Abstract
The formation of macropores in silicon during electrochemical etching processes has attracted much interest. Experimental evidences indicate that charge transport in silicon and in the electrolyte should realistically be taken into account in order to be able to describe the macropore morphology. However, up to now, none of the existing models has the requested degree of sophistication to reach such a goal. Therefore, we have undertaken the development of a mathematical model (phase-field model) to describe the motion and shape of the silicon/electrolyte interface during anodic dissolution. It is formulated in terms of the fundamental expression for the electrochemical potential and contains terms which describe the process of silicon dissolution during electrochemical attack in a hydrofluoric acid (HF) solution. It should allow us to explore the influence of the physical parameters on the etching process and to obtain the spatial profiles across the interface of various quantities of interest, such as the hole concentration, the current density, or the electrostatic potential. As a first step, we find that this model correctly describes the space charge region formed at the silicon side of the interface.
Highlights
Macropores have first been obtained upon electrochemical dissolution of n-type silicon in hydrofluoric acid (HF)-based electrolytes [1,2,3,4,5], in conditions where the current is limited by the supply of photogenerated holes to the electrochemical interface
We present a mathematical analysis as well as numerical simulations of our model and show that it exhibits two new key features that are important for the description of pore formation: at equilibrium, a large space charge region is present on the semiconductor side of the interface, and the application of an external potential yields a nonlinear current-voltage characteristic of Schottky type
It can be seen that the model correctly reproduces the change in conduction mechanism: whereas the hole current is much larger than the ion current inside the silicon, the opposite is true in the electrolyte
Summary
Macropores have first been obtained upon electrochemical dissolution of n-type silicon in hydrofluoric acid (HF)-based electrolytes [1,2,3,4,5], in conditions where the current is limited by the supply of photogenerated holes to the electrochemical interface. A noticeable contribution has been performed by Lehmann and Rönnebeck [18] who tried to extend to the p-Si case the generally admitted model accounting for macropore formation on n-Si, the so-called Lehmann's model [19] These authors assumed that in the case of p-Si, the electrode is under depletion conditions and that the silicon/electrolyte interface behaves as a Schottky diode. Since the approach is based on linear stability analysis, it has some intrinsic limitations in describing the pore development and propagation It has been refined by Chazalviel et al, who described the practical case where the electrochemical dissolution is under both charge transport and reaction rate control [22]. It appears that taking into account charge transport in the semiconductor and in the electrolyte is needed for accounting for pore formation but that new modeling tools need to be developed in order to account for the pore development and morphology
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