Density of state distributions

FIG. 1. Schematic density of states distribution. Bands of (mobile) extended states exist due to short-range order. Long-range disorder causes tails of localized states, whereas dangling bonds show up around midgap. The dashed curves represent the equivalent states in a crystal. 

Fig. 11 Temperature dependence of the hole mobility in PMPSi at different electric fields. Full curves are calculated using the theory by Fishchuk et al. [70], The fit parameters are the width a of the density of states distribution, the activation energy (which is p/2), the electronic exchange integral J, and the intersite separation a. From [70] with permission. Copyright (2003) by the American Institute of Physics...

Fig. 19 The effect of doping on the density of states distribution in a disordered organic semiconductor at variable concentration of charged dopants. The energy scale is normalized to the width of the DOS, expressed through a, of the undoped sample. The parameters are the intrinsic site concentration V and the dopant concentration N. From [125] with permission. Copyright (2005) by the American Institute of Physics...

Arkhipov VI, Heremans P, Emelianova EV, Adriaenssens GJ, Bassler H (2002) Weak-field carrier hopping in disordered organic semiconductors the effects of deep traps and partly filled density-of-states distribution. J Phys Condens Matter 14 9899... 

Traditionally, charge-carrier transport in pure and doped a-Se is considered within the framework of the multiple-trapping model [17], and the density-of-state distribution in this material was determined from the temperature dependence of the drift mobility and from xerographic residual measurements [18] and posttransient photocurrent analysis. 

The semiconductor nanocrystallites work as electron acceptors from the photoexcited dye molecules, and the electron transfer as sensitization is influenced by electrostatic and chemical interactions between semiconductor surface and adsorbed dye molecules, e.g., correlation between oxidation potential of excited state of the adsorbed dye and potential of the conduction band level of the semiconductor, energetic and geometric overlapping integral between LUMO of dye molecule and the density of state distribution of the conduction band of semiconductor, and geometrical and molecular orbital change of the dye on the... 

Starting from a medium of effective cells, the calculation of the physical quantities is immediate. For the density-of-states distribution, we take the trace on all the wave vectors K of the superlattice and on all the sites of the cell (Jf is the number of cells of the superlattice) ... 

This MCPA calculation has been carried out for the triplet naphthalene mixed crystal, with a square cell of nine sites (3 x 3). The density-of-states distribution for cA = 30% is shown in Fig. 4.14. One first notices that the smoothed shape disagrees generally with the numerical-simulation spectrum. The finest structure, at the maximum of the spectrum, corresponds to a configuration with a guest molecule A completely surrounded by host... 

Figure 4.14. Comparison of the MCPA density-of-states distribution with numerical results. There is improvement over the CPA calculations.

From now on, we wish, in the spirit of the site percolation in electrokinetics (Section IV.C.4.a), to neglect the bond correlations. Thus, we consider an effective medium around the energy vA where the excitation will propagate it is clear that this medium correctly describes the propagation, but that it will not correctly describe, for example, the density-of-states distribution, since it contains also fictitious B sites at the energy vA. Therefore, by means of this restriction, the HCPA method is then directly transferable to the naphthalene triplet lattice, with probability cL = cA of having a passing bond (4.83). The curves of Fig. 4.18 are likewise transferable, but, because of the fictitious B sites, the density of states around vA is not normalized at the real concentration of the A sites (as was possible for the CPA cases cf. Fig. 4.11). 

The disorder inherent in hydrogenated amorphous silicon gives rise to tails in the density of state distribution near the band edges. Calculations by... 

In practice AFGS is related to both the surface potential and to the flat-band voltage Vf. On the other hand, Vf is related to the virtual gate, which takes into account the presence of the solution as it has been shown in some details in Eqs. (3) and (4). A derivation of Id that does not take into account one of the two hypotheses for the density-of-states distribution considered in Ki-shida el al. (1983) could be more difficult nevertheless, a dependence on gate voltage will always be present and in any case could always be determined by experimental procedure. Also in this case, the 7d control will be exercised by the virtual gate, which contains, in ultimate analysis, the information on the ion concentration in solution. 

Yuen et al. [143] recently studied the pH dependence of the open-circuit potential and voltammetric peaks of anodic Ir oxide films (AIROFs) and sputtered Ir oxide films (SIROFs). These workers observed a 85 mV per pH unit variation of the main redox peaks for the AIROF films, and a 59 mV per pH unit variation in the case of the SIROFS. An electronic density-of-states distribution constructed for the AIROF films was found to be different in acid and base, which may indicate a pH-driven structural transformation for these films, which is reflected in a super-Nemstian pH response. On the other hand, a less structured electron density-of-states distribution, which is essentially pH-independent, appears to be applicable in the case of the SIROF layers. 

Fig. 1.6. Schematic density of states distribution for an amorphous semiconductor showing the bands, the band tails, and the defect states in the band gap. The dashed curves are the equivalent density of states in a crystal.

The energy bands are no longer described by the -k dispersion relations, but instead by a density-of-states distribution N E), illustrated in Fig. 1.6. Also the electron and hole effective masses must be redefined as they are usually expressed as the ciu-vature of (k). 

Fig. 1.9. The density of states distribution near the band edge of an amorphous semiconductor, showing the localized and extended states separated by the mobility edge.

Fig. 3.2. Schematic molecular orbital model of the electronic structure of amorphous silicon and the corresponding density of states distribution.

The model in Fig. 3.2 is sufficient to predict the general features of N E), but much more detailed calculations are needed to obtain an accurate density of states distribution. Present theories are not yet as accurate as the corresponding results for the crystalline band structure. The lack of structural periodicity complicates the calculations, which are instead based on specific structural models containing a cluster of atoms. A small cluster gives a tractable numerical computation, but a large fraction of the atoms are at the edge of the cluster and so are not properly representative of the real structure. Large clusters reduce the problem of surface atoms, but rapidly become intractable to calculate. There are various ways to terminate a cluster which ease the problem. For example, a periodic array of clusters can be constructed or a cluster can be terminated with a Bethe lattice. Both approaches are chosen for their ease of calculation, but correspond to structures which deviate from the actual a-Si H network. 

The Si-H bonds add further features to the density of states distribution. The Si-H bonding electrons are more localized than the Si-Si states and lead to sharper features in the density of states. One set of calculations, shown in Fig. 3.4, finds a large hydrogen-induced peak... 

The density of states distribution in Fig. 3.16 represents the best current estimates for low defect density a-Si H. The results are sufficiently accurate to use in calculations of the transport and recombination etc., but are continually being refined by new and more accurate experiments. 

Thermal emission measurements are generally based on electrical transport and in most cases involve the effects of a trapped space charge, Q. The two main ways of extracting information about the density of states distribution are from the release time of the charge from the traps... 

DLTS experiments are performed either by measuring the temperature dependence of the capacitance at a fixed time after the application of the reverse bias or the time dependence is obtained at constant temperature (Johnson 1983). The result is an equivalent measure of N E), but the exponential dependence of the release time on energy in Eq. (4.17) means that a wide range of times are needed to measure the full energy range. Figs. 4.17 and 4.18 show examples of the density of states distribution for n-type a-Si H obtained using both techniques. A broad defect band 0.8-0.9 eV below (, is observed. 

Fig. 4,17. Some examples of the density of states distribution of n-type a-Si H obtained from DLTS. Samples with the largest phosphorus concentration have the greatest density of states at the middle of the gap. The Fermi energies of the different samples are indicated (Lang el al. 1982a).

Fig. 4.20. The density of states distribution obtained from space charge limited current measurements on undoped a-Si H. The various symbols represent different samples and deposition conditions. Field efiect (FE) and DLTS data are shown for comparison. is the substrate temperature during growth (Mackenzie, LeComber and Spear 1982).

Fig. 4.20 (Mackenzie et al. 1982). The deduced density of states distribution is fairly constant in material deposited at 300 increasing...

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