Electrode macroporous

In the simplified transport model, we lump the resistance inside the electrode with that in the spacer channel. To describe the current-voltage relation, we will not assume a constant resistance but include how the resistance increases when the salt concentration goes down. We assume that at each moment in time the salt concentration within the electrode macropores (the transport pathways in the electrode) is the same as in the spacer channel. Therefore, we can use a single relation between J, A(()tr, and c (with c being the salt concentration, assumed equal in spacer channel, macropores, and recycle vessel), resulting for J in... 

The main difference from the alkaline dissolution scheme is the hole needed to initiate step 1 of the divalent reaction. The polarizing effect on the Si backbonds is the same for Si-F and Si-OH. From this similarity a certain crystal anisotropy is expected for the divalent reaction, too. Faceting along (111) planes in HF electrolytes is observed when the current density is close to JPS and micro PS formation becomes suppressed. This is the case for the electrode surface shown in Fig. 2.4 or at the tips of macropores as shown in Fig. 9.13b. 

Photogenerated carriers are needed for the formation of macropores in n-type electrodes, as discussed in Chapter 9. 

The process described above is expected to produce a random distribution of active and passive spots on the electrode interface. But the electrode surface may also be artificially patterned prior to anodization in order to form nucleation centers for pore growth. This may be a lithographically formed pattern in said passive film or a predetermined pattern of depressions in the electrode material itself, which become pore tips upon subsequent anodization. The latter case applies to silicon electrodes and is discussed in detail in Chapter 9, which is devoted to macropore formation in silicon electrodes. 

An electric field in the semiconductor may also produce passivation, as depicted in Fig. 6.1c. In semiconductors the concentration of free charge carriers is smaller by orders of magnitude than in metals. This permits the existence of extended space charges. The concept of pore formation due to an SCR as a passivating layer is supported by the fact that n-type, as well as p-type, silicon electrodes are under depletion in the pore formation regime [Ro3]. In addition a correlation between SCR width and pore density in the macroporous and the mesoporous regime is observed, as shown in Fig. 6.10 [Thl, Th2, Zh3, Le8]. 

For p-type electrodes with doping densities below 1018 cm-3 diffusion and thermionic emission of charge carriers across the SCR is dominant. For p-type doping densities below 1016 cm4 this charge transfer is associated with the formation of macropores, as discussed in Chapter 9. 

Another mechanism that can produce significant anodic pore tip currents across the SCR in low doped n-type electrodes (< 1018 cm-3) is collection of minority carriers (holes). Minority carriers can be generated by illumination or by injection from a p-type region. Macropore formation is observed in this regime, as discussed in Chapter 9. 

If the pore density is plotted versus the doping density of the silicon electrode, it can be seen that the micropore density is independent of doping, while the macropore and mesopore densities increase linearly with doping density, as shown in Fig. 6.10. This is a consequence of the QC formation mechanism being independent of doping, while the SCR-related mechanisms are not, as discussed in Section 6.2. 

Fig. 6.10 Pore density versus silicon electrode doping density for PS layers of different size regimes. The broken line shows the pore density of a triangular pore pattern with a pore pitch equal to twice the SCR width for 3 V applied bias. Note that only macropores on n-type substrates may show a pore spac-...

This section is devoted to the formation mechanisms that have been proposed as being responsible for formation of macropores on p-type and n-type silicon electrodes. 

In contrast to p-type electrodes, an n-type electrode is under reverse conditions in the anodic regime. This has several consequences for pore formation. Significant currents in a reverse biased Schottky diode are expected under breakdown conditions or if injected or photogenerated minority carriers can be collected. Breakdown at the pore tip due to tunneling generates mainly mesopores, while avalanche breakdown forms larger etch pits. Both cases are discussed in Chapter 8. Macropore formation by collection of minority carriers is understood in detail and a quantitative description is possible [Le9], which is in contrast to the pore formation mechanisms discussed so far. 

Having discussed the causes of pore wall passivity, we will now focus on the active state of the pore tip, which is caused by its efficiency in minority carrier collection. Usually the current density at the pore tip is determined by the applied bias. This is true for all highly doped as well as low doped p-type Si electrodes and so the pore growth rate increases with bias in these cases. For low doped, illuminated n-type electrodes, however, bias and current density become decoupled. The anodic bias applied during stable macropore formation in n-type substrates is... 

Macropore formation on p-type silicon electrodes was first observed for anodization in water-free mixtures of anhydrous HF and an organic solvent [Pr7, Ril]. Later it was observed that organic HF electrolytes with a certain fraction of water [Pol, We5], or even non-organic, aqueous HF electrolytes [We2, Le21], are also sufficient for the formation of macropores on p-type Si electrodes. This indicates that macropore formation on such electrodes cannot be ascribed to the chemical iden-... 

The growth of a macropore on a p-type substrate can be initiated by artificial etch pits. The growth of predefined pore arrays is observed to be more stable than the growth of random pores on flat electrodes [Chl6, Le21]. If a slit is used for pore initiation the formation of trenches separated by thin walls has been observed on (100) p-type substrates [Oh5]. Note that for slits along the (110) direction the walls become (110) planes, in contrast to trenches produced by alkaline etchants, for which only (111) oriented walls can be formed on (110) oriented silicon substrates. 

A specific feature of macropore formation in n-type silicon is the possibility of controlling the pore tip current by illumination and not by applied bias. This adds another degree of freedom that is not available for mesopore or macropore formation on p-type substrates. The dark current density of moderately doped n-type Si electrodes anodized at low bias is negligible, as shown in Fig. 4.11, therefore all macropore structures discussed below are formed using illumination of the electrode to generate the flux of holes needed for the dissolution process. Illumination, however, is not the only possible source of holes for example, hole injection from a p-doped region is expected to produce similar results. 

Fig. 9.9 SEM micrograph of an n-type silicon electrode with an etched macropore array (5 2 cm, (100), 3 V, 350 min, 2.5% HF). Pore growth was induced by a square pattern of pits produced by standard lithography and subsequent alkaline etching (inset upper right). In order to measure the depth dependence of the growth rate, the current density was periodically kept at 5 mA cm 2 for 45 min and then reduced to 3.3 mA crrf2 for 5 min. This results in a periodic decrease in the pore diameter, as indicated by the white labels on the left-hand side. After [Le9].

A lower limit of bias is given by the onset of unstable macropore formation. This is shown in Fig. 9.13, which shows the pore morphology and the corresponding formation conditions in the current density-voltage plot The current density J is held constant by the intensity of the backside illumination, so that the influence of the applied bias can be studied independently. At -0.4 V, versus a platinum wire as a pseudoreference electrode, the current density is constant over the... 

Fig. 9.15 Cross-sections of macropore arrays parallel to the electrode surface (a) for a square, (b) for an ordered and (c) for a random pattern. The pores (black squares)...

Note that during macropore formation in p-type silicon electrodes the pore tip current density is usually well below JPS, and so Eqs. (9.1) to (9.5) are not applicable to p-type macropore formation [Le21]. 

The pore growth direction is along the (100) direction and toward the source of holes. For the growth of perfect macropores perpendicular to the electrode surface (100), oriented Si substrates are required. Tilted pore arrays can be etched on substrates with a certain misorientation to the (100) plane. Misorientation, however, enhances the tendency to branching and angles of about 20° appear to be an upper limit for unbranched pores. For more details see Section 9.3. 

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