Experimentally Derived Catalytic Etching Kinetics for Defect-Utilized

Article pubs.acs.org/JPCC

Experimentally Derived Catalytic Etching Kinetics for Defect-Utilized Dual-Porous Silicon Formation Tae-Ki Woo,† Sarah Eunkyung Kim,† and Hyo-Sok Ahn*,§ †

Nano/IT Fusion Program, Graduate School of NID Fusion Technology, and §MSDE Program, College of Techno-Management Convergence, Seoul National University of Science and Technology, 172 Gongneung 2-dong, Nowon-gu, Seoul, 139-743 Korea S Supporting Information *

ABSTRACT: A kinetic model of defect-utilized dual-porous structure (DPS) formation of silicon, composed of amorphous porous structure (APS) and defect-followed mesoporous structure (DMPS), is proposed. It is found that a defect site is preferentially removed while creating the oblique DMPS of high aspect ratio, and the DMPS is wholly covered with the APS which is gradually grown through applied etching time but finally saturated. It is suggested that the APS growth is progressed by the chemically enhanced-oxygen diffusion, which is driven by catalytic chemical reactions, and the APS dissolution depends on the oxygen concentration of the APS itself. On the basis of these results, we describe the DPS formation using fundamental reaction kinetics and Fick’s law of diffusion. Understanding the APS growth mechanism is profound and potentially useful for prediction and controlling of the porous Si growth in the conventional HF/HNO3/H2O etching system. The DMPS development at the defect sites is ca. 22 times faster than the defect-free sites due to varied physicochemical properties. This analytical approach is a new attempt to describe the porous silicon formation mechanism as well as the conventional HF/HNO3/H2O etching procedure and further opens a new domain for the viability of defect engineering.

1. INTRODUCTION Porous structures of silicon have aroused tremendous interest due to their applicability to various fields, ranging from optoelectronics1,2 to photovoltaics3−5 and biosensors.6 Diverse porous structures such as macro-porous structures,7−9 straight nanoporous structures,10 zigzag-shaped nanoporous structures,11 fractal-geometric porous structures,12−15 and spongelike amorphous porous structures16−18 have been developed by adopting several chemical methods such as wet electrochemical etching by anodization of silicon in electrolyte of HF,2,4,5,7,15,17 metal-assisted chemical etching by catalytic reaction of many kind of metals functioning as a cathode in HF,3,9,11,19,20 and stain etching by HNO 3 or various oxidants/HF mixtures.4,5,18,21−24 These pore-structuring methods produce a great variety of geometries and show distinct characteristics in their detailed reaction schemes; however, decisive reactions governing most of these methods can be expressed as silicon oxidation and silicon oxide dissolution.23,25,26 The silicon oxidation is described with one of the following processes: holetransferring to the silicon by electric potential7,13,15,17,26−28 or oxidant18,21,23,29−33 or oxidant with metal-assisted catalytic reaction,3,9,11,19,20,34 and diffusion of oxidizing species into the silicon.22,24,35−38 The following silicon oxide dissolution is enacted by HF in all these cases. Recently, we developed a functionalized dual-porous structure (DPS) of silicon, showing distinct optical properties due to its structural features and geometries, which was © 2012 American Chemical Society

constructed by using a defect-utilized method combining the preferential etching and the stain etching (MC-PESE).39 Like other pore-structuring methods, it is formed by the silicon oxidation and oxide dissolution processes, but with the notable reactivity and diffusivity of the defect site in silicon which is intentionally created by mechanical grind process. In this article, the DPS formation procedures and its geometric features are summarized and the analytical modeling is attempted to discuss the formation kinetics of the DPS which consists of the amorphous porous structure (APS) and the defect-followed mesoporous structure (DMPS). A catalytic reaction behavior is observed in this MC-PESE, and a phenomenological similarity with the conventional thermal oxidation model40 is confirmed in the APS growth. Based on these findings, a kinetic model for the APS is developed. We also present the quantitative description of the DMPS formation kinetics with our proposed model. The kinetic model, simultaneously describing both the atomistic and mesoscopic pore-structuring, is newly introduced.

2. EXPERIMENTAL SECTION Boron doped p-type (ca. 25 Ω·cm) silicon (001) 8 in. wafers were used. For defect site generation the backside of wafer was Received: January 11, 2012 Revised: March 3, 2012 Published: March 5, 2012 7040

dx.doi.org/10.1021/jp300351d | J. Phys. Chem. C 2012, 116, 7040−7049

The Journal of Physical Chemistry C

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Figure 1. Configuration of characterized defective structures and DMPSs: (a) TEM image of defective structures with selected area electron diffraction (SAED) pattern. (b) AFM image of the ground sample showing the ground traces and glide bands. (c) Cross-sectional TEM image of the DMPS etched during 30 s with SAED pattern. (d) SEM image of the DMPSs etched during 150 s. Red arrows show a width of the DMPS.

ground using DGP8670 Grinder/Polisher (DISCO Ltd.). 49 wt % HF solution (T. J. Baker Ltd.), 61 wt % HNO3 solution (Junsei Ltd.), and deionized (D.I.) water were used to prepare HF/HNO3/H2O mixtures. Wet etching process was conducted by dipping a ground sample in a Teflon container filled with 100 mL mixture of various concentration ratios with magnetic stirring at 60 or 200 rpm, or without the stirring. The MCPESE was conducted in the concentration ratio of 1:1:8 (HF:HNO3:H2O; mole fraction) with a magnetic stirring at 60 rpm. More details for the fabrication conditions and procedures of the DPS were described in our previous paper.39 Measurement of the etched thickness of bulk silicon was performed using a Dektak-150 3D-profiler instrument (Veeco Ltd.), operated in a direct stylus-scanning method. For surface observation atomic force microscopy (AFM), scanning electron microscopy (SEM), and high resolution scanning Auger microscopy (HRSAM) were used. AFM was performed in a DI 3100 instrument (Veeco Ltd.) which was operated at 512 × 512 resolution in a 10 × 10 μm2 scan by tapping mode. SEM was conducted by an S-4200 instrument (Hitachi Ltd.) with a resolution of 1.6 nm using an incident electron beam of 15 keV. HRSAM was performed in a PHI-700 instrument (ULVACPHI Ltd.) using an incident electron beam of 5 keV. Transmission electron microscopy (TEM) were used for structural characterizations, which was performed in a TecnaiF20-G2 instrument (FEI Ltd.) using an acceleration voltage of 200 keV. Highly magnified TEM images were utilized for fast Fourier transform (FFT)-processing using a DigitalMicrograph software (Gatan Ltd.). For elemental/chemical analysis a depth profiling was conducted using Auger electron spectroscopy (AES), performed in a PHI-700 instrument (ULVAC-PHI Ltd.) using an incident electron beam of 5 keV and an Ar-ion sputtering of 2 keV. The most flat regions of ca. 500 × 500 nm2

were used for incident areas of the electron beam for all the etched samples. For quantitative analysis of the APSs we used a calculation method41 expressed as follows: I /F [A]atomic% = A A × 100 ∑ I /F

(1)

where A is an element, I is the intensity, and F is the sensitivity factor. Based on the standard SiO2, the sensitivity factors of silicon and oxygen were defined, and using the peak-to-peak height ratio of the Si−O bonds in the SiLVV and in the OKLL the intensities were determined.42

3. RESULTS AND DISCUSSION 3.1. Defective Structure Generation and Development of DMPS. Figure 1, panels a and b, shows the defective structures created by a mechanical grind process in crosssectional and plane views. These were obtained by TEM and AFM, respectively. In the cross-sectional image, severe crystallographic defects (dark contrast in this bright field image) are shown along the subsurface, parallel with the axis of grind direction (black arrow; ⟨110⟩). The majority of defects are located in ca. 1−1.3 μm depth, where structures are complexly tangled and highly strained by the defects (hereafter this region is referred to as the highly damaged region, HDR). Some of the defects are solely distributed in a considerable depth range of ca. 3−5 μm, which are the candidates of the DMPS.39 In the plane image, the peaks and valleys are shown in rows with the grind direction (⟨110⟩), and the densely propagated waves marked by dotted circles are found, which are grind grooves and glide bands. The grooves are traces wearing out in a cutting mode grind43 and the glide bands are a sign of the existence of successive slip planes with the collective dislocations.44,45 Coarse grind causes severe damage to the 7041



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Figure 2. Configuration of the characterized thickness and morphology of the APSs and the etched thickness of bulk silicon: (a) High resolution TEM image of the APS with the inset of its FFT image. Scale bar represents 2 nm. (b-g) Cross-sectional TEM images with the inset of HRSAM images of 15, 30, 60, 90, 120, and 150 s etched samples’ APSs. Scale bars of TEM and HRSAM images represent 100 nm and 1 μm, respectively. (h) Thickness of APS and the etched thickness of bulk silicon through etching time scale. The thickness is based on the average of TEM image measurement in relatively plat regions out of the DMPS and only in the plateaus of APSs except the etch-pitted regions for 120 and 150 s etched samples. Error represents standard deviations from N = 10−12 regions.

Table 1. Dimension of the DMPS with the Obtained Aspect Ratioa etching time (s) length (l), μm width (w), μm aspect ratio (l/w)

5

10

15

30

60

90

120

150

0.84 ± 0.27 0.21 ± 0.03 4.00

2.50 ± 0.58 0.39 ± 0.05 6.41

3.75 ± 1.02 0.50 ± 0.09 7.48

3.81 ± 1.20 0.51 ± 0.08 7.47

3.76 ± 1.36 0.68 ± 0.11 5.53

3.62 ± 0.98 0.90 ± 0.14 4.04

3.25 ± 1.09 1.26 ± 0.27 2.58

2.68 ± 0.87 1.79 ± 0.38 1.50

a

Length is based on the average of measurements of large number of TEM images for statistical calculation. Length only reflects the solely developed DMPSs showed as unobstructed, rather than intersected or overlapped one. Error represents standard deviations from N = 10−33 pores. Width is based on the average of measurements of several SEM images with an aid of image-calculation-software. Width only reflects the DMPSs propagated diagonal to the ⟨110⟩ grind direction. Error represents standard deviations from N = 18−25 pores.

variation of the DMPS indicates a similar trend with the etched thickness of bulk silicon (Figure 2h) due to the absence of active dissolution of the defect site.39 Table 1 presents the etching time-varying dimension of the DMPS with obtained aspect ratio. From comprehensive standpoint it is concluded that geometry of the DMPS is tentatively determined by the preformed defect site which corresponds with starting geometry of the DMPS. However, once the DMPS is formed, the geometry is governed by the etching kinetics of the defect-free site, thus being sensitive to the etching duration. 3.2. APS Growth. Figure 2a-g show that the APSs wholly cover the DMPSs with themselves as an amorphous phase without any crystalline particles in thickness variation through an applied etching time. Figure 2h summarizes the thickness variation as the follows. The APS growth is initiated at a time between 10 and 15s (Figure S1), and the growth rapidly progresses in the early stage, but the rate of growth decreases to the late stage, finally being saturated. Compared with the etched thickness of bulk silicon,39 this APS growth kinetics is

subsurface of processed material, especially in brittle materials,43,46−48 and which is our purpose in this study because the intentional defect is skeleton of the DMPS. In our study, both the HDR and the distributed defects behave mainly in the ⟨110⟩{111} slip system of Si,47 thus resulting in the threedimensional defective structure formation.39 Via the MC-PESE, the HDR are stripped out while the deeply distributed defects being preferentially removed, which is due to the high diffusivity and reactivity of the defect sites.39 As a result, the DMPSs are formed as shown in Figure 1c. The DMPSs created along the major slip planes, {111}, of silicon prove that the defect-followed preferential etching occurs in this MC-PESE. As shown in Figure 1d, the densely distributed glide bands, referring to the upper side of the HDR, are replaced with the more loosely distributed pores after the MCPESE. It is the result of the HDR removal and the development of distributed defects to the DMPSs. The HDR removal and the distributed defect removal are completed at least before 10 and 15 s, respectively.39 After 15 s, the length and width 7042



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Figure 3. AES montages of the APS obtained from depth profiling of the 90 etched sample with a schematic bond state figure: (a) Montage of SiLVV: straight red and blue arrows indicate kinetic energies assigned by Si−O and Si−Si bond-related Auger transitions, respectively. (b) Montage of OKLL: straight red arrow indicates kinetic energy assigned by Si−O bond-related Auger transition.

diffusion into silicon depending on the applied etching time.21,22,24,35−38,55 To investigate the APS dissolution by HF, dipping the etched samples in a 49 wt % HF solution was conducted for 5 min. Figure 4 displays the atomic ratio of the HF-treated APS of 90 s etched sample as a representative. It proves that HF is able to actively dissolve the APS up to the stoichiometric composition of ca. SiO0.3.22,56 In the same treatment, such dissolution characteristic was hardly found in a 15 s etched sample, but it occurred in all other samples with almost the same atomic ratios. In the case of dipping samples in a 5 wt % HF for 5 min, the dissolution hardly occurred in all samples. However, in the case of dipping for 2 h, very similar results occurred with the case of the 49 wt % HF treatment. From these results we can confirm that HF actively debonds the Si−O bond but very slowly debonds the Si−Si bond.57−61 Thus, we dictate that the dissolution of the APS by HF actively proceeds through the depth just before the HF meets a strong Si−Si bonding network. Possibly, the more oxygen quantity that is in the APS, the faster the dissolution should occur and vice versa. On the basis of the APS dissolution study, we can account for the APS growth aspect with the etched thickness of bulk silicon as follows. From the APS growth initiation to 30 s, the APS is soundly grown by oxygen diffusion while being weakly attacked by HF, attributed to the sparse oxygen quantity and the highly diluted HF concentration.59,62 The APS growth progresses, but the macroscopic dissolution of bulk silicon starts at around 30 s, owing to the increased oxygen quantity enough to be dissolved. After that, the APS dissolution and the growth rate gradually increase and decrease up to 120 s, respectively, but being commonly saturated after 120 s. Here, it is noted that the grown APS thickness is a final fruit resulting from the parallel but competitive reactions between the oxidation by oxygen diffusion and the dissolution by HF.21 Accordingly, it means that the oxygen diffusion rate is faster than the dissolution rate until 120 s but these rates became the same to be in an equilibrium state after 120 s. 3.3. Autocatalyst Effect to Reaction Kinetics. The reason for the increasing oxygen diffusion rate, confirmed from the increasing dissolution rate, is considered as the existence of so-called ‘autocatalyst’.29−32,35−38,55 The autocatalyst is a kind of reactive oxidant species among lots of intermediate species produced during etching process.29−32,35,37,55 In fact, the

anomalous because its kinetics goes in opposite direction against the bulk silicon dissolution kinetics despite the APS lying on the bulk silicon (DMPS). Figure 3 representatively displays the SiLVV and OKLL montages of the APS of 90 s etched sample through depth profiling in a function of kinetic energy of Auger electron. The SiLVV montage shows an elemental Si peak at 92 eV (blue arrow)49,50 and a peak at 78 eV, originated from the Si−O bond (red arrow),51−54 from the top of APS to the depth. The intensities at 92 and 78 eV increase and decrease to the depth, respectively. At last, at the edge of the APS, the intensity at 92 eV becomes similar to that of bulk silicon, and one at 78 eV is annihilated. In the corresponding OKLL montage a peak at 506 eV, originating from the Si−O bond,53 is exhibited as a decreasing intensity gradient to the depth of the APS. These results show that both the chemical bonds of Si−Si and Si−O simultaneously reside in the APS, and oxygen amount is decreasingly distributed to the depth of APS. Quantitative analysis (Figure 4) also reveals that quantity of the oxygen transported into the APS increases with an increase of etching time but is saturated in ca. SiO1.3 at 120 s.42,51 These phenomena accurately correspond with the APS growth aspects. Thus, the APS growth can be described by the oxygen

Figure 4. Atomic ratios of the APSs through the depth as a function of sputter time for the 15−150 s etched samples and HF-treated 90 s etched sample. 7043



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oxidation is performed mainly by the reactive oxidant29−32,35,37 rather than direct HNO3. The induction period prior to an observable macroscopic reaction is direct evidence,21,29−32,37,55 and the oxidation only by HNO3 requiring very long duration (several hour) and certain thermal condition (∼120 °C) to form thin oxide film (. After 120s noted as C section, the growth rate of the APS is almost equivalent to the no-growth rate of the APS, which is expressed by changing the mark, ≫, in eq 15 to ≈. In this section we have derived the APS kinetic model, valuable for understanding the mechanistic reaction procedures and useful for prediction and controlling of the APS growth. From the derivations, we can know that this APS growth kinetics is a resultant phenomenon of complex interlinked

(10)

where 1

⎪

NHF is the number of HF molecules required to dissolve a unit volume of the APS. Equation 13a is approximated to the etched thickness of bulk silicon (Figure 2h). Therefore we can modify eq 12 to the following:

Integrating this differential equation from an initial oxide thickness, Xi, to a final thickness, Xaps, is forwarded to the following equation:

A=

⎪

⎪

FHF h = HF (CHF,b − CHF,s) NHF NHF

For outer and interface conditions of the APS, CO,o ≈ Ceff.O because the reactive oxidant very actively reacts with the surface to diffuse oxygen and CO,I ≈ 0 due to the kinetics of this model being in the regime of “diffusion-controlled” as demonstrated in Figure 4.40,68 As simplified approximation, we can derive that, if Naps is the number of oxygen incorporated into a unit volume of APS, the growth rate of APS is described by the following differential equation: dxaps

⎪

where

Ceff.O kdiffuse

⎫ A⎧ t+τ ⎬ ⎨ 1+ 1 − 2⎩ A2 /4B ⎭

xaps =

which gives only a grown thickness of APS as a function of time, excluding its dissolution by HF. To reflect the no-growth of the APS, we redefine the growth rate of the APS (eq 9) as the competitive expression.

F3 = kapsCO,i

1

(11a)

Solving eq 11 yields the form

⎛C ⎞ O,o − CO,i ⎟ F2 = DO,aps⎜⎜ ⎟ xaps ⎝ ⎠

Feq = F1 = F2 = F3 =

(11)

2DO,apsCeff.O Naps (10a) 7046



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because (v) implicitly assumes that the DMPS development rate is equivalent to the APS growth rate.

reactions, significantly influencing each other as a function of concentration but eventually depending on the potential oxidant and HF, and this model requires the experimental confirmation for the completeness of itself. 4.2. Kinetics of DMPS Development. Very fast development of the DMPS (Table 1)39 is due to the prominent diffusivity and reactivity of the defect site. To describe the DMPS development kinetics we consider a simple defective structure, one-dimensionally propagated and regarded as an equivalent defect state through its length,69 which is placed on an intermediate stage of defect removal as shown in Figure 6.

dxdev .l = dt

dxdev.v = dt

Ceff.O,DMPS ⎡ 1 x 1 ⎤ ⎥ + dev.l + Naps⎢ DO,aps k aps ⎦ ⎣ kdiffuse Ceff.O,DMPS

⎡ 1 x 1 ⎤ ⎥ + dev.v + Naps⎢ D ′O,aps k ′aps ⎦ ⎣ k ′diffuse

(16)

where Xdev.l and Xdev.v are development thicknesses to the lateral and vertical directions, respectively, Ceff.O,DMPS is the effective concentration of oxygen contributing to the DMPS development, k′diffuse, D′O,aps, and k′aps are same terms as kdiffuse, DO,aps, and kaps but are assigned at the defect site. As already mentioned, chemical reactivity and diffusivity of the defect site are higher than those of the defect-free site, which means enlarged magnitudes of constants and coefficients. Thus, we can use our experimental results of the defect site and defectfree site, referring to the length and width developed from 10 to 15s (Table 1), to calculate the constants and coefficient variations. The calculated development rates of the length and width are, respectively, ca. 251 and ca. 12 nm/s, which can be expressed as the following: 12nm/s = Figure 6. Schematic illustration of the DMPS development model one-dimensionally behaved along the defect site (length) and against the defect-free site (width).

251nm/s =

On the basis of our TEM study we assume for this model that (i) the defective structure is dissolved to form the DMPS followed to the defect site in vertical direction, which becomes the length of the DMPS, and against the perfect crystalline silicon walls in lateral direction, which become the width of the DMPS. For simplicity, (ii) each of these directional developments is assumed as only one-dimensional behavior as depicted by the red arrows. As already confirmed, the vertical development is very fast but the lateral development is relatively slow, and there is no obvious variation of the width through the length (Figure 1).39 Thus, we can assume that (iii) the difference of the lateral development rate through the length is negligible. We can thereby approximate that (iv) the concentration distribution of reagents in the DMPS is equivalent through the length, which leads to both the vertical and lateral developments being in an equivalent ambient conditions. We utilize the length and width of the DMPSs developed during from 10 to 15 s. In this period the grown thickness of the APS is just a few nanometers (Figure 2) and the DMPS development is in a mesoscopic scale. Thus, (v) we can neglect this slight APS growth in this DMPS development calculation. By virtue of this simplification, we can express the DMPS development rates as the following (eq 16) using a differential mass balance equation, which is same form with the (eq 9),

Ceff.O,DMPS ⎡ 1 x 1 ⎤ ⎥ + dev.l + Naps⎢ DO,aps k aps ⎦ ⎣ kdiffuse Ceff.O,DMPS ⎡ 1 x 1 ⎤ ⎥ + dev.v + Naps⎢ D ′O,aps k ′aps ⎦ ⎣ k ′diffuse

(17)

Although the Xdev.l and the Xdev.v of each diffusivity term are differently denoted to express the different directional developments, in practice, these are same because these mean the APS thicknesses of both the directions, which are commonly negligible in this period. Hence, we can rewrite eq 17 as the following expression only using the constants and coefficient: ⎡ ⎤ 1 1 1 ⎥ + + 21.86⎢ ⎢⎣ k′diffuse D′O,aps k′aps ⎥⎦ 1 1 1 = + + kdiffuse DO,aps k aps

(18)

This simple equation shows that the chemically enhancedoxygen diffusion, solid-state diffusion and interface reactioninvolved lumped property of the defect site is ca. 22 times larger than that of the defect-free site in the equivalent ambient conditions of this etching system, and also means that the distribution of the defect site strictly determines vertical development of the DMPS due to its exceedingly fast development rate. In this section we have calculated the DMPS development kinetics based on appropriate assumptions, which notifies a significant difference between the defect site and defect-free site in their development kinetics. The most important point should be the quantitatively disclosed properties of the defect site how about deviated from that of the defect-free site, which 7047



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is a critical knowledge for this defect-utilized pore-structuring technology.

5. SUMMARY In this study we developed a kinetic model for the defectutilized DPS formation. In the experimental observations, we confirmed that the intentional defect sites were preferentially removed while producing the DMPSs of high aspect ratios, and the defect removal was perfectly accomplished within 15 s. During the DMPS development, the APS growth and final saturation due to the rate difference and equivalence of the competitive oxidation and dissolution through etching time were also verified. These behaviors were strongly related to the autocatalyst generation, responsible for the chemically enhanced oxygen diffusion into silicon. According to the oxygen concentration of the APS, HF dissolved the APS at a different rate. Based on these experimental results and rational assumptions, a kinetic model using fundamental reaction kinetics and Fick’s law of diffusion was derived. The kinetic model accounted for the APS growth kinetics upon the conventional etching system but required the experimental confirmation for the completeness of itself. Using the developed APS growth kinetic model, we also described the DMPS development kinetics which had a development rate of the defect site that was ca. 22 times faster than that of the defect-free site due to varied physicochemical properties (chemically enhanced-oxygen diffusion, solid-state diffusion, and interface reaction). Analytical modeling is a new approach to describe the DPS formation kinetics and enhances the possibility for defect-utilized pore-structuring technology.

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ASSOCIATED CONTENT

S Supporting Information *

Cross-sectional HRTEM images for the APS formation and the definition of the APS growth initiation time; confirmation for the stain and rate-limiting factors and the induction period; existence and accumulation of the autocatalyst. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-2-970-6307; e-mail: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. J.-P. Ahn and J.-M. Kim at Nano-Analysis Center, Korea Institute of Science and Technology, for discussion about TEM analysis. This study was financially supported by Seoul National University of Science and Technology. The additional support by the Practical Application Project of Advanced Microsystems Packaging Program of the Korea Ministry of Knowledge Economy is also highly acknowledged.

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REFERENCES

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