Multiphysics simulation accelerates the development of electrochemical etching
JENNIFER A. SEGUI, COMSOL, Inc., Burlington, MA.
A team of researchers from Germany use multiphysics simulation to elucidate the impact of important process variables in the electrochemical etching of silicon and make progress toward the integration of the process for commercial applications.
Electrochemical etching, also referred to as anodization, represents a flexible process that is used to produce well-controlled three-dimensional structures in silicon. There are many variables that affect the etching process and therefore complicate the integration of the technique into mass production. In their work, Alexey Ivanov of Furtwangen University, Ulrich Mescheder of Furtwangen University, and Peter Woias of the University of Freiburg-IMTEK (all located in Germany) are developing an approach to further understand the electrochemical etching of silicon through the use of multiphysics simulation. Their work can ultimately facilitate the efficient integration of electrochemical etching into large-scale silicon wafer process. In correspondence with Alexey Ivanov, he explains that the "???process has some properties, such as high surface quality and electrically controlled formation of 3D forms, which make this process unique for some applications where other micro structuring techniques are not applicable."
Two specific modes of operation for the electrochemical etching of silicon in hydrofluoric acid (HF) have been identified that are particularly relevant to industry-scale process. These modes, depicted in FIGURE 1, are selected through control of the electrical current density and electrolyte solution concentration governing the electrochemical reaction. In the first mode, a low current density and high concentration solution result in an electrical current dominated process that creates a porous silicon layer. This porous silicon can be incorporated as a micro-channel filter in microfluidics, according to Ivanov.
|FIGURE 1. Two modes of electrochemical etching of silicon wafer include (a) porous silicon formation and (b) electropolishing.|
The second mode of operation is achieved through application of a high current density and low concentration solution where the result is a diffusion controlled electropolishing process. The electropolishing of silicon using this technique creates surfaces with roughness on the order of nanometers enabling its use in the most demanding optics and microfluidics applications as shown in FIGURE 2.
|FIGURE 2. Smooth and well-controlled electrochemical etching of a silicon wafer to produce a master mold for polycarbonate optical lenses.|
Parameters that affect the resulting etch forms in silicon include the electrolyte concentration and temperature, silicon substrate dopant type and concentration, magnitude of applied current, and mask opening dimensions. In this article, we further explain the electrochemical etch process and mechanism, etch form development particularly for the two primary modes of operation, and the use of multiphysics simulation to better understand the impact of each parameter on the etching process.
Electrochemical etching of silicon
The electrochemical etching of silicon is performed using an HF-ethanol electrolyte solution. A silicon substrate with insulating stress-free silicon nitride (SiNx) layer on the front side is submerged into an HF-stable tank containing the electrolyte solution and two platinum electrodes as shown in Fig. 1. A positive electric potential is applied to the anode while the cathode remains grounded. The SiNx layer on the front side of the silicon substrate serves as a mask or template to guide the formation of structures during the etch process. For clarity, we explain the process and mechanism of electrochemical etching for p-type silicon (10-20 Ohm??cm, (100)-Si, and ~ 520??m thickness), however, the technique can also be modified for use on other substrate types. For p-type silicon of this low resistivity, the back side of the wafer should be highly doped in order to form an ohmic contact with the electrolyte.
At low current density (low supply of holes) and high HF concentration (high supply of fluoride-ions) silicon atoms are directly dissolved with consumption of two holes per silicon atom (e.g. with a reaction valence of 2):
In this mode, silicon atoms are dissolved selectively from the substrate producing pores of various shapes that are etched into the silicon. The skeleton of porous silicon remains crystalline.
At higher current densities (higher supply of holes from silicon) and lower HF concentration in the electrolyte (lower supply of fluoride-ions), the mechanism of silicon dissolution has two steps. In the first step, anodic oxidation takes place under the supply of four holes per silicon atom:
The second step runs without consumption of positive charge from the substrate and consists of silicon dioxide dissolution in HF:
Thus, dissolution of silicon in electropolishing mode runs with a reaction valence of 4.
The current flow through a p-type silicon (p- Si) sample with front side SiNx masking layer is shown schematically in FIGURE 3A. In the beginning of the process, there is a higher etch rate near the edges of the mask, and a so-called edge-effect (convex) shape is observed as indicated in Figure 3b. Etch form transformation from convex to concave, in Figure 3c, has been observed in the experiments for longer etching times.
|FIGURE 3. Etch form development during the electrochemical etching of silicon: (a) schematic cross-section of a silicon sample, arrows represent current flow, (b,c) profile of structure etched through a 600 ??m circular opening in a SiNx masing layer in 30 wt% HF at 2.5 A/cm2 for (b) t = 1 min and (c) t = 10 min; measured with a stylus profilometer; straight regions on both sides of the concave profile are measurement artifacts.|
Two mechanisms are proposed to explain shape development. First, the specific current density distribution in silicon leads to the formation of a convex shape at the beginning of the process. The current is more concentrated at the edge when compared with the center of the structure. Etching deeper into the substrate will lead to formation of a more concave shape assuming that the conductivity of the electrolyte and substrate are similar.
Additionally, the shape conversion can be assisted by ionic transport in the electrolyte for the particular case of a diffusion-controlled etching process. The resulting concentration of reacting ions is then critically dependent on geometric parameters such as mask thickness and opening size. The ion concentration will change during etching and will convert the etch shape from convex to concave (isotropic). This is a well-known phenomenon in wet chemical etching.
Simulation of the electrical and diffusion etch processes
The two mechanisms of shape transformation described in the previous section appear to play different roles in the etching process depending on the applied current and electrolyte concentration. As a first step on the way to a full model of the electrochemical etching process, Ivanov and his colleagues simulated the electrical and diffusion mechanisms separately. The respective models are presented in this section.
For both cases, the models have been simulated in 2D with axial symmetry. The geometry of the models consists of the computational domains shown in FIGURE 4d.
|FIGURE 4. Model geometry and demonstration of the moving mesh feature available in COMSOL Multiphysics. (a-c) Moving mesh front changing from convex to concave etch form as time lapses; (d) computational domains defined in the model including a predefined etch form as an initial condition that is necessary for the simulation to proceed.|
The movement of the etch front was implemented with the moving mesh feature demonstrated in Figures 4a-c, where the dynamic deformation of the interface between the silicon substrate and the "predefined etch form" is driven by the electrochemical reactions. A further enhancement of the simulation process for deep etch forms was achieved by applying the automatic remeshing feature. The simulation was performed in COMSOL Multiphysics.
The Electric Currents physics available in COMSOL Multiphysics has been applied to all domains for simulation of the current flow in the model. Etch front movement for two values of electrolyte conductivity were simulated. The parameters defined for the domains are summarized in Table 1. For the boundary between the initial etched region and the silicon substrate (etch front), a prescribed mesh velocity in cylindrical coordinates is defined by:
where jr and jz are the r and z components of the current density vector, and KE is a constant for the electrical model that takes into account the density of silicon and the reaction valence. If we assume electropolishing mode, i.e. no porous silicon formation, then:
where z is the reaction valence, e is the elementary charge, MSi is the molar mass of silicon, ??Si is the density of silicon and NA is the Avogadro constant. For the reaction valence of 4:
During simulation, an electric potential of 1 V was applied to the anode while the cathode was grounded.
|FIGURE 5. Resulting etch forms from the electrical models with low electrolyte conductivity and opening diameter in the masking layer of 200 ??m (left) and 1000 ??m (right).|
As an example, the resulting etch forms for opening diameters of 200 ??m and 1000 ??m in the SiNx masking layer are shown in FIGURE 5. Corresponding current and potential distributions for the models with an opening diameter of 1000 ??m are shown in FIGURE 6.
|FIGURE 6. Current density (left) and potential distribution (right) for the electrical model with the low conductivity electrolyte and mask opening diameter of 1000??m at the end of the process. Arrows on the current density plot represent current flow.|
For the electrical model, the researchers note that in the beginning of the process there is higher current density near the edges of the SiNx masking layer leading to the formation of the convex edge effect etch form. However, there is a discrepancy in the further development of the etch shapes. In the electrolyte with low conductivity, convex shapes transform into concave during the etching process as shown Figures 5 and 6. In the highly conductive electrolyte, however, deeper parts of the etch form near the edges of the opening lead to a further increase in current. This is due to a lower resistance in regions that are filled with highly conductive electrolyte and causes the edge effect to become self-amplifying.
The Transport of Diluted Species physics available in COMSOL Multiphysics interface has been applied to the simulation of diffusion in electrolytes.
The following parameters have been used in the model:
- initial electrolyte concentration
- diffusion coefficient for HF and HF2-
- reaction rate variable defined for the boundary between electrolyte and the silicon substrate for the 1st order reaction (where a reaction rate constant k = 1 m/s is assumed in order to provide a diffusion-controlled process)
For the boundary between the electrolyte and the silicon substrate domains (etch front), a prescribed mesh velocity is defined as follows:
Where nr and nz are normal vectors and KD is a constant for the diffusion model:
where m is a number of fluorine atoms needed for dissolution of one atom of silicon. In the electropolishing mode, six atoms of fluorine are required in the reaction of silicon dioxide dissolution. Then:
For the boundary between the electrolyte and the silicon substrate, an inward flux equal to -R has been defined. The concentration was fixed to c0 for the top, left, and right side boundaries of the electrolyte.
For all opening diameters in the SiNx masking layer, the formation of a convex shape in the beginning of the process with subsequent transformation to a concave shape was observed.
Due to diffusion limits, concave isotropic form is achieved when the distance from the opening in the masking layer to the etch front becomes comparable to the diameter of the opening. For opening diameters of 40??m and 800??m, concave form is observed at depths of 10.5??m and 276??m, respectively. Further supply of chemical species to the reaction site through the opening in the masking layer after this depth can be regarded as a point source that is equally distant from all the points in the etch front. This creates a uniform etch rate along the etch front.
The diffusion model is limited in scope in that it only considers diffusion transport in electrolytes. There are other transport phenomena in the process such as convection and drift and so their influence on etch form will need to be evaluated in further work.
The electrochemical etching of silicon in HF represents a versatile process that depends on many variables. The use of multiphysics simulation to investigate the impact of process variables will lead to a viable commercial process that is relevant for a range of substrate types and applications. This article is based on an article by A. Ivanov and U. Mescheder, "Dynamic Simulation of Electrochemical Etching of Silicon with COMSOL," presented at the COMSOL Conference 2012, October 10-12, 2012, Milan, Italy.
JENNIFER A. SEGUI is a technical Marketing Engineer, COMSOL, Inc., Burlington, MA.