Band bending, calculation

Consider the case of small band bending, in which eo4>(x) first order, and calculate the distribution of the potential. 

Fig. 3. Like a photoelectrochemical cell, such a powder includes sites for photo-induced oxidation and reduction, but no external current flow accompanies these transformations. Photoactivity is also maintained as the size of the particle decreases to the colloidal range although the absorption characteristics, the quantum efficiency of charge separation, and the kinetics of interfacial electron transfer may be influenced by the particle size. On sufficiently small particles, for example, the calculated space-charge width necessary for effective band bending may exceed the dimensions of the particle.

The field is a function of band bending voltage V and since V depends on x, field is also a function of x. We first calculate the charge distribution and the field Fx as a function of the surface potential Vs. The gate voltage is then calculated by adding the drop across the insulator to Vs. To calculate the drain current we use the following equations [157],... 

Fig. 8.14. Theoretical plots showing competition between recombination and current doubling. Calculated for a surface state density of 5 x 10,2cm "2. The surface state is located 0.3eV below the bulk Fermi level. Donor density 1.5 x I0,ftcm. Arinj 5 x 104s" rccn = 2 x 10 7 s. Band bending values (a) 0.40 eV, (b) 0.35 eV, (c) 0.30 eV, (d) 0.2 eV. Note the transition in the IMPS response from current from current doubling control at 0.4 eV to...

As discussed above, the band bending in semiconductor particles may be small and in this situation photogenerated charge carriers may either recombine or separate via diffusion. In the case of the latter, the charge carriers may ultimately diffuse to the particle surface where they participate in the reactions described in Section 9.2.1. Calculations of photogenerated... 

A-Si H has a smoothly varying density of states, so that Eq. (9.8) applies when the band bending is small compared with the width of the defect band, which is about 0.2 eV. When the voltage is larger, the charge depends on the shape of the density of states and W cannot easily be calculated. 

Fig. 4. Band bending in a thin film on a metal substrate where the calculated value of the space-charge layer width, IF, exceeds the film thickness, Lt, so that excess charge appears on the metal. In this situation, the field assists the separation of photoexcited carriers throughout the entire film.

Fig. 11. Calculated field-effect conductance for the structureless density of states and a density of states with a peak in the vicinity of , shown in Fig. 12, as indicated by the solid and dashed lines, respectively. Different mediods of analysis were used curves a and b, with no approximations curve c, using zero temperature statistics curves d and e, employing an assumed parabolic band-bending profile. [After Powell (1981).]...

All potentials given in Fig. 3 are referenced to the potential at the interface between the semiconductor and the current collector. This choice of reference potential is arbitrary, and is used here to emphasize the degree of band bending and straightening in the semiconductor. A number of researchers (see, e.g., Refs. 17 and 19) have reported that the potential of the solution is independent of current and illumination intensity when referenced to an external quantity such as the Fermi energy of an electron in vacuum. This concept does not have strict thermodynamic validity because it depends upon the calculation of individual ionic activity coefficients38 however, it has proved useful for the prediction of the interaction among semiconductors and a variety of redox... 

To calculate the band bending changes from the changes in the resistance, one has to use the following dependency ... 

The only difference compared with the accumulation layer for the p-type SMOX is that the electrons are the charge carriers and that the accumulation is therefore described by a downward band bending. Again, here one has to solve the Poisson equation (Morrison, 1977) with its solution, the average electron concentration % can be calculated. One obtains ... 

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