The mechanism of galvanic/metal-assisted etching of silicon
© Kolasinski; licensee Springer. 2014
Received: 16 May 2014
Accepted: 29 July 2014
Published: 26 August 2014
Metal-assisted etching is initiated by hole injection from an oxidant catalyzed by a metal nanoparticle or film on a Si surface. It is shown that the electronic structure of the metal/Si interface, i.e., band bending, is not conducive to diffusion of the injected hole away from the metal in the case of Ag or away from the metal/Si interface in the cases of Au, Pd, and Pt. Since holes do not diffuse away from the metals, the electric field resulting from charging of the metal after hole injection must instead be the cause of metal-assisted etching.
Electroless etching of silicon induced by an oxidant in acidic fluoride solutions was first described by Fuller and Ditzenberger , Turner , and Archer  in a regime that produces nanocrystalline porous silicon. These porous films exhibit colors induced by white light interference effects and scattering; hence, they were called stain films and the process stain etching. Kolasinski [4–6] has recently unambiguously demonstrated that hole injection into the Si valence band initiates etching and is the rate-determining step in the overall etch process. Furthermore, the connection of hole injection to the electronic structure of Si is what leads to the inherently self-limiting nature of stain etching that produces nanostructures. This is because quantum confinement leads to a downward shift in the valence band when Si features drop below approximately 2 nm in a critical dimension. The downward shift of the valence band with decreasing feature size decreases the rate of hole injection into the pore walls of the porous film, which effectively passivates the walls toward further electroless etching.
Two extremely versatile variations on stain etching have gained considerable interest because they are capable of producing not only patterned films within Si devices but also ordered arrays of pores or nanowires [7, 8]. The first process is called galvanic etching. It was demonstrated in a controlled manner by Kelly and co-workers [9–12]. In galvanic etching, a planar metal film is deposited on a wafer (either on the front face or on the back face). Upon exposure of the wafer to an oxidant + HF solution, the metal catalyzes hole injection from the oxidant. The second process is metal-assisted etching. Li and Bohn  recognized that the presence of metal localizes etching to the vicinity of the metal. Therefore, if well-spaced metal nanoparticles are used as a catalyst, pores can be etched. If a metal film with an array of openings is deposited, the substrate beneath the metal is etched with the unetched Si beneath the openings being left as nanowires with roughly the same size as the openings.
The purposes of this report are to demonstrate that the mechanism proposed in the literature to explain both galvanic and metal-assisted etching is incorrect and to propose a new one on the basis of an understanding of the band structure of the system.
The mechanism proposed in the literature [7, 12, 13] to explain galvanic and metal-assisted etching is analogous to stain etching. In stain etching, a hole is injected directly into the Si valence band wherever the oxidant collides with the surface. Direct measurements of etch rates and comparison to Marcus theory demonstrated  that each hole injected is used to etch one Si atom. Because of the random nature of oxidant/surface collisions, optimized stain etching produces thin films of porous Si (por-Si) with randomized pores but uniform lateral porosity (porosity gradients from top to bottom of the film are observed for thick films). In contrast, metal-assisted etching is concentrated on the region of the metal/Si interface.
There are, however, several problems with the literature model of metal-assisted etching. First, as shown in many reports [7, 8], the pore left by the etch track of a metal nanoparticle is usually surrounded by a microporous region. Within the literature model, this is ascribed to holes diffusing into the Si away from the metal. Second, if holes are produced at the metal/Si interface - which lies at the bottom of the metal nanoparticle not exposed to the solution - how is the HF solution transported there to facilitate etching? Third, why does the hole leave the metal since the Fermi level lies above the bulk Si valence band?
The transport of holes is determined by the band structure of the metal/Si interface. Hot holes injected far below EF will relax to EF in less than a femtosecond. At the Fermi velocity, this means that they can travel no more than a few nanometers before they cool to the top of the band. In any case, according to Marcus theory, the majority of holes are injected at EF. Thus, we need not consider hot hole transport. Below, we will show that an approximate calculation of the electronic structure at the metal/Si interface using the Schottky-Mott relationships [14, 15] does not support the idea of hole diffusion away from the metal/Si interface. Instead, the charge stays on the metal nanoparticle, which generates an electric field. The charged metal then effectively acts like a localized power supply that induces anodic etching.
Etching was performed on (1) Si(100) 0 to 100 Ω cm p-type test grade wafers, (2) Si(111) mechanical grade n-type wafers (both University Wafer, Boston, MA, USA), or (3) unpolished single crystal reclaimed wafer chunks (Union Carbide Corporation, Houston, TX, USA). Chunks were sieved to obtain a narrow size distribution (3.35 to 4.75 mm). The sample size was large enough (approximately 2 g) to ensure constant initial surface area. The silicon was cleaned by ultrasonication in acetone then ethanol followed by rinsing in water. After etching, samples were rinsed in water and ethanol, then dried in a stream of Ar gas. V2O5 (Fisher certified grade (Thermo Fisher Scientific, Waltham, MA, USA)), HOOH (EMD Chemical (Gibbstown, NJ, USA), 30% solution in water), and HF (JT Baker (Phillipsburg, NJ, USA), 49% analytical grade) were used to create stain etchants. Metal deposition was performed galvanically by adding a few drops of 0.1 to 1 mM metal salt solution to HF, resulting in metal coverage of about 5% of the Si surface. The Si wafers with metal deposits were then transferred directly to the stain etchant with a droplet of deposition solution covering the wafer. In this manner, the H-terminated surface and the deposited metal nanoparticles were never exposed to the atmosphere and potential contamination. Aqueous salt solutions used for deposition include PdCl2 (Sigma-Aldrich (St. Louis, MO, USA), reagent plus, 99%), AgNO3 (ACS certified, >99.7%), H2PtCl6 (EMD Chemical, 10% (w/w) solution), and CuCl (Allied Chemical (Morristown, NJ, USA), reagent grade 98%).
Results and discussion
where ni is the intrinsic density of donors in Si, nD is the donor density in n-type Si and nA is the acceptor density in p-type Si. From the work of Novikov , the value of the intrinsic work function can be obtained, E i = 4.78 ± 0.08 eV. The intrinsic donor density is ni = 1.08 × 1010 cm-3 at 300 K . Here, I use typical donor densities of nD = 1 × 1015 cm-3, which corresponds to 5 Ω cm, and nA = 1 × 1015 cm-3, which corresponds to 14 Ω cm. Accordingly, EF - E i = 0.296 eV on n-type Si and E i - EF = 0.296 eV on p-type Si. The doping density is not critical as changing the values from 1014 cm-3 to 1016 cm-3 will only change EF - E i by ±0.06 eV, i.e., less than the uncertainty in Ei.
Work function Φ , experimental Schottky barrier on n -type Si , calculated Schottky barriers, and , and standard electrochemical potential E°
Three other commonly used metals for metal-assisted etching, all of which can be deposited by galvanic displacement deposition from solution, are Au, Pt, and Pd. These are all high work function metals compared to Si. In all three cases, the bands bend upward.
As discussed by Tung , the Schottky-Mott relationships are an approximation to the true Schottky barrier height because the presence of surface states, reconstructions, or lack of an abrupt interface can lead to lower values. This is corroborated by comparison of the experimental values on n-type Si to the calculated values in Table 1. The values for Ag are close to the ideal value. In all other cases, interfacial chemical and structural changes reduce the barriers below the ideal values. However, the shape of the band bending is always correctly predicted by the Schottky-Mott relations. Therefore, they can be used to characterize the qualitative shape of the bands at the interface, and deviations from ideal character will not be important for hole injection into the valence band as discussed below.
It is not the Schottky barrier itself that is of interest; rather, it is band bending and the energy of the Si valance band at the interface that are important. This is because a hole must be transferred from the metal to the Si valence band to induce etching. The Schottky-Mott analysis allows us to calculate the energy of the Si valence band maximum at the interface, which is labeled E in Figures 1 and 2. Holes naturally relax to the highest available energy in a band, whereas electrons relax to the lowest energy in the band. The definition of the Schottky barrier height is the energy required to move a charge carrier from the metal to the Si interface; however, the carrier changes from p-type to n-type Si. On p-type material, the Schottky barrier height is the energy required to move a hole from the metal to the Si valence band at the interface. Therefore, the Schottky barrier height is the same as the energy of the Si valence band maximum at the interface. On n-type material, the Schottky barrier height is the energy required to move a hole from the Si conduction band at the interface to the metal. This value is not directly relevant to the discussion of etching. Rather, it is again the energy of the Si valence band maximum at the interface E that is required. A nonideal interface may introduce gap states between the conduction and valence bands, which affects the Schottky barrier height. However, the introduction of gap states does not change E. Therefore, any inaccuracies in the Schottky-Mott relationships will not change the direction of band bending and should not affect the conclusions of the model presented here.
Figures 1 and 2 show that Ag is clearly different than all other metals. Holes injected into Ag are more stable in Ag than they are either in Si or at the Ag/Si interface. In the three other cases, holes injected into the metal should immediately move to the metal/Si interface where band bending will hold them. Therefore there should not be any diffusion of holes away from the metal particles in any case and Ag cannot inject holes into Si. Nonetheless, metal induced etching is observed for all four of these metals and etching is observed away from this interface as evidenced by photoluminescent por-Si formation surrounding the metal nanoparticle. These observations call for an alternative mechanism to explain etching.
I propose that rather than thinking of the metal particles as sources of holes, they should be thought of in terms of charged particles with some density of holes injected by the oxidizing agent. The charge they hold creates an electric field in their vicinity. The potential difference induced by this electric field will change the hole density in the region around the nanoparticles including regions far from the nanoparticle just as would the application of a bias at a nanoelectrode. With a sufficiently large field, the hole density can be raised in the surrounding area sufficiently to facilitate electrochemical etching or even electropolishing, just as in anodic etching when the entire sample rather than just a local portion of the sample is biased.
Using the methods we previously developed  to determine the stoichiometry in stain etching without a metal catalyst, we have found that the stoichiometry of both hole injection and H2 production vary for the four different metals shown here. We have shown that stain etching was dominated by a valence 2 process . The observation of strong visible photoluminescence was confirmation of the production of nanocrystalline nanoporous Si. Metal-assisted etching using VO2+ as the oxidant in the presence of a few percent of a monolayer of Ag or Au nanoparticles exhibited the same stoichiometry. In the presence of Pt, a valence 4 process dominated, which led to rapid production of photoluminescent nanoporous Si. Pd acted much differently. Whereas none of the other metals induced etching in the absence of VO2+, consistent with prior reports , we found that etching at a very slow rate begins in the presence of Pd even in the absence of VO2+. In addition, whereas the rate follows steady first-order kinetics with respect to VO2+ consumption, just like all the other metals and stain etching in the absence of metals, neither H2 production nor the valence of etching is constant for Pd. Etching in the presence of Pd is at first dominated by electropolishing and then proceeded by a mixture of electropolishing and valence 2 porous Si production. In all four cases, the rate of etching in the presence of a metal is significantly faster than for stain etching, i.e., the metal nanoparticles catalyze the injection of holes compared to the rate at a bare Si surface. Preliminary results  on the stoichiometry of metal-assisted etching have been reported, with a detailed report to follow (Kolasinski KW, Barclay WB, Sun Y, Aindow M: The stoichiometry of metal assisted etching of Si in V2O5 + HF and HOOH + HF solutions. In preparation).
The mechanism of metal-assisted etching
We need to explain the production of an etch track that is very close to the size of the metal particle and the formation of porous Si remote from the particle. From the results of anodic etching [6, 24, 25], it is well known that there are three electrochemical pathways for Si etching: (1) current doubling (valence 2 process), which leads to the formation of visibly photoluminescent nanoporous Si, (2) current quadrupling (valence 4 process), which leads to visibly photoluminescent nanoporous Si, and (3) electrochemical oxide formation (valence 4 process) followed by chemical removal of the oxide by HF(aq), which leads to electropolishing. Electropolishing occurs above a critical voltage/current density, which can be related to a nonlinearity introduced by water dissociation, which is a precursor to oxide formation . When concentrations and voltages are appropriately adjusted, etching on the edge of the electropolishing regime can lead to current oscillations caused by competition between oxide formation and the various etching processes [26–28].
Our results indicate that stain etching  as well as etching in the presence of Ag and Au  are dominated by the current doubling pathway. Etching in the presence of Pt is dominated by the current quadrupling pathway. In contrast, the initial lack of nanoporous Si in the presence of Pd indicates that etching is dominated by electropolishing, though it is subsequently accompanied by current doubling etching.
The band structure of the metal/Si interface does not facilitate the diffusion of charge away from a metal after an oxidant has injected a hole into the metal. Therefore, the holes injected into the metal are not directly available to induce etching in Si. It is proposed here that the catalytic injection of holes by an oxidant in solution to a metal (film or nanoparticle) in metal-assisted etching (MAE) leads to a steady state charge imbalance in the metal. This excess charge induces an electric field in the vicinity of the metal and biases the surrounding Si. Close to the metal, the potential is raised sufficiently to induce etching with electropolishing character. Further away from the metal, the potential is sufficient to induce etching that leads to the formation of porous silicon by either a valence 2 or valence 4 process. The balance between valence 2 etching, valence 4 etching, and electropolishing varies depending on the chemical identity of the metal.
KWK is a Professor of Chemistry as well as a Chartered Chemist (Royal Society of Chemistry) with a Ph.D. in Chemical Physics from Stanford University and a B.S. in Chemistry from the University of Pittsburgh.
Experiments concerning the stoichiometry of metal-assisted etching to be reported elsewhere were performed together with William B. Barclay, now at the University of Maine. Electron microscopy in support of these experiments was performed with Yu Sun and Mark Aindow at the University of Connecticut. KWK would like to thank Stéphane Bastide, Institut Chimie et Matériaux Paris-Est, CNRS for a stimulating discussion that motivated these calculations. This work has been supported by West Chester University.
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