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`Anisotropic Etching of Crystalline Silicon in
`Alkaline Solutions I. Orientation Dependence
`and Behavior of Passivation Layers
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`ARTICLE in JOURNAL OF THE ELECTROCHEMICAL SOCIETY · NOVEMBER 1990
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`3612 J. Electrochem. Soc., Vol. 137, No. 11, November 1990 (cid:14)9 The Electrochemical Society, Inc. 5. J. Bloem and L. J. Giling, in "Current Topics in Mate- rial Science," Vol. 1, E. Kaldis, Editor, pp. 147-342, North-Holland Publishing Company, Amerstdam (1987). 6. W. G. J. H. M. van Sark, G. Janssen, M. H. J. M. de Croon, and L. J. Giling, Semicond. Sci. Technol., 5, 16 (1990). 7. Ibid., 36 8. M.H.J.M. de Croon and L. J. Giling, This Journal, 137, 2867 (1990). 9. J. van de Ven, G. M. J. Rutten, M. J. Raaijmakers, and L. J. Giling, J. Cryst. Growth, 76, 352 (1986). 10. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, "Trans- port Phenomena," pp. 249-260, John Wiley & Sons, New York (1960). 11. M.Abramowitz and I.A. Stegun, "Handbook of Mathe- matical Functions," pp. 446-452, Dover Publications, New York (1970). 12. W. G. J. H. M. van Sark, M. H. J. M. de Croon, G. Jans- sen, and L. J. Giling, Semicond. Sci. Technol., 5, 291 (1990). 13. P. R. Hageman, X. Tang, M. H. J. M. de Croon, and L. J. Giling, J. Cryst. Growth, 98, 249 (1989). 14. M. H. J. M. de Croon and L. J. Giling, Prog. Crystal Growth and Charact., 19, 125 (1989). 15. M. H. J. M. de Croon and L. J. Giling, To be published. Anisotropic Etching of Crystalline Silicon in Alkaline Solutions I. Orientation Dependence and Behavior of Passivation Layers H. Seidel Messerschmitt-B6lkow-Blohm GmbH, D-8000 Munich 80, Germany L. Csepregi Fraunhofer-Institut fi~r FestkSrpertechnologie, D-8000 Munich 60, Germany A. Heuberger Fraunhofer-Institut fiir Mikrostrukturtechnik, D-I O00 Berlin 33, Germany H. BaumgSrtel lnstitut fi~r Physikalische Chemic, Freie Universit~it Berlin, D-IO00 Berlin 33, Germany ABSTRACT The anisotropic etching behavior of single-crystal silicon and the behavior of SiO2 and Si3N4 in an ethylenediamine- based solution as well as in aqueous KOH, NaOH, and LiOH were studied. The crystal planes bounding the etch front and their etch rates were determined as a function of temperature, crystal orientation, and etchant composition. A correlation was found between the etch rates and their activation energies, with slowly etching crystal surfaces exhibiting higher acti- vation energies and vice versa. For highly concentrated KOH solutions, a decrease of the etch rate with the fourth power of the water concentration was observed. Based on these results, an electrochemical model is proposed, describing the aniso- tropic etching behavior of silicon in all alkaline solutions. In an oxidation step, four hydroxide ions react with one surface silicon atom, leading to the injection of four electrons into the conduction band. These electrons stay localized near the crystal surface due to the presence of a space charge layer. The reaction is accompanied by the breaking of the backbonds, which requires the thermal excitation of the respective surface state electrons into the conduction band. This step is con- sidered to be rate limiting. In a reduction step, the injected electrons react with water molecules to form new hydroxide ions and hydrogen. It is assumed that these hydroxide ions generated at the silicon surface are consumed in the oxidation reaction rather than those from the bulk electrolyte, since the latter are kept away from the crystal by the repellent force of the negative surface charge. According to this model, monosilicic acid Si(OH)4 is formed as the primary dissolution prod- uct in all anisotropic silicon etchants. The anisotropic behavior is due to small differences of the energy levels of the back- bond surface states as a function of the crystal orientation. Anisotropic etchants for crystalline silicon have been known for a long time (1-3). Their first applications in- cluded the etching of V-grooves on <100> silicon or U- grooves on <110> silicon, in order to fabricate MOS tran- sistors for high power and high current densities (4). In- creasing attention has been paid to this etching technol- ogy, after recognizing its unique capabilities for micromachining three-dimensional structures (5-9). Due to the strong dependence of the etch rate on crystal direction and on dopant concentration, a large variety of silicon structures can be fabricated in a highly controllable and reproducible manner. Typical structures include thin membranes, deep and narrow grooves, and cantilevers with single or double sided suspension. Important fields of application include the fabrication of passive mechanical elements, sensors, and actuators, as well as micro-optical components (8, 10). Among the best known examples are sensors for pressure (8), acceleration (11), and flow (12), as well as ink jet nozzles (13), connectors for optical wave- guides (14), and major components of a gas chromatograph (15). All anisotropic etchants are aqueous alkaline solutions, where the main component can be either organic or inor- ganic. The first organic system was proposed in 1962 and consisted of hydrazine (N2H4) and water with the addition of pyrocatechol (C6H4(OH)2) (16). It was shown that pyro- catechol is not a necessary component, and might well be omitted (2). Experiments were made with iso-2-propyl al- cohol as a third component, which was shown to act as a moderator (3). In a later work, hydrazine was substituted by ethylenediamine (NH2(CH2)~NH2), which is more stable and less toxic than the former (2). Purely inorganic aqueous solutions of KOH and NaOH have been known to etch silicon anisotropically for a long time (1). A different system with improved etching behav- ior was obtained by the addition of isopropyl alcohol (17).
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`J. Electrochem. Soc., Vol. 137, No. 11, November 1990 (cid:14)9 The Electrochemical Society, Inc. 3613 In general, all aqueous solutions containing hydroxides of other alkali metals, like LiOH, and CsOH (18) perform in a similar manner. Aqueous solutions of ammonium hydrox- ide (NH4OH), were also reported to etch anisotropically (19). The same type of solution with the addition of H202 is frequently employed for the cleaning of silicon wafers (20). More complicated derivatives of ammonium hydroxide, e.g., so-called quaternary ammonium hydroxides like tet- ramethyl ammonium hydroxide (N(CH3)4OH) and choline ((CH3)3N(CH2CH2OH)OH) can also be used as anisotropic etchants (21). General Considerations Solutions consisting of ethylenediamine, water, and py- rocatechol (EDP) are among the most widely employed. Many essential results concerning the composition of this system and its crystal orientation dependence were re- ported in the work done by Finne and Klein (2). They found that pyrocatechol can be omitted, so that in its most primitive form, the etchant solely consists of ethylenedia- mine and water. With nonaqueous ethylenediamine no etching was achieved, indicating that water is an active and necessary component. The maximal etch rate oc- curred at an ethylenediamine to water molar ratio of ap- proximately 1:2. By the addition of pyrocatechol, a strong increase of the etch rate by a factor of three was obtained, saturating at a concentration of approximately 4 mole per- cent (m/o). For the three main silicon crystal orientations <100>, <110>, and <111>, Finne and Klein found an etch rate ratio of 17:10:1. The effects of further additives were studied by Reisman et al. (22). They found that when exposing the EDP solu- tion to oxygen, 1,4-benzoquinone and other products are formed, leading to an increase of the etch rate and a darkening of the solution. This effect can be avoided by continuously purging the etching apparatus with an inert gas (2, 22). They also found that trace quantities of pyra- zine (C4H4N2) lead to an increase of the etch rate. However, similar to pyrocatechol, this effect nearly saturates at a concentration of 3g pyrazine per liter ethylenediamine. Since commercially available ethylenediamine usually contains an unknown trace amount of pyrazine, Reisman et al. (22) proposed to intentionally add enough pyrazine to the solution so that the saturation level is reached. For the ethylenediamine-water-pyrocatechol system several recipes were proposed. Reisman et al. developed two specific solutions optimized for use where either a high etch rate is required ("F"), or where slower etch rates and/or lower temperatures are desired ("S") (22). Their specific compositions are listed in Table I, together with a recipe used by Finne and Klein ("T") (2) and another one proposed by Bassous ("B") (23). For both solutions suggested by Reisman et al. (22) an activation energy of 0.36 eV on <100> silicon was found, which increased to 0.47 eV when no pyrazine was added. Furthermore, they determined an anlsotropy ratio for the <100>/<111> silicon etch rates of 19 and 13.5 with and without pyrazine, respectively. Finne and Klein were the first authors to publish reac- tion equations for the etching process (2). Based on a chemical analysis of the reaction products and on the ob- servation that hydrogen evolves during etching in a stoi- chiometric ratio of approximately 2 H2/Si, they proposed an oxidation-reduction step with hydroxide ions and water reacting with the silicon surface, followed by a che- lation stage involving pyrocatechol Si + 2(OH)- + 4H~O -~ Si(OH)6-- + 2H2 [1] Si(OH)6- + 3C6H4(OH)2---> Si(O2C6H03-- + 6H20 [2] They assumed the chelation to be the slow step, unless pyrocatechol was added at a concentration exceeding 4 mole percent (m/o). In that case they considered the oxida- tion reaction to be rate limiting. Pyrocatechol was as- sumed to act mainly as an agent to increase the solubility of the silicon compound, thus increasing the reaction rate. The above mentioned oxidation-reduction equation was used by several authors in later publications without Table I. Composition of different EDP solutions published by Finne and Klein (2), Reisman et al. (22), and Bassous (23) Type S (22) F (22) B (23) T (2) Water ml 133 320 320 470 ED 1 1.0 1.0 1.0 1.0 Pyrocatechol g 160 320 160 176 Pyrazine g 6 6 major modifications (22, 24). The gross reaction proposed in this equation does not provide an obvious explanation for the anisotropic behavior of the etchant. For this pur- pose it must be broken up into its fundamental reaction steps. It was noticed by several workers that residues might appear on the silicon surface. The occurrence of this phe- nomenon depends on the composition of the solution and on its saturation level with silicon. For EDP solutions, Reisman et al. (22) have found that this tendency increases with the water content of the solution. With respect to the aging of the solution, quantitative results were given by Wu et al. (25). They found that in a one liter solution (type F and type B) at a temperature of 100~ a maximum amount of 10g silicon can be etched without producing solid resi- dues. This value was slightly higher for the F etchant which was attributed to its larger content of pyrocatechol. A chemical analysis of the residues showed that they con- sisted mainly of SiO~ with additional trace amounts of re- action products. The work of Abu-Zeid et al. (26) showed that, for ethyl- enediamine-based solutions, the silicon etch rate can be in- creased considerably by stirring. They also showed that the etch rate depends on the effective silicon area being exposed to the solution and its geometry. An increase can be observed, when the area of the active region gets smaller. These results indicate that diffusion processes in- fluence the silicon dissolution rate considerably. For hydrazine water solutions a very similar behavior to the one observed in EDP solutions was found (3, 27, 28). At a temperature of 118~ an etch rate ratio of 16:9:1 for the {100}:{110}:{111} planes was determined, which is compa- rable to EDP (28). When underetching convex corners, (211) was identified as an etch bordering plane with a very high etch rate (3, 27). Among the inorganic solutions, the one most frequently used is based on KOH. The first detailed study on a ternary mixture of KOH, water, and isopropyl alcohol was given by Price in 1973 (17). His major observations were the fol- lowing: the maximal etch rate occurred at a KOH concen- tration of 10-15 weight percent (w/o) when no alcohol was added, and around 30% KOH with alcohol. In general, the addition of isopropyl alcohol leads to a decrease of the etch rate. On <100> silicon the activation energy was found to be between 0.52 and 0.69 eV. He found no effect of stirring on the etch rate, indicating that the reaction is not diffu- sion limited. Under optimum conditions, Price observed an etch rate ratio of 35:1 for the {100}/{111} crystal planes (17). A much higher anisotropy ratio of up to 500:1 for the <110> to <111> etch rates in a highly concentrated 55% KOH solution was reported by Kendall (29, 30). Further data on the etch rates of <110> and <111> silicon as well as SiO2 were given by Clark and Edell (31). For KOH solu- tions with a concentration between 9 and 54 w/o, they found the following ranges of activation energies: 0.6-0.8 eV for <110>, 0.4-0.9 eV for <111>, and 0.8-1.0 eV for SIO2. In a work done by Palik et al. (32) the etching process of KOH on silicon was monitored in situ by Raman spectros- copy. From these experiments the main reaction species was determined to be OH-. They proposed SiO2 (OH)z-- to be the primary etching product with subsequent polymer- ization. The following overall gross reaction was suggested by them (33) Si + 2H~O + 2 OH- --> Si(OH)202-- + 2H2 [3] From experiments done with isopropyl alcohol added to the KOH solution, they conclude that the alcohol does not
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`3614 J. Electrochem. Soc., Vol. 137, No. 11, November 1990 (cid:14)9 The Electrochemical Society, Inc. participate chemically in the reaction. In a later work (34), Palik et al. included energy level considerations, stating that the etching reaction transfers an electron from OH- into the silicon surface bond and then back to the etch products. A more detailed break down of the reaction equations, including the transfer of charge was suggested by Raley et al. (24). They assumed that four electrons are injected into the conduction band by an initial oxidation reaction, which are later consumed in a reduction step Si + 2 OH- --> Si(OH)2 ++ + 4e- [4] Si(OH)2 ++ + 4e- + 4H20 ~ Si(OH)6-- + 2H2 [5] In the literature published to date several attempts were undertaken to explain the anisotropic behavior of these etchants. Price indicated that a correlation between the available bond density of different crystal planes and the etch rate could exist (17). However, it is difficult to explain etch rate ratios of about 100:1 when the bond density only varies by a factor of two. Another proposal was made by Kendall who argues that {111} planes get oxidized more rapidly than others and therefore could be covered with a thin oxide layer immediately after immersion into the etchant (29). Palik et al. assume that the anisotropy might be attributable to differences in activation energies and in backbond geometries on different surfaces (33). In this paper, experimental results on the orientation de- pendence of the silicon etch rate for several solutions as a function of composition and temperature will be given. An attempt will be made to give a model valid for all anisotro- pic silicon etchants, explaining the underlying mecha- nism. Furthermore, results on the etch behavior of the most widely used passivation layers SiO2 and Si3N4 will be reported. The effects of dopants on the silicon etch rate will be dis- cussed in an accompanying paper (35). Experimental In the experiments, n- and p-type Czochralski grown 3 in. wafers with <100> and <110> orientation were used. The resistivity was 1-10 ~-cm, corresponding to an impur- ity concentration of approximately 1 - 1015 - 1 (cid:12)9 1016 cm -3. For passivation, these wafers were either thermally oxi- dized or a CVD silicon nitride layer was deposited. In order to obtain detailed data on the crystal orientation dependence of the etch rate, a fan shaped or wagon wheel shaped masking pattern was employed, consisting of radi- ally divergent segments with an angular separation of one degree (36-40). This pattern was transferred to the passiva- tion layer. Thus, alternating segments of bare silicon and regions covered with silicon dioxide or silicon nitride were obtained. The size of a chip containing one such pattern was 16 (cid:12)9 16 mm 2. In order to achieve a more accurate angu- lar resolution, particularly in the neighborhood of {111} planes, where the etch rate is a very sensitive function of the angular orientation, a second pattern with segments and spaces differing by an angle of 0.1 ~ and with a total an- gular spread of 4 ~ was used. For etch rate studies on passivation layers, wafers covered with thermal SiO2 (1000~ wet), CVD-SiQ (Sill4, N20, 800 ~ and 900~ and CVD-Si3N4 (Sill4 and NH3, 900~ were prepared and diced to the same chip size mentioned above. The samples were etched in an oil-heated, double-walled glass vessel. The temperature was varied between 20 ~ and 115~ and was controlled with an accuracy of -+0.2~ In order to keep the composition of the etchant constant, the vapors were recondensed in a water cooled reflux con- denser. In the case of EDP solutions, an additional nitro- gen purge was applied, in order to prevent changes of the etch properties due to contact with atmospheric oxygen (2, 12). The inorganic etchants employed in the experiments were KOH, NaOH, and LiOH with concentrations in the range of 10-60, 24, and 10%, respectively, where all values are in weight percent. In some experiments, isopropy] al- cohol was added to a 20% KOH solution according to the following recipe: 1 liter H20, 312g KOH, 250 ml isopropyl alcohol. The only organic etchants used were EDP solu- tions, among which a composition type "S" introduced by Reisman et al. was employed most frequently (Table I). This choice was made because it is applicable in a wide temperature range which is important for obtaining reli- able data on activation energies. After etching the chips masked with a wagon wheel pat- tern, a blossom-like figure developed. This phenomenon is due to the total underetching of the passivation layer in the vicinity of the chip center, leaving an area of bare exposed silicon. The radial extension of this area depends on the crystal orientation of the individual segments, leading to a different amount of lateral underetching. The pattern de- veloped on a <100> test sample etched in an EDP solution is shown in Fig. 1. Visual inspection of such blossom-like patterns was only used for a qualitative evaluation of the anisotropy. In order to obtain quantitative results, the lateral etch rates were determined by measuring the width w of the overhanging passivation layer with an optical linewidth measurement system (LEITZ Latimet). This is illustrated in Fig. 2, show- ing a schematic cross section of the test chip after etching. Additionally, the depth d of the etch grooves and the orien- tation of the etch bordering planes were determined by means of a mechanical stylus profiler and laser reflection methods, respectively (41). Similar measurements were performed on chips with the 0.1 ~ pattern. Fo~ determining the etch rate of the passivation layers, their thicknesses were measured by ellipsometry before and after etching. Results Morphology of the etched silicon surfaces.--After etching a partially masked silicon surface, two regions of interest arise. One is the bottom surface obtained from vertical etching, the other consists of the laterally under-etched sidewalls developing along the edges of a masking pattern. When using EDP solutions, the surfaces generally tend to be quite smooth, particularly on etched bottom surfaces of <100> wafers. Also, the laterally under-etched sidewalls of the passivated segments are generally smooth. How- ever, as indicated in Fig. 3, a certain waviness can be ob- served on fast etching sidewall crystal planes. On etched surfaces of < 110> wafers with relatively large areas exposed to the etchant, a linearly textured structure develops which can be recognized with the naked eye. When viewed under a scanning electron microscope, as shown in Fig. 4, these textured surfaces appear to be bounded by well-defined, slanted crystal planes. As has been observed in numerous previous studies, {111} crystal planes form perfectly smooth lateral side- walls, both on <100> and on <110> wafers, and for all etchants investigated (5, 6). In case of alkaline etchants like KOH, the vertically etched bottom surfaces of <100> and <110> wafers turn out to be relatively smooth. However, when using a solu- Fig. 1. Etch pattern emerging on a masked test wafer with the orien- tation <100> after etching in an EDP solution type S. The residual oxide at the center is due to the finite resolution of the mask.
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`J. Electrochem. Soc., Vol. 137, No. 11, November 1990 (cid:14)9 The Electrochemical Society, Inc. 3615 Fig. 2. Schematic cross section of a silicon test chip covered with a star-shaped masking pattern after etching. tion of low concentration (below 30%), a tendency for the formation of pyramids can be observed on <100> wafers. The laterally underetched sidewalls of the masked seg- ments generally appear to be fragmented, as demonstrated in the micrographs of a <110> wafer shown in Fig. 5a and b. Both pictures show a steep-walled mesa rising over a more gently sloped shoulder. Within this formation patches with smooth {111} surfaces can be observed. They are surrounded by jagged surfaces which could not be identified as any particular crystal plane. Etch limiting crystal planes.--By means of laser reflec- tion measurements, as indicated in Fig. 2, the crystal orien- tation of the planes bounding the laterally underetched segments was determined for the case of EDP etchants. These planes are shown in Fig. 6 for <100> and <110> wa- fers in the form of stereographic projection diagrams. For both wafer orientations they can be characterized by the Miller indexes {hhk} where h and k are integers with h -> k. This was found for all EDP compositions and tempera- tures applied. As mentioned above and indicated in Fig. 4, a linearly textured structure develops on bottom surfaces of etched <110> wafers. The crystal orientation on the long steps in this texture was found to be close to {331}. On the basis of these results, it is surprising to observe the formation of smooth, laterally underetched {110} surfaces on <100> wafers, when using EDP solutions. A similar surprise is the formation of smooth, flat-etched bottoms when etch- ing narrow grooves bounded by vertical {111} planes on <110> wafers. This phenomenon is probably attributable to the different geometrical situation of a flat, large sur- face, as compared to a small sidewall bounded by concave corners. For silicon surfaces etched by KOH, the resulting crys- tallography depends on the composition of the etchant. Furthermore, as mentioned above, only a limited number of crystal planes can be identified. For relatively high KOH Fig. 3. Fast etching sidewalls on a <100> silicon wafer after expo- sure to an EDP solution type S. Fig. 4. Main surface of a <110> silicon wafer after etching in an EDP solution type S. concentrations, exceeding 35%, these planes are shown in the stereographic projection diagrams in Fig. 7. In contrast to EDP solutions, vertical {100} planes emerge on <100> wafers (Fig. 7a) when a masking pattern with an angle of 45 ~ to the flat is used (39). When misaligning such a pattern by a few degrees with respect to this 45 ~ line, the vertical smooth sidewall remains, but an inclined shoulder begins to form in the corner. When misalignment exceeds a few degrees, a similar situation as shown in Fig. 5a develops. The crystal planes marked in the central region of the <110> diagram, Fig. 7b, correspond to the slanted shoul- ders depicted in Fig. 5b. The vertical {111} planes on <110> wafers rise over an inclined shoulder of {311} planes. Such a shoulder does not arise when using EDP so- lutions. Lateral etch rate as a function of crystal orientation.- As mentioned above, it was found for EDP solutions that etch bordering crystal planes develop, which are charac- terized by the indexes {hhk} (h >- k). The lateral underetcb rates of these planes on <100> and <110> wafers for a temperature of 95~ are shown in the polar coordinate dia- grams in Fig. 8. Apart from the sharp absolute minima at {111} planes, relative minima occur at {110}. The maximal lateral etch rate is observed for {331} planes. The differences of the lateral underetch rates of crystal planes occurring several times on the same diagram, e.g., in Fig. 8b, are due to different slanting angles of these planes. The immediate result of the measurement is the projection of the etch rate onto the surface of the wafer. The true etch rate can be calculated by multiplying the ap- parent lateral underetch rate, as measured by the over- hanging film of the passivation layer, by the sine of the in- clination angle O. This factor can be given as a function of the lateral alignment angle ~ in the wafer plane. When the <110> direction, which corresponds to the intersecting line of the {100} wafer plane and the resulting etch border- ing {111} plane, is taken as ~ = 0 ~ the following formula applies 0 ~ -< ~ < 45 ~ [6] 1 sin O = 1 tan2 ( 450 - 4) + 2 For <110> wafers again with the <110> direction taken as = 0 ~ which in this case corresponds to the intersecting line of the {110} wafer plane and the {111} planes with an inclination angle of 35.3 ~ , the correction factor is given by sin O = ~l tanZ~ + 1 0 ~ ~ -< 54.7 ~ [7] 2tan 2~-2 t~+3
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`3616 J. Electrochem. Soc., Vol. 137, No. 1t, November 1990 (cid:14)9 The Electrochemical Society, Inc. Fig. 5. Laterally underetched sidewall of a masked segment on a <110> wafer after exposure to a 50% KOH solution. The edges of the masked segment diagonally crossing the picture had an angular misalignment of (a, left) 32 ~ and (b, right) 42 ~ with respect to the [110] direction, which is. parallel to the 35.3 ~ inclined {111 } planes. When an angular correction is applied according to these equations, the etch rates of the same crystal planes with different inclinations nearly coincide. The result of such a transformation on a <110> wafer is shown in Fig. 9. For KOH solutions, similar polar coordinate diagrams for <100> and <110> wafers are shown in Fig. 10. These results are in general agreement with the KOH data of de Guet et al. (42). In comparison to the results obtained with EDP (Fig. 8), it is remarkable that the peak etch rates are far more pronounced. However, since the sidewalls are not particularly flat, the resulting etch rates can be attributed to specific crystal planes only for some orientation angles. All other etch rates are average values for surfaces com- posed of many different crystal planes. The lateral etch rate in the vicinity of {111} crystal planes is extremely sensitive to small angular misalignments. This can be seen from high resolution measurements, the results of which are shown in Fig. 11 for EDP and KOH so- lutions. The etch rate increases by about a factor of two for a misalignment of 1 ~ on a <100> wafer. On a <110> wafer, this effect is even more pronounced due to the faster varia- tion of crystal planes as a function of misalignment (29). Thus, in practical applications where large aspect ratios are important, precise alignment is crucial. Temperature dependence of the etch rates.--The tem- perature dependence of the vertical etch rate on <100> wafers for various EDP and KOH solutions is shown in Fig. 12. For an EDP solution type S an activation energy of 0.40 eV was determined. For KOH solutions, values be- tween 0.57 and 0.62 eV were found. On <110> surfaces, the results were 0.33 eV for EDP and again between 0.57 and 0.62 eV for KOH solutions. The activation energies Ea and pre-exponential factors Ro were determined according to the Arrhenius law R = Ro (cid:12)9 exp(-EJkT). The experimental results obtained on <100> and <110> wafers are listed in Table II for <100> and <110> wafers for all etchants investigated. A feature of general interest for many practical applica- tions of anisotropic silicon etching is the ratio of the etch rates of the main crystal planes {100}, {110}, and {111}. The {100} and {110} rates were determined by vertically etch- ing <100> and <110> wafers. The <111> etch rate was de- termined by laterally underetching segments on < 100> or <110> wafers with an angular separation of 0.1 ~ The re- sults for an EDP solution type S are shown in Fig. 13. It can be seen that the slower the etch rate, the higher is the activation energy. As a consequence, the etch rate ratio of <110>/<111> as well as <100>/<111> increases from 30:1 1~o~11o 1~ lO0 001 0ol Fig. 6. Stereographic projection diagrams of crystal planes bounding the etch front when laterally underetching a masking pattern on (a, left) <100> and (b, right) <110> wafers in an EDP solution.
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`J. Electrochem. Soc., Vol. 137, No. 11, November 1990 (cid:14)9 The Electrochemical Society, Inc. 3617 100 ~00 001 ITi.~I~[ 001" Fig. 7. Stereographic projection diagrams of crystal planes bounding the etch front when laterally underetching a masking pattern on (a, right) <100> and (b, left) <110> wafers in a KOH solution with a concentration exceeding 30%. near the boiling point of the solution to about 150:1 and 100:1, respectively, at 50~ A similar behavior can be ob- served for KOH solutions. <110> etches about 60% faster than <100>, with nearly identical activation energies of 0.61 and 0.59 eV, respectively. The activation energy of <111> is approximately 0.7 eV. The etch rate ratio of <110>:<100>:<111> was found to vary from 50:30:1 at 100~ to about 160:100:1 at room temperature. These re- sults show that the anisotropy ratios are roughly compa- rable between EDP and KOH. However, as mentioned ear- lier, the exact values of these etch ratios depend on the effective area exposed to the solution, especially in EDP solutions (26). The temperature dependence for the lateral etch rates of different crystal planes on <100> wafers was measured for an EDP solution type S. The results are shown in the Ar- rhenius diagram in Fig. 14 where the parameter of the dif- ferent curves refers to the polar alignment angle of the edge of the masking pattern with respect to the <110> di- rection. As can be seen from this diagram, the activation energy is higher on crystal planes with a lower etch rate. This situation is indicated in more detail in Fig. 15a, and b, where the activation energy and the pre-exponential fac- tor are shown as a function of orientation angle, corres- ponding to specific crystal planes. The activation energies vary between 0.25 and 0.52 eV. KOH etchants reveal a similar behavior. However, in this case the orientation angle cannot always be correlated to a specific crystal plane, as mentioned above. The activation energies were found to vary between 0.58 eV and approxi- mately 0.7 eV, which is in good agreement with earlier re- ports of 0.51-0.64 eV (30) and 0.57-0.71 eV (31) for <100> and <110> at low and high KOH concentrations, respec- tively. Influence of etchant composition and concentration.- For very high KOH concentrations exceeding 15 w/o the silicon etch rate decreases when raising the concentration further, as indicated in Fig. 16. It was found that for very high concentrations the data could best be fitted by assum: ing a proportionality to the fourth power of the molar water concentration. For the full range of concentrations investigated, the best fit for the etch rate R was obtained by taking R ~ [H20] 4 [KOH] 1/4. When isopropyl alcohol is added to a KOH solution, a general decrease of the etch rates can be observed, which is about 20% for <100>, but almost 90% for <110>. This is shown in Fig. 17 for a 20% KOH solution with and without the addition of 250 ml isopropyl alcohol per liter water.