Holes diffusion

Jia,., Fujitani, Mv Yae, S., and Nakato, Y., Hole diffusion length and temperature dependence of photovoltages for n-Si electrodes modified with LB layers of ultrafine platinum particles, Electrochim. Acta, 42, 431,1997. 

Macro pores on p -Sidue to hole diffusion in space charge layer39... 

The current i flowing in photoexcited n-type semiconductor electrodes equals the sum of the photoexcited hole current i >h, the limiting current of hole diffusion ip. itB, and the current of hole recombination inc as shown in Eqn. 10—44 ... 

The mechanism operating within a polymer LED involves injection, via a metal electrode, of electrons into the conduction band and holes into the valence band of the polymeric semi-conductor. The electrons and holes diffuse towards each other and then combine to form an exciton, which can move along the polymer chain. These excited states then decay to the ground state with a characteristic fluorescence. 

It has then to be concluded that the charge transfer in the ferrocene/ferroci-nium couple in this specific solvent is a fast process at the timescale of the hole diffusion in the semiconductor space charge layer. However, at the present time, it seems that the constraints arising from the construction of a perfectly tight device will hinder the development of these electrochemical photovoltaic cells. 

Since one starts off with a larger hole concentration in the //-type of material than exists in the //-type of material, there will initially be more holes taking the p — // random walk titan the n — // random walk. One has stated in microscopic language that there will be diffusion of holes in the// —> // direction [Fig. 7.21(b)]. What is the result of this p—m hole diffusion The net p transport of holes leaves a negative charge on the p material and confers a positive charge on the n material [Fig. 7.21(c)]. A potential difference develops [Fig. 7.21(d)]. Further, this charging of the two sides of the interface and the resultant potential difference acts precisely in such a manner as to oppose further //—>// hole diffusion (Fig. 7.22). 

Here Dp is the hole diffusion coefficient and Lp = (Dptp)112 is the diffusion length, where tp is the hole lifetime. This expression for ijjm coincides with a known formula (see, for instance, Middlebroock, 1957) for the saturation current of a p- junction. 

Photocurrent measurements permit the determination of the hole diffusion length Lp. As was already noted, comparison of measured and calculated polarization curves allows Lp to be determined by a fitting procedure. For example, Butler (1977) and Wilson (1977) obtained for W03 and TiOz the values of Lp equal to 0.5 x 10-4 and 4 x 10-4 cm, respectively. 

Woodall et al.36 have analyzed the relationship between surface recombination velocity and the steady state band gap luminescence in GaAs. They calculate for 534nm excitation that a decrease in vs from 106cm/sec to 104cm/sec will triple the quantum efficiency at a 2.5Mm deep p-n junction if the hole diffusion length, Lp, is 3jim, and the electron diffusion length, L is 4/im. 

In the above, L is the hole diffusion length, t is the lifetime, p0 is the equilibrium hole density, and is the equilibrium band bending voltage. These equations are good approximations when 5 is not too small and are equivalent to that given in (2J where the exchange current parameter is used instead of the charge transfer rate constant. More accurate... 

The hole diffuses in the crystal until it is trapped or reacts with an impurity or with a photoelectron (recombination). A hole trapped at a crystal defect could be neutralized by ejection of a neighboring silver ion into an interstitial position (6,7) or combination with a silver ion vacancy, but still could recombine with an electron or react with a silver atom or other agent. 

The absorption of energy by the grains produces conduction electrons and either free or trapped holes. The conduction electrons and the holes diffuse initially by a three-dimensional random walk. In chemically sensitized crystals, the holes are trapped by products of chemical sensitization which thus undergo photo-oxidation. Rapid recombination between a trapped hole and an electron is avoided by the delocalization as an interstitial Ag ion of the nonequilibrium excess positive charge created at the trapping site. Latent pre- and sub-image specks are formed by the successive combination of an interstitial Agi ion and a conduction electron at a shallow positive potential well. 

In nanosized particle film electrodes, photogenerated holes can be rapidly transferred to the semiconductor/electrolyte interface and there be captured by the redox species in the electrolyte. In this way, the recombination losses can be diminished. This is of great importance for semiconductors like hematite with a very short hole diffusion length (2-4 nm). Another advantage is the large internal surface area, which characterize nanostructured semiconductor film electrodes. The latter decreases the current density per unit area of semiconductor / electrolyte interface. 

Since local space-charge neutrality does not hold at the oxide interfaces, the above expression for the current is restricted to the interior zone [28] where local space charge neutrality has been found [46] to be a good approximation. This is illustrated for the case of cation vacancy (or anion interstitial) and electron-hole diffusion by Fig. 17. Thus, the domain of validity is not 0 but instead is 5 < [Pg.75]

Fig. 8.4. Profile of light intensity at the semiconductor electrolyte junction. W is the width of the depletion layer and L, is the hole diffusion length. The penetration depth of the light...

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