Methods and apparatus for nanolapping

1 . A lapping system for lapping portions of a workpiece, the system comprising:

a lap being defined by a surface, wherein portions of the surface are a lapping surface; and wherein the lapping surface has a coating; wherein the coating enhances material removal from a workpiece in a lapping process; and

a scanning probe microscope having a tip and a substrate;

wherein the scanning probe microscope controls lapping motion of the lap and workpiece.

2 . The lapping system of claim 1 wherein the lap is the tip and the workpiece is the substrate.

3 . The lapping system of claim 1 wherein the lap is the substrate and the workpiece is the tip.

4 - 17 . (canceled)

18 . A lap having a lapping surface for lapping portions of a workpiece, the lap comprising:

a plurality of lap segments, wherein each lap segment has a lapping surface; and wherein the lapping surfaces of the lap segments are oriented to form the lapping surface of the lap.

19 - 21 . (canceled)

22 . The lap of claim 20 wherein the lapping surface of the lap is a track having a polygonal shape; and

the track is bounded by a space defined by a cube having edge dimensions of about 200 μm or less.

23 . A method of fabricating a lap, the method comprising:

cutting a silicon wafer along the 110 crystallographic plane;

etching a track of a first shape in the silicon wafer, the track has a first sidewall, a second sidewall, and a bottom surface, the first and second of sidewalls being approximately perpendicular to a top surface of the silicon wafer;

cutting the silicon wafer in a plurality of pieces; and

arranging the plurality of pieces to form the lap;

wherein the lap has another track having second shape; and

the other track is a lapping surface

24 . The method of claim 23 wherein the other track is bounded by a space defined by a cube having edge dimensions of about 200 μm or less.

25 - 27 . (canceled)

28 . A lap having a lapping surface for imparting shape onto portions of a workpiece, the lap comprising:

a body; and

a set of surface portions bounding the body;

wherein the lapping surface is comprised of a subset of the surface portions; and

the lapping surface is bounded by a space defined by a space defined by a cube having edge dimensions of about 200 μm or less.

29 . The lap of claim 28 and further comprising at least another lapping surface comprised of a another subset of the surface portions;

wherein the other lapping surface is bounded by a space defined by a cube having edge dimensions of about 200 μm or less.

30 . The lap of claim 29 wherein the lapping surface forms a first track and the other lapping surfaces forms a second track.

31 - 86 . (canceled)

87 . A lapping method for lapping portions of a workpiece, the method comprising:

controlling movement of the workpiece and a first lap relative to each other with a scanning probe microscope;

controlling movement of the workpiece and a second lap relative to each other with a scanning probe microscope;

lapping the workpiece into a first shape with the first lap; and

lapping the workpiece into a second shape with the second lap.

88 - 122 . (canceled)