Effective 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. 

The quantum efficiency of photo electrochemical reactions may vary from 2 to 4 the effective dissolution valence may vary from 2 to 4 and the efficiency of hydrogen evolution may vary from zero to near 1 depending on light intensity and potential. 

This fast removal of Si-F species can be ascribed to the weakening of the Si backbonds induced by the strong polarizing effect of F [Ubl], The weak back-bonds are then attacked by HF or H20. This reaction scheme for the dissolution process is supported by quantum-chemical calculations [Trl]. The observed dissolution valence of two for Jelectron injection current and Si-F bond density [Be22] are experimental findings that are in support of the divalent dissolution mechanism, as shown in Fig. 4.3 [Lei, Ge7, Ho6]. 

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. 

The smallest pores that can be formed electrochemically in silicon have radii of < 1 nm and are therefore truly microporous. However, confinement effects proposed to be responsible for micropore formation extend well into the lower mesoporous regime and in addition are largely determined by skeleton size, not by pore size. Therefore the IUPAC convention of pore size will not be applied strictly and all PS properties that are dominated by quantum size effects, for example the optical properties, will be discussed in Chapter 7, independently of actual pore size. Furthermore, it is useful in some cases to compare the properties of different pore size regimes. Meso PS, for example, has roughly the same internal surface area as micro PS but shows only negligible confinement effects. It is therefore perfectly standard to decide whether observations at micro PS samples are surface-related or QC-related. As a result, a few properties of microporous silicon will be discussed in the section about mesoporous materials, and vice versa. Properties of PS common to all size regimes, e.g. growth rate, porosity or dissolution valence, will be discussed in this chapter. 

The soluble divalent SiF2 compound is in turn transformed by disproportionation into SiF6 and elemental amorphous silicon. This mechanism is responsible for the effective dissolution valence of Si, which was found to be equal to 2 in the range of potential between 0 and +0.4V/SCE. 

The effective dissolution valence is defined as the average number of electrons flowing through the external circuit per dissolved silicon atom. It reflects the nature of the reactions during the dissolution processes, e.g., the extent of electrochemical reactions relative to the chemical reactions. For silicon, the effective dissolution valence of... 

FIGURE 5.21. Effective dissolution valence of p-Si and n-Si as a function of anodic current density in 2.5% HF. (Reprinted from Lehmann. 1993, with permission from Elsevier Science.)... 

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). 

The efficiency of hydrogen evolution and effective dissolution valence are directly correlated, and their relation varies with potential, illumination, and doping of the silicon. The overall relation among these two parameters and the factors are summarized in Fig. 5.23. 

FIGURE 5.23. Summary of effective dissolution valence and hydrogen evolution efficiency as a function of potential for different materials and illumination conditions. L is illumination intensity. 

Deviation of 60 mV/decade can be seen in Table 5.3 under different conditions. In addition to the potential distribution in the two double layers, there are two other possible causes for the deviations. The first is possible potential drops in other parts of the electrical circuit, e.g., in the electrolyte and semiconductor. The second possibility is the change of effective surface area due to the formation of a porous silicon layer during the course of i-V curve measurement. In addition, if the reaction is controlled by a process involving the Helmholtz layer, the apparent Tafel slope may be smaller than the 60 mV/decade as would be expected from the formula, B = kTI23anq, because the effective dissolution valence n is not a constant with respect to potential but varies from 2 to 3 in the exponential region. 

The overall reaction valence from reactions (5.8) to (5.10) is 4, which accounts for the reactions occurring in the electropolishing region in HF solutions. To account for the effective dissolution valence of 2 at potentials below the passivation potential (potential of the peak current, A), it was proposed that silicon reacts directly with HF. 

Reaction (5.12) results in Hz evolution which is of chemical nature and is responsible for the effective dissolution valence of 2. The Turner-Memming model explains the overall characteristics of the anodic reactions, that is, two different reaction paths in HF and in non-HF solutions passivation by an oxide film at high anodic potentials evolution of hydrogen to account for the effective dissolution valence being less than 4. However, it lacks the details to account for phenomena such as surface termination by hydrogen, current multiplication, and variation of effective dissolution valence. 

The results presented in the previous sections show that the anodic reactions on a silicon electrode may proceed via different paths depending on the conditions and that those in HF solutions and those in KOH solutions are rather different. They also show that the mechanistic models proposed for the reactions in HF and KOH solutions from the many studies in the literature are largely separated. However, in both HF and KOH solutions, the silicon/electrolyte interface is fundamentally similar differing only in the concentrations of hydroxyl and fluoride ions. Thus, a reaction scheme must be coherent with respect to the experimental observations in both FIF and KOH solutions. For comparison. Table 5.8 summarizes the characteristic features of the reactions occurring on silicon in FIF and KOH, in terms of nature of the reaction, rate, effective dissolution valence, photoeffect, and uniformity of the surface. 

TABLE 5.9. Effective Dissolution Valence and Conditions for Different Reaction Paths Shown in Figs. 5.70-5.73... 

Quantitative analysis of the data shows that a H2 molecule is gena-ated for two dissolved Si atoms, indicating that the effective dissolution valence of silicon is 3. According to Kooij et the etching reactions on/ -Si and n-Si are different in terms of the involvement of the charge carriers. For the p-Si the reaction is... 

As discussed in Chapter 5, the effective dissolution valence of silicon, n, can vary between 2 and 4 depending on the type of silicon, potential, and illumination intensity. In general, n increases with increasing anodic current density for all types of silicon substrates as shown in Fig. 5.21. The value of n sharply changes at the peak current... 

For p-Si in the PS formation region, n tends to increase with doping concentration particularly at high doping concentrations as shown in Fig. 8.8 for n-Si the effect of doping concentration on dissolution valence is seen to depend on current density. It decreases with increasing illumination intensity as shown in Fig. 8.9. Substrate orientation has little effect on n as shown in Fig. 8.10. ° ... 

Evolution of hydrogen gas occurs during the formation of PS. It is the result of the chemical reaction responsible for the effective dissolution valence of less than 4. Figure 8.11 shows that the amount of hydrogen gas is proportional to the time of anodization. When the anodization is stopped, the hydrogen evolution still continues at a lower rate. In situ F TIR studies indicate that the H-termination of the silicon surface is preserved during PS formation on The silicon atoms on the surface are... 

The amount of chemical reactions relative to electrochemical reactions determines the amount of anodic hydrogen evolution and the value of effective dissolution valence. 

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