Dissolution valence

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. 

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]. 

Fig. 4.5 Dissolution valence nv as a function of anodic current density for low doped p-type and strongly illuminated, low doped n-type samples (<1017cnT3, 2.5% HF, at RT). For current densities belowJPS the samples were measured with and without the microporous layer. This produces a minor difference in indicated by two data points.

The first of the four characteristic currents to J4 has a prominent position. It indicates the crossover from a charge supply limited reaction to a kmetically and mass transfer limited reaction. This crossover is accompanied by pronounced changes in charge state, chemical dissolution reaction, dissolution valence, pore formation and anodic oxide formation. Therefore its dependence on other parameters, such as crystal orientation, temperature or H F concentration deserves further investigation. In the literature Jt is usually termed /crl JPS or JPSL. In the following the symbol JPS will be used. 

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 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 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 ... 

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 etching rate at room temperature is proportional to the Xep2 pressure, with rates as high as 12 nm s at 1.4x 10 Torr [42]. This etch rate corresponds to an equivalent etching current of about 7 mAcm on a (100) surface and assuming a dissolution valence of 2. 

Recent work on etching of silicon in anhydrous HF solutions has shown that silicon is dissolved with a dissolution valence of 4 and with no hydrogen formation [111]. This result also shows that OH groups are an essential component of the etching reaction in aqueous solutions. 

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... 

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