Diffusion of holes

Many theories on the formation mechanisms of PS emerged since then. Beale et al.12 proposed that the material in the PS is depleted of carriers and the presence of a depletion layer is responsible for current localization at pore tips where the field is intensified. Smith et al.13-15 described the morphology of PS based on the hypothesis that the rate of pore growth is limited by diffusion of holes to the growing pore tip. Unagami16 postulated that the formation of PS is promoted by the deposition of a passive silicic acid on the pore walls resulting in the preferential dissolution at the pore tips. Alternatively, Parkhutik et al.17 suggested that a passive film composed of silicon fluoride and silicon oxide is between PS and silicon substrate and that the formation of PS is similar to that of porous alumina. 

Annealing the system at temperatures close to its softening point allows recrystallisation to occur and the grain size to increase. This process again progresses by diffusion of holes through the structure and it is quite clear from Equation (2.33) that this process will be assisted by elevated temperatures. 

For n-type electrodes in the dark, the transfer of anodic holes reduces the concentration of interfacial holes (minority carriers) so that the quasi-Fermi level pEfj of interfacial holes is raised beyond the Fermi level efcso (pej > ertso) of the electrode interior, hence, a positive overvoltage Up sc emerges due to the diffusion of holes in the electrode as shown in Eqn. 10-31 ... 

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). 

Fig. 7.21. When a junction between a p-type and an n-type of semiconductor is established (a), a diffusion of holes and electrons in the opposite direction takes place (b). This results in a separation of charge (c) and the formation of an electrical potential difference across the interface (d).

Fig. 7.22. The established electric field opposes further diffusion of holes across the interface.

Hence, when diffusion of particles occurs, there is a corresponding diffusion of holes. Instead of treating ionic diffusion as a separate subject, therefore, one can consider hole diffusion and write the Stokes-Einstein relation (Section 4.4.8) for the diffusion coefficient of holes... 

Macro pores on p -Si due to a rate limiting process by diffusion of holes in the space charge layer Lehmann Ronebeck ... 

First-principle simulations of the excitation dynamics, charge localization, and charge transport in liquid hydrocarbons. Are there excitons, Rydberg states, and exciplexes in liquid hydrocarbons What are the mechanisms for localization of electrons and holes in non-polar liquids What is the mechanism for rapid diffusion of holes and excited states What determines the fragmentation pathways of triplet and singlet excited states ... 

In Section 4.2 we have described electrode reactions which were partly limited by the deficiency of electrons or holes in the corresponding energy bands. A typical example was the current-potential behavior in Figure 12. The anodic current at the n-type electrode was limited by the diffusion of holes and the cathodic current at the p-type electrode by the diffusion of electrons toward the surface. It was further mentioned that these currents could be enhanced by light absorbed by the electrode. 

However, the nature of intermolecular interactions not only depends on the center-of-mass distances between the relevant pairs but also on the orientation of the molecules with respect to each other. In Figure 8.5, the unique intermolecular contacts and their molecular structures, as derived from g(f) for benzene in both the polymorphs, are shown. Benzene I has two contacts consisting of L-shaped (A) and V-shaped (B) dimers. In benzene II, the two contacts are T-shaped (A) and slipped-parallel (B) dimers. Similarly, naphthalene I consists of one T-shaped (A) dimer and two slipped-parallel (B) and (C) dimers, whereas naphthalene II consists of one slipped-parallel (A) dimer, one V-shaped (B) dimer, and one twisted slipped-parallel (C) dimer, respectively. Such different molecular orientations with respect to each other at a given distance would govern the diffusion of holes and electrons, which requires detailed modeling. 

Consider Equation 21.6 in which the diffusion of holes from the p- to the n-type material is balanced by the gradient of the contact potential. If the p-side is connected to the positive terminal of a battery (holes flow from + to —, electrons from — to +), some of the electrons that had diffused into the p-side are taken up by the battery. This applied voltage V reduces the contact potential as seen in Figure 21.4 as well as the electric field across the depletion zones as seen in Figure 21.5 and more electrons can diffuse across the jimction. The positive terminal of the battery continues to supply holes to the p-material by taking up excess electrons while the electrons flowing from the negative terminal of the battery continue to annihilate the excess holes that were injected into the n-type material. 

Robertson and coworkers [24] also view the structural relaxation as a free volume reduction via the mechanism of a diffusion of holes, in response to molecular relaxation events along the chains. 

---