Quasi-Fermi energy

This structure is ideal, but complicated. It requires 3 different materials, an absorber and 2 membranes, which should have a large band gap but different electron affinities Xe> in order to give rise to the barriers. We see that this structure transforms the difference between the quasi-Fermi energies of the absorber into a difference between the Fermi energies cf,i<-r and f,right in the n- and p-contacts, which is the voltage V multiplied by the elementary charge e. 

Before the transfer starts, the energy distribution of electrons takes the form of a Fermi-Dirac distribution function. While the number of electrons is decreasing steadily with time, the distribution of electrons keep the form of a Fermi-Dirac distribution function. This constancy of the distribution is due to the fact that the capture rate of free electrons by the localized states is much faster than the loss of free electrons caused by the transfer when the occupation probability of localized states is not approximately one. Therefore, electrons are considered to be in their quasi-thermal equilibrium condition i.e., the energy distribution of electrons is described by quasi-Fermi energy EF. Then the total density t of electrons captured by the localized states per unit volume can be written as... 

Several other sources of external excitation result in metastable defect or dopant creation in a-Si H. Most have the characteristic property that a shift in the Fermi (or quasi-Fermi) energy causes a slow increase in the density of states and that annealing to 150-200 °C reverses the effect. The phenomena are therefore similar in origin to the optically-induced states and fall within the same general description of departures from the thermal equilibrium state induced by excess carriers. 

The photoconductivity (from now on assumed to be only from electrons) is also expressed in terms of a quasi-Fermi energy, describing the quasi-equilibrium of band tail carriers. 

The second expression uses the experimental information about the conductivity prefactor derived in Eq. (7.19). The descriptions of the photoconductivity in terms of the recombination lifetimes or the quasi-Fermi energies are equivalent. 

Recombination is evidently controlled by trapping into defect states, consistent with the other recombination measurements. The recombination transitions through defects with two gap states are illustrated in Fig. 8.24, with electrons and holes captured into either of the two states. This type of recombination is analyzed by the Shockley-Read-Hall approach which distinguishes between shallow traps, for which the carrier is usually thermally excited back to the band edge, and deep traps, at which the carriers recombine. A demarcation energy, which is usually close to the quasi-Fermi energy, separates the two types of states. The occupancy of the shallow states is determined by the quasi-equilibrium and that of the deep states by the recombination processes. No attempt is made here at a comprehensive analysis of the photoconductivity, which rapidly becomes complicated. Instead some approximate solutions are derived which illustrate the processes. 

The maximum voltage deUvered by the dye-sensitized solar cell corresponds to the difference between the potential corresponding to the quasi-Fermi energy... 

Fig. 2. Space-charge region for deep depletion. In the deep-depletion region the charge density is approximately constant as determined by the position of the quasi-Fermi energy. Parameters are defined in the text.

As time progresses (see 1 = 1 ), region A will eventually disappear as the system loses its memory of the initial conditions. Finally (t — ), region B will disappear as the new equilibrium is attained. However, for larger reverse ambient bias, a region similar to B will persist at a characteristic quasi-Fermi energy near midgap (see the previous discussion in Section 2). 

At pH 7 versus NHE. 3Fe(OH)2 Fe(OH)2Cl /i H2O where 3 > n > 2 (63), [Fe(II)4 Fe(III)2 (0H)i2]2+ [S04 2H20]2- (64), Single crystal. Quasi-Fermi energy level for electrons. This is the Fermi energy level under illumination (nonequilibrium conditions). For n-type semiconductors where electrons are the majority carriers, the quasi-Fermi energy level is approximately equal to the Fermi energy level (65),... 

Fig. 7 Transient absorption data showing the decay of the cation state of Ru(dcbpy>2(NCS)2 adsorbed on a nanocrystalline Ti02 electrode with an ethanol/D-l M tetrabutylammonium triilate electrolyte for different applied potentials 0, 100, 200, 300, and 400 mV (circles, right to left) [33]. Lines were calculated using the simulatirai procedure described in [32] assuming one catirai pCT nanoparticle. The parameters obtained fiorn fitting are a = 0.37, 0.4, 0.47, 0.58, 0.81 and quasi Fermi energy Ep as a ratio of k T of 25.1, 21.1, 17.9, 15.5, 13.1 (right to left). Reproduced with permission from [32] 2002 American Chemical Society...

The curves are for different illumination intensities. Each curve is characterized by the quasi Fermi energy E. The good agreement with experiment combined with the conclusion that long-time behavior of the recombination kinetics is determined solely by the trap energy distribution has led to widespread acceptance of the trapping model. 

For TOF experiments blocking contacts, e. g. A1 for hole transport, have to be used to avoid trap filling due to an unduly large dark current. The quasi-Fermi energy Sfp can be estimated from [69]... 

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