Rapidly Renewable Lap: Theory and Practice

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  • Rapidly Renewable Lap: Theory and Practice

    Chris J. Evans (21, Robert E. Parks, David J. Roderick, Michael L. McGlauflin National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

    Received on January 8,1998

    The Rapidly Renewable Lap (RRL) uses a textured substrate over which thin films are slumped. The substrate provides the geometry of the lap and a localized texture, depending on the film thickness, properties, and means by which it is deformed over and adhered to the substrate. Abrasives, added to the film, lap or polish without touching or changing the substrate geometry. Depending on process parameters, the RRL gives brittle or ductile (two-body) lapping. This paper has two major themes: it describes the RRL and some applications; and it shows that some relatively simple lapping models predict of process characteristics.

    Keywords: Lapping, polishing, abrasion

    1. Introduction Lapping and polishing are probably the oldest manufacturing professions, with applications dating back to Neolithic man1 and with published process descriptions starting in the 16th century2. Today, these processes are cruaal to the semiconductor3 and many other industries. Not surprisingly, lapping and polishing have been widely investigated and were the subject of two recent CIRP keynote papers45.

    Lapping and polishing processes (except "non- contact" processes such as float polishing6 and elastic emission machining-/) involve the mechanical interaction of three elements: the workpiece surface, the sluny partide, and the surface of the lap. The workpiece geometry is determined by the lap shape, which may change in-process, while surface finish and sub-surface damage are affected by numerous parameters such as load, speed, work and lap material properties, slurry temperature and chemistry. Often the lap properties which optimise finish are not ideal for form control.

    The Rapidly Renewable Lap8 (RRL) separates the functions of figure and finish control and can be used for a broad range of lapping and polishing processes9 (Table 1). It is highly repeatable, and hence makes process investigations easier. In developing and applying the RRL technology, we have gained experience that is summarized in the first part of this paper. That experience indicated RRL characteristics that are contrary to expectations based on classical optical shop experience and on the published literature. The second part of the paper, therefore, desuibes a simple process model defined to help understand system behavior and a set of experiments aimed at validating that model.

    2. Essential features of the RRL The basic idea of the RRL is a lap comprising two parts: a stable textured substrate onto which is held a film that conforms or partially conforms to the substrate's local texture. Abrasives may be embedded in the film, or a sluny applied. The substrate may be flat or have a long radius of curvature; sharply radiussed substrates will cause film puckering.

    A number of implementations of the basic RRL idea are possible. We have focussed on the use of vacuum to both hold the film in place and cause it to partially conform to the

    texture in the substrate (Figure 1). This has been implemented on two kinematically different polishing machineslo; a 300 mm diameter conventionall 1 over-am polisher and a three station 300 mm lapper. In each case, the only required machine modification was to drill out the spindle and add a vacuum union. Implementation on a 600 rnm diameter polisher is nearing completion.

    Polymer or metal Impervious film or pad

    Backing plate

    Spindle G Figure I: The rapidly renewable lap concept

    Table 1: RRL applications have used a number of combinations of materials Film

    Mylar Polyethylene Polyetherether- ketone (PEEK) Themal shrink wrap Kyanar Polyurethane Abrasive papers


    Alumina Diamond Silicon carbide Chrome oxide Cerium oxide Colloidal silica Colloidal alumina

    Work material Copper Aluminum Anodized aluminum Niobium Stainless steel Electroless nickel Filter glass Fused quark Laser phosphate glass Silicon Sapphire Silicon carbide Silicon nitride

    Annals of the ClRP Vol. 47/1/1998 239

  • For much of our work we have used porous ceramics as the lap substrates. These are available with pore sizes up to 5 mm. Particularly*convenient are foamed silicon carbides12 with 4-12 poredun , which can readily be ground with a resin bond diamond wheel to create a plane of small plateaux. Once the substrate is mounted on the polishing machine, final adjustments to figure can be made using diamond abrasives and appropriate laps. In some polishing applications, control of temperature is considered Critical, leading to the introduction of cooling channels in the cast iron lapping plates of commercially available machines. We have shown that the ceramic substrates can be replaced with metal plates which are compatible with cooling channels and have texture machined into the surface.

    A variety of polymeric and metal films have been used. Most of the polymer films deform elastically over the substrate texture, although 75 pm polytetrafluorethylene (PTFE) crept and failed in a matter of minutes. Aluminum foils (12 and 25 pm thick) deform plastically. Polyurethane and similar pads currently used for industrial chemomechanical polishing (CMP) applications have also been used. Conventional thickness pads performed in the same manner as when used on a conventional lap; the substrate texture propagated through specially thinned pads (0.5 mm), offering the prospect of providing textures on different spatial scales.

    Clearly the construction of the RRL leads to some specific and desirable characteristics: 1. 2.






    The substrate defines the geometry of the finished part; The abrasive never touches the substrate, so its shape never changes; No adhesives are used, so the film may be changed in seconds, allowing rapid changes of abrasive size or type knowing that the part will "fit"; Varying the texture in the substrate changes the spatial scale of lap surface texture; Varying the applied vacuum changes the amplitude of the lap surface texture Additional control of lap surface texture can be obtained by changing the micro-texture of the film

    Experience with the RRL As indicate above, the RRL has been applied to a broad range of lapping and polishing processes (Table 1). Rather than try to follow conventional, inconsistent, process nomenclature, we will class@ processes by the three primary modes of material removal observed in RRL applications to date.

    3.1 Fracture mode lapping In the fabrication of glass, ceramic and crystalline components most of the material removed is via the initiation and propagation of fracture. In the dassical optics shop, fixed abrasive roughing operations are typically followed by fine "grinding" using alumina or silicon carbide abrasives and a cast iron tool. Similar lapping operations are used, for example, in silicon wafer processing and the manufacture of silicon carbide automotive water seals for automobile uses.

    Similar processes have been implemented on the RRL using 75 pm thick Mylar films. Silicon carbide abrasives up to 25 pm have been used to lap sapphire and alumina used to lap a range of glasses, from a soft filter glass to fused silica. Data on removal rates for the latter process are given in Figure 11. Two qualitative observations differentiate surfaces prepared in this mode on the RRL from those prepared more conventionally: 1. The 'gray' glass surfaces have finer scale fracture, observed from the surface, than those prepared on a cast iron tool using the same abrasive size;

    Pores intersected by randomly selected lines on the surface


    2. These surfaces clean up quickly and uniformly when changing from lapping with alumina to polishing with ceria. Gray fused silica surface prepared using 9 pm alumina can be polished uniformly to a 1 nm rms finish13 in less than 10 minutes, although it is not clear that all the sub-surface damage has been removed at this stage.

    Note also that, unlike the 2-body ductile diamond lapping process described below, this process involves significant wear of both the work material and the lap film. Figure 2 shows scanning electron micrographs of wear on Mylar film. Experience shows that film life under representative conditions on the 300 mm lapper (30 rpm, 0.75 glmm2) is about 8 hours. The process described here may fall between the classic definitions of two- and three-body abrasive wearl4-15 :

    "Two-body abrasive wear occurs when a rough surface or fixed abrasive particles slide across a surface to remove material. In three-body abrasive wear, the particles are loose and may move relative to one another, and possibly rotate, while sliding across the wearing surface."

    From observation of the surfaces produced, there is no way to determine what proportion of the abrasive particles interacting with the surface are sliding or rolling. Whatever the mechanism, the surfaces produced are nearly isotropic, fine- scale fractured surfaces.

    Figure 2

    3.2 Two-body ductile lapping Over a broad range of materials, we have obsewed that rapid stock removal with low damage is obtained when diamond abrasives are used in a "two-body" rather than a 'threebody" material removal (or abrasion) regime. Such a removal regime is assumed to occur when abrasive grits become embedded in the lap so that no rolling occurs. This mechanism has been referred to as "closed threebody abrasive weat"6; in the application, however, the analogy to grinding suggests that it be described as a twGbody process.

    Twebody ductile lapping has been achieved on the RRL on metals, single crystals such as silicon and sapphire, and ceramicsg. The newly generated surfaces are characterized by a network of continuous smooth fracture free "scratches". Other removal mechanisms seen in some circumstances are: (a) three-body abrasion, characterized by linear surface tracks of fluctuating width and depth obviously caused by rolling of the abrasive; and (b) spalling out of material as a result of brittle fracture. Here we will describe primarily our experience with silicon lapping.

    3.2.1 Silicon wafer lapping A number of 100 mm diameter silicon wafers have been diamond lapped under a range of conditions. The wafers were mounted using commercial 'Yemplates"l7, which

  • comprise a wetted felt backer with a polymer annulus which constrains the wafer radially but allows the wafer to conform to the lap surface, thus ensuring uniform removal.

    Lapped and etched wafers, with an initial roughness18 ranging from 4.8 to 17.9 pm Rt (0.35 to 1.1 pm Rq), were lapped on Mylar with both oil-based and aqueous diamond slumes at loads up to 2.25 g/mm2. With 3 pm to 17 pm diamonds, surfaces were generated with no evidence of surface fracture (Figure 3). At larger diamond sizes, under these conditions there was some evidence of lines of fracture, possibly introduced by rolling diamonds. Changing to a softer film (polyethylene) allowed ductile lapping with diamonds as large as 45 pm.

    In the course of these tests, we observed that for diamond sizes greater than 6 pm, the time taken to remove the etch pits (ie the removal rate) appeared independent of diamond size. Surface finish, however, is a strong function of abrasive size. Changing from Mylar to a harder film, aluminum foil, and 1 pm diamond gave comparable removal rates and finishes of the order of 1 nm ms.

    Figure 3: Nomarski micrographs of ductile lapping of silicon using 3 pm diamond showing (let?) incomplete removal of etch pits and (right) final surface. Marker bar is 50 pm

    Figure 4: Nomacski micrographs showing (let?) as- lapped silicon suface using 6 pm diamond and (right) the effect of a 3 minute Schimmel etch, which revealed no subsurface fracture. Marker bar is 50 pm

    3.2.2 Subsurface damage in crystalline materials Rroduction of apparently fracture free surfaces is a necessary, but not suffiaent condition in production of semiconductor substrates and some crystalline optics. Previous researchers1 920 have indicated that apparently fracture-free surfaces produced on silicon and other crystalline materials may have substantial dislocation densities. For the 2-body ductile lapping process described here, rocking cunre21, X-ray topography22, etching9 (Figure 4) and our CMP data all indicate a significant dislocation density in the subsurface region.

    3.3 CMP using the RRL As indicated earlier, the RRL can be used for a variety of chemomechanical polishing processes. Ceria has been used with Mylar films to polish glasses, chrome oxide on Mylar to polish silicon nitride, and colloidal silica on polyurethane to polish copper, tungsten, silicon oxide and silicon. Where polymer films have been used, the most obvious advantage of the RRL is the ease of changing process, typically from fracture mode lapping to polishing. Where pads are used, the primary advantage demonstrated so far is that no adhesives

    are used: thus the pad may be changed in a matter of seconds, rather than the 30 minutes or more typical of current practice in the IC industry.

    4. Simple psuedo-static indentation model of ductile lapping In using both the rapidly renewable lap and other laps in the two-body mode, we have observed that there is some empirical relationship between the material properties of the workpiece and those required from a usable lap. Specifically, it seems that the work must always be somewhat harder than the lap. In addition we have observed counterintuitive behaviors compared with common optical shop practice. In this section of this paper, therefore, we present a simple model of the process (see also Brown23) and of the conditions under which hmbody abrasion would be expectedEminate.

    Work Work ............ 70- .::..,\ .... ... . ,:_.. . To-. ._ .. ., . * ,.... , i .. -.. './". .._ ..


    _,: ,?.'

    Lap Figure 5 Figure 6

    \ /

    Material removed Figure 7

    Consider (Figure 5) a particle lodged between a lap and the harder work. With no relative motion, we can consider this as a simple indentation process. Now, indentation hardness is defined as the pressure on the projected indentation area. Thus, for example, Vickers hardness obtained is derived from the geometry of the indenter as:

    (1) 2F. sin 68'

    tiv = D2

    where F is the load and D the measured diagonal of the square impression. The diamond abrasive will usually be a regular polyhedron; the geometric factors are different, but:

    where throughout this paper ki (i = 1 ..13) is a set of constants combining geometric terms and physical properties such as the densrty of diamond (eg Eq 10 below).

    The penetration depth into elher work (dlhh or lap (do is proportional to the diagonal length D, and, for a regular polyhedron, the geometric constants are the same on both sides of the contact: Thus, for a fixed normal load F:

    7 r


    Consider next the effect of applying a lateral force. If no rolling takes place then, for material removal to take place, the shear strength of the material must be exceeded along some failure surface. For a section through the abrasive partide (Figure 6), that failure surface may be approximated as a plane at some angle u to the surface and the cutting force will be given by the product of the shear strength, T and the area of the failure surface. Note that a is a function of the rake angle; thus if the "abrasive" is rotated to some asymmetric orientation. a will change. For any regular polyhedron, the change in a will be the same on both sides of the contact (i.e. work and lap).

    Now, for a sliding diamond shaped indenter with an included angle of 2p let us assume the shape of the failure

    24 1

  • surface may be approximated as hwo triangles as indicated in Figure 7. Clearly the area in question is the sum of those triangles whose area Ai (i=Wor L) is:

    Rotating the abrasive about an axis normal to the surfaces will change the angles a and p but, by symmetry, they will be the same for both lap and work. Hence the functional form 0 is irrelevant and:

    Note that if the surface is approximated as a spherical segment of radius d;, a conical surface of included angle a and base radius dj, or segment of an ellipsoid, its area can still be expressed as in Eq (5). Now for the work to be machined and the abrasive to remain locked in the lap:

    To the extent that k3 is the same for lap and work, substituting (3) and (5) into (6) gives:

    Ai = di2. @(a,/3) (4)

    A, = k3df (5)

    A L r l ~ 4 y r w (6)

    This simple analysis, ignoring for example any time- dependent materials properties and chemical or frictional effects on embedding, leads to the intuitively reasonable result that for two body lapping of the work to take place, the ratio of shear strength to hardness for the lap must be larger than that for the work material. There are two addlional limitations. First the load must not be supported diredly on the lap surface or via a hydrodynamic film such that the abrasive penetration into the work remains elastic. Second. if the abrasive particle becomes sufficiently large, compared with the penetration depth d, then the moment will be such that rolling will be favored over sliding.

    4. I Process predictions based on the 2-body modd If the simple doublesided indenter model introduced above has any validity, it should also be able to predict the effect of varying process conditions. For a process removing stock uniformly over an entire surface, the removal rate is the average of the removal by the distribution of grits. This "average" may (or may not) be heavily weighted toward some particular grits in the distribution. However, provided that the shape of the distribution is constant, the removal rate will be related to a characteristic grit of size s.

    If there are a very large number of active grits, the removal rate (or surface recession, dhldf) )will be proportional to the penetration depth, dw and the surface speed, V. Hence, from Eqn (3):

    -= k4Vdw = k s V E (8)

    where Fj is the force per grit. This model suggests that the removal rate is proportional to FIE, in contradiction to Preston's equation24.

    An alternative model is to consider that the active cutting grits are relatively widely spaced on the lap. In this case the removal rate is controlled by the volumetric removal rate per grit, itself proportional to d,,,?. Hence:

    _ - 5 dt HW dh - kGVNd& = k7VN - (9)

    where N is the number of grits . Eq (9) has the functional form of Preston's equation.

    Consider next the effect of abrasive size, s, on removal rate. If the shape of the size distribution does not change as the characteristic size, is changed (by the slurry supplier), then we can characterise the slurries by the mean of their size distributions, s. Assume that, for simpliaty, the slurry comprises a fixed weight of regular polyhedral abrasive grits per unit volume of slurry. For a fixed volume of slurry supplied

    to the lap, the number of grits in contact, N, is inversely proportional to 3. Thus the force per grit is:

    F," ' x F s 3 Now if the removal rate is given by the average penetration into the work, substituting Eq 10 into Eq (8) gives:

    ie removal rate is proportional to $Q, while for widely separated cutting grits, substituting Eq (10) into Eq (9) gives:

    (1 2) 1 Fs3 F

    dt s3 H, H* - kgV--= kgv- dh --

    ie removal rate is independent of particle size. Note that these removal rate predictions will only be valid in the range where:

    no rolling takes place; and there is no significant load support from the lap surface interacting directly with the work or from a hydrodynamic film.

    Surface finish, 0, should be directly proportional to the penetration of the characteristic grit, ie for fixed conditions:


    r = klodw = kll\ j$

    ie, finish is predicted to be proportional to s3/2.

    surface speed on the part, Eq (8) gives: Recalling that F,=FN, for a fixed grit size and

    ie for a fixed load, removal rate is proportional to N - I n in the case of many active grits while Eq (9) gives:

    F F dh dt NHw . H,

    k7N - = k7 - -= suggesting that, within the bound of the model. removal rate is independent of concentration.

    4.2 Experimental tests All samples used in the tests described below have, in the surface, a small dimple produced either using a 0.5 mm diameter drill or by polishing a shallow spherical indentation. The indentation is measured, with respect to the polished surface, using a scanning white light interferometer18 and the ten-point height used as an indication of depth. Examination of the bottom of the dimple shows that it is not being lapped.

    In our previous work, the effect of load on removal rate has been evaluated for 50 mm diameter [IOO] siliconlo and electroplated nickel-phosphorus samples. Over the pressure range 0.3 g/rnm2 -1.5 g / m d using 9 and 12 pm diamond, removal rate appeared linear with load.

    1, I

    - - _ - - - - _ _ - - _ _ _ - - - - - silicon

    fractured Si - 0 L - - . ._ - .--L 0 10 20 30

    Diamond size, pm

    Figure 8: Removal rates for overarm polisher, 300 mm diameter I0 poredcm Sic RRL, Mylar film, water-based slurries, 0.9 @rnd pressure, 35 rpm spindle speed, I0 stmkedmin arm speed


  • To evaluate the effect of grit size on removal rate, a series of slurries were obtained with the same concentration of diamond and self-similar size distributions. These were used to lap 50 mm diameter samples of silicon and electroplated nickel-phosphorus (Figure 8). For the nickel phosphonrs. removal rate is constant for grit sizes from 6 um to 30 pm. Silicon shows a doubling of its removal rate at 30 urn, but the surface also shows fracture. Both materials show a drop in removal rate at 3 pm, presumably due to some load support by the hydrodynamic film or directly from the Mylar. As noted above, changing to an aluminum film restored the removal rate even for 1 ktm diamond.

    Figure 9 shows rms surface finish versus diamond size. Slumes from several suppliers were used, which contributes to the scatter. Linear and 3/2 power tits through this data have indistinguishable correlation coefficients.

    30 +

    f 20

    E :+ 5 .- + v) 10

    8 * 0 4.-- -

    0 10 20

    Diamond size, mm

    Figure 9: Finish achieved on overarm polisher; conditions as for Figure 8

    0 0.5 1

    Relative concentration

    Figure 70: Effect of concentration when lapping under identical conditions to Fig 8, except that the load was 1.3 @ m d and the substrate was machined aluminum rather than foamed silicon cahide

    Figure 10 shows the effect of concentration. A nominal 17 pm aqueous based sluny containing a mass fraction 0.5% diamond was diluted up to 50:l using the proprietary "extendel" from the sluny supplier. The removal rates at 25:l and 50:l are indistinguishable from that achieved using pure extender; note that the Mylar film is coated with colloidal silica.

    5. Fracture mode lapping models and experiments From the previous sedons it is clear that a simple indentation model successfully predicts behavior in what we have called 2-body ductile lapping, where the number of diamonds actually removing material is vely small. Are similar simple models available for the fracture mode case?

    Recall the work of Evans and Marshall25 who predicted that the material removed by a sliding grit, mg, which initiates and propagates radial fracture will be proportional to

    Pn9/8 , where Pn is the peak normal penetration force on the grit. Hence, in a lapping with fixed abrasives causing fracture:

    _ - dh - k,,VNrng = k,3VNP:'8 dt

    In accordance with Preston's eqn, this predicts that removal rate will be linear with speed. As above, substituting FJVfor Pn leads to the prediction that, for fixed load, removal rate will be proportional to and N118. Again noting that N is proportional to 3 leads to the prediction that removal rate will be proportional $18.

    Figure 11 shows results obtained with alumina abrasives lapping 70 mm square fused quartz samples offset so that the edge of the part just stays on the 300 mm diameter lap on the continuous lapper.

    .- C 0.6 E

    6 E

    z 0 5 - A. 0 4 -

    0 3 .

    0 2 ~


    - > p 0 1 .

    Conc. = 130 g/ l , 9prn grit

    z = 0 - - * - ._ . -- - - 5 10 15 20 25 30

    Speed, rpm

    0 2 5 . c .- g 02, E ai 0 1 5 E



    - 0 1 m > 0 E 0 0 5 . cu

    [ r j

    0 . 0

    10 rpm, 0.75 g/mm2, 130 gll

    Alumina size, pm

    - I 9 004 , 10 rpm, 0.75 glrnmz, 9 pm grit 0 I $ 0 0 2 -

    Concentration, g/l

    Figure 1 7 : Removal rates for fused qua& lapped with alumina on Mylar films over a 4 poredcm foamed silicon carbide lap. Sluny supplied at 15 mfmin

    6. Discussion It should be noted that our selection of baseline conditions in all the experiments reported in this paper has been guided by conventional practice. Hence relatively little diamond is used in "ductile" lapping, whereas concentrated alumina slurries are used in fracture mode glass lapping.

    The simple model of 2-body ductile lapping based on widely separated diamonds correlates well, within the stated limits of applicability, with the experimental results for removal rate. We have not attempted to predict removal rates


  • for different material systems from first principles, only to predict trends within a given system. Thus we have been able to ignore such variables as surface chemistry, work hardening, the ratio of ploughing to cutting, etc 26.

    The predicted and observed behaviours in what we call 2-body ductile lapping are unexpected from the perspective of the abrasive wear of metals, where strong correlations between wear rate and abrasive size (particularly below about 100 pm) are typically reportedl5-27. Such data has generally been obtained with bonded abrasive papers, where the separation between active grits is of the same order as the grit size28. For the results reported here in Figure 10, for example, we estimate the separation between active cutting diamond to be over 30 times the size.

    Dwyer-Joyce et a116 show data from bearing wear tests where, at concentration similar to the 0.1 level in our Fig 10, identical wear rates for 3 pm and 4 pm diamonds, the largest they use. Samuels29. in his studies of metallographic polishing with diamonds, shows a peak removal rate for relatively small diamonds (2-4 pm) , with significant decreases when larger or smaller diamonds are used. The drop with increased size he associates with the ability of the diamond to embed in the fibres of the lapping cloth used.

    The experimental results (Figure 11) from the fused quartz lapping tend to support the simple sliding grit mode125. For example, the removal rate scales approximately with $8; more data over a wider range of conditions is required. As Ling and FinnieSO note, later workers have produced slightly different correlations of radial crack extent to peak pressure that would modify slightly the predictions of the simple slider model; more detailed experiments are required, however, to justify the use of refined models. Furthermore, alternative models based, for example, on removal by rolling grits should be compared with the data given here.

    7. Conclusions This paper has described the principle of the Rapidly Renewable Lap and reviewed experience in its use. The next steps in the development of the technology will include development of doublesided lapping implementations and scaling up to larger machines. Additional work is also need to evaluate performance in chemo-mechanical polishing.

    Simple models of two distinctly dierent lapping processes provide guidance to trends in process performance. Additional work is required to improve the models, for example to indude analytrc treatments of the limits of validity, and to evaluate effects such as sub-surface damage in fracture mode lapping. We do not suggest that all modes of lapping are described by the models discussed here.

    8. Acknowledgments The authors are grateful for the helpful comments and contributions of M. A. Davies, J. Dagata, D. Black, L. K. Ives, T. W. h a n g , R. S. Polvani, J. Pedula, R. D. Deslattes and A. Henins (NISn and E. W. Jensen (Rodel Inc). Diamond slumes for some experiments were provided by Rare Earth Sciences Inc. This work was supported in part by the National Semiconductor Metrology Program at NIST.

    9. References

    (1) Woodbury. R. S., 1958, History of the Grindincl Machine, Technology Press, Boston, Ma (2) Twyman F. ,1952, Prism and Lens Making, Hilger and Watts, London (3) Tonshoff H. K., Von Schmieden W., lnasaki I., Konig W., Spur G., 1990 "Abrasive Machining of Crystal Silicon" Annals of the CIRP, 39/2: 621

    (4) Venkatesh , V. C., Inasaki, I., Tonshoff, H.K., Nakagawa T., Marinescu I.D., 1995, Observations on Polishing and Ultra- Precision Machining of Semi-conductor Substrate Materials, Annals of the CIRP Vol. 44/2/95. p. 61 1 (5) Komanduri R., Lucca D. A., Tani H., 1997 'Technological Advances in Fine Abrasive Processes" ClRP Annals Vol 46Q. pp545-596 (6) Namba, Y.,Tsuwa. H., Wada, R., 1987, Ultra-precision float polishing machine, ClRP Annals Vol. 36/1/87, p. 21 1 (7) Tsuwa H., lkawa N., Mori Y., Sugiyama K.. 1979 "Numerically controlled elastic emission machining" ClRP Annals, 2811 : 193 (8) Evans C. J. and Parks R. E., 1995 "Rapidly Renewable Polishing Lap", Proc. SPIE. 2536 248-55 (9) Parks R. E., Evans C. J., Roderick D.J., Dagata J., 1997 "Applications of the Rapidly Renewable Lap" Proc. SPIE, 3134; 240-251 (10) Evans C. J., Parks, R. E.. Roderick D. J. and Evans B. A. "Experiences with the Rapidly Renewable Lap Optical Fabrication and Testing Workshop,. 1996 Technical Digest Series, Vol7. pp 131-33 (1 1) Rogers and Clarke overarm polisher. Lapmaster lapper. Strasbaugh 6CA 600mm polisher. Specific commercial equipment is identified to fully describe the experimental procedures. Such identification does not imply any endorsement of the product by the National Institute of Standards and Technology, nor that the product is necessarily the best for the purpose. (12) HTTec Ceramics, Alfred. NY (1 3) W K O TOP0 3D, 40x objective (14) Burwell J. T., 1958 "Survey of possible wear mechanisms" Wear, 1, 1958:119-141 (1 5) Misra A., Finnie I., 1982 "A review of the abrasive wear of metals" Trans. ASME, 10494-101 (1 6) Dwyer-Joyce R. S., Sayles R. S., loannides E., 1994, "An investigation into the mechanisms of dosed three-body abrasive wear" Wear, 175:133-142 (1 7) Rodel TA, Rodel Inc, Newark, DE (1 8) W K O Rollscope scanning white light interferometer, 1.2 x 0.9 mm F.o.V., 368x236 pixels (19) Puttick K. E., Whitmore L. C.. Chao C. L. and Gee A. E. Transmission electron microscopy of nanomachined silicon uystals" Phil. Mag A, 69:91-103 (20) Shibata T. ,Atsuchi O., Kurihara K., Makino E., lkeda M., 1994 "Cross section transmission electron microscope observations of of diamond tumed single crystal silicon surfaces" Appl. Phys. Letters, 65:2553-2555 (21) Parks R. E., Evans C, Bartos A. ,1994, "Diamond polishing of silicon" OSA 1994 Technical Digest Series,

    (22) Black D. Personal communication (23) Brown N. J. ,1990 "Optical Fabrication" Lawrence Livermore National Laboratory, MISC 4476 rev 1 (24) Preston, F. W. 1922. Trans Opt Soc 23:141 (25) Evans A. G., Marshall D. B. 1981" Wear mechanisms in ceramics" in Fundamentals of Friction and Wear (ed. D. A. Rigney) ASME Press, NY, pp439-52 (26) Suh N. P. 1986: Tribophvsics, Prentice-Hall, NJ (27) Moore M. A.:1974"A review of two-body abrasive wear" Wear.27: 1-1 7 (28) Mulheam T. 0.. Samuels L. E. ,1962 "The abrasion of metals: a model of the process" (29) Samuels L. E., 1984 "Effects of type and size of diamond abrasives on material removal rates in metallographic polishing" Metallography 17:1941 (30) Ling E., Finnie I., 1989 "Subsurface fracture and the wear of brittle solids" Key Engineering Materials, 33:49-76