Journal of The Electrochemical Society, 149 ~3! C180-C185~2002!0013-4651/2002/149~3!/C180/6/$7.00 © The Electrochemical Society, Inc.

C180

Dimensional Constraints on High Aspect Ratio SiliconMicrostructures Fabricated by HF Photoelectrochemical EtchingG. Barillaro, z A. Nannini, and F. Pieri

Dipartimento di Ingegneria dell’Informazione: Elettronica, Informatica, Telecomunicazioni Universita`di Pisa, 56126 Pisa, Italy

The fabrication of macropores in crystalline silicon by photoelectrochemical etching in a hydrofluoric acid electrolyte is investi-gated. It is shown that the dimensional constraints on the pore diameters, which, in previous literature, are considered to dependon substrate doping, can be significantly relaxed. We show that it is possible to fabricate arrays of square section macropores withsides ranging from 2 to 15mm using the same n-doped~2.4-4V cm! silicon substrate. Moreover, we demonstrate that macroporearrays with pitch variation up to 100%~8 and 16mm! can be simultaneously grown on the same silicon sample. The same processis used to fabricate arrays of silicon walls with different spacing and pitch as well. A simple model, based on the coalescence ina single pore of multiple stable pores, is proposed to explain the experimental data.© 2002 The Electrochemical Society.@DOI: 10.1149/1.1449953# All rights reserved.

Manuscript submitted July 9, 2001; revised manuscript received October 19, 2001. Available electronically February 8, 2002.

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Electrochemical etching of silicon in hydrofluoric acid~HF! elec-trolyte is a well known technique for the formation of porosilicon.1,2 The dissolution of silicon in the electrolyte is activatedholes. In p-silicon electrodes holes are the majority carriers, soit is possible to produce porous silicon simply by etching the samin an HF-based solution, even in the dark. For n-type silicon,majority carriers are electrons, so that it is necessary to geneholes in order to produce porous silicon. Depending on the silidoping and on the type of the anodized silicon substrate, diffepore morphologies can be obtained. In fact, microporous laycharacterized by random pores with nanometric dimensions caeasily grown on p-type substrates,3 while macroporous layers withmicrometric straight pores can be obtained from n-type substra4

In the last case, by illuminating the rear surface of the wafer wsufficiently energetic photons, holes can be generated in thestrate by a process of photon absorption. Under anodic biasingditions, the photogenerated holes move to the front surface andcon dissolution takes place. Initially, the electric field concentratesharp defects on the flat wafer surface. Surface defects thereforas seeding points for macropore formation. As the etch progresthe electric field still concentrates at the pore tips, where most ofinjected holes react with the electrolyte. Fewer holes are then aable for the dissolution of the sidewalls, that are therefore proteagainst dissolution.5 By prepatterning the wafer surface with defesites it is possible to determine where macropores will form. KOetching after a standard photolithographic step can be used to cpyramidal notches in the required positions which can act asarray of defects. Both random5,6 and prepatterned7 macropore arrayswith high aspect ratio~up to 250! were fabricated through the wafethickness8 and on the whole wafer.9-11 The macropore morphologysignificantly depends on the anodization conditions, such as cudensity, etching time, HF concentration, temperature, and biaswell as on substrate properties, such as doping and orientation

The feasibility of different pore geometries and patterns and tdependence on growth conditions was discussed in detail bymann et al.12 Although the pore diameter could be related to tporosity alone, which can be accurately controlled by varyingcurrent density, they report that the substrate resistivity severelyits the range of feasible pore diameters; they propose a rule of thgiving the appropriate substrate resistivity in ohms per centimetethe square of the desired pore diameter in micrometers. Theyreport that the sensitivity to the macropore growth process onrelation between pitch and doping density is so high that a reducof the pitch by only 3% changes a perfect pore pattern to an imfect one.

The main purpose of this paper is to show that, although

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above limit is actually undeniable, the diameter of the porespitch can be varied on a wide range independently of the subsresistivity. Regular macropore arrays with sides ranging from 2mmup to 15mm were fabricated using a silicon substrate with 2.4-4Vcm resistivity. Moreover, macropore arrays with a change inpitch of 100% were simultaneously fabricated on the same samThe fabrication process is described, and the macropore formatidiscussed.

We also report the feasibility of this process to fabricate haspect ratio silicon structures as wall arrays with different thicknand pitch.

Finally, a model for the pores formation, which is able to explathe experimental results, is proposed. The model is based onself-organization and coalescence of several stable pores to fosingle one and includes the commonly accepted model of macroformation as a particular case for small dimensions of the patte

Fabrication Process

The experimental setup used for macropores formationsketched in Fig. 1. The electrochemical cell is made of polyrafluoroethylene~PTFE! and has a volume of 400 cm3. The frontside of the silicon sample is in contact with the electrolyte. Telectrolyte composition is 1:2:17~vol! HF ~48%!: C2H5OH ~99.9%!:H2O. Ethanol is added to reduce hydrogen bubble formation atsample surface, a technique commonly used for microporous silformation.13 For the same reason, the solution is stirred duringanodization process. The area of the sample exposed to the elelyte is about 0.6 cm2 and has a circular shape. Electron hole paare generated by illuminating the back side of the sample with aW halogen lamp, 20 cm from the sample, through a circular windin the metal foil used to provide the electrical contact to the samThe power supply of the lamp can be varied to modulate the etchphotocurrent. The counter electrode is a platinum wire immerinto the electrolyte, close to the sample surface~about 5 mm!. AnHP4145B parameter analyzer is used to apply the anodizationage and to monitor the etching current. All the experimentsexecuted at room temperature. The sample material is an n-silicon wafer,^100& oriented, 2.4-4V cm resistivity, 550mm thick,single-side polished.

A preliminary study of Si-HF electrochemical system was carrout in order to find the region for stable pore growth. TypicalJ-Vcurve obtained for our Si-HF system for high light intensity~about150 W! is shown in Fig. 2. In agreement with the literature,5 acurrent limit peakJps 5 35 mA/cm2 at 2.5 V, separating siliconporous formation and electropolishing regimes, was observed inanodic region of the characteristic.

Random macropore arrays were then fabricated for several eing currents belowJps and constant anodization voltage of 3 Vabove the voltage of the current limit peak, as suggested in Re

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Journal of The Electrochemical Society, 149 ~3! C180-C185~2002! C181

The macropore average diameter has been estimated by scaelectron microscope~SEM! observations in about 2mm, in agree-ment with the literature data.5

The same silicon substrate was used to fabricate regularaspect ratio structures, following the fabrication process sketcheFig. 3. A silicon dioxide layer~5000 Å thick! was grown on thesample by thermal oxidation~Fig. 3a!. A pattern was defined usingstandard photolithographic process. The patterns were arraysquare holes of different side and pitch, and arrays of straight lwith different width and pitch. Some of the studied dimensionssummarized in the first column of Tables I and II. A buffered hdrofluoric acid~BHF! etch was then used to transfer the patternthe silicon dioxide~Fig. 3b!. Pyramidal notches were created bKOH etching through the patterned silicon dioxide~Fig. 3c!. Elec-trochemical etching in HF was then used to fabricate regular sttures in the silicon substrate~Fig. 3d!, using the above describeelectrochemical cell. The last step of the process was a dryingperformed in air at 95°C for 10 min. The fabricated samples wfinally cleaved to allow SEM observations of the cross sections

Figure 1. Electrochemical cell used for macropore fabrication.

Figure 2. Typical J-V curve for the HF-Si electrochemical system undexamination.

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Results and Discussion

Patterned pores with sides ranging from 2mm up to 15mm werefabricated starting with the aforementioned silicon substrate, usthe above detailed process. The sample porosity was changetween 25 and 90%, starting with a fixed initial pattern and onvarying the etching current. In Fig. 4 an SEM cross section osquare hole array with pitch of 16mm having pores with side of 15mm, corresponding to 90% of porosity, is shown. Macroporesabout 35mm deep, corresponding to 20 min of etching time.

The porosityp of the array, defined as the ratio between tvolume of etched silicon and the total initial volume, is determinat the steady state, by the etching current densityJ according to therelation p 5 J/Jps, whereJps is the critical current density at thepore tips.8 Varying the etching current density is then a viable wto control the porosity of the sample under etching. Conseque

Figure 3. Schematic steps for prepatterned macropore fabrication.

Figure 4. SEM cross section of a macropore array with a pitch of 16mmhaving pores with sides of 15mm. The porosity of the fabricated array i90% according to the density current used in the experiment.

Journal of The Electrochemical Society, 149 ~3! C180-C185~2002!C182

Table I. Condition of fabricated macropore arrays for different dimensions and porosities. An X means a flawless sample, a B means lateralbranching, while ‘‘ Õ’’ means a sample that cannot be fabricated„see text….

Hole square array

Porosity

,25% 25% 50% 75% 80% 85% 90%

2 mm pitch 4mm / X X X X X X4 mm pitch 8mm B X X X X X X8 mm pitch 16mm B B X X X X X

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starting with the same initial pattern, it is possible to changegeometrical dimensions of the pores. Indeed, for an orthogonaltern of square holes with pitchr , where the pitch is defined as thperiod of the pattern, the pore sides is, from simple geometricaconsiderations,s 5 rp1/2.

In Table I some of the fabricated structures are summarized.each row, we report in the first column of the table the KOH startpattern~shape and geometrical dimensions of pattern before theodization process! and in the next columns the porosity values otained for the fabricated samples. In the table we indicate with athe patterns obtained without any defect, while the B indicasamples in which branching of the pores occur; finally, the ‘‘sodus’’ character means that the sample cannot be fabricated withspecified porosity value~as is clarified below!. For instance, in thelast row of the table we can see that starting from an initial KOsquared hole array with 8mm side and 16mm pitch, it is possible tovary the porosity of the anodized sample from 50 to 90%, usinproper etching current. No branching of primary pores is obserfor the above specified porosity. It must be noted that, in the abexample, a value of porosity of 90% corresponds to pores with sof 15 mm, while the width of the silicon walls between two adjacepores is 1mm. When the porosity is 25% or lower, branchingprimary pores is observed in the silicon wall separating pores. F25% porosity, the initial pattern was simply transferred to the silicsubstrate; the side of pores and the wall thickness between thjacent pores of anodized sample remains 8mm as in the mask. Inorder to explain the use of the solidus character we observe thatto the fact that the average diameter of the random pores is abomm for the used substrate, it is not possible to fabricate samplesporosity requiring pores with diameters less than 2mm. This is, forinstance, the case reported in Table I for a porosity,25% withstarting pattern 2mm side, 4mm pitch square hole array.

No limit for upper porosity is found in our samples. As matterfact, branch-free, regular macropore arrays with porosity up to 9were fabricated~see Table I!. On the contrary, it is evident fromTable I that a porosity lower limit exists. Below the lower poroslimit secondary pores,100& oriented, grow in the silicon walls separating the primary ones. This effect was explained by considethe width of the walls separating neighboring primary pores. Icommonly accepted8 that the macropore growth process is ruledthe extension of the space charge region around the pore tips, swhen the wall width between neighboring pores is about twiceof the space-charge region, too few holes penetrate in the silwall to promote silicon dissolution, and no pores grow in the silicbetween adjacent ones. On the contrary, when the wall thickbecomes wider, more holes, generated deep in the substratediffuse into the silicon walls and reach the Si-HF interface, whthey react with the electrolyte giving rise to the growth of secondpores.

The space-charge region widthw for the electrochemical systemunder investigation can be estimated from the Schottky contheory14

w ' ~2««0VJ/eND!1/2

with « and «0, respectively, the dielectric constant of Si and tvacuum permittivity,VJ junction voltage, e elementary charge, aND the concentration of donors. All the experiments were perform

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with an anodization voltage of 3 V; assuming that all the voltadrops at the silicon-electrolyte interface, we obtain an excessmation of w ranging between 1.4 and 1.7mm for the silicon sub-strate doping we used. In our samples, branching of primary poreobserved when the wall thickness between near pores is greater4 mm, which is more than twice that of the space-charge width. Tresult does not completely agree with the predictions for macropformation in n-type silicon which are based on the aforementiospace-charge region model. Results in agreement with our exments were reported by Follet al.15 for random macropores in asilicon wafer with the same orientation and similar resistivity. Thfact seems to suggest that hole diffusion in the substrate is probthe main limiting effect for pore branching, but other phenomeshould also be considered in order to properly model the pbranching, for instance, the ohmic resistance in the narrow nonpleted region between adjacent pores could play a role as well.

The experimental data suggest that for macropore array fabtion, once the substrate resistivity is fixed, no higher limit existsporosity; any increase of it simply results in larger pores and thinwalls separating pores. A limit was found, however, for the thicknof the silicon walls separating adjacent pores. In fact, once the inpattern is given, a minimum value always exists for the porositythe macropore array, corresponding to a maximum width forsilicon wall separating pores. Below this porosity limit it is npossible to fabricate branch-free patterned pores.

Arrays with different dimensions can be grown on the same scon sample, once the porosity~that is, the etching current density!has been chosen. Two different patterns with a 100% pitch variawere fabricated on the same sample; an SEM top view is showFig. 5. The initial pattern in the oxide was constituted by two arra4 mm squares with a pitch of 8mm, and 8mm squares with a pitch

Figure 5. SEM top view of two difference macropore arrays with 100pitch variation. A macropore array with 14mm side and 16mm pitch ~left!was fabricated simultaneously with an array with 7mm side and 8mm pitch~right!. Random macropores present in the area between the arraysdestroyed by the drying step.

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Journal of The Electrochemical Society, 149 ~3! C180-C185~2002! C183

of 16mm. With a proper choice of the current, a pore array with amm side and a 16mm pitch ~Fig. 5, left! and an array with a 7mmside and a 8mm pitch ~Fig. 5, right! were simultaneously fabricatedA SEM cross section of the Fig. 5 left array is shown in Fig. 6. Poshown in Fig. 5 and 6 are 35mm deep, corresponding to 20 min oetching time with 27 mA/cm2 etching current density. Interestinglythe obtained porosity is greater than that of the initial pattern~25%for both arrays!, and it is found to be about 75% in both arrays,agreement with the current density used in the experiment. It mbe noted that the abrupt end of the pattern does not lead to brancof pores.

Wall arrays were also fabricated, using KOH patterned stralines as initial nucleation sites for electrochemical silicon etchiDimensions and porosity of the fabricated structures are summa

Figure 6. SEM cross section of a macropore array. Thickness of the wal1 mm, while the side of pore is 7mm, corresponding to 75% of porosityPores shown are about 35mm deep. It is evident that 16 stable pores groand join to build the single structure~zoom!.

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in Table II, in a similar manner to the macropores case of TablAgain, no limit is found for higher porosity. However, as in the caof macropore arrays, a lower limit exists, but it is clear from Tablethat the maximum allowable width of silicon walls is significantgreater~up to 6mm! than the maximum width in square arrays. Thcould be explained by considering the field effect of corner existin the macropore arrays between four neighboring pores. In facthe wall array no angles exist focusing electric field lines, so thareduced number of holes, coming from the substrate, are presethe silicon walls, due to insignificant drift field effect. So, it shoube again considered that not only the space-charge layer, buthole path resistance and geometrical shape of the fabricated stures could influence the thickness of the silicon walls in the eltrochemical etching and thus the lower limit of the porosity. A SEcross section of a wall array is shown in Fig. 7. The array wobtained by the anodizing of a KOH pattern of 4mm wide straightlines with a pitch of 8mm. Thickness of the walls is about 2mm,while the spacing is 6mm, corresponding to 75% porosity, accoring to the current density used in the experiment. The wallsabout 25mm deep.

The above reported experimental results do not completely awith the commonly accepted limits reported in Ref. 12. As alreapointed out, the theoretical relationship concerning porosity apore diameter only depends on the etching current density; howein Ref. 12 the substrate resistivity was found to be crucial forpore diameter. This is reasonable when the macropore growthcess is supposed to depend only on the extension of the space-cregion at the pore tips. In fact, if the stable pore diameter reduwith the depletion region width, which in turn depends on the doing density of the substrate, a misadjustment of pitch and/or dopdensity leads to branching of pores for high doping densities odying pores for low doping densities. The region of stable pdiameters is, then, a narrow function of the substrate resistivity.the basis of their results the sensitivity of the system to small va

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Figure 7. SEM cross section of a wall array. Thickness of the walls is ab2 mm, while the spacing is 6mm, corresponding to 75% porosity. The walshown are 25mm deep.

Table II. Condition of fabricated wall arrays for different dimensions and porosities. For the meaning of symbols refer to Table I.

Wall array

Porosity

,25% 25% 50% 75% 80% 85% 90%

2 mm pitch 4mm / / X X X X X4 mm pitch 8mm B X X X X X X8 mm pitch 16mm B B B X X X X

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Journal of The Electrochemical Society, 149 ~3! C180-C185~2002!C184

tions of pitch or doping~for instance, a reduction of the pitch bonly 3%! should change a perfect pore pattern to an imperfect oA rule of thumb for selection of silicon substrate was given,i.e., thesquare of the desired pore diameter~in micrometers! gives the ap-propriate substrates resistivity~in ohms per centimeter!. For ex-ample, 2mm pores could be growth only using a 4V cm n-typesubstrate, and it should not be feasible to fabricate regmacropore array with a side up to 15mm using our substrate. Moreover, the fabrication of regular macropore array with a pitch vation of about 100% should not be possible.

On the basis of exhaustive SEM investigation of the fabricastructures, we suggest a macropore growth model which is abexplain our experimental results. It is known that stable randmacropore growth on surfaces without prestructured nucleationis preceded by two phases of pore nucleation and redistributio15

We suggest that the same nucleation and redistribution phasesexists for stable macropore growth also on prestructured siliconface. Moreover, we postulate that the phase of pore redistributioa crucial step for HF electrochemical silicon etching. The evolutmodel for HF electrochemical silicon regular macropore formatprocess is schematically shown in Fig. 8. For the first time, shalmacropores are formed in correspondence to pre-existing desites~Fig. 8a and b!. The surface density of the shallow macroporcould be relatively high, about the defect density of a polishedcon surface~106 defects/cm2). When the silicon between neighbo

Figure 8. Schematic steps of time evolution model for HF electrochemsilicon etching~macropore formation!.

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ing primary pores is not too thick, according with data reportedTable I and Table II, no secondary pores grow deep in the siliconof the predetermined defects, indeed, because the electric fielocalized at the created notches, few holes can reach the Sinterface through the silicon separating the etched pitch. Due tofact that most of the holes coming from the substrate are collectethe sharper and deeper KOH defects any initial dissolution reacout of the predetermined defects cannot proceed further and onfew holes are available for dissolution of the flat silicon surface.

It is known that an equilibrium density for stable randomacropores growth exists, which depends on silicon substrate rtivity and anodization parameters~voltage, current density!. A redis-tribution phase starts, then, as soon as the nucleation process tnates. In this phase, some pores stop growing and terminwhereas other pores, collecting more holes, continue to growcreasing their diameter. Similarly we postulate that, a redistribuprocess starts, because the density of the macropores growigreater than the equilibrium density. Thus, the diameter of the gring pores increases to reach the value of stable random pores~about2 mm for the used substrate! ~Fig. 8c and d!. As soon as this redis-tribution process terminates, the phase of stable pore growth syielding an arrangement of pores that is stable and does not sig

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Figure 9. SEM cross sections of two wall arrays fabricated starting withmm straight lines and a pitch of 4mm, and different current densities. Thwidth of the initial notch is close to the diameter of stable pores. At 5porosity~top!, corresponding to 2mm pores and walls, a single pore growseach site, while at 90% porosity~bottom!, corresponding to 0.4mm poresand 3.6mm walls, two pores grow at each site.

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Journal of The Electrochemical Society, 149 ~3! C180-C185~2002! C185

cantly change anymore~Fig. 8e and f!. The overall structure growsdeep without further modification of dimensions and shape.

Interestingly, the number of pores growing in the predeterminnotch depends on its dimensions. If the typical dimension ofnotch is approaching the diameter of stable random pores, onlypore grows in correspondence of the single defect, as reported bcommonly accepted model for macropore formation.8 When the di-mension of the defect is much greater than the diameter of thedom pores, more pores grow in the defect site and coalesce, crea structure with a greater dimension. For instance, a 2mm pitch, 4mm square array was fabricated with only one macropore growineach pyramidal notch, while a 4mm pitch, 8mm square array wasfabricated with four macropores growing and joining in each siteboth the experiments, it was necessary to hold the etching decurrent at 0.25Jps, corresponding to 25% of porosity, in orderfabricate a pore array having the same geometrical dimensionthe initial KOH pattern. In fact, we found that the number of stapores growing into a single prepatterned defect depends also oetching current, once the dimension of the defect is fixed. Thidirectly related to the dimension of the obtained structure. As maof fact, it can be noted that starting from a KOH pattern of squholes with a side of 4mm and a pitch of 8mm, when the usedetching current is raised at 0.75Jps, corresponding to 75% of porosity, the number of stable pores growing and joining increafrom four ~J 5 0.25Jps! up to sixteen~see Fig. 6, zoom!. This is theexplanation of the result that, once the initial pattern is assigned,possible to vary the porosity of the fabricated sample simplyvarying the anodization current density. In Fig. 9 are shownSEM cross sections of two wall arrays, anodized with proper crents to obtain porosities respectively, of 50%~up! and 90%~bot-tom!. The same initial pattern, straight lines 2mm width with a pitchof 4 mm, was used as a seeding pattern for both arrays. It is evithat only one pore grows for 50% of porosity, while two pores grand join to assemble the final structure for 90% of porosity, accoing to the above discussed macropore growth model.

Similar results about the growth of several pores in a sinpredetermined defect were reported using isotropic wet etchingRIE notches as seeding points.16 In Ref. 16 it is reported that, due tthe higher current density at the corners of any primary notch,electrochemical etching initially starts at the four corners. In osample a KOH etching was used for seeding points formationthat inverse pyramidal defects were fabricated as initial defeNonetheless, as discussed above, the number of the pores groand joining at any notch can be higher than four. Our results sug

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that, though the effect of the corners is significant in the procesmacropore formation, other aspects, as the dimension of theterned defect and the etching current density, as well as the shathe defect~square hole or straight line!, should be taken into accounto properly model the electrochemical etching of the substrate.

Conclusions

In this paper a study of the photoelectrochemical formationprepatterned macropores on a silicon substrate with 2.4-4V cmresistivity is reported. Dimensional constraints for macroporemensions as a function of the resistivity of the substrate are shto be significantly less severe than those reported in the prevliterature. Macropore arrays with sides ranging between 2 andmm, as well as arrays of walls with comparable dimensions, wfabricated on the same substrate. A simple physical model basethe coalescence of several smaller random pores, which includecommonly accepted model as a particular case, is proposed toplain the experimental data. This increased flexibility in the choof the dimensions could allow new applications of the photoelecchemical etching technique in the field of silicon microfabricatio

Universitadi Pisa assisted in meeting the publication costs of this artic

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