0268-1242_27_6_065001

Controlling the shape and gap width of silicon electrodes using local anodic oxidation and

anisotropic TMAH wet etching

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Semicond. Sci. Technol. 27 (2012) 065001 (11pp) doi:10.1088/0268-1242/27/6/065001

Controlling the shape and gap width ofsilicon electrodes using local anodicoxidation and anisotropic TMAH wetetchingJalal Rouhi1, Shahrom Mahmud1, Sabar Derita Hutagalung2,Nima Naderi1, Saeid Kakooei3 and Mat Johar Abdullah1

1 Nano-Optoelectronic Research (NOR) Lab, School of Physics, Universiti Sains Malaysia,11800 Pulau Pinang, Malaysia2 School of Materials and Mineral Resources Engineering, Universiti Sains Malaysia,14300 Nibong Tebal, Pinang, Malaysia3 Department of Mechanical Engineering, Universiti Teknologi Petronas, 31750 Perak, Malaysia

E-mail: [email protected]

Received 8 February 2012, in final form 12 March 2012Published 23 April 2012Online at stacks.iop.org/SST/27/065001

AbstractA simple method for fabricating silicon electrodes with various shapes and gap widths wasdesigned using the special properties of anisotropic tetramethylammonium hydroxide(TMAH) wet etching and local anodic oxidation (LAO). A statistical system was used for theoptimization of the parameters of the LAO process to facilitate a better understanding andprecise analysis of the process. Analyses of the interaction effects among the significantfactors of LAO showed that the relative humidity and applied voltage were interdependent.They had the strongest interaction effect on the dimensions of the oxide mask. TMAH with aconcentration of 25% was used as an etchant solution in (1 0 0) silicon with a rectangular oxidemask. The observed undercutting at convex corners, tip shape of emitters and gap widths ofelectrodes were exactly consistent with theoretical studies. Combination of the LAO methodand anisotropic TMAH wet etching was successfully used to fabricate Si nano-gap electrodes.This fabrication method of sharp and round tip emitters was simple, controllable and fasterthan common techniques. These results indicate that the method can be a new approach forstudying the electrical properties of nano-gap electrodes.

(Some figures may appear in colour only in the online journal)

1. Introduction

Nano-gap electrodes with nanometer junctions allow theconsideration of tunnel junctions for single-electron transportdevices. One of the most interesting and frequently discussedtopics on nano-gap electrodes is the field-emission effect.The field-emission characteristics of nano-junctions aresignificantly affected by geometric factors (e.g., the distancebetween electrodes and the radius of curvature of the emitterapex) and the work function of emitter materials. Given thatemission arises from the emitter tip, emission currents can be

different according to the tip geometry (e.g., sharp, round andblunt) [1].

There are various techniques for creating nano-gapelectrodes, including nano-imprint lithography [2], electro-migration methods [3], electroplating technique [4], focusedion beam lithography and electron beam lithography [5, 6].

Local anodic oxidation (LAO) lithography using atomicforce microscopy (AFM) is a convenient method for creatingnanometer-scale structures, nano-electronic devices [7, 8] andsensors. In previous studies, LAO has been presented as a verypromising tool for fabricating lines and nanodots on several

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Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

Table 1. The ranges of variables and experimental design levels.

Levels

Parameters 1 0.5 0 0.5 1Relative humidity (%) A 40 55 60 75 80Applied coltage (V) B 4 5 6.5 8 9Tip speed (m s1) C 0.1 0.25 0.55 0.85 1

types of materials [912]. Previous studies have indicated thatwriting speed, applied voltage and relative humidity (RH) aremajor operational parameters to control the LAO process anddetermine oxide dimensions [1315].

Anisotropic tetramethylammonium hydroxide (TMAH)wet etching has been extensively used to fabricate simplestructures such as cantilevers and pressure sensors. Based onthe capabilities of TMAH wet etching and LAO, this studyfocused on controlling the shape and value gap of electrodesby combining these two methods.

2. Experimental details

2.1. Materials

LAO was carried out on a p-type Si (1 0 0) wafer witha resistivity of 0.7510 cm at room temperature usingSPI3800N AFM. The contact mode tip was coated with Cr/Ptwith a resonance frequency of 13 KHz and a force constant of0.2 N m1. The RH was controllable from 40% to 80% with anaccuracy of 1%. All runs were conducted at the contact modeof the AFM tip.

A silicon-on-insulator (SOI) wafer was used as a substrateto fabricate nano-gap electrodes with a 100 nm thicknessdevice layer above a 150 nm buried oxide layer. Furthermore,the p-type (1 0 0) silicon device layer had a resistivity of110 cm. The buried oxide layer in the SOI wafer was usednot only as an insulator between the device and the handledsilicon layer, but also as the etch-stop for the wet etching.TMAH with concentration of 25% was used in the wet etchingprocess.

2.2. Statistical design using the response surfacemethodology (RSM) on the LAO process

The tip speed, applied voltage and RH are effective parametersfor improving LAO on semiconductor surfaces in air [16].Although LAO is important for the fabrication of nano-devices,no LAO optimization study has been reported yet. The DesignExpert Software (Version 6.0.6, Stat-Ease, Inc., USA) wasused in the current work to create a regression model andperform statistical as well as graphical analyses.

The variables in this survey included three numericalfactors: (A) RH, (B) applied voltage and (C) tip speed. Theranges of variables and experimental design levels used areindicated in table 1.

The first requirement for RSM is the design of theexperiment to determine the number of required runs andprovide a credible measurement of the desired response [17].Consequently, the numbers of experimental runs determined

Figure 1. Topographic images and line profiles of the runs of 7, 9, 3,13 and 15.

from the central composite design (CCD) were 20 runsbased on the eight factorial points, six axial (star) pointsand six center point replications. Optimizations were alsoperformed for two responses. Table 2 shows the completedesign matrix for the actual oxide height and width responsesof the experiments. The height of the lines is determined fromthe line profiles, and the mean of the five points per line. Oxidewidth is determined from the mean of five full-width half-maximum (FWHM) per line. Figure 1 shows the topographicimages and line profiles of the number of required runs.

Multiple regression analysis on the experimental data wasperformed to develop the mathematical models for the desiredresponses as a function of selected variables. The quadraticequation model for predicting the optimal point can bewritten as

Y = 0 +k

i=1iXi +

k

i=1iiX

2i +

i

j=i+1i jXiXj + , (1)

where Y represents the responses (oxide height and width);0, i, ii and ij are the constant, ith linear, quadratic andlinear model coefficients, respectively; Xi and Xj are codedindependent variables (RH, applied voltage and tip speed),and is the standard error. The quality of the model wasdemonstrated by the R-squared value. R-squared is the squareof the correlation between the models predicted values and theactual values. The square of the correlation ranges from 0 to 1.The greater the R-squared, the better model fit is indicated. Thestatistical significance of the model was evaluated by analysisof variance (ANOVA) using the mean square of residual errorand values of regression.

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Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

Table 2. Experimental design and results.

Variable in coded levels

Design points Point type A (%) B (V) C (m s1) Height (nm) Width (nm)

1 Fact +1 +1 +1 3.41 +/ 0.06 191 +/ 42 Fact 1 +1 +1 1.74 +/ 0.03 129 +/ 23 Fact +1 +1 1 4.92 +/ 0.09 220 +/ 44 Fact 1 1 1 0.42 +/ 0.01 111 +/ 25 Fact +1 1 +1 0.93 +/ 0.02 119 +/ 26 Fact +1 1 1 1.26 +/ 0.02 139 +/ 37 Fact 1 +1 1 3.03 +/ 0.05 163 +/ 38 Fact 1 1 +1 0.36 +/ 0.01 70 +/ 19 Axial +0.5 0 0 2.12 +/ 0.04 173 +/ 3

10 Axial 0 0.5 0 1.85 +/ 0.03 148 +/ 311 Axial 0.5 0 0 1.88 +/ 0.03 161 +/ 312 Axial 0 +0.5 0 2.94 +/ 0.05 176 +/ 313 Axial 0 0 +0.5 1.68 +/ 0.03 177 +/ 314 Axial 0 0 0.5 2.48 +/ 0.05 179 +/ 315 Center 0 0 0 2.14 +/ 0.04 166 +/ 316 Center 0 0 0 1.95 +/ 0.04 165 +/ 317 Center 0 0 0 1.92 +/ 0.03 170 +/ 318 Center 0 0 0 2.12 +/ 0.04 168 +/ 319 Center 0 0 0 1.89 +/ 0.04 171 +/ 320 Center 0 0 0 1.99 +/ 0.04 167 +/ 3

2.3. Anisotropic TMAH wet etching

In this work, TMAH with concentration of 25% was used in thewet etching process because the etching rate of the SiO2 layerin a TMAH solution is approximately ten times lower than thatin a KOH solution. Consequently, the SiO2 layer can be used asa mask in the anisotropic etching process for a long time. Theetching rate of the SiO2 layer increases with increased etchingtemperature, but slightly decreases at TMAH concentrationsgreater than 5 wt.% [18]. The surface roughness also increaseswith decreased TMAH concentration. An etched surface isvery smooth at high concentrations, but contains many hillocksat low concentrations [19].

2.3.1. Initial estimation of the value gap in the nano-oxide mask. Previous studies have investigated the etchingbehavior of silicon crystals, including the three main crystalorientations (1 0 0), (1 1 0) and (1 1 1) [2022].

The etched gaps on the (1 0 0) silicon layer bounded byconverging (1 1 1) planes have an angle of 54.74 with the(1 0 0) surface. As shown in figure 2, the minimum gap widthafter etching (W o) is estimated using the following relation:

Wo = WSi

2YSi, (2)

where YSi is the thickness of the silicon device layer in a SOIwafer, W Si is the size of the etched gaps on the wafer surface,Wm is the value gap in the nano-oxide mask, x indicates thevariation between the mask opening and the intersection of the(1 1 1) planes etched with the mask due to undercutting and tis etching time (figure 2).

After the determination of the etching rates of the (1 0 0)and (1 1 1) planes, Wm can be defined to obtain the desired gapwidth after etching.

2.3.2. Undercutting at a convex corner on a (1 0 0) siliconsurface. Undercutting occurs at the corners of a convex

Figure 2. Cross-sectional view of the etched profile of a (1 0 0)oriented SOI wafer.

rectangular or square structure [19]. As shown in figure 3(a),the convex corner was constituted by two (1 1 1) planes thatintersect at edge r1r2.

In this case, undercutting may occur in three regions,including edge r1r2, the region in the proximity of pointr1 and the region in the proximity of point r2. Correspondingto the theorem of Sequin [23] (based on the kinematic wavetheory) and the theorems of WulffJacodine [24] (based on theequilibrium thermodynamic theory), a convex corner keepsits convex shape after etching regardless of the number ofnew crystal planes that emerged. Identically, a concave cornerremains concave after etching independent of the number ofnew crystal planes. New planes at convex corners are caused

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Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

(a) (c)

(b)

Figure 3. Schematic representation of convex corner undercutting: (a) convex corner constituted by the two (1 1 1) planes which intersect atthe edge r1r2, (b) undercutting configuration of convex corner and (h k l) planes appeared and (c) top view of convex corner undercutting.

by the fastest etching planes, whereas those at concave cornersare caused by extremely slow etching planes.

The two (1 1 1) sidewalls at the convex corner of edger1r2 have the slowest etching rates. Planes with etching ratesfaster than those of (1 1 1) planes may emerge, but only thosethat have the fastest etching rates [25]. Figure 3(b) showsthe undercutting configuration of a convex corner. Inasmuchas silicon single crystals belong to the m3m point-symmetrygroup [26], if an undercut plane(h k l)appears, a crystal plane(h k l)also emerges. In the proximity of point r1, the (1 1 1)sidewall and the (1 0 0) oxide mask form a concave corner. Theetching rate of the SiO2 mask is almost zero and the (1 1 1)plane has the slowest etching rate among the silicon crystals.Therefore, there is no crystal plane with a slower etching rate.As a result, new planes cannot emerge at this concave corner.

According to figure 3(c), the angle formed by theintersecting lines of the bevel planes with the oxide masksurface ( ) depends on the solution concentration. For the25% TMAH solution, the measured was 22 1 and thebevel planes were specified as (3 1 1) [2729].

Figure 4 schematically shows bevel planes emerging atthe tip apex.

3. Results and discussion

3.1. Optimization of effective parameters for LAO

3.1.1. Coded experimental model equations for oxide heightand width. The optimum levels of key parameters and theeffects of their interactions on the oxide height and widthwere determined by the CCD of RSM. The ANOVA for theoxide height and width showed that the model was significantbecause values of Prob > F were less than 0.05, indicating that

Figure 4. Schematics of bevel planes appearing in tip apex.

model terms were significant; in contrast, values of Prob >F greater than 0.05 showed that the model terms wereinsignificant [30]. In fact, the P-value is the smallest levelof significance that could be used to reject the null hypothesis,H0. Thus, the smaller the value is, the more significantits corresponding coefficient and the contribution towardthe response variable [31]. Insignificant model terms weresubsequently removed to improve the model. The ANOVAresults obtained after removing the non-significant terms forthe oxide height and width are indicated in tables 3 and4, respectively. The F-value is the mean square (regression)divided by the mean square (residual). The high F-value

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Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

Table 3. ANOVA for the oxide height as the desired response (reduced models).

Source Sum of squares DF Mean square F-value Prob.> F Comments

Quadratic 20.02 7 2.86 132.95

Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

(a)

(b)

Figure 5. Parity plots between the predicted and actual data of(a) the oxide height and (b) the oxide width in the oxidation process.

Therefore, the greatest interaction is that between the RH andapplied voltage.

The three-dimensional plot (figure 8) shows that atany amount of RH between 40% and 80%, the oxideheight increases correspondingly with the applied voltage.With a constant applied voltage, the oxide height increasessignificantly with increased RH from 40% to nearly 66%.After this point, the oxide height remains almost constant withfurther increased RH to 70%, above which the oxide heightdecreases.

The shape and size of the water meniscus are importantfactors affecting the oxide growth. Water molecules aredissociated by the electric field. Hydroxyl anions then migrateto the substrate and react with the silicon atoms of silicon

(a)

(b)

Figure 6. Two-dimensional interaction plot between (a) relativehumidity and applied voltage, (b) applied voltage and tip speed onthe oxide height.

oxide. As shown in figure 9, a thicker water meniscus formsaround the tipsample junction with increased humidity. Thequantity of hydroxyl anions migrated by the electric field in thelateral direction also increases [32]. With increased humidity,the water meniscus widens and the amount of hydroxyl anionswithin it increases. Consequently, the oxide width increasesand the height decreases. This process greatly depends on thevalue of water available for adsorption. A higher humidityresults in a thicker water meniscus, and correspondingly, theanodized surface area becomes larger and wider. Figure 10illustrates the surface plot of the interaction effect of the RHand applied voltage on the oxide width. The tip speed was keptat 0.2 m s1.

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Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

(a)

(b)

Figure 7. Two-dimensional interaction plot between (a) RH andapplied voltage, (b) RH and tip speed on the oxide width.

High RH increases the quantity of ionic diffusion througha water layer on the Si surface and reduces the Faradaiccurrent. The Faradaic current generates considerable lateralionic diffusion that causes further growth of the oxide width.

3.2. Fabrication of the nano-oxide mask using the LAOmethod

LAO is often used as a mask for fabricating nano-electronicdevices. By placing oxide lines adjacent to each other, oxidemasks with various shapes can be fabricated by controlling theLAO process parameters. Figure 11 shows an oxide mask withsquare shape. LAO was utilized to fabricate an oxide mask forcreating nano-gap electrodes on the SOI wafer.

Figure 8. Response surface 3D plot indicating the effect of theinteraction of RH and applied voltage (AB) on the oxide height,with the tip speed set at 0.45 m s1.

(a)

(b)

Figure 9. Schematic representation of LAO of a silicon surface:(a) the low and (b) the high humidity conditions.

3.3. Etching rate of a (1 0 0) silicon surface using 25% TMAH

Wet etching is not very effective if the depth and width ofthe etched dimension are not controllable. Consequently, theoptimal experimental conditions for measuring the etching rateof (1 0 0) silicon were determined.

Anisotropic wet etching experiments were performedon a (1 0 0) oriented p-type silicon with a resistivity of

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Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

Figure 10. Three-dimensional plot indicating the effect of theinteraction of RH and applied voltage (AB) on the oxide width, withthe tip speed set at 0.2 m s1.

Figure 11. AFM image of oxide mask fabricated by LAO.

0.7510 cm. A square-shaped silicon oxide mask was used

as the etching mask material, and was transferred onto the Si

wafers by LAO.

Figure 12 compares the etching rates of a (1 0 0) silicon

layer using 25% TMAH at various etching temperatures

obtained by Shikida et al [33], Chen et al [18], Tabata

et al [34] and this study. The etching rate in this work is almost

identical with those obtained by Shikida et al and Tabata et al

but is different from that by Chen. The discrepancy may be

due to the use of a stirrer during the etching process.

Figure 12. Comparison of the etching rate of the (1 0 0) siliconsurface among different studies.

Figure 13. AFM image of nano-oxide mask transferred by LAO andspecifications of oxide mask in the electrode tip.

3.4. Controlling the shape of the emitter tip and gap width ofelectrodes

The oxide mask was transferred onto the silicon device layerusing the LAO method (figure 13). SiO2 as a mask materialhas probably the most applications in nano-fabrication. It canbe easily grown on silicon layers by LAO. The selectivityof SiO2 to silicon in TMAH is excellent. The SiO2 etchingrate is much lower than that of silicon. SiO2 can also beeliminated readily using wet etching solutions, such as adiluted hydrofluoric acid (HF) solution.

According to equation (2), Wm can be estimated by thefollowing equation:

Wm = Wo +

2YSi 2tR(1 1 1)sin

. (5)

8

Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

(a)

(b)

Figure 14. (a) FESEM, (b) AFM image and profile of round tipemitter formed.

The etching rate of the (1 0 0) plane using 25% TMAH at70 C is 4.11 nm s1. Therefore, the etching time required toachieve an etching depth of 100 nm (thickness of the Si devicelayer in the SOI wafer) is about 25 s. The (1 1 1)/(1 0 0) etchingrate ratio is almost 0.035 [33, 34]. Thus, the etching rate ofthe (1 1 1) plane was measured as 0.14 nm s1. According toequation (5), a gap of about 190 nm in the nano-oxide maskis needed to obtain 55 nm gap junctions. Figure 13 shows thatthe nano-oxide mask transferred onto the silicon (1 0 0) devicelayer of the SOI wafer has a triangular shape in all convexcorners. As shown in figure 13, the oxide mask is 1500 nm inlength and 500 nm in width in the electrode tip.

A TMAH solution with a concentration of 25% was usedfor the anisotropic wet etching of the silicon layers. The etchingtemperature was kept at 70 C during the experiments. Thenano-gap electrodes were constructed by removing the siliconoxide mask using HF (2%) for 22 s.

The average corner undercutting ratio L/y for convexcorners is about 3.7 for 25% TMAH [35]. Undercutting inthe corners and tip apex of the electrodes are shown infigure 14. Undercutting convex corners appear as mentionedin section 2.3. The created round tip emitters according to the

(a)

(b)

Figure 15. (a) AFM image of nano-oxide mask and specificationsof oxide mask in the electrode tip. (b) FESEM image of sharp tipemitter with 35 nm gap.

above conditions are also shown in figure 14(a). Figure 14(b)demonstrates the AFM image and profile of round tip emitterformed. Si nano-gap electrodes are approximately 1 0 0 nm inthickness and are very smooth on the surface. By changing thetip dimensions in the oxide mask and increasing the etchingtime, sharp tip emitters are obtained (figure 15). As shownin figure 15(a), the width of the tip in the right oxide maskis decreased from 500 to 340 nm, and the gap width of theoxide mask is decreased from 190 to 160 nm. The etchingtime is also increased to 28 s. Given that the etching rate of(3 1 1) planes is more than that of (1 1 1) ones, the (1 1 1) planerapidly vanishes and L increases with increased etching time(figure 4). As a result, a sharp tip emitter with a 35 nm gap isformed.

The fabricated oxide mask may have some shadowstructures even under a controlled condition (figure 15(a)).Consequently, the pad is not precisely formed as a squareshape and there is a shadow around the pad. This phenomenonmay be caused by the high electric field created on the AFMtip. The electric field can form thin layers of oxide shadows

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Semicond. Sci. Technol. 27 (2012) 065001 J Rouhi et al

around the oxide mask at high RH values in a sample chamber.Considering the high selectivity of TMAH to SiO2, the shadowstructures may remain on the device after the TMAH etchingprocess and change the pad shapes (figure 15(b)). To ourknowledge, the current study is the first to report on the use ofthe LAO method and wet etching to control the shape and gapwidth of electrodes.

4. Conclusions

In this study, the shape and gap width of electrodes weresuccessfully controlled using anisotropic TMAH wet etchingand LAO. A statistical system was used for the individualand interaction effects of the RH, applied voltage and tipspeed on the LAO process. This system helped facilitatea better understanding and precise analysis of the process.The RH and applied voltage were interdependent and hada significant interaction effect on the width and height ofoxide lines. A nano-oxide mask was transferred onto a siliconsurface by the LAO method. Electrodes were formed usingwell-controlled nano-oxide mask dimensions and anisotropicTMAH wet etching. The current work showed for the firsttime that TMAH wet etching and LAO can be used together asappropriate methods for controlling the shape and gap value ofelectrodes. Undercutting phenomena at convex corners werevery consistent with those in previous studies. The value ofthe gap spacing between two electrodes and the tip shape ofemitters were predictable and in full accordance with the statedtheory. The etched surface was very smooth. This method forthe fabrication of round and sharp tip emitters was simple,controllable and faster than common techniques.

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1. Introduction2. Experimental details2.1. Materials2.2. Statistical design using the response surface methodology (RSM)on the LAO process2.3. Anisotropic TMAH wet etching

3. Results and discussion3.1. Optimization of effective parameters for LAO3.2. Fabrication of the nano-oxide mask using the LAO method3.3. Etching rate of a (1 0 0)silicon surface using 25 TMAH3.4. Controlling the shape of the emitter tip and gap width of electrodes

4. ConclusionsReferences