Quasi Fermi potential

During permanent illumination of the semiconducting oxides without Ag support, a stationary state different from the thermal equilibrium is formed. It is characterized by the appearance of the quasi-Fermi potentials of electrons and holes shifted closer to the band edges. 

To locate the approximate redox potentials of the reactive electron-hole pair, the quasi-Fermi levels of the powders were measured as summarized above. The plots of photovoltage versus pH for TH and a series of H2[PtCl6]/TH materials are summarized in Fig. 3. From the inflection point (pHo), the corresponding quasi-Fermi potentials at pH 7, as obtained via Eq. (11) taking = 0.059V, are —0.58V (P25) and —0.54V (TH). The flat-band potential of a single crystal of anatase was reported to be —0.59 V (pH 7) (31). Relative to the value of TH the quasi-Fermi level is shifted anodically by 0.05, 0.09, and... 

Bandgap Energies and Quasi-Fermi Potentials of Electrons... 

Organic transistors are thin-fllm transistors. In contrast to the most common inorganic field-effect transistors they operate in depletion (off-state) and accumulation (on-state). The current is determined by the gradient of the quasi-Fermi potential along the channel. Thus, one ean write, e.g., for a p-channel transistor of width w... 

A direet applieation of the eontinuity equations in Eq. (11.66) to the current density equations leads to second-order differential equations in the potential and the two carrier densities. This is one method of formulating the equations. A second method is to use a Quasi-Fermi potential representation where the new variables are exponentially related to the carrier densities by die relationships ... 

In terms of electric potential and Quasi-Fermi potentials, the three semiconductor device equations then become ... 

To complete the formulation a set of boundary conditions are needed for the three solution variables. The reader is referred back to Figure 11.22 which shows the physical geometry of a p-n junction to which this set of equations is to be applied. In equilibrium a built-in voltage exists across the junction with the n-side positive with respect to the p-side. This static equilibrium potential has previously been demonstrated by solving just Poisson s equation and t5q)ical solutions are shown in Figures 11.23 or Figure 11.26. For the equilibrium case, the current densities are zero and the two Quasi-Fermi potentials are zero at all points along the device. 

They actually contain more physical effects such as high injection and ohmic resistance affects than do the low voltage solutions. For Eleetrieal Engineers, the total current would be just as important, or perhaps more important than the potential profile and Quasi-Fermi potentials. The current can be evaluated from the three solution variables in a straightforward manner but will not be done here since the emphasis is on solving coupled nonlinear BV equations and tins can be done without evaluating the total current. A calculation of the current is left to flie interested Eleetrieal Engineers. 

Figure 11.31. Solutions of potential and Quasi-Fermi potentials for Listing 11.26.

II. 33. It can readily be seen that the solution for the Quasi-Fermi potentials,... 

Figure 11.37. Magnitudes of Quasi-Fermi potential derivatives near the two boundaries of the p-n junetion problem. For an applied voltage of 0.3 Volts.

To explore this question, consider the electron current density in terms of the electron Quasi-Fermi potential as ... 

From these it can be seen that the carrier drift velocities can be directly related to the derivatives of the Quasi-Fermi potentials as ... 

Figure 11.38. Solution for potential and Quasi-Fermi potentials for semiconductor p-n junction with modified boundary conditions and long lifetime. Compare with Figure 11.31 for short lifetime case.

These can be reduced to a set of three coupled differential equations which are first order in the time derivative and second order in the spatial derivative. As in Chapter 11 it is convenient to introduce the Quasi-Fermi potentials through the relationships ... 

Figure 12.13 shows a graph of one of the solution variables as obtained by Listing 12.11 and saved in the file listl2 1 l.dat. This is for the hole Quasi-Fermi potential. The other two variables are not shown at fliis time. In general the plot is... 

Figure 12.13. Transient response ofhole quasi-Fermi potential around p-n junction for applied step voltage of 1 Volt with 10 time steps per decade in time.

Hole Quasi-Fermi potential as a funetion of time for five spatial... 

---