'Wagon-wheel' mask as a tool to study anisotropy of porous silicon formation rate
© Astrova and Zharova; licensee Springer. 2012
Received: 5 May 2012
Accepted: 27 July 2012
Published: 27 July 2012
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© Astrova and Zharova; licensee Springer. 2012
Received: 5 May 2012
Accepted: 27 July 2012
Published: 27 July 2012
Relationship between the rate of electrochemical formation of mesoporous Si and the crystallographic directions has been studied by local anodization of wafers through a mask having the form of narrow long wedges radiating from the center in all directions (‘wagon-wheel’ mask). The etching rates were found from the side etching under the thin transparent n-Si mask. On p+-substrates of various orientation diagrams characterizing the distribution of pore formation rates over different directions in the wafer plane were constructed for the first time. The wagon-wheel method was applied to study the current dependence of the anisotropy. It was found that the orientation-related difference between the pore formation rates is 5% to 25%, depending on the crystallographic direction and the etching current density. At a current density of approximately 9 mA/cm2, the etching rates are related as V 100:V 113:V 110:V 112:V 111 = 1.000:0.900:0.836:0.824:0.750. A general tendency is observed toward weakening of the anisotropy with increasing current. The highest rate always corresponds to the <100 > direction, and the rate ratio between the other directions varies with increasing current, which leads to a change of their sequence.
Analysis of the pore formation rate in relation to a crystallographic direction is important both from the standpoint of fundamental science, for understanding the nature of the porous structure formation, and from the practical standpoint, for solving various technological tasks based on utilization of porous silicon (por-Si) [1–5] or for creating a birefringent optical medium based on nanostructured silicon [6, 7]. It is known that individual pores in meso-porous silicon form a dense array with a stable front propagating in the bulk of the crystal. Despite that individual pore channels in this array display strong anisotropy of their motion (microscopic anisotropy), the anisotropy in the propagation of the pore front (macroscopic anisotropy) is rather weak. Porous silicon has been intensively studied in the last two decades; however, the information about the macroscopic anisotropy of the electrochemical etching rate is scarce [8–12], and its quantitative characteristics are at all lacking. A possible reason is that no appropriate method of study has been developed so far. Recently, we suggested the method of local anodization of p-Si wafers through a mask in the form of narrow long wedges radiating from the center in all directions (‘wagon-wheel’ mask) , previously used to examine only the chemical etching anisotropy for Si in alkaline solutions [14, 15]. The under-etching for this mask depends on the motion rate of the porous-layer boundary along different crystallographic directions lying in the sample plane and makes it possible to determine quantitative parameters of the anisotropy.
The present study is concerned with the anisotropy of pore formation in heavily doped (degenerate) p+-Si. The wagon-wheel procedure is used to construct diagrams of the etching rate distribution over different crystallographic directions, and the orientation dependence of the motion rate of the pore front is analyzed in relation to the etching current.
We used this potential shift to selectively form pores in differently doped areas.
The starting material in our experiments was p+-Si. (111), (100), and (110) wafers were cut from the same ingot doped with boron to a concentration of 2 × 1019 cm−3 (6 mΩ⋅cm). To form the mask for local anodization, we formed n-Si layers either by local diffusion of phosphorus at 1,100 °C (p-n junction depth x j = 3 μm) or by ion implantation (dose 5 × 1015 cm−2) with subsequent annealing (x j ≈ 1.4 μm). The surface concentration of phosphorus was N s = 1020 cm−3. The local doping with phosphorus was performed using thermally grown SiO2 film prepatterned by photolithography.
The wagon-wheel mask EA-3 had the form of 72 beams with an angular width Δθ = 2° radiating with a step θ = 5°. The beam length was 1 cm; the full anodization area, 3.14 cm2, of which the unmasked part constituted 60%, i.e., 1.88 cm2. The anodization was performed in a 1:1 HF-ethanol electrolyte in the galvanostatic mode at I = const for 7 to 120 min to a depth of approximately 50 μm. This corresponds to a change in the current density from j0 at the start (t = 0) to j f = 0.65 j0 by the end of the process. The anodization rate was found as V(θ) = w(θ)/t, where t is the etching duration. Experiments on the current dependence were performed with (110) wafers. In these experiments, the product I⋅t was kept constant. To enable reading of R(θ), the mask was provided with a scale whose divisions indicated the distance R from the mask center and the angle θ (see Figure 4a). The scale marks were formed by n-Si strips and points on the beams opened for anodization. To find the under-etch length for the mask produced by diffusion, we introduced a correction for the increase in the n-type beam width x due to the side diffusion of phosphorus, w c = w + x (see Figure 1b), where x = 0.8x j . In the case of ion implantation, this correction is negligible and can be disregarded.
It can be seen in Figure 2a that the upper part of the mask, heavily doped with phosphorous, becomes porous, with only the deeper part remaining intact. This agrees with inequality (1) when n+ is preferably etched. As soon as the etching front reaches n-Si, p+-Si substrate becomes predominantly etched. For this reason, the n-Si prevents anodization. The formation of the porous material from the upper layer of n+-Si results in upward-bent mask edges in Figure 2b, formed upon dissolution of porous silicon. The phosphorus concentration in the region of lateral diffusion beneath the oxide mask is lower than that in the opened window, and therefore, this part of n-Si at the mask edge was passivated under anodization. As for the layer ion-implanted with phosphorus, we found that it works upon a high temperature treatment at 1100 °C for 10 min, when the moderately doped n-Si becomes thick enough. Both masks are transparent to the visible light of the microscope. We found that the dark field mode is preferable.
Parameter A for different crystallographic orientations and etching currents
Two intersection points of the curves A(I) can be seen in Figure 8. The intersection of A111 and A110 means that at currents I < 350 mA the minimum anodization rate is observed for the <111 > direction, and at I > 350 mA for the <110 > direction. Near the second intersection point of the curves for A112 and A110 at I ≈ 40 mA, the motion rates of the pore front along the <112 > and <110 > directions become approximately the same, and anodization of Si (111) wafers in this mode yields a diagram on which preferred directions cannot be distinguished. Therefore, it was necessary to use a high etching current for recording an anisotropy on (111) wafers (see Figure 5a,d). The ratio between the rates V 110 and V 100 experiences the minimal variation over the whole range of currents under study. Therefore, the rate diagram for (100) wafers in the form of four petals could be obtained at all the currents.
It should be noted that, despite the simplicity and clarity, patterns of this kind are rather inconvenient for obtaining quantitative characteristics, especially in the case of a weak anisotropy. Similarly to the beveled edge in measurements of small depths, the wagon-wheel procedure makes it possible, by extending the pattern, to raise the measured value by a factor of several tens and to record small differences in w.
The observed macroscopic anisotropy results from certain morphology of porous silicon, which is, in turn, produced by anisotropic formation of separate pores in silicon on the microscopic level, when the reaction predominantly occurs at the pore tip. The situation can be roughly described as follows: individual pores possess preferred growth directions and form main channels with dead-end branches. Depending on the angle between the crystallographic axis and the preferred motion direction of the main channels, the ‘road’ in the general front propagation direction (along the electric field) is more or less ‘wandering.’ It is the shape of the trajectory of separate pores and their diameter that, in the end, determine the propagation rate of the pore front.
According to the existing concepts , the anisotropy must be manifested most clearly when the pore formation rate is limited to the greatest extent by the kinetics of the chemical reaction, i.e., at low currents. The dissolution rate of silicon depends on the strength of its bonds, which varies between different crystallographic planes [17, 18]. Direct silicon dissolution is known to demonstrate the most pronounced anisotropy . Our data confirm that, at all the currents, the highest etching rate V of p+-Si is characteristic of the <100 > directions, whereas the <111 > direction is the slowest only at low currents: V 111 < V 112 < V 110 < V 113 < V 100. The rates for the <112 > and <110 > axes swap places when the current was raised, and further increase in the current changes the slowest direction from <111 > to <110>. The general weakening of the anisotropy with increasing current density can be attributed to the increased role of oxidation and to growing importance of mass-transfer process inside pores.
The wagon-wheel method is an effective tool for studying the etching rate anisotropy for mesoporous silicon, which can determine etching rates simultaneously for numerous crystallographic directions. This method can be well performed with the role of a mask played by a thin layer of n-type silicon on a p-Si substrate. This mask can be easily fabricated by local diffusion or ion implantation of a donor impurity. A study of how the anodization rate depends on current at various orientations demonstrated that, on the whole, the macroscopic anisotropy with respect to the dominating rate along the <100 > direction becomes weaker with increasing current density, and the relative rates for different directions change places. At high currents, the <110 > direction becomes the slowest, instead of <111>, and the rate along <112 > starts to exceed that along <110 > already at not-too-high currents.
scanning electron microscopy.
The study was financially supported by the EU Programme FP/2007-2013 under grant agreement N 256762 and by an RF Presidential grant for Russian Scientific Schools, NSh - 3008.2012.2. The authors thank V.P. Ulin for the helpful discussions.
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