Analysis of p-Si macropore etching using FFT-impedance spectroscopy
© Ossei-Wusu et al.; licensee Springer. 2012
Received: 30 April 2012
Accepted: 20 June 2012
Published: 20 June 2012
The dependence of the etch mechanism of lithographically seeded macropores in low-doped p-type silicon on water and hydrofluoric acid (HF) concentrations has been investigated. Using different HF concentrations (prepared from 48 and 73 wt.% HF) in organic electrolytes, the pore morphologies of etched samples have been related to in situ impedance spectra (IS) obtained by Fast Fourier Transform (FFT) technique. It will be shown that most of the data can be fitted with a simple equivalent circuit model. The model predicts that the HF concentration is responsible for the net silicon dissolution rate, while the dissolution rate selectivity at the pore tips and walls that ultimately enables pore etching depends on the water content. The ‘quality’ of the pores increases with decreasing water content in HF/organic electrolytes.
The formation of macropores in silicon was first discovered by Lehmann and Föll in the 1990s ; macropores in this case were etched into n-type silicon under backside illumination using HF/aqueous electrolytes. They came up with a model (usually referred to as the Lehmann model) that essentially relied on the geometry of the space charge region to explain pore formation. The model is only applicable to n-type silicon, and it took almost half a decade before Propst and Kohl succeeded for the first time in etching macropores in p-type silicon (with rather ‘bad’ pore morphologies) using acetonitrile as a base for an almost water-free electrolyte . Since then, the use of electrolytes based on organic solvents such as dimethylformamide (DMF), dimethylacetamide (DMA), dimethyl sulfoxide, and ethanol have been shown to enable macropore etching in p-type silicon, and several models emerged dealing with this. For example, Ponomarev and Lévy-Clément [3, 4] attempted to correlate the etching of macropores in p-type Si to a covering (and thus passivation) of the pore walls by the organic molecules, whereas Wehrspohn et al. emphasized differential current flow based on the resistivity of the wafer and the electrolytes and even reported the first p-macropores etched by using aqueous electrolytes . In 2000, Christophersen et al. proposed H-termination as the passivation mechanism of the pore walls . Meanwhile, it was shown that lithographically pre-structuring the sample has a major influence on the ease of macropore etching in p-type substrates and the quality of the pores (far more pronounced than in n-type substrates) [7–10]. Not much data seem to exist about the role of the HF concentration in p-macropore formation.
In this investigation, emphasis was placed on the effect of the HF and water concentrations while using organic solvents as major ingredient of the electrolytes. The different morphologies of the pores etched, as well as the importance on the dissociation rate of HF in the solvents, will be reported. FFT impedance spectra, which were taken in situ every 2 s, were analyzed and compared to the final pore morphologies.
HF and water concentrations in the various electrolytes used
2.5 wt.% HF
5 wt.% HF
7.5 wt.% HF
10 wt.% HF
Concentrations are always given in weight percent so that differences in the densities of the organic electrolytes were not relevant. The experiments with DMA 2.5%(x) electrolytes always produced rather ‘bad’ pore morphologies and were therefore ignored.
While the use of these organic solvents is not new in the electrochemistry of silicon [2, 3, 8, 12, 13], in this work, we used only newly prepared electrolyte to perform the experiments, and the volume of the organic solvents used for each preparation was the same (190 ml) for all the experiments, ensuring comparable residual contents of water. The pores were etched for 30 min with a constant current density of j = 10 mA/cm2. In situ FFT-IS measurements were performed every 2 s; recording a spectrum took 1 s. The IS employed 24 frequencies in a range of 5 Hz to 20 kHz. All spectra could be fitted quite well by a simple equivalent circuit consisting of one series resistance in series with three circuits with a resistor parallel to a capacitor (RpCp components). Thus, there are seven independent R/C parameters, and these parameters were extracted in situ. From these parameters, three time-constant τ = RC that were also displayed in situ could be constructed. To the best of our knowledge, this is thus the first investigation of p-macropores where relevant data other than currents and potentials were obtained during etching. A detailed description of the model and procedures with respect to in situ FFT impedance are described in [14–16]. A fully integrated laboratory etching system of ET&TE GmbH (Kiel, Germany) controlled all parameters of the etching procedure. The pore morphologies were examined by a scanning electronic microscope and were compared with the FFT-IS measurements for further analysis.
Pore morphology and geometry
On the other hand, maintaining the HF/water concentration at 10%(11%) and repeating the experiment using DMA as a solvent, the etched pores had much smoother pore walls (Figure 1c) similar to those etched with DMF 5%(5.4%) (Figure 1a) but were shorter in length (around 40 μm) and slightly bigger in diameter (around 1.7 μm). Further, the morphology of the pores etched using DMA 10%(3.8%) shown in Figure 1d was nearly identical to that of the pores etched with DMF 5%(5.4%) in Figure 1a. This shows that both the HF concentration and the water content are important for the pore formation. For almost the same water content, DMA needs approximately double the HF concentration in comparison to DMF to produce the same pore structure. We postulate that this is linked to the different dissociation rates of the HF in the solvents, which is well known to have a big impact on the pore etching [13, 17]. It should be mentioned that pores etched with DMA 5%(5.4%) electrolyte had smooth walls but shorter lengths (around 20 μm) and bigger diameters (around 2.2 μm) than those produced with DMA 10%(3.8%).
Pore etching is a very complicated process in which all the parameters involved should be in their optimal regime to produce comparable results. Pore formation mechanisms, which have been studied in detail by many authors [1, 2, 18–20], take into consideration the nucleation of the pores, oxide formation and dissolution, diffusion limitations and thus local changes of, e.g., the HF concentration as the pores get longer, current flow at the pore tips related to local field strengths, the leakage current (current that flows in the dark) through the pore walls, the selectivity of the hydrogen (H2) passivation of the pore walls and tips, and much more.
Detailed descriptions of the importance of doping concentration, lithography pre-structuring KOH etch pits, and the kind of solvent can be found in [8, 9, 21–25]. None of the models, however, has anything to say on the impedance underlying the etching process. Here, we will limit the discussion to the data presented, except to point out that, without the seeded nucleation, no good pores would have been obtained in most cases and that most of the models mentioned above do not consider the influence of nucleation on pores.
DMF 5%(5.4%) and DMA 10%(3.8%) produced nearly identical pores as far as morphologies are concerned. This most likely indicates that the dissociation rate of HF in a particular solvent is an (obviously) important parameter, which has impact on the pore formation (as it has also been mentioned by [13, 17]). If, for the time being, one accepts this as the reason for the difference between the solvents, it follows that the HF dissociation in DMA should be smaller than in DMF.
In this paper, we will only address some more general features, which can be extracted from the FFT impedance data shown in Figure 5. Most astonishing is the result shown in Figure 5h; the sum of the transfer resistances Rp2 and Rp3 is constant and thus independent of the water concentration (and of the HF concentration). Although the reason for this is not clear, it cannot be treated as a trivial or self-explaining result. Like in the case of energy conservation, system parameters that do not change but are conserved hint at fundamental properties of a system. Here, the sum of the two transfer resistances that are related to the large time constants τ2 and τ3 (i.e., the slow processes) stays constant. To some extent, this can be seen as a necessity for etching ‘good’ macropores in p-Si since constancy of Rp2 + Rp3 is not a general feature of macropore formation. Many experiments that produce only ‘bad’ pores do not show this effect. This indicates strongly that the slow processes related to the large time constants are essential for the formation of good macropores in p-Si. Comparing Figure 5a and Figure 5e or Figure 5b and Figure 5f, respectively, the two large time constants show a simple dependence on the water concentration (two straight lines), while the relation to the HF concentration is not that clear. Thus, it is probably the water concentration which has the most direct impact on the two slow processes.
Comparing Figure 5c and Figure 5g, the transfer resistance Rp3 depends linearly on the HF concentration, while two straight lines are found as a function of water concentration, so in contrast to the time constants, the transfer resistances depend mainly on the HF concentration. The sum of the three transfer resistances just describes the linear response in the steady state (i.e., ω ≥ 0); in other words, the amount of silicon etched away depends, as clearly expected, mainly on the HF concentration. In contrast, the pore quality depends decisively on the water concentration. High pore quality is achieved if etching proceeds only at pore tips and not at the pore walls; the results thus give strong indications that, for p-Si, the water concentration in the organic solvent has a strong impact on the passivation of the pore walls. The results shown in Figure 2 may be seen as a direct check of this statement. Although the electrolyte DMF 5%(5.4%) allows for very good pore formation when etching for 30 min, reaching a pore depth of 50 μm, strong differences in using DMF 5%(1.5%) are found when etching for much longer times (540 min), reaching pore depths of 450 and 520 μm, respectively. The insets show the large differences especially in the morphology of the pore walls. In the experiment using higher water concentration, the walls are rougher close to the pore tips, and close to the top, the pore walls are nearly destroyed, while for DMF 5%(1.5%), the pore walls are much more stable and smoother.
It has been demonstrated that the HF concentration and the water content of DMA- and DMF-based electrolytes are essential for the quality of macropores etched into lithographically pre-structured low-doped p-type silicon. The achievable pore lengths, pore diameters, and the pore wall smoothness depend on both parameters (and the solvent). From in situ impedance data, it can be concluded that the HF concentration is mainly responsible for the volume of silicon dissolved, while the water content is instrumental for the selectivity of the etching between pore tips and walls. The water content is thus instrumental for the pore wall stability and, therefore, the maximum achievable lengths of the pores.
The authors thank the FhG ISIT for the silicon wafers used in this work. We also express our sincere appreciation to Dr. E. Quiroga-González, J. Bahr, and Mrs. K. Brandenburg for the lithographical structuring of the wafers, fruitful discussions, and technical help.
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