite well developed now [1-5] and was applied successfully to the study of radiation defects [6-8], dilute alloys and processes in highly defective solids [9-11]. Mobile particles or defects in solids inavoidably interact and thus participate in a series of diffusion-controlled reactions [12-18]. Three basic bimolecular reactions in solids and liquids are dissimilar particle (defect) recombination (annihilation), A + B —> 0 energy transfer from donors A to unsaturable sinks B, A + B —> B and exciton annihilation, A + A —> 0. 

The interpretation of the interband transition is based on a single particle model, although in the final state two particles, an electron and a hole, exist. In some semiconductors, however, a quasi one-particle state, an exciton, is formed upon excitation [23,24]. Such an exciton represents a bound state, formed by an electron and a hole, as a result of their Coulomb attraction, i.e. it is a neutral quasi-particle, which can move through the crystal. Its energy state is close to the conduction band (transition 3 in Fig. 2), and it can be split into an independent electron and a hole by thermal excitation. Therefore, usually... 

In course of subsequent work Bubeck, Tieke, and Wegner discovered that the action spectrum for photopolymerization of undoped diacetylene multilayers extends into the visible provided some polymer formed in course of previous UV-irradiation is present. Since obviously excitation of the polymer can sensitize the reaction this effect has been termed self-sensitization. Checking the absorption spectrum of the polymer produced via self-sensitization assured that the final product is identical with the product obtained under UV excitation of the monomer. Later work by Braunschweig and Bassler demonstrated, that the effect is not confined to multilayer systems but is also present in partially polymerized single crystalline TS-6, albeit with lower efficiency. Interestingly, the action spectrum of self-sensitization follows the action spectrum for excitation of an electron from the valence band of the polymer backbone to the conduction band rather than the excitonic absorption spectrum of the polymer which is the dominant spectral feature in the visible (see Fig. 21). The quantum yield is independent of the electric field, whereas in a onedimensional system the yield of free carriers, determined by thermal dissociation of optically produced, weakly bound geminate electron-hole pairs, is an linear function of an applied electric field 29.30,32,129) Apparently, the sensitizing action does not... 

Reviews of the application of electrical measurements in solid state decompositions have been given by Kabanov [52]. Electrical conductivity measurements, both a.c. and d.c. studies, have been used to characterize the species that participate in the thermal decomposition of ammonium perchlorate [53,54] (this reaction is discussed in Chapter 15). Other studies have been concerned with the mechanisms of oxide decompositions [55,56]. Torkar et al. [56] conclude from electrical conductivity evidence that the decompositions of alkali oxides are more complicated than exciton formation processes. 

Many kinetic studies of the thermal decomposition of silver oxalate have been reported. Some ar-time data have been satisfactorily described by the cube law during the acceleratory period ascribed to the three-dimensional growth of nuclei. Other results were fitted by the exponential law which was taken as evidence of a chain-branching reaction. Results of both types are mentioned in a report [64] which attempted to resolve some of the differences through consideration of the ionic and photoconductivities of silver oxalate. Conductivity measurements ruled out the growth of discrete silver nuclei by a cationic transport mechanism and this was accepted as evidence that the interface reaction is the more probable. A mobile exciton in the crystal is trapped at an anion vacancy (see barium azide. Chapter 11) and if this is further excited by light absorption before decay, then decomposition yields two molecules of carbon dioxide ... 

Comparison of the thermal energy required to excite an exciton with the activation energy for electronic conductivity allows determination of U and t], the on-site electron-electron repulsion and the intra-dimer one-electron transfer integral. We find U % 1,3 and 1,1 eV tj 0,4 and 0,35 eV for the Rb+ and TMB+ salt, respectively. ... 

PbN(,. Dedman and Lewis [144] studied the photoconductivity of PbN crystals as a function of Ught intensity, temperature, and time. A prominent feature of their spectra is a peak at 407.0 nm in the region of strong absorption. Based on temperature coefficient measurements, the peak was interpreted to arise from transitions to an exciton level 0.86 eV below the bottom of the conduction band. Application of the Mott relation between thermal and optical band gaps (via the ratio of dielectric constants) led to a band-gap value of 3.9 eV. Cook and coworkers [145] also observed a peak in photocurrent at 406.0 nm, and, based on its enhancement with thermal decomposition, attributed it to the presence of interstitial nitrogen. 

Figure 1. Energy-level diagram used in the interpretation of the mechanism of slow thermal decomposition. An electron from an azide ion in the metal azide is promoted directly from the valance to the conduction band, transferred via the intermediate exciton levels introduced by impurities or defects, or promoted to the conduction band of the metal formed by decomposition, i// is the electron affinity of the solid azide compound and 0 the work function of the metal.

For Na, K, and Ba azides no such simple correlation can be made. The activation energy of the alkali-metal azides is not high enough for promotion of an electron even to the first exciton level. On the other hand, the mechanism proposed by Mott specifically to explain the thermal decomposition of barium azide is energetically more favorable. In this mechanism, an electron is first promoted to the conduction band of the metal to form metal, which catalyzes the reaction. Young [16], in fact, observed that the decomposition of potassium azide is promoted in the presence of potassium vapor, which prevents the evaporation of potassium nuclei as they are formed by decomposition. 

Electrons and holes can be produced by thermal motion or the absorption of light. Excitons are electron/hole pairs. Excitons are produced when an electron takes up energy, but not a sufficient amount to escape the hole produced. Consequently, the electronic charge of an exciton is zero. The exciton can transport energy but cannot conduct an electric current. Empty lattice sites are called site defects or vacancies. Atoms residing in sites between lattice ponts are called interstitial defects. 

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