Conduction band parameters

Electron Level Position. One essential condition of spectral sensitization by electron transfer is that the LUMO of the dye be positioned above the bottom of the conduction band, eg, > —3.23 eV in AgBr or > —4.25 eV in ZnO (108). To provide the desired frontier level position respectively to the valence and conduction bands of the semiconductor, it is necessary to use a polymethine with suitable electron-donor abiHty (Pq. Increasing the parameter (Pq leads to the frontier level shift up, and vice versa. Chain lengthening is known to be accompanied by a decrease of LUMO energy and hence by a decrease of sensitization properties. As a result, it is necessary to use dyes with high electron-donor abiHty for sensitization in the near-ir. The desired value of (Pq can be provided by end groups with the needed topological index Oq or suitable substituents (112). 

The bending of the graphite planes necessary to form a buckytube changes the band parameters. The relevant dimensionless parameter is the ratio a/R, where a ( = 3.4 A) is the lattice constant and R is the buckytube radius. For / = 20 A, the shift is expected to alter the nature of the conductivity[13-16j. In our buckybundle samples, most of material involves buckytubes with R > 100 A confirmed by statistical analysis of TEM data, and we assume that the elec-... 

If an electronic equilibrium is set up on the surface, the parameters ij°, rr, and r/+ are strictly fixed. Their values are determined by the position of the Fermi level at the crystal surface, which will be characterized here by the quantity ea or +. These latter quantities are the distances from the Fermi level to the bottom of the conduction band or, accordingly, to the top of the valency band in the plane of the surface. Evidently,... 

The parameters jj°, -rr, and i)+ as functions of es or + are schematically presented in Fig. 5 in accordance with (5). We see that when the Fermi level is displaced from bottom to top in Fig. 5 (i.e., as it moves away from the valency band and approaches the conduction band), the quantity t increases monotonically and jj+ decreases monotonically, i.e., the relative number of particles in the negatively charged state increases, and the relative number of particles in the positively charged state decreases. As to the quantity r ° characterizing the relative content of the neutral form of chemisorption, it passes through a maximum when the Fermi level is monotonically displaced. 

Since the asymmetry parameter is dependent on the conduction band characteristics, i.e., specifically, on the density of states around Ep, it can be expected that the broadening effect is stronger for those actinides which still have some weak itinerant 5 f character, i.e., 5f electrons at Ep even in the nearly localized situation. 

All TSRs involve the release of trapped charge carriers into either the conduction band or valence band and their subsequent capture by recombination centers and recapture by other traps (retrapping). Their experimental investigation is undertaken with the goal of determining the characteristic properties (parameters) of traps cap-tnre cross sections, thermal escape rates, activation energies, concentration of traps. 

Process (b) is characterized by two steps (1) electrons or holes are captured at the corresponding recombination centers (2) the captured electrons or holes recombine with holes of the valence band or with electrons of the conduction band before their thermal reexcitation. The parameters of the recombination centers... 

A transition of this kind from metal to insulator will occur when some parameter, for instance the specific volume, the c/a ratio or the composition in an alloy, changes in such a way that two bands cease to overlap, producing a full valence band and an empty conduction band with an energy gap between them (see Fig. 4.1). A simple case is that due to the change in volume of a divalent metal. In any divalent metal, if the volume increases sufficiently, an s-like valence band will separate off from a p-like conduction band, the density of states going from the form of Fig. 1.13(b) to that of Fig. 1.13(c). The most favourable case is mercury,... 

The parameter (v) is the average thermal velocity of an electron, Nc the density of states in the conduction band, g the degeneracy of the deep level, and A x = EQ — ET the electron transition energy. Equation (9) also relates the capture constant to the emission rate because of the definition... 

Thus, we see that a plot of In n/T3/2 versus 1/T should be a straight line of slope - do//c at low temperatures. At high temperatures, n approaches a constant, since all available (uncompensated) electrons from the donor of interest have entered the conduction band. The four parameters that may be determined from a fit of Eq. (12) are N0, NAS - NDS, EO0, and (0Do/0Di)exp(aD/7c). We assume that m is known. 

Unfortunately, the redox potential of the Pt4 + /3+ couple is not known in literature. Although some stable Ptm compounds have been isolated and characterized (37), the oxidation state III is reached usually only in unstable intermediates of photoaquation reactions (38-40) and on titania surfaces as detected by time resolved diffuse reflectance spectroscopy (41). To estimate the potential of the reductive surface center one has to recall that the injection of an electron into the conduction band of titania (TH) occurs at pH = 7, as confirmed by photocurrent measurements. Therefore, the redox potential of the surface Pt4 + /3+ couple should be equal or more negative than —0.28 V, i.e., the flatband potential of 4.0% H2[PtClal/ TH at pH = 7. From these results a potential energy diagram can be constructed as summarized in Scheme 2 for 4.0% H2[PtCl6]/TH at pH = 7. It includes the experimentally obtained positions of valence and conduction band edges, estimated redox potentials of the excited state of the surface platinum complex and other relevant potentials taken from literature. An important remark which should be made here is concerned with the error of the estimated potentials. Usually they are measured in simplified systems - for instance in the absence of titania - while adsorption at the surface, presence of various redox couples and other parameters can influence their values. Therefore the presented data may be connected with a rather large error. 

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