Fermi level differences

This equation is obtained by using eqs. 22 and 23 from Bolton et al. (1980). In the range where eq. 2.78 is valid, the quasi-Fermi level difference fi should be as small as possible in order to avoid recombination losses, i.e., p. = -i- qrj +. ... 

Fig. 9a-c. Shift of energy bands of WSe2 in presence of different redox agents. A different kinetics (surface position of quasi Fermi-level), different surface states as well as a different charging of surface states can be involved... 

Figure 1. Space-charge distribution of the excited current carriers p along z-coordinate within one period of superlattice structures (a) No. 4 and (b) No. Ai as a function of the quasi-Fermi level difference AF at 20 K.

Figure 2. Dependence of the effective energy gap Eg on the quasi-Fermi level difference AF in the superlattice No. 4 at 20 K (a) and 300 K (b). Thin curves represent the quasi-Fermi level for electrons Fe relative to the top of the valence band, dashed curves correspond to the quantum energy of the spontaneous recombination spectrum maximum hvmax.

Essential changes in the concentrations of charge carriers and accordingly in the potential profile and emission spectra are observed when the quasi-Fermi level difference AF exceeds, e.g., for the superlattice No. 4 the value of 0.9 eV. Then, the chemical potential for electrons in the n-type layers becomes positive and the degeneration begins. For superlattice No. 4i it occurs at a smaller value of AF. 

When a semiconductor comes in contact with another material of Fermi level, different from the semiconductor, a junction is formed. This can be formed between -type and p-type semiconductors, or a metal and a semiconductor, or a semiconductor and a redox electrolyte. 

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

Electrons excited into the conduction band tend to stay in the conduction band, returning only slowly to the valence band. The corresponding missing electrons in the valence band are called holes. Holes tend to remain in the valence band. The conduction band electrons can estabUsh an equihbrium at a defined chemical potential, and electrons in the valence band can have an equiUbrium at a second, different chemical potential. Chemical potential can be regarded as a sort of available voltage from that subsystem. Instead of having one single chemical potential, ie, a Fermi level, for all the electrons in the material, the possibiUty exists for two separate quasi-Fermi levels in the same crystal. 

Fig. 6. Self-consistent band structure (48 valence and 5 conduction bands) for the hexagonal II arrangement of nanotubes, calculated along different high-symmetry directions in the Brillouin zone. The Fermi level is positioned at the degeneracy point appearing between K-H, indicating metallic behavior for this tubule array[17. ...

The metallic electrode materials are characterized by their Fermi levels. The position of the Fermi level relative to the eneigetic levels of the organic layer determines the potential barrier for charge carrier injection. The workfunction of most metal electrodes relative to vacuum are tabulated [103]. However, this nominal value will usually strongly differ from the effective workfunction in the device due to interactions of the metallic- with the organic material, which can be of physical or chemical nature [104-106]. Therefore, to calculate the potential barrier height at the interface, the effective work function of the metal and the effective ionization potential and electron affinity of the organic material at the interface have to be measured [55, 107],... 

A semiconductor can be described as a material with a Fermi energy, which typically is located within the energy gap region at any temperature. If a semiconductor is brought into electrical contact with a metal, either an ohmic or a rectifying Schouky contact is formed at the interface. The nature of the contact is determined by the workfunction, (the energetic difference between the Fermi level and the vacuum level), of the semiconductor relative to the mclal (if interface effects are neglected - see below) 47J. 

Equation (5.21) is based on the electrochemical way of counting the energy difference between zero (defined throughout this book as the potential energy of an electron at its ground state at "infinite" distance from the metal) and the Fermi level Ep (Eq. 5.15). The latter quantity must not be confused with the Fermi energy go which is the energy difference between... 

Figure 5.18. Schematic representation of the density of states N(E) in the conduction band and of the definitions of work function d>, chemical potential of electrons p, electrochemical potential of electrons or Fermi level p, surface potential x> Galvani (or inner) potential

Thus the difference jJ02-(S) Po2 (M) is the thermodynamic driving force for O2 backspillover from the support onto the catalyst surface as already discussed in Chapter 3 and as proven by AC Impedance spectroscopy, STM, TPD and XPS as reviewed in Chapter 5. It should be noted in equations (11.4) and (11.5) that the Fermi level of the metal is also the Fermi level of the support. 

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