Macropores growth rate

The experimentally observed parabolic increase in pore depth and linear decrease in concentration shown in Fig. 9.18 c indicate that Eq. (9.6) is valid [Le9]. The macropore growth rate decreases linearly with l according to Eq. (9.6). If, therefore, a constant pore diameter is desired for a macropore array, a decrease in etching current or illumination intensity, respectively, with time is required. 

If one studies the growth rate as a function of anodization current density for different PS structures prepared in the same electrolyte, as shown in Fig. 6.5, some inherent laws can be observed. In the regime of stable macropore formation on n-type silicon the growth rate is found to be virtually independent of the applied current density. This is simply a consequence of JPS being present at any pore tip, as described by Eq. (9.5). For the growth rate rPS (in nm s 1) of micro PS in ethanoic... 

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... 

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].

In contrast to the micro- and mesoporous regimes, for which only a few empirical laws for the growth rate and porosity are available, the detailed pore geometry for macropore arrays in n-type silicon can be pre-calculated by a set of equations. This is possible because every pore tip is in a steady-state condition characterized by = JPS [Le9]. This condition enables us to draw conclusions about the porosi-... 

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) ... 

Fig. 9.17 Calculated growth rates of macropores for nv=2 and nv=4 (lines) and experimentally obtained initial macropore etch rates rp (squares) versus the HF concentration Chf of the electrolyte (J/JPS = 0.2S, 1015 crrT3 n-type, RT, square pattern). After [Le9],...

Anchorage-dependent cells can be grown on solid or macroporous microcarrier beads and these can then be superfused with nutrient medium in the spectrometer. The advantages of the system include direct contact between the perfusate and the cells (see below) and growth of the cells at rates comparable to those found in tissue culture dishes. A disadvantage, with solid beads, is the relatively low cell density obtainable due to the large sample volume occupied by the beads. 

The rate of growth of macropores observed on -Si is independent of current density when the current density at the tip equals J. The pore diameter was related by Lehmann to the ratio of actual current density to peak current density... 

A recent systematic study of macropore formation performed on various doped n-type Si substrates with rear illumination, by Foil and coworkers [106] showed that a strong influence of the SCR on the average macropore density is indeed observed in accordance with the Lehmann model [72] (i.e. an increased anodic bias decreases the density of pores), except for highly doped Si. It was observed that an increasing anodic bias increases the pore density, in contrast to the prediction. The pore growth seems to be dominated by the chemical-transfer rate and most likely calls for a chemical passivation mechanism of the macropore walls. 

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