Scanning probe and electron microscope probes and their manufacture

Abstract

Methods are described for the economical manufacture of Scanning Probe and Electron Microscope (SPEM) probe tips. In this method, multiple wires are mounted on a stage and ion milled simultaneously while the stage and mounted probes are tilted at a selected angle relative to the ion source and rotated. The resulting probes are also described. The method provides sets of highly uniform probe tips having controllable properties for stable and accurate scanning probe and electron microscope (EM) measurements.

Claims

1. A SPEM probe or batch of SPEM probes, wherein each SPEM probe comprises: a rod having a thickness in the range of 1 to 2000 μm, and comprising a single tip at one end; a probe tip that is substantially oxide free as characterized by having less than 5 nm of oxide as imaged by TEM; wherein the probe tip has: a cone angle of 5 to 45°; and a diameter of curvature of 1 to 35 nm; and further comprising a shape having at least one of the following morphologies: wherein a silhouette of the probe has a tip that can be described by a sphere with the diameter of curvature of the tip apex; wherein the silhouette has a longitudinal axis that corresponds to the longitudinal axis of the probe; and wherein two straight line segments of equal length can be drawn, each of which is tangent to this sphere, and intersect the silhouette at two points with one point on either side of the silhouette opposite the same length on the longitudinal axis of the probe, and wherein the thickness of the silhouette increases monotonically from the two tangent points to the two intersection points and the edge of the silhouette lies farther from the tip longitudinal axis than the two straight line segments at every point along the edge of the silhouette from the tip apex to each of the two intersection points, no matter what length straight line segments are chosen (or wherein the straight line segments are drawn to intersect the probe silhouette at 1 μm, or 100 nm, or 50 nm down the longitudinal axis of the probe from the tip apex); or wherein a silhouette of the probe conforms to a profile f(x) described by the functional form:
f(x)=a.sub.0+a.sub.1x+a.sub.2x.sup.2+a.sub.3x.sup.3+b.sub.1x.sup.1/2+b.sub.2x.sup.1/3, where f(x) is the distance of the surface of the probe from the longitudinal axis of the probe, measured along a line perpendicular to the longitudinal axis, the coefficients a.sub.0, a.sub.1, a.sub.2, a.sub.3, b.sub.1, b.sub.2 are real numbers, and x is the distance in nm that ranges from 0 to L, with 0 being the longitudinal axis position where the probe profile is tangent to the probe apex sphere, where a.sub.0 is in the range of 1 to 50 nm, where a.sub.1 is 0 or is in the range 0.2 to 4, where a.sub.2 is 0 or is in the range of 0.004 to 0.08 nm.sup.−1, where a.sub.3 is 0 or in the range of 0.00008 to 0.0016 nm.sup.2, where b.sub.1 is 0 or in the range of 1.4 to 28 nm.sup.1/2, and where b.sub.2 is 0 or in the range of 2.7 to 54 nm.sup.2/3; or a shape defined by two arcs of a circle, each arc being tangent to one of a pair of opposing parallel sides of a cylindrical wire body wherein the two arcs are defined by a circle having a radius equal to between 1 and 20 times (in some embodiments between 5 and 7 times) the wire body diameter D, and wherein the two arcs meet at the tip apex; or a biconic shape wherein, with reference to FIG. 9, L.sub.2>L.sub.1; L.sub.1/L is in the range of 0.05 to 0.4 or 0.1 to 0.3; ϕ.sub.1/ϕ.sub.2 is in the range of 1.1 to 2.0, or 1.2 to 1.8, or 1.1 to 1.3; R.sub.1 is in the range of 10 to 1 μm or 20 to 200 nm; and L is in the range of 30 nm to 1 μm or 50 nm to 500 nm, or 50 nm to 100 nm; and R.sub.2 is in the range 1 to 2000 μm, or 250 to 1000 μm; or a shape defined by a power series wherein, with reference to FIG. 10, the shape is within the area encompassed by rotating a curve y=R(x/L).sup.n about an x-axis defining the longitudinal probe axis, where n is in the range of 0.6 to 0.9 or 0.7 to 0.8; or a shape defined by a Haack series wherein, with reference, to FIG. 11, where y=[R(θ−½ sin 2θ+C sin.sup.3 θ).sup.1/2]/π.sup.1/2; where θ=arccos(1−2x/L); where C is in the range of 0.00 to 0.667 or 0.0 to 0.3.

2. The SPEM probe or batch of SPEM probes of claim 1 wherein a silhouette of the probe has a tip that can be described by a sphere with the diameter of curvature of the tip apex; wherein the silhouette has a longitudinal axis that corresponds to the longitudinal axis of the probe; and wherein two straight line segments of equal length can be drawn, each of which is tangent to this sphere, and end at two points with one point on either side of the silhouette opposite the same length on the longitudinal axis of the probe, and wherein the thickness of the silhouette increases monotonically from the tip apex to the two points and the edge of the silhouette lies farther from the tip longitudinal axis than the two straight line segments at every point along the edge of the silhouette from the tip apex to each of the two points, no matter what length straight line segments are chosen (or wherein the straight line segments are drawn to intersect the probe silhouette at 1 μm, or 100 nm, or 50 nm down the longitudinal axis of the probe from the tip apex).

3. The SPEM probe or batch of SPEM probes of claim 1, comprising a batch of SPEM probes mounted on a stage.

4. The batch of SPEM probes of claim 1, wherein each SPEM tip has a cone angle in the range of 9° to 15°.

5. The SPEM probe or batch of SPEM probes of claim 1, wherein each SPEM tip has a diameter of curvature of 1 to 10 nm.

6. The SPEM probe or batch of SPEM probes of claim 1, wherein each SPEM probe comprises a cylindrical rod having a rod diameter in the range of 250 to 500 μm.

7. The SPEM probe or batch of SPEM probes of claim 1, wherein the probes have striations indicative of ion milling.

8. A method of manufacturing or studying an integrated circuit comprising using the SPEM probe of claim 1 for nanoprobing or atomic force probing.

9. The method of claim 8 comprising using the probe for nanoprobing; wherein the step of nanoprobing comprises electrical testing.

10. The SPEM probe or batch of SPEM probes of claim 1, wherein a silhouette of the probe or each probe in the batch of probes conforms to a profile f(x) described by the functional form:
f(x)=a.sub.0+a.sub.1x+a.sub.2x.sup.2+a.sub.3x.sup.3+b.sub.1x.sup.1/2+b.sub.2x.sup.1/3, where f(x) is the distance of the surface of the probe from the longitudinal axis of the probe, measured along a line perpendicular to the longitudinal axis, the coefficients a.sub.0, a.sub.1, a.sub.2, a.sub.3, b.sub.1, b.sub.2 are real numbers, and x is the distance in nm that ranges from 0 to L, with 0 being the longitudinal axis position where the probe profile is tangent to the probe apex sphere, where a.sub.0 is in the range of 1 to 50 nm, where a.sub.1 is 0 or is in the range 0.2 to 4, where a.sub.2 is 0 or is in the range of 0.004 to 0.08 nm.sup.−1, where a.sub.3 is 0 or in the range of 0.00008 to 0.0016 nm.sup.2, where b.sub.1 is 0 or in the range of 1.4 to 28 nm.sup.1/2, and where b.sub.2 is 0 or in the range of 2.7 to 54 nm.sup.2/3.

11. The SPEM probe or batch of SPEM probes of claim 1, wherein the SPEM probe or each probe in the batch of probes comprises a shape defined by two arcs of a circle, each arc being tangent to one of a pair of opposing parallel sides of a cylindrical wire body wherein the two arcs are defined by a circle having a radius equal to between 1 and 20 times the wire body diameter D, and wherein the two arcs meet at the tip apex.

12. The SPEM probe or batch of SPEM probes of claim 1, wherein the SPEM probe or each probe in the batch of probes comprises a biconic shape wherein, with reference to FIG. 9, L.sub.2>L.sub.1; L.sub.1/L is in the range of 0.05 to 0.4; ϕ.sub.1/ϕ.sub.2 is in the range of 1.1 to 2.0; R.sub.1 is in the range of 10 nm to 1 μm; and L is in the range of 30 nm to 1 μm; and R.sub.2 is in the range 1 to 2000 μm.

13. The SPEM probe or batch of SPEM probes of claim 1, wherein the SPEM probe or each probe in the batch of probes comprises a biconic shape wherein, with reference to FIG. 9, L.sub.2>L.sub.1; L.sub.1/L is in the range of 0.1 to 0.3; ϕ.sub.1/ϕ.sub.2 is in the range of 1.2 to 1.8; R.sub.1 is in the range of 20 to 200 nm; and L is in the range of 50 nm to 500 nm; and R.sub.2 is in the range 250 nm to 1000 μm.

14. The SPEM probe or batch of SPEM probes of claim 13, wherein the SPEM probe or each probe in the batch of probes comprises a biconic shape wherein, with reference to FIG. 9, L.sub.2>L.sub.1; L.sub.1/L is in the range of 0.1 to 0.3; ϕ.sub.1/ϕ.sub.2 is in the range of 1.2 to 1.8; R.sub.1 is in the range of 10 nm to 1 μm; and L is in the range of 30 nm to 1 μm; and R.sub.2 is in the range 250 nm to 1000 μm.

15. The SPEM probe or batch of SPEM probes of claim 1, wherein a silhouette of the probe or each probe in the batch of probes comprises a shape defined by a power series wherein, with reference to FIG. 10, the shape is within the area encompassed by rotating a curve y=R(x/L).sup.n about an x-axis defining the longitudinal probe axis, where n is in the range of 0.6 to 0.9.

16. The SPEM probe or batch of SPEM probes of claim 1, wherein a silhouette of the probe or each probe in the batch of probes comprises a shape defined by a power series wherein, with reference to FIG. 10, the shape is within the area encompassed by rotating a curve y=R(x/L).sup.n about an x-axis defining the longitudinal probe axis, where n is in the range of 0.7 to 0.8.

17. The SPEM probe or batch of SPEM probes of claim 1, wherein the SPEM probe or each probe in the batch of probes comprises a shape defined by a Haack series wherein, with reference to FIG. 11, where y=[R(θ−½ sin 2θ+C sin.sup.3 θ).sup.1/2]/π.sup.1/2; where θ=arccos(1−2x/L); where C is in the range of 0.00 to 0.667.

18. The SPEM probe or batch of SPEM probes of claim 17, wherein the SPEM probe or each probe in the batch of probes comprises a shape defined by a Haack series wherein, with reference to FIG. 11, where y=[R(θ−½ sin 2θ+C sin.sup.3 θ).sup.1/2]/π.sup.1/2; where θ=arccos(1−2x/L); where C is in the range of 0.0 to 0.3.

19. The SPEM probe or batch of SPEM probes of claim 2 wherein a silhouette of the probe has a tip that can be described by a sphere with the diameter of curvature of the tip apex; wherein the silhouette has a longitudinal axis that corresponds to the longitudinal axis of the probe; and wherein two straight line segments of equal length can be drawn, each of which is tangent to this sphere, and end at two points with one point on either side of the silhouette opposite the same length on the longitudinal axis of the probe, and wherein the thickness of the silhouette increases monotonically from the tip apex to the two points and the edge of the silhouette lies farther from the tip longitudinal axis than the two straight line segments at every point along the edge of the silhouette from the tip apex to each of the two points, no matter what length straight line segments are chosen.

20. The SPEM probe or batch of SPEM probes of claim 1 wherein a silhouette of the probe has a tip that can be described by a sphere with the diameter of curvature of the tip apex; wherein the silhouette has a longitudinal axis that corresponds to the longitudinal axis of the probe; and wherein two straight line segments of equal length can be drawn, each of which is tangent to this sphere, and end at two points with one point on either side of the silhouette opposite the same length on the longitudinal axis of the probe, and wherein the thickness of the silhouette increases monotonically from the tip apex to the two points and the edge of the silhouette lies farther from the tip longitudinal axis than the two straight line segments, wherein the straight line segments are drawn to intersect the probe silhouette at 1 μm, or 100 nm, or 50 nm down the longitudinal axis of the probe from the tip apex.

21. The SPEM probe or batch of SPEM probes of claim 1 wherein the rod comprises a material selected from the group consisting of beryllium copper (Be—Cu) alloy, platinum (Pt), iridium (Jr), platinum-iridium (Pt—Ir) alloy, tungsten (W), tungsten-rhenium (W—Re) alloy, palladium (Pd), palladium alloy, gold (Au), and commercial alloys (NewTek™, Paliney 7™ (Pd along with small percentages of Ag, Au, Pt, Cu, and Zn), Paliney H3C and Paliney C (Pd alloys with Pd, Ag, and Cu)).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic illustration of the inventive process.

(2) FIG. 2 shows angles in the process.

(3) FIG. 3 illustrates the cone angle and diameter or curvature of the SPEM probe.

(4) FIG. 4 illustrates a tip (dark, central tip) having an oxide coating (seen as a lighter coating). The small rectangular bar in the left hand corner is a scale showing the length of 10 nm.

(5) FIG. 5 illustrates a tip (dark, central tip) without an oxide coating. The small rectangular bar in the left hand corner is a scale showing the length of 10 nm.

(6) FIG. 6 shows four representative examples of probes after ion milling. Striations can be seen on the surface of these probes parallel to their longitudinal axis. They appear after exposure to an impinging beam of Ar ions.

(7) FIG. 7 is a diagram showing a bullet shaped probe.

(8) FIG. 8 shows the descriptive geometry of a probe with a bullet shape given by a tangent arc radius equal to 6 wire body diameters.

(9) FIG. 9 illustrates the descriptive geometry of a probe with a biconic shape.

(10) FIG. 10 illustrates the descriptive geometry of a probe with a shape given by rotating the curve y=R(x/L){circumflex over ( )}n about the x-axis.

(11) FIG. 11 illustrates the descriptive geometry of a probe with a shape given by the Haack series.

DETAILED DESCRIPTION

(12) The SPEM probe is manufactured from a piece of wire (defined as a material having a length to diameter ratio of at least 5, preferably at least 10, more typically at least 100 or, in some embodiments, in the range of 10 to 1000). Wire pieces for the starting materials preferably have a diameter between 0.15 mm and 1.00 mm and a length in the range of 0.5 to 3 cm, more preferably 1.5 to 2.5 cm and are etched or machined to a point. The probe materials may be any of the materials conventionally used for SPEM probes. Thus, in preferred embodiments, the probe comprises a material selected from the group consisting of beryllium copper (Be—Cu) alloy, platinum (Pt), iridium (Jr), platinum-iridium (Pt—Ir) alloy, tungsten (W), tungsten-rhenium (W—Re) alloy, palladium (Pd), palladium alloy, gold (Au), and commercial alloys (NewTek™, Paliney 7™ (Pd along with small percentages of Ag, Au, Pt, Cu, and Zn), Paliney H3C and Paliney C (Pd alloys with Pd, Ag, and Cu)), and cemented metal carbides, borides or nitrides, such as tungsten (W), titanium (Ti), niobium(Ni), or tantalum (Ta) carbide cemented with cobalt (Co), nickel (Ni), iron (Fe), chromium (Cr), molybdenum (Mo), platinum (Pt), iridium (Jr), rhodium (Rh), palladium (Pd), rhenium (Re), ruthenium (Ru), and osmium (Os), or mixtures thereof. A preferred list of probe body materials comprises tungsten, platinum iridium, and tungsten carbide cemented with cobalt, nickel, or mixtures of cobalt and nickel. These materials may be used by themselves or with a coating of one or more layers such as polytetrafluoroethylene (PTFE); magnetic coatings, such as iron, cobalt, chromium or platinum alloys; diamond; diamond-like-carbon (DLC), Ag; Au; C; boron nitride; silicon nitride; silicon dioxide; metal oxides, such as aluminum oxide; metal nitrides, such as titanium nitride or aluminum titanium nitride; metal carbides, such as tungsten carbide; metal borides such as hafnium diboride (HfB.sub.2) or titanium diboride; metal carbonitrides, such as titanium carbonitride; ceramics; or other hard coatings, such those containing chromium. Suitable methods for applying such coatings are known in the literature; for example, in Jensen et al., J. Am. Chem. Soc. 110, 1643-44 (1988); Jayaraman et al., J. Vac. Sci. Technol. 23, 1619 (2005); and Jayaraman et al., Surface & Coatings Technol. 200, 6629-6633 (2006), all of which are incorporated herein by reference. We have prepared SPEM probes from W and Pt—Ir having the advantageous properties of cone angle and diameter of curvature discussed in this description. We have also prepared SPEM probes with HfB.sub.2 coatings having the discussed advantageous properties. The inventive method may also utilize non-conductive wires, in some embodiments selected from the group consisting of diamond, diamond-like carbon, silicon, undoped silicon, metal oxides such as alumina or zirconia, silicon dioxide, silicon carbide, silicon nitride, boron nitride, boron carbide, glass, cementitious materials, plastics, rubber, silicon rubber, organic polymers and resins such as phenolic, epoxide, polyisocyanurate, polyurethane, ethylene propylene diene monomer rubber (EPDM), polyimide, polyvinyl chloride, polystyrene, polyether ether ketone (PEEK), polypropylene (PP), polyethylene terephthalate (PET), polyethercsulfone (PES), polyethylene imine (PEI), ethylene-chlorotrifluroethlyene polymer (ECTFE), polybutylene terephthalate (PBT), polytetrafluoroethylene (PTFE) and fluorinated ethylene propylene polymer (FEP), fiberglass, cellulose, mineral (rock or slag), mica, porcelain, clay, aluminosilicate, wood, cotton, ceramic, paper, fiber glass composites, plastic fibers, and natural fibers, and combinations thereof. A preferred list of nonconductive wire materials includes diamond, zirconia, silicon carbide, and silicon nitride. The materials listed above are believed to behave similarly under the ion milling conditions described in this description and likewise are believed to result in similar finished SPEM probes.

(13) Before processing the wire pieces according to the inventive method, the wire pieces may be pre-sharpened by known methods. Preferably, this is done by electrochemical etching by a technique such as that described by Zhang et al., which is referenced above. Typically, a coating, if present, is applied after the electrochemical etch. The coating can be applied either before or after the ion milling process described here, and HfB.sub.2 coatings have been applied after the ion milling such that little or no additional sharpening is needed.

(14) A schematic view of the inventive process is illustrated in FIGS. 1-3. A batch of wire pieces 18 is fixed onto a stage 10 (also called a support). A “batch” of wire pieces (or SPEM probes) refers to a group of 5 to 10,000; preferably 10 to 1000 wire pieces. The stage is then rotated around a central axis 16 that is perpendicular to the top surface of the stage 10, typically at a rate of at least 0.01 revolution per minute (rpm), preferably in the range of 1 to 100 rpm, in some embodiments in the range of 50 to 70 rpm. Typically, the wire pieces in a batch are arranged in a circular or square array, and the long axes of the wire pieces 18 are approximately parallel with the central axis of rotation 16 of the stage 10. The stage 10 and ion beam 20 are disposed within evacuation chamber 14. The entire batch of wires should be exposed to the broad ion beam 20 generated by broad beam ion source 12. Thus, the size of the rotating array of wires (square or other shape) should be enveloped by the size of the ion beam 20. In some preferred embodiments, the ion beam has a circular area (perpendicular to the beam direction 26) with a diameter of 5 to 50 cm, in some embodiments 5 to 20 cm. The ion flux from the source is in the range of 10.sup.14 to 10.sup.17 ions/cm.sup.2s. The ions are preferably obtained from neon, argon, xenon, or krypton gases, or mixtures of these gases. In addition to the inert gases, hydrogen, oxygen, and nitrogen can be used individually, in combination with each other and/or in combination with neon, argon, or krypton, for ion processing. Gases such as methane or acetylene can be used to modify the surface properties. Preferably, the ion beam is made up of Ar ions. Neutral Ar atoms may also be present as chamber background pressure used to operate the ion source. Also, electrons may be present as a means of collimating the ion beam and to enable processing of non-conducting samples by preventing charge buildup from the ions. The angle 28 between the direction of incident ion beam and axis of rotation is known as the ion angle, which may be set in the range of 5° to 90°, preferably 10° to 70°, preferably 15° to 65°, in some embodiments 15 to 25°, and in some embodiments 45° to 55°. The ion beam is set to an ion energy in the range of 100 eV to 3500 eV; preferably 200 eV to 3000 eV, more preferably 500 eV to 2500 eV, in some embodiments in the range of 1000 eV to 2000 eV, and in a specific embodiment about 1500 eV. The exposure to the ion beam is preferably conducted with a current density of 0.1 to 1 mA/cm.sup.2, more preferably from 0.2 to 0.8 mA/cm.sup.2, still more preferably from 0.4 to 0.6 mA/cm.sup.2. In preferred embodiments, the time for exposure can be for 20 to 120 minutes; preferably for 30 to 90 minutes; or 60 minutes to 120 minutes; or more than 120 minutes; and may be for about 60 minutes. However, these times could be about two orders of magnitude shorter for ion fluxes in the 10.sup.17 ions/cm.sup.2s range. In some embodiments, the angle 28 is changed one or more times during the milling process; for example, starting with a relatively large angle to quickly remove material from the wire and moving to more oblique incident angles to control the shape of the probe. In other embodiments, the angle may also be moved continuously during the milling process.

(15) Another advantage of the present invention is that it is self-limiting. The probe arrives at a final shape for a given angle, and then, while the tips continue to be exposed to the ion source, the probe shortens but maintains the same shape during prolonged milling.

(16) When the milling is complete, the ion beam exposure is stopped and the wires are removed from the stage. The resulting probes comprise a probe body 22 and a tip characterizable by a cone angle 24 (also called taper angle or tip angle) and diameter of curvature 32. There should be a single tip on each probe body 22 since multiple tips on a probe results in inferior properties. Typically, the probes have striations, which are indicative of ion milling. The probe tips preferably have cone angles of 5° to 45°, more preferably in the range of 5° to 30°, still more preferably in the range of 5° to 15°, and still more preferably in the range of 9° to 15°. The diameter of curvature is preferably in the range of 1 to 35 nm; in some embodiments in the range of 5 to 35 nm, or 10 to 35 nm, or 15 to 30 nm. In some embodiments, the tip is substantially oxide free. These unique and novel properties are enabled by the methods of the present invention. These properties, or any selected combination of these properties (including, in some preferred embodiments, any of the shape characteristics described below), are present on individual probes and are preferably present on all or at least 80% or at least 90% of a batch.

(17) In general, this technique creates tips that are substantially cylindrically symmetrical about the tip axis. Some degree of asymmetry is tolerable, but the most useful tips are those that are reasonably symmetrical, as could be judged by a person experienced with working with SPEM probes. The properties of SPEM probes can be measured by electron microscopy, typically transmission electron microscopy (TEM).

(18) In an embodiment, the sample holder for field directed sputter sharpening is adapted to hold the longitudinal axis of the conductor to be sharpened at a selected angle (for example a predetermined angle with respect to the longitudinal axis of an ion beam). In an embodiment, the ion acceleration voltage is between about 550 eV and 5 keV and the voltage applied to the conductor is ten volts or more and preferably 100 V or more.

(19) The processing conditions described above can be combined with the field directed sputter sharpening (FDSS) method, in which an electrical potential difference, either positive or negative, is applied to the tip so as to modify the flow of ions around the tip. FDSS is described by Lyding and Schmucker in U.S. Pat. Nos. 8,070,920 and 8,819,861 which are incorporated herein as if reproduced in full. The difference between the ion accelerating voltage and the tip voltage is sufficiently large that sputtering of the tip occurs, but not so large that the influence of the tip voltage is negligible. The directed sputtering in FDSS cannot be used to produce the bullet shape that is characteristic of preferred embodiments of the present invention, but FDSS may be utilized where sharper tips are needed. In FDSS, it is necessary that the probes be electrically conductive and a potential is applied to the probe. In contrast to FDSS, the present invention can be operated in the absence of a potential applied to the wires; in other words, the stage (including mounted wires) can be grounded during the sputtering process. In addition, in contrast to FDSS, the present invention can be performed upon nonconductive probes.

(20) The ability of a probe to image on the nanometer scale and also be mechanically robust depends on both the diameter of curvature of the tip and also the shape of the probe near the tip. If the cone angle of the near-tip region is too small, the probe will be mechanically too flexible to be useful for applications in which the probe must be placed in contact with the surface. If the cone angle of the near-tip region is too large, the probe will not be suitable for applications in which more than one probe is used simultaneously in close proximity to one another. One example of a technique that requires both a mechanically robust probe and that involves the use of multiple probes in close proximity is fault testing of microelectronic circuits. For such applications, it is advantageous for the near-tip region of the probe to have not only a cone angle within a certain specific range, but also a convex or “bullet shape” One of the features of the current invention is that a probe with bullet shape can be obtained.

(21) The methods of the present invention enable the production of tips in which the near apex region of the tip has a different geometry than the cone-like geometry typically seen. The near apex region is defined as the portion of the probe between the apex and a distance L from the apex along the longitudinal axis of the probe. In one embodiment L is 1 micrometer. In another embodiment, L is 100 nm, and in a further embodiment L is 50 nm.

(22) The following sections provide mathematical descriptions of the geometry of the probes near the apex. In all cases, the shape of a probe is measured by TEM; although some minor roughness may be observed on an atomic level; the shape is measured by disregarding or smoothing out the roughness/noise as is typically observed by TEM.

(23) An electron microscopy image is obtained at a resolution of 10 nm or better, preferably at 1 nm. A silhouette of the tip is obtained from which two profiles can be obtained, one on either side of the silhouette. In embodiments relevant to the current invention, the silhouette is approximately bilaterally symmetric with respect to the longitudinal probe axis. The probe has a tip 71 that can be described by a sphere 72 with the diameter of curvature of the tip apex. Two straight line segments 73, 74 of equal length are drawn, each of which is tangent to this sphere at points 75 and 76, and which intersect at two points 77, 78, one on either side of the silhouette edge 79 (see FIG. 7). In some embodiments, the two straight line segments 73, 74 intersect the probe silhouette at 1 μm, 100 nm, or 50 nm along the longitudinal probe axis. If the thickness 80 of the probe silhouette increases monotonically from the tangent points 75, 76 to the two intersection points 77, 78, and the profile lies farther from the tip longitudinal axis than the two straight lines at every point between the tangent points to the tip and the two intersection points, no matter what length straight line segments are chosen, then the tip has a bullet shape. Shaded region 81 shows the area outside a cone.

(24) The geometry of a probe from the tangent point where the probe profile meets the spherical end of the probe to a distance of L from the tangent point is often nearly or completely axially symmetric. In one embodiment, the geometry of the probe can conform to a profile f(x) that can be described by the functional form:
f(x)=a.sub.0+a.sub.1x+a.sub.2x.sup.2+a.sub.3x.sup.3+b.sub.1x.sup.1/2+b.sub.2x.sup.1/3,
where f(x) is the distance of the surface of the probe from the longitudinal axis of the probe, measured along a line perpendicular to the longitudinal axis, the coefficients a.sub.0, a.sub.1, a.sub.2, a.sub.3, b.sub.1, b.sub.2 are real numbers that can be positive, negative or zero, and x is the distance that ranges from 0 to L, with 0 being the longitudinal axis position where the probe profile is tangent to the probe apex sphere. This functional form describes probes with near apex regions that can be cylindrical, conical, convex or concave in shape. In one embodiment of the bullet shaped probe, the probe region from 0 to L is parabolic in shape, which corresponds to a.sub.0 and b.sub.1 being non-zero and all the other coefficients being zero. The coefficient a.sub.0 will typically have values in the range of 1 to 50 nm. The coefficient a.sub.1 will typically either be 0 or have values in the range 0.2 to 4 if x is in nm. The coefficient a.sub.2 will typically be 0 or have values in the range of 0.004 to 0.08 nm.sup.−1 if x is in nm. The coefficient a.sub.3 will typically be 0 or have values in the range of 0.00008 to 0.0016 nm.sup.−2 if x is in nm. The coefficient b.sub.1 will typically be 0 or have values in the range of 1.4 to 28 nm.sup.1/2 if x is in nm. The coefficient b.sub.2 will typically be 0 or have values in the range of 2.7 to 54 nm.sup.2/3 if x is in nm.

(25) Another kind of bullet shape is defined in FIG. 8. In this embodiment, if the diameter of the cylindrical wire body is D, the profile of a bullet-shaped probe in the near apex region as defined above is described by two arcs of a circle of radius equal to a multiple of D, each arc being tangent to one of a pair of opposing parallel sides of the cylindrical wire body. In some embodiments, the two arcs are defined by a circle having a radius equal to between 1 and 20 times, preferably between 5 and 7 times the wire body diameter D. The two arcs meet at the apex of the probe. At this meeting point, the apex is defined by a diameter of curvature that in one embodiment is less than 10 nm. The two arcs may or may not be tangent at the point of intersection to the cylindrical portion of the wire. When the circles are tangent to the cylinder portion, this is a tangent shape. When the circles are not tangent to the cylinder portion, this is a secant shape.

(26) In other embodiments, the probe tip has a biconic shape (see FIG. 9) wherein L.sub.2>L.sub.1; L.sub.1/L is in the range of 0.05 to 0.4 or 0.1 to 0.3; ϕ.sub.1/ϕ.sub.2 is in the range of 1.1 to 2.0, or 1.2 to 1.8, or 1.1 to 1.3; R.sub.1 is in the range of 10 to 1 μm or 20 to 200 nm; and L is in the range of 30 nm to 1 μm or 50 nm to 500 nm, or 50 nm to 100 nm; and R.sub.2 is in the range 1 to 2000 μm, or 250 to 1000 μm. In this case, whether a given probe has this morphology is determined by dividing L into 5 equal parts and the points defining each part, beginning at the sharp end, forms a shape that falls within the claimed ranges.

(27) In some embodiments, the probe tip has a shape generated by rotating the curve y=R(x/L).sup.n about an x-axis defining the longitudinal probe axis, where R and L are defined as in the FIG. 10, and n is in the range of 0.6 to 0.9 or 0.7 to 0.8. In this case, whether a given probe has this morphology is determined by dividing L into 5 equal parts and the points defining each part, excluding the point at the sharp end, forms a shape that falls within the claimed ranges.

(28) In some embodiments, the probe tip has a shape defined by the Haack series (see FIG. 11):

(29) where y=[R(θ−½ sin 2θ+C sin.sup.3 θ).sup.1/2]/π.sup.1/2

(30) where θ=arccos(1−2x/L)

(31) where C is in the range of 0.00 to 0.667 or 0.0 to 0.3

(32) and where R, L, and x are defined as above.

EXAMPLES

(33) Tungsten wire pieces of diameter between 0.15 mm and 1.00 mm and about 2 cm in length are etched to a point with a diameter of curvature of less than 100 nm using known procedures (see the previously cited Zhang et al.). These etched wire pieces are then secured onto a flat stage such that the long axes of the wires are perpendicular to the surface of the stage, with the tips pointing away from the stage surface. The stage is then attached to a rotation mechanism that is located inside an evacuation chamber as shown in FIG. 1. The stage is tilted so that the long axes of the wire pieces are oriented at a pre-specified angle, called the ion angle, ranging from 0 to 90° with respect to the incident argon ion beam. In another embodiment of the invention, the angle is varied during ion beam processing.

(34) The broad beam ion source used was a Kaufman type source, which produces a nearly uniform ion beam across its exit aperture. The exit aperture is 10 cm in diameter. In addition to emitting ions, the source incorporates a neutralizer filament that thermionically emits electrons, which create space charge neutrality and prevent the ion beam from blooming. The tips to be sputtered were located about 30 cm from the exit aperture of the ion source. The ion energy range used with the source is 100 eV to 1500 eV and the ion beam current can range from 10 mA to 100 mA. These conditions correspond to a flux range from 7×10.sup.14 ions/cm.sup.2s to 7×10.sup.15 ions/cm.sup.2s.

(35) Specific processing conditions used argon ions at an energy of 1500 eV and a flux of 3×10.sup.15 ions/cm.sup.2s. During ion processing, the sample holder is rotated on its axis at about 60 rpm, and the typical processing time is 60 minutes.