Kinetic Investigation on the Confined Etching System of n-Type

Article pubs.acs.org/JPCC

Kinetic Investigation on the Confined Etching System of n‑Type Gallium Arsenide by Scanning Electrochemical Microscopy Jie Zhang, Jingchun Jia, Lianhuan Han, Ye Yuan, Zhong-Qun Tian, Zhao-Wu Tian, and Dongping Zhan* State Key Laboratory for Physical Chemistry of Solid Surfaces and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China ABSTRACT: Confined etchant layer technique (CELT) has been proved an effective electrochemical microfabrication method for both 3D microstructures and a supersmooth surface. From a physical chemistry viewpoint, the confined etching system of n-GaAs includes an etchant generation reaction from Br− to Br2 (E) followed by two parallel reactions: the confining reaction between Br2 and L-cystine (C1), and the etching reaction between Br2 and n-GaAs (C2). In this paper, the homogeneous EC1 process is investigated first through the tip generation/substrate collection (TG/SC) mode of scanning electrochemical microscopy (SECM), and the reaction rate of C1 is determined as (8.0 ± 1.0) × 103 dm3 mol−1 s−1; second, the heterogeneous EC2 process is investigated through the feedback mode of SECM, and the reaction rate of C2 is determined as (3.2 ± 0.5) × 10−2 cm s−1; third, a deformed geometry finite element model is established to simulate the etching topography coupling E(C1∥C2) processes by using the obtained data. The theoretical profiles of pits etched at different concentrations of scavenger, L-cystine, are analyzed and compared with experimental results. This model allows the prediction of spatial resolution of CELT as a function of reaction rates of C1 and C2 but also of the concentration of scavenger.

1. INTRODUCTION Microfabrications are the cutting-edge technologies in modern manufacturing industries such as the ultralarge scale integration (ULSI),1 the microelectromechanical system (MEMS),2 precision optics3 and micro total analytical system (μTAS).4,5 Gallium arsenide (GaAs) is a direct band gap semiconductor with high saturated electron velocity and high electron mobility, which makes it widely used in microwave frequency integrated circuits, infrared light-emitting diodes,6 laser diodes,7 and solar cells.8 In the real GaAs devices, 3D microstructures have to be fabricated to perform special functions. Because the GaAs wafer is fragile, nanoimprint is not applicable. Further, direct writing techniques, e.g., laser beam writing, usually change the surface component and leave surface damage due to the applied high-power energy.9 Wet chemical etching is the most frequently adopted method to make a 3D microstructure on GaAs wafer.10,11 However, the microfabricating processes as well as the target shapes are difficult to control due to not only the isotropic etching processes but also the unknown chemical kinetics. Electrochemical techniques play important roles in microfabrications, which can work on fragile materials without surface damage.12−16 Cathodic deposition and anodic dissolution are employed to make 3D microstructures. However, the materials of the workpieces should be conductive and act usually as the working electrode. Therefore, these techniques do not work for semiconductors and insulates. Another approach is the localized chemical etching induced by electrochemical generation of etchant.12,17−19 Although scan© 2014 American Chemical Society

ning electrochemical microscopy (SECM) has been employed to perform localized etch, it is difficult to control the spatial resolution due to the lateral diffusion of electrogenerated etchant. To improve the spatial resolution of SECM micropatterning, Heinze’s group proposed a “chemical lens” technique in which ligands were used to shift the deposition potential of metal ions so that only the surviving metal ions can be reduced on the substrate.20−22 In this way even a metal wire thinner than the electrode size can be obtained. On the other hand, to improve the spatial resolution of SECM microimaging on the enzyme activity, Wittstock and Schuhmann employed catalase to consume the hydrogen peroxide produced by the interreaction between glucose and glucose oxidase.23 In 1992, Tian et al. proposed the confined etchant layer technique (CELT) in which scavengers were employed to compact the depletion layer of the electrogenerated etchant.24 Most importantly, the SECM tip electrode is replaced by a large-area mold with complex microstructure, which makes CELT a potential but accurate microfabrication method for mass production. Generally, CELT includes three basic chemical processes: the etchant is generated on the surface of the mold electrode (working electrode) through an electrochemical reaction, which can react with a scavenger in the electrolyte. Due to this subsequent coupling reaction, the diffusion distance of etchant is confined very close to the Received: June 6, 2014 Revised: July 22, 2014 Published: July 23, 2014 18604

dx.doi.org/10.1021/jp5056446 | J. Phys. Chem. C 2014, 118, 18604−18611

The Journal of Physical Chemistry C

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surface of mold electrode. This subsequent coupling reaction is termed as a confining reaction while the depletion layer of etchant is termed as the confined etchant layer (CEL). Finally, the mold electrode approaches the substrate to ensure the etching reaction occurs. Thus, the etching precision is controlled by the thickness of the CEL. In brief, the confined etching system is composed of an electrochemical reaction (E) followed by two parallel subsequent chemical reactions, i.e., the confining reaction (C1) and the etching reaction (C2). CELT has been proved a useful method not only for the 3Dmicrostructure fabrication on different materials, such as silicon, GaAs, metals, and alloys,25−29 but also for surface polish and planarization.30 Recently, we proposed an “electrochemical mechanical micromachining” method, in which a microelectrode tip was employed to perform cutting and milling processes.30 We also developed a leveling method for CELT microfabrication by determining the feedback current of the redox loop of Br2 between the platinum tip and the GaAs substrate.31 Different from traditional electrochemical microfabrications, CELT can work on different materials no matter the conductivity of the workpieces because it is actually a wet chemical etching method induced by in situ electrochemical modulations. To study the kinetic properties of a confined etching system, it is very important to evaluate, screen, and design the technical parameters of CELT processes. In this paper, scanning electrochemical microscopy (SECM) is employed to investigate the kinetic properties of the confined etching system of n-GaAs. SECM has been widely applied to the study of the interface etching kinetics32−34 and electrochemical reaction followed by a homogeneous catalytic process.35−39 Recently, SECM together with arbitrary Lagrange−Eulerian (ALE) simulation was employed to study the kinetics and topography of the etching process.40−42 However, these reports involve only the EC2 coupling systems. Here we present the kinetic investigations on the confined etching system, which is a E(C1∥C2) process: (1) Tip generation/substrate collection (TG/SC) mode is employed to investigate the homogeneous confining reaction between Br2 and L-cystine (EC1). The reaction rate of C1 is derived as (8.0 ± 1.0) × 103 dm3 mol−1 s−1. (2) Current feedback mode is adopted to investigate the localized heterogeneous etching reaction of n-GaAs by Br2. The reaction rate of C2 is determined as (3.2 ± 0.5) × 10−2 cm s−1. (3) A deformed geometry finite element model is proposed to simulate the E(C1∥C2) process by using the obtained kinetic rates. The simulation results are in harmonious accordance with the experimental results.

is the etching reaction (eq 3), and RSSR refers to L-cystine. The reactive rate constant of eq 2 and the net rate constant for bromine consumption in eq 3 are defined by K1 and K2, respectively. The reaction order of bromine and L-cystine in eq 2 is considered as 1. It should be noted that these reaction equations express the main processes with a consideration of the mass balance of the confined etching system. There might be some intermediate steps or side-reactions, such as the radical recombination (Br•) during the oxidation of Br− on Pt electrode,43−45 the possible reaction between Br2 and L-cystine related byproducts,46,47 and the removal of surface oxides (i.e., Ga2O3 and As2O3) by sulfuric acid.12,17 However, these can be negligible when determining “apparent” rate constants because, to some extent, they can be considered as a part of reactions 2 and 3. Furthermore, we have not observe a decrease of electrocatalytic current (EC1 processes) during the experiment, which indicates that the tip contamination can be ignored. In conclusion, the full reaction schemes could be simplified as a competition between two subsequent reactions C1 and C2. To study the kinetics of the EC1 process, we consider only the coupling case between eqs 1 and 2. For the TG/SC mode of SECM used herein, the time-dependent mass transport as well as the solution reactions in axisymmetric cylindrical coordinates are governed by ∂C Br− = DBr−∇2 C Br− + 10K1C Br2C L ‐ cystine ∂t

∂C Br2 ∂t

= DBr2∇2 C Br2 − 5K1C Br2C L ‐ cystine

∂C L ‐ cystine ∂t

(5)

= DL ‐ cystine∇2 C L ‐ cystine − K1C Br2C L ‐ cystine −3

2

(4)

(6)

−1

where C (mol cm ) and D (cm s ) represent the concentration and diffusion coefficient of species in solution, respectively. The geometry for finite element model is shown in Figure 1, where a is the radius of Pt wire; rsub is the radius of Pt substrate electrode; rglass is the radius of sealing glass outside the

2. THEORY AND SIMULATIONS The chemical processes happening in the confined etching system of n-GaAs can be simplified as follows, E: 16Br − → 8Br2 + 16e−

(1)

C1: 5Br2 + RSSR + 6H 2O → 2RSO3H + 10Br− + 10H+ K1

(2) Figure 1. Schematic diagram of the axisymmetric cylindrical geometry used for the simulation of E(C1∥C2) processes. The numbers in bold represent the boundary numbers as defined in the text. Boundary 3 represents the Pt substrate electrode in the TG/SC mode and the initial shape of n-GaAs substrate in the feedback mode. Boundaries I and II with dashed lines represent the cross-sectional profile of the pit in the deformed geometry model.

C2 : 3Br2 + GaAs + 3H 2O → Ga 3 + + AsO33 − + 6Br − + 6H+

K2

(3)

where E is the electrochemical reaction for the generation of etchant Br2 (eq 1), C1 is the confining reaction (eq 2) while C2 18605



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GaAs before etching, and h is the depth of the etched pits. The boundaries are defined the same as for TG/SC mode except the boundary 3 (heterogeneous etching of n-GaAs), which is defined by eqs 14 and 15. The commercial finite element package Comsol Multiphyisics 4.3b is used to simulate the E(C1∥C2) etching process. The arbitrary Lagrange−Eulerian (ALE) method has been successfully applied to model the removal or addition of material.48,49 Here we use the ALE method to simulate the development of domain during etching. The movement of boundaries was described as follows: boundaries 2, 4, 5, 6, and 7 are fixed, while boundary 1 is fixed in the R dimension but free to move in the Z dimension. For the movement of boundary 3, the tangential movement in the R dimension is fixed and the normal velocity to the n-GaAs surface in the Z dimension is defined as

Pt wire; and d is the distance between tip and substrate electrode. The simulations are carried out with RG = 2. The numbers represent the boundaries defined as follows. On the insulation/symmetry boundary 1, 4, and 5, there is no flux normal to the boundaries for all species, i, which is described by

∇Ci·n ⃗ = 0

(7)

where n⃗ is the inward unit vector normal to the surface and i represents Br−, Br2, and L-cystine. On boundary 2, the generation of Br2 on Pt tip electrode under diffusion-limited conditions is C Br− = 0,

C Br2 =

1 * C Br− , 2

∇C L ‐ cystine·n ⃗ = 0

(8)

−

where C*Br− is the bulk concentration of Br . Because L-cystine is electroinactive at the same potential, there is no flux normal to the tip surface for L-cystine. On boundary 3, the collection of Br2 on the Pt substrate electrode under diffusion-limited conditions is described by * −, C Br− = C Br

C Br2 = 0,

∇C L ‐ cystine·n ⃗ = 0

νZ = K 2C Br2 /ρ

ν GaAs Br2

where ρGaAs is the molar density of n-GaAs (ρGaAs = 3.71 × 104 mol m−3) and νBr2 is the stoichiometry of bromine (νBr2 = 3).

(9)

3. EXPERIMENTAL SECTION 3.1. Chemicals and Materials. Silicon doped gallium arsenide wafers were purchased from China Crystal Technologies Co., China. Before the etching, n-GaAs was rinsed with acetone and deionized water. All chemicals used in the experiments (KBr, H2SO4, L-cystine) are analytical grade or better and provided by Sinopharm Co., China. All aqueous solutions were prepared with deionized water (18.2 MΩ, MilliQ, Millipore Corp.). 3.2. Instrumentation and Procedures. The ultramicroelectrode (UME) was fabricated by sealing a Pt wire with 25-μm diameter (99.99%, Alfa Aesar) in a glass capillary under vacuum using a heating resister coil. The sealed Pt wire was connected to a copper wire using conductive silver epoxy. Then the UME was polished and sharpened to RG = 2. The true radius was characterized through steady-state voltammetry.50 SECM measurements were performed with a CHI 920c SECM workstation (CH Instruments Inc.). The counter electrode was a Pt wire while the reference electrode was an Ag/AgCl electrode with a saturated KCl aqueous solution. For the TG/SC mode, a Pt disk electrode with 500 μm diameter worked as the substrate electrode to collect the bromine, which was not scavenged by L-cystine. First, the tip was positioned at a precise distance from the substrate electrode through the purely diffusion-controlled positive approach curves in 5 mM KBr, 0.5 M H2SO4 solution. During positioning, the tip potential is held at 1.1 V to generate Br2 while the substrate potential is biased at 0.6 V to collect Br2. After positioning, the tip potential was scanned linearly from 0.6 to 1.4 V. Meanwhile, the substrate was held at 0.6 V to collect Br2 generated by the tip electrode. The currents across both tip and substrate were recorded at different tip−substrate distances by withdrawing the tip from the substrate. The same experiments were performed in 5 mM KBr, 0.5 M H2SO4 solution, with 2 mM and 5 mM L-cystine. The collection coefficient (η) was calculated by the current responses of the tip and substrate electrodes. For the feedback mode, n-GaAs was used as the substrate in 5 mM KBr, 0.5 M H2SO4. The approach curve based on oxygen reduction current was used to position the tip precisely. Then, the tip potential was biased at 1.1 V to generate Br2 and

On the boundary 6 and 7, the concentration of all species is equal to bulk solution, which is * −, C Br− = C Br

C Br2 = 0,

C L ‐ cystine = C L*‐ cystine

(10)

The tip and substrate currents are calculated by a

i tip =

∫0

isub =

∫0

nFD rsub

∂C Br− 2πR dR , n = 1 ∂Z

nFD

∂C Br− 2πR dR , n = 1 ∂Z

(11)

(12)

The normalized current is defined by itip/i∞ and isub/i∞ where i∞ = 4.43nFDBr−aC*Br− for RG with 2.20 The collection coefficient (η) is defined by η = isub/itip. Now discuss the kinetics of the coupling EC2 process between eqs 1 and 3. The heterogeneous etching of Br2 on nGaAs is considered to be a first-order reaction process. For the current feedback mode of SECM used herein, the timedependent mass transport for axisymmetric cylindrical coordinates is governed by

∂C i = Di ∇2 C i ∂t

(16)

(13) −

where i represents Br and Br2. The geometry of the finite element model is the same with TG/SC mode (Figure 1) except that the Pt substrate is replaced by a n-GaAs substrate. The boundaries are also defined the same as TG/SC mode except the boundary 3. As for boundary 3, the interfacial etching of n-GaAs is described by −DBr2∇C Br2·n ⃗ = K 2C Br2

(14)

−DBr−∇C Br−·n ⃗ = −2K 2C Br2

(15)

Finally in the case of the E(C1∥C2) processes, a deformed geometry condition is introduced. The time-dependent mass transport is defined by eqs 4, 5, and 6. The finite element model involving a deformed geometry is the same as the feedback mode (Figure 1) except the dotted lines I and II, which represent the geometric profile of etched n-GaAs substrate. d represents the distance between the tip and n18606



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Figure 2. SECM characterization of the EC1 process. (A) Linear sweep voltammograms at 25-μm-diameter Pt UME with a scan rate of 50 mV s−1. (B) TG/SC voltammograms obtained with different tip/substrate separation. The tip potential was scanning from 0.6 to 1.4 V (vs Ag/AgCl) to generate Br2. Meanwhile the substrate electrode (500 μm diameter) was biased at 0.6 V (vs Ag/AgCl) to collect Br2. (C) Current feedback curves of the substrate electrode in the TG/SC mode. (D) The TG/SC collection efficiency as a function of log(d/a). For (B), the solution contained 5 mM KBr, 0.5 M H2SO4, and 2 mM L-cystine; for the others, the solutions contained 5 mM KBr, 0.5 M H2SO4, and 0 mM L-cystine (curve 1), 2 mM Lcystine (curve 2), and 5 mM L-cystine (curve 3). The solution represented by curve 4 contained 5 mM L-cystine and 0.5 M H2SO4. The solid lines are experimental results, and the symbols represent simulation results.

electrochemical oxidation of L-cystine alone is 1.47 nA at 1.1 V (curve 4). Compared with the catalytic current of the EC1 process, the direct oxidation of L-cystine at the electrode/ solution interface can be neglected. It is reasonable, in the TG/ SC mode, to hold the tip potential at 1.1 V to generate Br2 and to hold the substrate potential at 0.6 V to collect Br2. Typical TG/SC voltammograms obtained in an aqueous solution containing 5 mM KBr, 0.5 M H2SO4, and 2 mM Lcystine with different tip−substrate distances are shown in Figure 2B. Both tip and substrate electrodes present welldefined steady-state current plateaus. The high collection efficiency makes the TG/SC mode qualified for the study of the coupling EC process. In the absence of L-cystine, the η is almost to 100% at the range of d < 2a. Due to the competition of eq 2, the tip current decreased to the steady-state current obtained in the bulk solution while the substrate current decreased to almost zero dramatically when the normalized distance between tip and substrate is larger than 2 (i.e., d/a > 2). By extracting the substrate current at 1.1 V with different tip−substrate distances in Figure 2B, we can get the feedback curves of the substrate electrode. Figure 2C shows the current feedback curves of the substrate electrode at different concentrations of L-cystine. The tip−substrate distance, within which the substrate electrode can capture Br2, was shortened with increasing concentration of L-cystine (Figure 2C). The results indicated that the thickness of CEL is compressed

approached the n-GaAs substrate to obtain the positive feedback current. No external potential was applied to the nGaAs substrate. The positive feedback was caused by the subsequent chemical etching reaction between Br2 and n-GaAs. A series of pits were etched on n-GaAs to identify the simulation results predicted by the deformed geometry model. To induce the etching process, the tip−substrate distance was fixed at 3 μm. Meanwhile, the tip potential was held at 1.1 V to generate Br2. The etching experiments on the n-GaAs surface were performed in the presence of 0 mM, 20 mM, and 40 mM L-cystine in an aqueous solution containing 20 mM KBr and 0.5 M H2SO4. A digital microscope (VHX-600 + 500F, KEYENCE Co.) and confocal laser scanning microscope (CLSM) (Olympus 4000, Olympus Co.) were employed to characterize the depths and profiles of the etch pits.

4. RESULTS AND DISCUSSION 4.1. Kinetic Investigation on the EC1 Process by TG/SC Mode. To demonstrate the homogeneous catalytic effect of Lcystine on the oxidation of Br−, voltammetric measurements were performed in an aqueous solution containing 5 mM KBr, 0.5 M H2SO4, and different concentrations of L-cystine. The linear scan voltammograms of the EC1 process are shown in Figure 2A. The diffusion-limited current for the oxidation of Br− at 1.1 V increased from 49.7 to 73.6 and 89.6 nA in the presence of 2 mM and 5 mM L-cystine. The heterogeneous 18607



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Figure 3. SECM characterization of the EC2 process. (A) Simulated normalized normal flux of Br2 on n-GaAs substrate with different K2 for d = 3 μm. Each normal flux curve is normalized by the maximum value at r = 0, 0.5 cm s−1 (0.0053 mol m−2 s−1), 0.1 cm s−1 (0.0037 mol m−2 s−1), 0.05 cm s−1 (0.0027 mol m−2 s−1), and 0.01 cm s−1 (0.00085 mol m−2 s−1). (B) Feedback curves on n-GaAs substrate with the tip potential at 1.1 V (vs Ag/ AgCl). The solid lines are experimental approach curves, and the symbols represent approach curves simulated with different values of K2.

obvious topological change of the n-GaAs substrate in the experimental time scale, the normalized flux of Br2 can be considered in proportion to the etching rate. Thus, the normalized flux represents the normalized shape of the pits, which are actually normalized by the depth of the pit.51 Figure 3A shows the simulated normalized flux of Br2 on n-GaAs substrate with different K2. With the increasing value of K2, the radius of the pits decrease and the depth of the pits increase. Figure 3B shows the experimental current feedback curve on nGaAs substrate as well as the simulated ones with different values of K2. The kinetic rate of the etching reaction (K2) can be obtained as (3.2 ± 0.5) × 10−2 cm s−1. The kinetic rate of the etching reaction also can be obtained through a deformed geometry model, i.e., the ALE method introduced in the theoretical section. Figure 4A shows the optical image of the pits etched in an aqueous solution containing 20 mM KBr and 0.5 M H2SO4 with different etching times. The cross-sectional profiles fit well with the simulated ones (Figure 4B). From eq 16, the value of K2 is obtained as 3.5 × 10−2 cm s−1, which is in harmonious accordance with the kinetic rate obtained from SECM feedback mode. The results confirm further that, in our experiments, the direct electron transfer between Br2 and n-GaAs is negligible and the SECM positive feedback is caused by the etching reaction. Supposing the tip−substrate distance is 2 μm, the mass transfer rate (D/d) is estimated as 9.0 × 10−2 cm s−1 by using a diffusion coefficient (D) value of Br− as 1.8 × 10−5 cm2 s−1.31 That means the etching reaction is not fast enough to meet a completely diffusion-controlled process. Consequently, the lateral diffusion of Br2 unconsumed by the etching reaction makes the size of the etch pit larger than the size of the tip electrode as depicted in Figure 4A. 4.3. Etching n-GaAs with the Coupled E(C1∥C2) Process. To improve spatial resolution of the etching process, a scavenger should be added in the working solution to confine the diffusion distance of Br2. Therefore, a confined etchant layer (CEL) would be formed on the tip electrode. The fabrication precision of CELT is determined actually by the thickness of CEL, which is relevant to the distance between mold electrode and workpiece, the rate constants of the confining reaction and the etching reaction, and the scavenger concentration. Because the rate constants of K1 and K2 were obtained, a deformed geometry finite element model was adopted to simulate the

through the EC1 process. From the limiting diffusion current at 1.1 V (Figure 2B), collection efficiencies (η) at different concentrations of L-cystine were obtained. Figure 2D shows the plots of η as a function of log(d/a). The simulation results match the experimental data very well. Phenomenally, in the case of 5 mM L-cystine, the TG/SC voltammograms are similar to those shown in Figure 2B. With constant concentration of KBr, the currents on both tip and substrate depend on the diffusion time of Br2 from tip to substrate (d2/DBr2), the reactive rate constant of eq 2 (K1), and the concentration of Lcystine. The catalytic reaction rate constant, K1, is the only variable to get the best fit data. The values of K1 of (8.0 ± 1.0) × 103 and (6.0 ± 1.0) × 103 dm3 mol−1 s−1 are obtained at concentrations of L-cystine of 2 mM and 5 mM, respectively. 4.2. Kinetic Investigation of the EC2 Process by Current Feedback Mode. When an UME approaches a conductor or reactive surface, positive feedback would be obtained if the substrate is conductive or reactive. In our experiments, it could be caused by both direct electron transfer on GaAs and etching reaction, through which Br− ions are regenerated and form a redox loop between the SECM tip and substrate. However, this depends on the doping type of GaAs.17 Because of the highly positive potential of Br2/Br− redox couple, in the case of n-GaAs, it is reasonable to hypothesize that the direct electron transfer is negligible and the positive feedback is almost due to the etching reaction. To figure out the net rate constant of the etching reaction, current feedback curves were obtained and fitted to the simulated curves. Because it takes only a few seconds to obtain one approach curve, the surface change of the n-GaAs substrate can be neglected. After each approach operation was finished, the tip was moved to a new place to get another approach curve. The etching rate of n-GaAs is relevant to the kinetics of the etching reaction and also the mass transport of reactants or products in solution. If the etching reaction were fast enough, the etching would be dependent only on the hydrodynamics of the etching system. Thus, no kinetic information can be obtained from the diffusion-controlled feedback curve. Meanwhile, the size of the etch pits and the diffusion of the etchant, Br2, will be highly localized. If the surface reaction were not so fast, the kinetics of the etching reaction would have a great influence on the profile of the etch pits. Because the etching reaction did not make an 18608



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Figure 4. Pits etched without the confining of L-cystine. (A) Optical image of the pits etched in a solution containing 20 mM KBr and 0.5 M H2SO4. The etching time is 100, 200, and 300 s from left to right. The tip−substrate separation is 3 μm. (B) The cross-sectional profiles (solid line) of the pits etched in (A) measured through confocal laser scanning microscope and the corresponding cross-section simulated by deformed geometry model (symbols) with K2 = 3.5 × 10−2 cm s−1.

coupled E(C1∥C2) process. Figure 5 shows the simulated concentration distribution of Br2 and the cross-section of the pits etched at 100 s in a solution containing 5 mM KBr and 0.5 M H2SO4 with 0 mM and 20 mM L-cystine. The initial tip− substrate distance was 3 μm. The dotted lines represent the initial surface of n-GaAs substrate before etching. It is obvious that the lateral diffusion of Br2 is confined closer to the electrode and, thus, the CEL becomes thinner in the presence of L-cystine. Although the flux of Br2 onto n-GaAs substrate is diminished, the spatial resolution will be promoted. Figure 6A shows the optical images of etching pits obtained at different concentrations of L-cystine. The simulated profiles of the pits by using the obtained values of K1 (8.0 × 103 dm3 mol−1 s−1) and K2 (3.2 × 10−2 cm s−1) match the experimental results very well (Figure 6B). The results prove that the kinetic rates of reaction C1 and C2 are reliable. In the absence of L-cystine, the diameter of the etch pit is 45.0 μm, which is much larger than the diameter of the platinum disk electrode (25 μm). In the presence of 20 mM and 40 mM L-cystine, the diameter of the etch pits decreases to 38.6 and 34.8 μm, respectively. The results indicate that the thickness of CEL is compacted by the subsequently parallel reactions. It should be noted that the etching efficiency is also decreased due to the consumption of Br2 by L-cystine. The depth of the pit obtained within the same etching time decreases with the increased concentration of L-cystine. However, because the removal amount is usually very small in microfabrications, it is worthy to promote the fabrication precision by decreasing the etching efficiency.

Figure 5. Simulated concentration distribution of the etchant Br2 and the cross-section of the pits in the axisymmetric geometry after etching for 100 s with K1 = 8.0 × 103 dm3 mol−1 s−1 and K2 = 3.2 × 10−2 cm s−1. The tip−substrate separation is 3 μm. The solution contains (A) 20 mM KBr and 0.5 M H2SO4 or (B) 20 mM KBr, 0.5 M H2SO4, and 20 mM L-cystine. The dotted lines represent the initial surface of nGaAs before etching.

5. CONCLUSIONS We demonstrated the methodology to study the complex electrode processes of CELT system (E(C1∥C2)), which is valuable in electrochemical microfabrication. First, the kinetics of the confining reaction between Br2 and L-cystine was studied through the TG/SC mode of SECM. The second-order rate constant, K1, is obtained as (8.0 ± 1.0) × 103 dm3 mol−1 s−1. Second, the kinetics of the etching reaction between Br2 and nGaAs was studied by the feedback mode of SECM. The rate constant, K2, is determined to be (3.2 ± 0.5) × 10−2 cm s−1. Fitting the experimental etching topography with the simulated cross-sectional profiles also results in K2 of 3.5 × 10−2 cm s−1. These kinetic parameters are important particularly for screening the confined etching systems. Third, a deformed geometry finite element model was developed to simulate the E(C1∥C2) processes of CELT. The concentration distribution of etchant and the theoretical profiles of etch pits have been analyzed and agree well with the experimental results. This model allows the prediction of spatial resolution as a function of kinetic rate of the confining and etching reactions, the concentration of scavenger, and the distance between tip and 18609



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Figure 6. Analysis of the pits etched by CELT. (A) Optical image of the pits etched in a solution containing 20 mM KBr and 0.5 M H2SO4; the concentrations of L-cystine are 0 mM, 20 mM, and 40 mM from left to right; the etching time is 100 s; and the tip−substrate separation is 3 μm. (B) The cross-sectional profiles (soild line) of the pits etched in (A) obtained through confocal laser scanning microscope, and the corresponding cross-section (symbols) simulated by deformed geometry model with K1 = 8.0 × 103 dm3 mol−1 s−1 and K2 = 3.2 × 10−2 cm s−1.

workpiece. In brief, this work proposed a SECM method not only for the screening of confining etching system for electrochemical microfabrications but also for the kinetic study of complex electrode processes. The simulations present in this paper are established as a general method to screen the confined etching system, and its applications in other III−V semiconductors are in process.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +865922185797. Fax: +865922181906. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the National Science Foundation of China (Grants 91023047, 21327002, 91323303, 21321062, and 91023006), the Natural Science Foundation of Fujian Province of China (Grant 2012J06004), and the Program for New Century Excellent Talents in University (NCET-12-0318) is appreciated.

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ABBREVIATIONS CELT, confined etchant layer technique; CEL, confined etchant layer; SECM, scanning electrochemical microscopy; TG/SC, tip generation/substrate collection; η, collection efficiency; UME, ultramicroelectrode 18610



Article

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Kinetic Investigation on the Confined Etching System of n-Type

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