The Dissolution Valence

While n.. shows no dependence on doping density, current density or electrolyte concentration in the electropolishing regime, it does in the PS regime [Le23, Fr6]. enerally n., increases with current density. This is shown for the mesoporous rein Fig. 6.9 a, and microporous regime in Fig. 4.6. From the data of the latter gure the dependence of n.. on formation current density J (in mA cm4) in etha-HF can be fitted to  

The dependence of ru, on PS formation parameters as discussed above reflects the dependence of nv on the microstructure of the porous film. A change of illumination 

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The formation of hydrogen does not occur in anhydrous organic solvents.32,33,63 Due to the lack of hydrogen evolution, dissolution valence is near 4 at all current densities. Addition of water in the organic solvents reduces the dissolution valence. 

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

A sufficiently anodic bias and the availability of holes are the two necessary conditions for the dissolution of silicon aqueous HF. In this case the Si dissolution rate is proportional to the current density divided by the dissolution valence. In all other cases silicon is passivated in HF this is the case under OCP, or under cathodic conditions, or under anodic conditions if the sample is moderately n-type doped and kept in the dark. If an oxidizing agent like HN03 is added silicon will already dissolve at OCP, but the dissolution rate remains bias dependent. If an anodic bias is applied the dissolution rate will be enhanced, whereas a cathodic bias effectively decreases the rate of dissolution. 

Electropolishing under galvanostatic conditions can be used to remove bulk silicon in a well-defined manner. This can for example be used to profile doping density or diffusion length versus the thickness of the sample, as discussed in Sections 10.2 and 10.3. The thickness D of the removed silicon layer can be calculated from the applied current density J, the anodization time t, the dissolution valence nv, the atomic density of silicon Nsi and the elementary charge e. 

As shown in Fig. 4.5, the dissolution valence n., shows a relatively constant value of 4 for electropolishing current densities well above JPS and a bias below 10 V. 

The steady-state condition (/ap=Jps) at the pore tip determines not only the pore diameter but also the pore growth rate. The rate rp of macropore growth can be calculated if the local current density at the pore tip is divided by the dissolution valence nv (number of charge carriers per dissolved silicon atom), the elementary charge e (1.602 xlO-19 C) and the atomic density of silicon Nsi (5xl022 cm-3) ... 

It should be emphasized that n.. and JPS, and therefore c and T, refer to the condition at the pore tip. The dissolution valence and the temperature can be assumed to be independent of pore depth. This is not the case for the HF concentration c. Because convection is negligible in macropores, the mass transport in the pore occurs only by diffusion. A linear decrease in HF concentration with depth and a parabolic growth law for the pores according to Pick s first law is therefore expected, as shown in Fig. 9.18 a. The concentration at the pore tip can be calculated from the concentration in the bulk of the electrolyte c, the pore length l, the diffusion coefficient DHf (Section 1.4) and the flow of HF molecules FHf. which is proportional to the current density at the pore tip ... 

In alkaline solutions, the effective dissolution valence at OCP, as shown in Table 5.1, is zero and changes only very slightly with anodic polarization before the passivation peak it is less than 0.4 at V. The dissolution reaction below the passivation potential is almost completely chemical. ° ° The dissolution valence in the passive region in alkaline solutions, which is not found in the literature, is likely close to 4 since the growth of anodic oxide films should be identical to that in HF solutions (see Chapter 3). 

Reaction paths (1) and (11) in Fig. 5.70 account for the anodic reactions onp-Si and illuminated n-Si in HF solutions at high light intensities. Path (1) is involved in the exponential region at an anodic potential much lower than Vp responsible for direct dissolution of silicon and dissolution valence of 2, while path (11) is involved at a potential above Vp responsible for the indirect dissolution of silicon through formation and dissolution of oxide and for the dissolution valence of 4. At a potential that is lower... 

Reaction path (1) shown in Fig. 5.71 is responsible for the dissolution valence and quantum efficiency of 4 observed on n-Si in HF solutions at low light intensities. It results in a dissolution valence and quantum efficiency of 4. This reaction path, which is a combination of reaction step (IV) in Fig. 5.69 and Eq. (5.29), is slow and is revealed only at a low light intensity when the reaction (1) is small. At high light intensities this reaction path is still active but the dissolution valence and quantum efficiency is less than 4 as reaction (1) becomes dominant. 

On the other hand, the decrease of tj) from 4 down to 2 is much more difficult to interpret. As already mentioned above, gravimetric experiments have shown that the decrease is due to a change in the dissolution valency of Si from IV to II. This analytical result is supported by the fact that H2 is formed as soon as the dissolution valency changes (Fig. 8.9), because H2 formation under anodic bias is only possible if Si is dissolved in the divalent state (see Eq. 8.3). Very recently, a model has been presented in which it is assumed that Si(I) (which is just a mobile surface radical) catalyses the divalent dissolution [23]. 

These results obtained with n-Si, seem to be in contradiction to those obtained with the p-type electrode. However, a quantum yield of 4> = 4 was found with n electrodes only at very low light intensities (<10 pW) which corresponds to a current of <5 pA cm. An analysis of the dissolution valency at p-electrodes, however, was not possible... 

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