Macropores formation mechanisms

According to the macropore formation mechanisms, as discussed in Section 9.1, the pore wall thickness of PS films formed on p-type substrates is always less than twice the SCR width. The conductivity of such a macroporous silicon film is therefore sensitive to the width of the surface depletion layer, which itself depends on the type and density of the surface charges present. For n-type substrates the pore spacing may become much more than twice the SCR width. In the latter case and for macro PS films that have been heavily doped after electrochemical formation, the effect of the surface depletion layer becomes negligible and the conductivity is determined by the geometry of the sample only. The conductivity parallel to the pores is then the bulk conductivity of the substrate times 1 -p, where p is the porosity. 

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. 

The average pore size of PS structures covers four orders of magnitude, from nanometers to tens of micrometers. The pore size, or more precisely the pore width d, is defined as the distance between two opposite walls of the pore. It so happens that the different size regimes of PS characterized by different pore morphologies and different formation mechanisms closely match the classification of porous media, as laid down in the IUPAC convention [Iu2]. Therefore the PS structures discussed in the next three chapters will be ordered according to the pore diameters as mostly microporous (d<2 nm), mostly mesoporous (2 nm50 rim). Note that the term nanoporous is sometimes used in the literature for the microporous size regime. 

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. 

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. 

An interesting question is whether such well-ordered pore arrays can also be produced in other semiconductors than Si by the same electrochemical etching process. Conversion of the macropore formation process active for n-type silicon electrodes on other semiconductors is unlikely, because their minority carrier diffusion length is usually not large enough to enable holes to diffuse from the illuminated backside to the front. The macropore formation process active in p-type silicon or the mesopore formation mechanisms, however, involve no minority carrier diffusion and it therefore seems likely that these mechanisms also apply to other semiconductor electrodes. 

Several qualitative models have been proposed to explain porous Si formation but none of them allow full explanation of the rich variety of morphology exhibited by porous Si and, in particular, the formation of the duplex layers (nano -I- macroporous). In addition, they possess very little predictive power. A majority of the models focussed on the pore propagation, whereas the mechanism of pore initiation received very little attention. A comprehensive review of the various models proposed to explain pore formation is found in excellent review articles by Smith and Collins [5], Parkhutik [12], and Chazalviel and coworkers [13]. Two main categories of models have been proposed. The first one is basically electrostatic in nature, based on the consideration that physical effects associated with the SCR play a major role in the pore-formation mechanism. The second category is based on computer simulations. 

The stable macropore formation obtained for an applied bias is sufficient to generate the critical current density (about 1 V). This understanding of the formation mechanism has allowed good control of the geometrical parameters of... 

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. 

Study of the formation mechanisms of cryogels on the basis of thiol-containing polymers Preparation and study of physicochemical properties and macroporous morphology of chitosan cryogels... 

Lehmann V, Griining U (1997) The limits of macropore array fabrication. Thin Solid Films 297 13 Lehmann V, Stengl R, Luigart A (2000) On the morphology and the electrochemical formation mechanism of mesoporous silicon. Mater Sci Eng B 69-70 11 Ogata YH, Kobayashi K, Motoyama M (2006) Electrochemical metal deposition on silicon. Curr Opin Solid State Mater Sci 10 163... 

Bengtsson M, Ekstrom S, Drott J, Collins A, Csoregi E, Marko-Varga G, Laurell T (2000) Applications of microstructured porous silicon as a biocatalytic surface. Phys Stat Sol 182 495-504 Bimer A, Li A-P, Muller F, Gdsele U, Kramper P, Sandoghdar V, Mlynek J, Busch K, Lehmann V (2000) Transmission of a microcavity structure in a two-dimensional photonic crystal based on macroporous silicon. Mat Sci Semicon Proc 3 487-491 Carstensen J, Christophersen M, Foil H (2000) Pore formation mechanisms for the Si-HF system. Mat Sci Eng B 69/70 23-28... 

Lehmann V, Foil H (1990) Formation mechanism and properties of electrochemically etched trenches in n-type silicon. J Electrochem Soc 137 653-659 Lehmann V, Ronnebeck S (1999) The physics of macropore formation in Low-doped p-type silieon. J Electrochem Soc 146 2968-2975... 

Slimani A, Iratni A, Chazalviel J-N, Gabouze N, Ozanam F (2009) Experimental study of macropore formation in p-type silicon in a fluoride solution and the transition between macropore formation and electropolishing. Electrochim Acta 54 3139-3144 Smith RL, Collins SD (1992) Porous silicon formation mechanisms. J Appl Phys 7LR1-R22 Starkov W (2003) Ordered macropore formation in silieon. Phys Status Solidi (a) 197 22-26 Steiner P, Lang W (1995) Micromachining applications of porous silicon. Thin Solid Films 255 52-58... 

Sadakane, M., Takahashi, C, Kato, N., Ogihara, H., Nodasaka, Y., Doi, Y., Hinatsu, Y., and Ueda, W. (2007) Three-dimensionally ordered macroporous (3DOM) materials of spinel-type mixed iron oxides. Synthesis, structural characterization, and formation mechanism of inverse opals with a skeleton structure. Bull. Chem. Soc. Jpn., 80, 677-685. 

The previous discussion has shown that the CIPS technique allows one to produce macroporous epoxy networks with either a narrow or bimodal size distribution. However, no indication has been given on the type of phase separation mechanism to yield these morphologies. As discussed earlier, the formation of a closed cell morphology can result either from a nucleation and growth mechanism or from spinodal decomposition. 

The polymerization mixture for the preparation of rigid, macroporous monolithic materials in an unstirred mold generally contains a monovinyl compound (monomer), a divinyl compound (crosslinker), an inert diluent (porogen), as well as an initiator. The mechanism of pore formation of such a mixture has been postulated by Seidl et al. [101], Guyot and Bartholin [102], and Kun and Kunin [103] and can be summarized as in the following text. 

The fact that adding a better solvent to the mixture results in a shift of the distribution to smaller pore sizes has been explained by the mechanism of pore formation, postulated for macroporous resins in the late 1960s [101-103]. The addition of a poor solvent causes the phase separation to occur early, whereas the precipitated polymer nuclei are swollen with monomers, which present a better solvating agent than the porogen. Due to the high monomer concentration within the globuli. 

Particle Size and Shape. The polymerization process for producing macroporous synthetic polymers (539) leads to the formation of spherical particles whose size can be controlled within certain limits. The popular XAD polymers are usually sold with approximately 90 of the total weight encompassing smooth beads with 20-50-mesh sizes. Most users incorporate a suspension step to remove the fines in their purification of the polymer, but they do not remove the small number of particles larger than 20 mesh. The particle size and distribution vary with different polymer batches, and it is advisable to mechanically sieve polymer beads and choose only those within the 20-50-mesh size for preparation of the adsorption columns. 

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