Band-bending

Fig. V-14. Energy level diagram and energy scales for an n-type semiconductor pho-toelectrochemical cell Eg, band gap E, electron affinity work function Vb, band bending Vh, Helmholtz layer potential drop 0ei. electrolyte work function U/b, flat-band potential. (See Section V-9 for discussion of some of these quantities. (From Ref. 181.)...

Fig. XVIII-19. Band bending with a negative charge on the surface states Eu, E/, and Ec are the energies of the valance band, the Fermi level, and the conduction level, respectively. (From Ref. 186.)...

Fig. 8. (a) Energy levels for the band model of silver haUde crystals. The band bending at the surface (-) is exaggerated. The extent of bending is at... 

K. Metder. AppL Phys. 12,75, 1977. PL measurements of surface state densides and band bending in GaAs. 

Thus it has been shown that thin insulating layers (in the nanometer range) at the interface metal/polymer in a PLED can significantly reduce the onset electric field necessary for EL [58-63]. This is still not fully understood and has been ascribed to band bending at the interface [64]. 

When a positive (negative) bias is applied to die metal, the bands bend downwards (upwards), as seen in Figure 14-4. 

Although the observations for PPV photodiodes of different groups are quite similar, there are still discussions on the nature of the polymer-metal contacts and especially on the formation of space charge layers on the Al interface. According to Nguyen et al. [70, 711 band bending in melal/PPV interfaces is either caused by surface states or by chemical reactions between the polymer and the metal and... 

In the depletion region for a band bending U - Ujb> 100 mV, where a reasonably low surface recombination velocity is found, the PMC signal can consequently be approached by... 

It is important to note that there may be at least two reasons for obtaining deviations from a purely exponential behavior for a PMC transient. These are a too high excess carrier generation, which may cause interfacial rate constants that are dependent on carrier concentration, and an interfacial band bending AU, which changes during and after the flash. For fast charge transfer, a more complicated differential equation has to be solved. 

The PMC transient-potential diagrams and the equations derived for PMC transients clearly show that bending of an energy band significantly influences the charge carrier lifetime in semiconductor/electrolyte junctions and that an accurate interpretation of the kinetic meaning of such transients is only possible when the band bending is known and controlled. 

Figure 7.13. The definitions of ionization potential, Ie, work function, , Fermi level, EF, conduction level, Ec, valence level Ev, and x-potential Xe without (a) and with (b) band bending at the semiconductor-vacuum interface.

More subtle effects of the dielectric constant and the applied bias can be found in the case of semiconductors and low-dimensionality systems, such as quantum wires and dots. For example, band bending due to the applied electric field can give rise to accumulation and depletion layers that change locally the electrostatic force. This force spectroscopy character has been shown by Gekhtman et al. in the case of Bi wires [38]. 

At the interface of the nitride (Ef, = 5.3 eV) and the a-Si H the conduction and valence band line up. This results in band offsets. These offsets have been determined experimentally the conduction band offset is 2.2 eV, and the valence band offset 1.2 eV [620]. At the interface a small electron accumulation layer is present under zero gate voltage, due to the presence of interface states. As a result, band bending occurs. The voltage at which the bands are flat (the flat-band voltage Vfb) is slightly negative. 

---