PS and Growth Kinetics

Characterization of PS and Growth Kinetics. A number of systematic studies were carried out to characterize the morphology and growth kinetics of PS from the mid-1970s to the early It was then established that the brown film 

Depletion Layer and Field Intensification Model. By the mid-1980s the overall scope of the conditions for the formation of PS and of the various morphological features were largely identified, although many details of PS morphology and the 

Based on an extensive investigation of the anodic i-V relations, dissolution valence, and PS morphology on a large matrix of silicon substrates, Beale el proposed a rather comprehensive model on the formation of PS. This was the first model that analyzed the i-V characteristics and correlated them with the current conduction mechanisms associated with silicon substrates of different types and doping concentrations. 

Because the spacing between pores is always less than the width of the depletion layer and PS has a very high resistivity, Beale et al. proposed that the material in the PS is depleted of carriers and the presence of a depletion layer is responsible for current localization at pore tips where the field is intensified. This intensification of field is attributed to the small radius of curvature at the pore tips. For lowly doped p-Si the charge transfer is by thermionic emission and the small radius of curvature reduces the height of the Schottky barrier and thus increases the current density at the pore tips. For heavily doped materials the current flow inside the semiconductor is by a tunneling process and depends on the width of the depletion layer. In this case the small radius of curvature results in a decrease of the width of the depletion layer and increases the current density at pore tips. The initiation was considered to be associated with the surface inhomogeneities, which provide the initial localized high current density at small surface depressions. 

The model of Beale et al. provided a deeper level of understanding of the current localization required for PS formation on different silicon substrates and pointed out the correlation between the relative dimension of pore size and the width of the depletion layer. Several concepts proposed in their model would be adopted and further developed in many of the later models such as those by FoU, Zhang, and Lehmann. However, because the model considered only the physical aspects of the semiconductor and none of the chemical reactions, it provided little insight for the change of pore size and other morphological features with current and HF concentration. Also, Beale s model assumed that the Fermi level of the semiconductor is pinned on the surface on the midgap which does not agree with the later experimental data. 

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