Patent Publication Number: US-8111080-B2

Title: Knee probe having reduced thickness section for control of scrub motion

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application of U.S. patent application Ser. No. 11/521,944, entitled “Knee Probe Having Reduced Thickness Section for Control of Scrub Motion”, to January Kister, filed Sep. 14, 2006, now U.S. Pat. No. 7,659,739 which is a continuation-in-part application of U.S. patent application Ser. No. 11/450,977, entitled “Knee Probe Having Increased Scrub Motion”, to January Kister, filed on Jun. 9, 2006, now U.S. Pat. No. 7,733,101 which is a continuation-in-part application of U.S. patent application Ser. No. 10/850,921 (now U.S. Pat. No. 7,148,709), entitled “Freely Deflecting Knee Probe with Controlled Scrub Motion”, to January Kister, filed May 21, 2004, and all of the specifications and claims thereof are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to probes for testing electronic circuitry. Particularly, the present invention relates to vertical probes having a rigid columnar structure and a suspension knee for controlled scrub motion. This invention relates to electrical probes for automated circuit and device testing. 
     2. Description of Related Art 
     In the field of electronic circuitry testing, scrubbing and contact force is an important factor in establishing a low resistance electrical contact between a probe tip and the test contact. During scrubbing, an eventual insulating oxide layer is removed in the interface between the contact tip and the test contact. Scrubbing is a microscopic shear movement of the probe tip along the test contact surface while a certain pressure is exerted from the probe tip onto the test contact. As size and pitch of test contacts decrease, it becomes increasingly difficult to tune the scrub motion irrespective of friction influences in the tip/contact interface. Also, as the integrated circuit (IC) manufacturers incorporate designs with IC pads and bumps placed over chip&#39;s active circuitry it becomes important that the scrub of the probe does not cause damage to the underlying circuitry. The size of the window of acceptable probe operation therefore, is restrained from one side by the contact resistance requirements calling for a sizable scrub, smaller scrub size required by smaller targets that need to be probed as pitches decrease, and smaller scrub (including depth) to avoid damage to the underlying circuitry. 
     The new generation of IC chips has pads that are placed over active circuitry in order to maximize use of the real estate. These types of chips are commonly referred in the industry as chips with “low-K dielectric”. The low-K dielectric refers to the fragile polymer-based insulator now placed between the pads and the underlying circuits for electrical purposes. It is not acceptable to damage the low-K dielectric during probing operations either. 
     In the prior art, well known buckling beam probes have been utilized to provide a combined resilient deflection and scrubbing. In order for a buckling beam probe to operate properly with a well defined scrub motion it needs to be rigidly held on its peripheral shaft and additionally guided close to the contact tip. This makes the buckling beam probe&#39;s assembly increasingly challenging with ever decreasing scale. Therefore, there exists a need for a probe that may be easily assembled in large numbers and small scale while providing a well definable scrub motion. The present invention addresses this need. 
     The contact resistance issue has also been addressed by probes having separate parts for scrubbing and for making electrical contact. For example, US 2004/0239352 considers dual probes having a contact probe and a separate scrub probe, where the scrub probe moves in such a way as to clean the part of the contact pad that will end up under the contact probe during test. In some cases (e.g., copper deposition manufacturing), circuit fabrication processes provide contact pads which are covered with a protective dielectric film (e.g., a silicon dioxide film). U.S. Pat. No. 6,727,719 considers a probe having an inner contact needle and an outer hard layer, where the hard outer layer is adapted for penetrating such a protective film. 
     An important consequence of decreasing probe and contact pad dimensions is that the current density at the probe-pad contact increases. This increased current density also raises issues which have not come up before in connection with large probes on large pads. More specifically, the current density can be high enough to form micro-welds between the probe and the pad due to local heating. Breaking these micro-welds as the probe is removed from the contact pad can lead to degradation of the probe tip (e.g., by accumulation of non-conductive material), thereby reducing probe reliability and/or lifetime. 
     Testing of electrical devices and circuits has been an important component of electronic manufacturing processes for some time. Such testing typically entails probing a circuit with a fixture including multiple flexible probes, each probe making electrical contact to a contact pad on the circuit chip. Various practical issues that have arisen in this context have been addressed in the prior art, especially in connection with providing reliable, low-resistance electrical contact. 
     It is well known that electrical contact between the probe and the contact pad can be hampered by the presence of non-conductive material on the pad and/or the probe (e.g., a thin oxide film). Accordingly, considerable attention has been devoted to details of how the tip of the probe moves relative to the contact pad in order to improve the resulting electrical connection. This relative motion is usually referred to as a scrub motion. For example, U.S. Pat. No. 5,923,178 considers a probe having a shape which provides a scrub motion which is primarily a rocking motion without appreciable sliding. U.S. Pat. No. 5,952,843 considers a probe having a canted tip portion to facilitate penetration of the passivation layer. U.S. Pat. No. 6,529,021 considers a probe arrangement where the probe tip can be made to move in a reciprocating manner to reduce contact resistance. 
     As circuit manufacturing technology continues to evolve to smaller critical dimensions, new practical issues relating to probing tend to arise which are not fully addressed by prior art approaches. For example, the decreasing size of contact pads as critical dimensions are reduced leads to increasingly demanding requirements on the ability to precisely control the probe scrub motion. Excessive scrub motion can cause loss of electrical contact, if the probe moves off the contact pad. 
     Accordingly, it would be an advance in the art to provide greater control of probe scrub motion. 
     BRIEF SUMMARY OF EMBODIMENTS OF THE PRESENT INVENTION 
     A preferably vertically assembled probe features a substantially rigid columnar structure and a connected suspension knee. The probe is held in assembly via its columnar structure. The suspension knee has a base arm laterally connecting at and propagating away from a connect end of the columnar structure. The base arm extends up to a lateral knee extension where a reverse arm continues from the base arm back in direction towards a central axis of the columnar structure. The reverse arm terminates in a contact tip in a tip offset to the column axis that is smaller than the lateral knee extension. During application of a contacting force onto the contact tip, a first deflection of the base arm and a second deflection of the reverse arm counter act in conjunction with base and reverse arms structural configuration. As a result, scrub motion may be well defined in direction and magnitude without need for additional guidance of the deflecting probe structure. 
     The entire probe is preferably symmetric with respect to a symmetry plane through the column axis and a tip axis, which is central with respect to a contacting face of the contact tip. The probe preferably has a continuous profile in a direction normal to the symmetry plane fabricated for example by electroplating. Base and reverse arms are preferably linearly protruding with a knee bent in between, which results in combination with continuous probe profile in a scrub motion highly in plane with the symmetry plane. 
     The probes may be arrayed with tight pitch that is less than the total width of the probe. Adjacent suspension knees may overlap while leaving sufficient clearance. The probes may be assembled via their columnar structures for example in a sandwiching fixture and clamping plates that provide a shearing clamping of the columnar structures. The probes may also be simultaneously fabricated in a probe comb including a number of probes linearly arrayed with a final assembly pitch and held together by a bridge connecting each of the arrayed probes on the peripheral end of the columnar structure. The bridge may be removed after a number of probe combs are stacked and fixed with respect to each other. 
     Improved probing is provided in one embodiment of the present invention using a knee probe where the knee curves away from the probe axis and then curves back to connect to the probe tip, crossing the probe axis on the way to the tip. The resulting lateral offset between the probe tip and the probe axis is a key geometrical parameter for predetermining the scrub motion provided by the probe in response to a predetermined contact force. The scrub motion preferably includes both a sliding motion and a rocking motion, where the sliding motion acts to clean the contact pad and the rocking motion acts to bring a clean part of the probe tip into contact with the freshly cleaned part of the contact pad. In preferred embodiments, the probe tip can include one or more relatively narrow “skates” for making contact to the contact pad. A dual skate configuration is especially appropriate when small dimples are at the centers of the contact pads. 
     Embodiments of the invention provide numerous advantages. The use of a probe having an “overshoot” knee as described above and in more detail below generally tends to increase the scrub motion compared to knee probes which do not “overshoot” the probe axis. In preferred embodiments, the invention makes use of multilayer probes, which facilitates the fabrication of probes having narrow “skates” on the probe tips. Such skates advantageously decouple the contact width (which should be small to increase contact for per unit area) from the probe width (which should be large enough to prevent motion in directions other than in the intended deflection plane). Multi-layer probes also allow the skate layers to be made of a suitable tip contact material, while the remaining layers are not constrained to be suitable tip contact materials. Dual-skate probe tips can be employed to probe contact pads having dimples at their centers (e.g., as provided by plating techniques for forming contact pads). In this case, the skates advantageously avoid the dimple, thereby avoiding issues relating to degraded electrical contact and increased mechanical stress on the probe tip that can arise when probing is performed directly at dimple locations. 
     To better appreciate the present invention, it is helpful to consider some aspects of prior work by the present inventor. In particular, U.S. patent application Ser. No. 11/450,977 by the present inventor considers a knee probe where the knee curves away from the probe axis and then curves back to connect to the probe tip, crossing the probe axis on the way to the tip. This configuration can be described as having a negative tip offset, in contrast to probes having no tip offset (i.e., the probe tip is aligned with the probe axis), or probes having a positive tip offset (i.e., the knee section does not cross the probe axis). Other parameters being comparable, probes having negative tip offset tend to provide longer scrub marks than probes having zero or positive tip offset. In some cases, it is desirable to decrease the scrub length provided by a probe having negative tip offset. 
     Such reduction in scrub length can be provided according to the present invention by modifying the probe shape. More specifically, the probe knee section includes a reduced thickness section to alter the mechanical behavior of the probe when contact is made. Providing a reduced thickness section of the probe makes it easier to deflect the probe vertically when contact is made. This increased ease of vertical deflection tends to reduce the horizontal contact force component responsible for the scrub motion, thereby decreasing scrub length. Here “thickness” is the probe thickness in the deflection plane of the probe (i.e., the plane in which the probe knee lies). 
     The reduced thickness section of the probe can be described in terms of a probe thickness function h(z), where z is distance along the probe, having a local minimum. A probe having uniform thickness would have a constant h(z), and a tapered probe would have a monotonically decreasing h(z). In either of these two conventional cases, h(z) would not have a local minimum. 
     Although reduction of scrub length for negative tip offset probes is one application of the invention, the invention is also applicable to probes having no tip offset and to positive tip offset probes. In general, embodiments of the present invention can provide improved control of scrub motion (e.g., by varying details of the reduced thickness section such as location, amount of thickness reduction, etc.), especially in combination with other probe parameters affecting scrub motion. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         FIG. 1  is a first perspective view of an exemplary probe in accordance with a preferred embodiment of the invention. 
         FIG. 2  is the first perspective view of a number of probes of  FIG. 1  in exemplary assembly array. 
         FIG. 3  is a top view of the probe array of  FIG. 2 . 
         FIG. 4  is the top view of the probe array of  FIG. 2  together with sandwiched fixture and clamping plate in aligned cutout position for probe insertion. 
         FIG. 5  is a second perspective view of the assembly of  FIG. 4 . 
         FIG. 6  is the second perspective view of the assembly of  FIG. 5  in shear clamp configuration. 
         FIG. 7  is the second perspective view of the assembly of  FIG. 6  with the top fixture plate being removed for illustration purpose. 
         FIG. 8  is a third perspective view of an exemplary probe comb of a number of linearly arrayed probes combined by a bridge. 
         FIG. 9  is a schematic front view of a suspension knee in deflected and non deflected condition. 
         FIGS. 10 ,  12 ,  14 ,  16 ,  17 ,  19  are colored front views of spectral displacement plots of variously configured suspension knees. 
         FIG. 11  is a colored front view of a spectral stress plot of the suspension knee of  FIG. 10 . 
         FIG. 13  is a colored front view of a spectral stress plot of the suspension knee of  FIG. 12 . 
         FIG. 15  is a colored front view of a spectral stress plot of the suspension knee of  FIG. 14 . 
         FIG. 18  is a colored front view of a spectral stress plot of the suspension knee of  FIG. 17 . 
         FIG. 20  is a front view of a multiradius contacting tip in initial contact with a test contact. 
         FIG. 21  is the front view with the multiradius contacting tip of  FIG. 20  in operational contact with the test contact of  FIG. 20 . 
         FIG. 22  is a fourth perspective view of a contacting tip with three tip segments. 
         FIG. 23   a  shows a first contact probe configuration according to an embodiment of the invention. 
         FIG. 23   b  shows an operational probe configuration according to an embodiment of the invention. 
         FIG. 24  shows a close up view of a probe tip making contact to a contact pad according to an embodiment of the invention. 
         FIG. 25  shows a close up view of a probe tip making contact to a contact pad according to another embodiment of the invention. 
         FIG. 26  shows a close up view of a probe tip making contact to a contact pad according to yet another embodiment of the invention. 
         FIG. 27   a  shows a photograph of a probe tip. 
         FIG. 27   b  shows a photograph of the probe tip of  FIG. 27   a  after 1,000,000 probing cycles according to an embodiment of the invention. 
         FIGS. 28   a - d  are photographs of probe array configurations suitable for use with embodiments of the invention. 
         FIG. 29  shows a depth profile for a scrub mark made in accordance with an embodiment of the invention. 
         FIG. 30  shows a probe according to a first embodiment of the invention. 
         FIGS. 31-32  show alternate embodiments of the invention having different tip offsets. 
         FIGS. 33-34  show alternate embodiments of the invention having different upper knee section thickness profiles. 
         FIG. 35  shows an embodiment of the invention having a tapered lower knee section. 
         FIG. 36   a  shows an embodiment of the invention in an initial contact configuration. 
         FIG. 36   b  shows an embodiment of the invention in an operating contact configuration. 
         FIG. 37  shows a probe according to another embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , a probe  1  in accordance with a preferred embodiment of the invention features a rigid columnar structure  2  having a peripheral end  21 , a connect end  22 , a knee opposing face  23 , a connect face  24 , a front face  25  and a back face  26 . The columnar structure  2  is preferably symmetric with respect to a central column axis CA. At the connect end  22 , a suspension knee  3  is laterally connecting via its base arm  32 , which propagates away from the column axis CA substantially up to a lateral knee extension PK. A reverse arm  34  continues from the base arm  32 . The reverse arm  34  propagates away from the lateral knee extension PK in direction towards the column axis CA with a reverse length RL. At the end of the reverse arm  34  is a contacting tip  35 . The contacting tip  35  has a contacting face  36  with a tip axis TA central with respect to the contacting face  36 . The tip axis TA is offset from the column axis CA in a tip offset TO. The tip offset TO is smaller than the lateral knee extension PK such that during application of a contacting force preferably along the tip axis TA a first deflection of the base arm  32  and a second deflection of the reverse arm  34  counteract, resulting in a predetermined scrub motion of the contacting tip  35 . The suspension knee  3  is connected to the rigid columnar structure  2  via a suspension connect  31 . 
     The probe  1  is preferably symmetric with respect to a symmetry plane SP that coincides with the column axis CA and the tip axis TA. As a preferred result, the scrub motion is substantially in plane with the symmetry plane SP. The probe  1  may have a continuous profile in direction perpendicular with respect to the symmetry plane SP such that the columnar structure  2  as well as the elements of the suspension knee  3  have substantially rectangular cross sections. 
     The columnar structure  2  has a first pair of adjacent faces and a second pair of adjacent faces, the first pair opposing the second pair. A first pair may be for example faces  24 ,  26  and a second pair may be faces  23 ,  25 . The probe  1  may be fabricated in a layered fabrication technique such as well known electroplating in combination with negative shaped mask. Relevant dimensions of the probe  1  include probe thickness TH, total probe width WT, column width CW, column height CH, tip offset TO, lateral knee extension BL and reverse arm length RL. In the preferred case of substantially linearly protruding base arm  32  and/or reverse arm  34 , relevant dimensions include also a base arm angle AB and reverse arm angle AR between a knee axis KA and their respective arms  32 ,  34 . The knee axis KA is a geometric element coinciding with a center of a knee bent  33  referencing the orientation of the knee bent  33  with respect to the column axis CA. The knee axis may be utilized to characterize the displacement behavior of the suspension knee  3  as depicted in the spectral displacement plots of  FIGS. 10 ,  12 ,  14 ,  16 ,  17 ,  19 . 
     In the  FIGS. 1-8 , the arms  32 ,  34  as well as the knee bent  33  and contacting tip  35  are depicted as having constant cross sections. Nevertheless, arms  32 ,  34 , knee bent  33  and contacting tip  35  may have tuned configurations to provide a scrub motion predetermined in direction and magnitude in response to a contacting force exerted onto the contacting face  36  during operational contacting of the probe  1  with a test contact as is well known in the art. Such tuned configurations and their influence on the scrub motion are described in more detail under  FIGS. 9-18 . 
     Referring to  FIGS. 2 ,  3 , multiple representations of probe  1  may be arrayed with a first pitch PX that is substantially smaller than the total width WT. Base and reverse angles AB, AR are selected such that for a given first pitch PX sufficient base arm clearance BC and reverse arm clearance RC is established for an unimpeded deflection of each suspension knee  3  within the array. The first pitch PX may be selected in conjunction with the column width CW such that a first gap GX remains at a minimum required for an assembly for the arrayed probes  1 . 
     Multiple representations of probe  1  may be arrayed in a two dimensional probe array  10  with the first pitch PX in a preferred direction parallel to the probes&#39; 1 knee axes KA and a second pitch PY preferably perpendicular to the first pitch PX. The second pitch PY may be selected in conjunction with the probe thickness TH such that a second gap GY remains at a minimum required for an assembly for the arrayed probes  1 . Providing the probes  1  in a configuration for a sole assembly via their rigid columnar structures  2  and for a scrub motion predetermined in direction and magnitude is highly advantageous for a tight interlaced array of the probes  1 . For example, probes  1  having a probe thickness TH of about 2 mils, a total width WT of about 8 mils and a column width CW of about 2 mils may be assembled with a first pitch PX of about 4 mils and a second pitch of about 3 mils. 
     Referring to  FIGS. 4-7 , the probes  1  may be fixedly held in a probe assembly  100  including fixture plates  4  that may be combined and/or part of a well known probe apparatus for testing electronic circuitry. Each fixture plate  4  has a number of fixing cutouts  41  with a contour larger than the rectangular cross section of the columnar structure  2 . Each fixing cutout  41  has two fixing faces  411 ,  412  that correspond to the first pair of adjacent faces  24 ,  25 . The probe assembly further includes a clamping plate  5  having a number of clamping cutouts  51  also with a contour larger than the rectangular cross section of the columnar structure  2 . Each clamping cutout  51  has two clamping faces  511 ,  512  that correspond to the second pair of adjacent faces  23 ,  26 . Fixing cutouts  41  and clamping cutouts  51  are fabricated into their respective plates  4 ,  5  with pitches PX and PY. 
     The clamping plate may be held with respect to the fixture plates  4  in an assembly position as seen in  FIGS. 4 ,  5  and a clamping position as seen in  FIGS. 6 ,  7 . In the assembly position, the clamping cutouts  51  align with the fixing cutouts  41  such that a columnar structure  2  may be inserted in the fixing cutouts  41  and the clamping cutouts  51 . In the clamping position, the clamping plate  51  is offset in a clamp direction DC relative to its assembly position. The clamp direction DC is in a clamp angle AC which preferably corresponds approximately with a diagonal between the enclosed edges of the first pair of adjacent faces  24 ,  25  and the second pair of adjacent faces  23 ,  26 . As a result of the angled clamping offset, the first pair of adjacent faces  24 ,  25  is forced into snuggle contact with the fixing faces  411 ,  412  and the second pair of adjacent faces  23 ,  26  is forced into snuggle contact with the clamping faces  511 ,  512  such that each probe is fixedly held in a predetermined pitch and orientation with respect to the fixture plates  4  and with respect to each other. 
     Plates  4 ,  5  may be fabricated from ceramic with the cutouts  41 ,  51  being deep trench etched as may be well appreciated by anyone skilled in the art. The clamping plate  5  may be forced into the clamping offset via any well known mechanical feature such as a screw pressing against a clamping access feature  55 . The clamping direction DC is self adjusting as long as the clamping force is applied in direction approximately complying with the predetermined clamping direction DC as may be well appreciated by anyone skilled in the art. The clamping plate  5  may be actuated without particular guides. Assembly position stoppers may be provided for the clamping plate to warrant alignment of the clamping cutouts  51  with the fixing cutouts  41  in assembly position. Positioning of the probes  1  in direction along the column height CH may be provided via an auxiliary stop plate (not shown) temporarily placed adjacent opposite an insertion side of the plate assembly such that the peripheral ends  21  contact the stop plate once fully inserted into the cutouts  41 ,  51 . After clamping, the stop plate may be removed. The probes  1  may be bonded in clamped position by an epoxy or other well known techniques. The cutouts  41 ,  51  may also be configured as conductively coated via holes conductively connected to peripheral terminals on the plates  41 , and/or  51 . The probes  1  may also be conductively accessed via well known wire bonding techniques bonding wires to the peripheral ends  21  as may be well appreciated by anyone skilled in the art. The fully fabricated probe assembly  100  may be inserted and/or assembled in a well known probe apparatus. 
     To facilitate the assembly of large numbers of probes  1 , a number of probes  1  may be simultaneously fabricated as a probe comb  11  as is exemplarily illustrated in  FIG. 8 . The probe comb  11  is held together by a probe bridge  6  connected to each of the arrayed probes&#39;  1  peripheral end  21 . A number of probe combs  11  may be stacked with second pitch PY in protrusion direction of the probe comb  11 , forming large two dimensional probe arrays. Individual probe combs  11  may be spaced apart by spacers that provide second gaps GY. The probe combs  11  may be held in alignment along second pitch PY direction by surrounding frame structures and/or by form features on both sides of the spacers. The form features may fit into the gaps GX. The probe combs  11  may alternately be assembled by inserting them with there probe bridges  6  in correspondingly shaped grooves of a template plate (not shown). 
     After the probe combs  11  are positioned with respect to each other, they may be fixed by use of a resin filled into the gaps between the probes  1 . After curing of the resin, the probe bridges  6  may be removed and the individual probes  1  conductively accessed as described above. 
     Suspension connect  31 , base arm  32 , knee bent  33 , reverse arm  34 , and contacting tip  35  may have various tuned configurations resulting in varying scrub motions. Referring to  FIGS. 9-13  a first tuned configuration is described in which a lateral scrub motion with respect to the tip axis TA is substantially zero. In  FIGS. 9-19 , numerals pertaining to the deflected elements of the suspension knee  3  have a suffix letter D, whereas numerals pertaining to non deflected elements of the suspension knee  3  have a suffix letter N. A contacting force resulting from the operative approach of the contacting tip  35  on a test contact  210  (see  FIGS. 20 ,  21 ) may act upon the contacting face  36 N/ 36 D along the tip axis TA. Where the tip axis TA crosses the base arm  32 N/ 32 D, the base arm  32 N/ 32 D has its local bending stresses at a minimum as can be seen in the spectral stress plots of  FIGS. 11 ,  13  and  15 ,  18 . At these low stress regions LS, LSN/LSD, the central base arm portion  321 D has its maximum angular central base arm deflection DAB 1  with respect to the central base arm portion&#39;s  321 N natural orientation and the peripheral base arm portion  322 D has its maximum angular peripheral base arm deflection DAB 2  with respect to the peripheral base arm portion&#39;s  322 N natural orientation. This is, because a first bending momentum acting on the central base arm portion  321 N/ 321 D is opposing a second bending momentum acting on the peripheral base arm portion  322 N/ 322 D. According to  FIG. 9 , the first bending momentum and the second bending momentum act counter clock wise or generally speaking in direction away from the upper portion of the column axis CA. The first bending momentum hinges thereby on the suspension connect  31  and the second bending momentum hinges on the knee bent  33 . 
     A third bending momentum acts on the reverse arm  34 N/ 34 D hinging on the knee bent  33  generally in direction opposite the second bending momentum. According to  FIGS. 10 ,  11 , the third bending momentum acts clock wise. First, second and third bending momentums result from the contacting force as may be well appreciated by anyone skilled in the art. The third bending momentum results in a maximum angular reverse arm deflection DAR with respect to the reverse arm&#39;s  34 N natural orientation. 
     The first tuned configuration includes dimensional and structural configurations of suspension connect  31 , central base arm portion  321 , peripheral base arm portion  322 , knee bent  33  and reverse arm  34  such that maximum local angular deflections DAB 1 , DAB 2  and DAR are substantially equal. An indication for the first tuned configuration is that the natural knee axis KAN of the non deflected suspension knee  3  is substantially parallel to the deflected knee axis KAD of the operationally deflected suspension knee  3 . 
     During deflection of the central base arm portion  321 N/ 321 D a lateral offset NOF may be introduced to the remainder of the suspension knee  3  due to the geometric conditions and geometric relations of the deflected and non deflected central base arm portion  321 N/ 321 D as may be well appreciated by anyone skilled in the art. The contacting tip  35  may be configured in length and deflection behavior such that the lateral offset NOF may be substantially compensated for. At the contacting face  36 D, the contacting tip  35 D may consequently have a maximum angular tip deflection DAT contributing to the scrub motion. Hence, in the first tuned configuration, the scrub motion includes substantially only angular movement of the contacting face  36 . 
     For a required contacting force, the operational deflection of the suspension knee  3  may be adjusted by configuring the elements of the suspension knee  3  for a leveled stress maxima as can be seen in the  FIGS. 12 ,  13 . There, the cross sections are adjusted with continuous thickness TH such that stress maxima propagate highly continuous along suspension connect  31 , central and peripheral base arm portions  321 ,  322 , knee bent  33 , reverse arm  34  and contacting tip  35 . Optimizing the suspension knee  3  with constant thickness TH is particularly preferred in combination with continuous profile of probe  1  and fabrication techniques layered in profile direction such as well known electroplating in combination with a negative mask corresponding to the contour of the probe&#39;s  1  continuous profile. Nevertheless, the suspension knee  3  may also be optimized by varying the thickness TH as may be well appreciated by anyone skilled in the art. 
     Referring to  FIGS. 14-16 , a second tuned configuration of the suspension knee  3  provides a scrub motion in direction towards the column axis CA. According to  FIGS. 14 and 15 , the second tuned configuration may be provided for a continuously shaped base arm  32  by extending the reverse arm  34  such that the tip axis TA divides the base arm into a central base arm portion  321  that is shorter than the peripheral base arm portion  322 . Consequently, the maximum angular deflection DAB 1  of central arm portion  321 D is smaller than the maximum angular deflection DAB 2  of the peripheral arm portion  322 D. Since base arm  32  and reverse arm  34  have substantially equal and continuous cross sections, DAB 2  is equal DAR. The summary of DAB 1 , DAB 2  and DAR results generally in a tilt of the displaced knee axis KAD in direction away from the upper portion of the column axis CA. With respect to  FIGS. 14 and 16 , the displaced knee axis KAD is tilted in clockwise direction with respect to the natural non deflected knee axis KAN. The resulting lateral scrub motion is in direction towards the central axis CA.  FIG. 15  depicts the corresponding stresses. 
     The same condition of DAB 1  being smaller than DAB 2  with DAB 2  being equal DAR is depicted in  FIG. 16 . There, the central base arm portion  321  is configured with larger bending stiffness than the peripheral base arm portion  322 . Even though the tip axis TA is at a distance to CA equal to the above described first tuned condition of  FIGS. 9-13 , the dissimilar structural configuration of both base arm portions  321 ,  322  is the prevailing condition determining the direction and magnitude of the scrub motion. 
     The teachings of  FIGS. 14-16  may be inverted to obtain a third tuned configuration in which the scrub motion is in a direction away from the central axis CA as may be well appreciated by anyone skilled in the art. Accordingly and as shown in  FIGS. 17 ,  18 , the suspension knee  3  is configured with the tip axis TA dividing the base arm  32  in a central base arm portion  321  that is longer than the peripheral base arm portion  322 . Despite continuous cross sections of base arm  32  and reverse arm  34 , DAB 1  being larger than DAB 2  results in a scrub motion away from the central axis CA irrespective of DAB 2  being equal DAR, which is illustrated in  FIG. 17  by the deflected knee axis KAD being rotated in counter clockwise direction with respect to the natural knee axis KAN or generally speaking, in the third tuned configuration the deflected knee axis KAD is rotated with respect to the natural knee axis KAN in direction towards the upper portion of the column axis CA. 
     Second or third tuned configuration may be obtained also by adjusting the reverse arm&#39;s  34  deflection behavior in conjunction with the peripheral base arm portion&#39;s  322  deflection behavior as illustrated in  FIG. 19 . There, the base arm portions  321 ,  322  are configured with equal deflection behavior such that DAB 1  equals DAB 2 . The reverse arm  34  on the other hand is stiffer than the peripheral arm portion  322  resulting in DAR being smaller than DAB 2  and consequently a third tuned configuration with a linear scrub motion away from the central axis CA. In case, the reverse arm  34  would be less stiff than the peripheral base arm portion  322 , the second tuned configuration would be established with the linear scrub motion towards the central axis CA. 
     As may be well appreciated by anyone skilled in the art, the teachings presented under the  FIGS. 9-19  may be well applied to configure various shapes of the suspension knee&#39;s  3  elements. Further more, the contacting force represented in the Figures by the tip axis TA may be adjusted in angle with respect to the column axis CA. Consequently, for a given geometry of the suspension knee  3 , first, second or third tuned configuration may be provided by assembling the probe  1  with its column axis CA in predetermined angle with respect to the contacting force defined by the probe apparatus in conjunction with the test contact  210  (see  FIGS. 20 ,  21 ) as may be well appreciated by anyone skilled in the art. For example, the probe  1  may be provided with a first tuned configuration in case of the tip axis TA being parallel to the column axis CA. Tilting such probe  1  in direction towards its knee  33  may result in a second tuned configuration whereas a tilting of such probe  1  in direction away from its knee  33  may result in a third tuned configuration. Tilting the probe  1  may be a convenient technique of fine tuning the linear scrub motion in direction and magnitude without need to remanufacture the probe  1 . 
     As taught under  FIGS. 9-19 , scrub motion may be adjusted for its lateral movement component in direction and, magnitude and for its angular movement component in magnitude as may be well appreciated by anyone skilled in the art. The advantageous combination of angular and lateral scrub motion adjustability may be combined with a multiradius contacting face  38  as illustrated in  FIGS. 20 ,  21 . The multiradius contacting face  38  may have at least a first contacting radius R 381  at the initial contacting region  381  where the multiradius face  38  initially contacts the test contact  210  of a tested electronic device  210 . An initial tip axis TA 1  may origin in the initial contacting region  381 . 
     As the probe  1  is brought into operational deflection with respect to the test contact  210 , the multiradius face  38  may be rotated with maximum tip deflection angle DAT such that an operational contacting region  382  comes into contact with the test contact  210 . An operational tip axis TA 2  may origin from the central interface between operational contacting region  382  and the test contact  210 . Between initial contacting at scrub start location SS and operational contacting, the multiradius face  38  prescribes a lateral scrub SL and an angular scrub equal DAT. Orientation of TA 1  and TA 2  may be affected by friction in the tip/contact interface CI as may be well appreciated by anyone skilled in the art. 
     The operational contacting region  382  has second contacting radius R 382  substantially larger than first contacting radius R 381 . The mulitradius face  38  hence features at least two radii R 381 ,  8382  that contribute to a smooth and continuously curvature of the multiradius face  38 . The two radii R 381 , R 382  may be selected in conjunction with the change of contacting force as a function of angular tip displacement such that contacting pressure in the tip/contact interface CI remains within a predetermined limit. 
     Referring to  FIG. 22 , area of and pressure in the tip/contact interface CI may also be adjusted by varying the contacting face thickness FT to levels less than the probe thickness TH. Also, the contacting tip  35  may be split into tip segments  351 ,  352 ,  353  of which one or more may provide contacting face(s)  36  or  38 . For that purpose, the probe  1  may be fabricated from a number of layers L 1 , L 2 , L 3  deposited in multiple steps for example by electroplating in combination with multiple masks as may be well appreciated by anyone skilled in the art. The layers L 1 , L 2 , L 3  may partially and/or fully extend across the probe&#39;s  1  profile contour and may be made of materials suitable for their particular task. For example, the layer L 2  illustrated in  FIG. 22  with the contacting face  36  may be fabricated from a material specifically suitable for probe tips such as rhodium. A single contacting face  36  or  38  may be placed centrally as shown in  FIG. 22 . Alternatively, dual contacting faces  36  or  38  may be provided by tip segments  351 ,  353 , one adjacent the front face  25  and the other adjacent the back face  26 . This may also assist in stabilizing the suspension knee&#39;s  3  deflection behavior within the symmetry plane SP and to reduce the risk of inadvertent lateral scrub motion deviations. 
     The contacting tips  351 ,  352 ,  353  may be arranged in a tripod like fashion with each contacting segment having a contacting face  36  or  38  for providing a self centering contacting on a test contact in the well known spherical configuration. The suspension knee  3  may be layered in direction along the symmetry plane SP. The layer configuration may also be adjusted in view of low surface resistance for high frequency current flow from the contacting tip  36  or  38  to the peripheral end  21  or the column  2 . Tip segments  351 ,  352  and  353  may also be fabricated from same material resulting in a monolithic structure. The spectral plots of  FIGS. 10-19  are generated with a commercially available FEA software. 
     Referring to  FIG. 23   a  shows, a “first contact” probe configuration is illustrated according to an embodiment of the invention.  FIG. 23   b  shows a corresponding operational probe configuration. Here “first contact” refers to the situation where a probe is in contact with a contact pad, but no contact force is applied. In contrast, an operational probe configuration makes contact with the contact pad with a predetermined contact force. Since the probe deforms in response to the contact force, the shape of the probe differs in the two cases. In particular, how the probe moves from the first contact configuration to the operational configuration is a key aspect of the invention. 
     A probe  2300  includes a shank  2302 , a knee section  2304  and a probe tip  2306  as parts of a single structure, as shown. Shank  2302  is straight and does not deflect appreciably during contact, so it is convenient to regard shank  2302  as defining a probe axis  2310  with which it is aligned. Knee section  2304  extends from shank  2302  to probe tip  2306 , and includes two parts. A first part of knee section  2304  starts at shank  2302  and extends outward from probe axis  2310  to reach a knee point  2312 . Knee point  2312  is a point of maximum separation from probe axis  2310 . A second part of knee section  2304  starts at knee point  2312  and extends to a tip location  2314 , such that probe axis  2310  is between knee point  2312  and tip location  2314 . A lateral tip offset  2316  is thereby defined between the probe tip and the probe axis. Probe tip  2306  is in contact with a contact pad  2320  defining a contact point  2324 . 
     Thus knee section  2304  can be regarded as extending outward for a certain distance D (the first part) and then curving back for a distance greater than D (the second part), thereby establishing the lateral offset  2316 . The present inventor has found that this probe configuration can provide improved probing performance. For comparison, U.S. patent application Ser. No. 10/850,921 by the present inventor considers a knee probe having a knee which curves back by a distance less than D (i.e., it does not overshoot the probe axis). 
       FIG. 23   b  shows the corresponding operational probe configuration for the example of  FIG. 23   a . Here contact pad  2320  is moved toward probe shank  2302  by a vertical displacement  2330 . Equivalently, a predetermined contact force is applied to the probe shank. For any particular probe design, there is a one to one relation (i.e., this relation is a mathematical function, which can be linear or nonlinear) between vertical displacement and contact force, as is well known in the art, so both ways of describing the operational configuration are employed interchangeably in the following description. Probe  2300  deforms under the contact force, and  FIG. 23   b  shows key parameters of this deformation. More specifically, contact point  2324 ′ on  FIG. 23   b  is farther from probe axis  2310  than the corresponding contact point  2324  on  FIG. 23   a . Thus the probe tip slides along the contact pad for a certain distance (i.e., the difference between  2316 ′ and  2316  on  FIGS. 23   a - b ). In addition to this sliding motion, the probe tip also “rocks” relative to the contact pad. This rocking motion can be more clearly appreciated by defining a “tip axis”  2318  on  FIG. 23   a  which is required to be parallel to probe axis  2310  and which passes through the contact point  2324 . In the operational configuration of  FIG. 23   b , tip axis  2318  is no longer parallel to probe axis  2310 . The angle between tip axis  2318  and probe axis  2310  on  FIG. 23   b  is a measure of the amount of rocking motion provided. 
     Thus the scrub motion provided in this example includes both a sliding motion of the probe tip relative to the contact pad, and a rocking motion of the probe tip relative to the contact pad. A key aspect of the invention is that parameters of the scrub motion (e.g., slide length and rocking angle) can be predetermined, in part, by geometrical parameters of the probe and by the predetermined contact force (or equivalently, predetermined vertical displacement). More explicitly, a probing method according to the invention includes: providing a probe having the general configuration of  FIG. 23   a  (i.e., having a knee section with an overshoot), making contact between the probe tip and a device under test, and applying a predetermined contact force to the probe shank, thereby providing a predetermined scrub motion of the probe tip on the contact pad. The scrub motion is predetermined in part by the contact force and by geometrical parameters of the probe. 
     The friction provided by the contact pad is also a relevant factor for determining the scrub motion, so probe designs and/or methods will typically need to account for variations in contact pad friction. The speed with which contact is made has also been found to be relevant. More specifically, the sliding motion length on the contact pad (also referred to as scrub length) tends to decrease as the relative contact velocity between probe tip and contact pad increases. Another method of further controlling the scrub length is by laterally moving the probe as contact is made. Lateral probe motion in the direction of the tip offset will increase the scrub length, and lateral probe motion in the opposite direction will decrease the scrub length. Such lateral probe motion can be provided by appropriate motion control of a chuck holding the probe (or probes), or by appropriate motion control of a stage holding the device under test. Further scrub length control can be provided by controlling relative velocity and/or lateral probe motion. Scrub length can be measured after probing has occurred by measuring the length of the mark left by the probe on the contact pad. Such measurements are important for verifying proper probe performance. 
     A scrub motion including both a sliding motion and a rocking motion has provided improved results in practice. Investigations indicate that the sliding motion acts to scrape non-conductive material from the contact pad to create an exposed area of the contact pad, and the rocking motion acts to bring a clean part of the probe tip into contact with the freshly exposed area of the contact pad. From  FIGS. 23   a - b , it is apparent that the rocking motion causes a different point of the probe tip to be in contact with the contact pad in the operational configuration than in the “first contact” configuration. Providing a scrub motion including both of these motions is therefore preferred. 
     Suitable materials for probe  2300  and probe tip  2306  are well known in the art, and any such materials can be employed in practicing the invention. Suitable tip materials are electrically conductive and wear-resistant, and include Rh and Cr. 
     Detailed design work in accordance with the above-identified principles of the invention has led to a point design as well as identification of some preferred parameter ranges. A point design for making contact to Cu or Al contact pads (or flat topped columns) has a tip offset ( 2316  on  FIG. 23   a ) of approximately 0 to 0.3 mm and preferably approximately 0.1 to 0.2 mm and more preferably approximately 0.18 mm, a knee offset (distance between knee point  2312  and probe axis  2310  on  FIG. 23   a ) of approximately 0 to 0.7 mm and preferably approximately 0.1 to 0.5 mm and more preferably approximately 0.31 mm, and a probe length (combined length of probe tip and knee section in Z direction on  FIG. 23   a ) of approximately 0 to 5 mm and more preferably approximately 1 to 3 mm and more preferably approximately 1.95 mm. In this point design, the probe width is approximately 0 to 0.2 mm and more preferably approximately 0.05 to 0.1 mm and more preferably approximately 0.076 mm, and the probe material is Nickel-Cobalt alloy. The tip offset is preferably in a range from about 0.05 mm to about 0.25 mm. The knee offset is preferably in a range from about 0.05 mm to about 0.5 mm. The probe length is preferably between about 0.5 mm and about 3.0 mm. 
     For a configuration with a small knee offset and large tip offset one can expect a longer scrub length. For a configuration with large knee offset and small tip offset, a shorter scrub length is expected. Large contact friction requires a probe design that generates larger horizontal reaction force typically produced with larger scrub length. Smoother, less frictional contact pad surfaces require a probe design producing a shorter scrub length. 
     As indicated above, for any particular probe, there is a predetermined relation between contact force and vertical deflection. As the probe stiffness increases, the amount of contact force required for a given vertical deflection increases. A typical vertical deflection in practice is about 75 μm (i.e. about 3 mils), and for this amount of deflection, the contact force is preferably between about 0.025 N and about 0.15 N (i.e., about 2.5 to 15 grams force), and is more preferably between about 0.08 N and about 0.10 N (i.e., about 8 to 10 grams force). The vertical deflection during contact is preferably between about 12 μm and about 125 μm and is more preferably between about 50 μm and about 75 μm. 
     Another way to describe probing according to the invention is in terms of parameters of the scrub mark left on the contact pad by the probe. The scrub mark width is preferably between about 3.0 μm and about 15.0 μm and is more preferably about 7 μm wide. The scrub mark depth is preferably between about 0.1 μm and about 2.0 μM and is more preferably about 0.6 μm.  FIG. 29  shows an example of a measured scrub mark depth profile. The scrub mark length is preferably between about 3.0 μm and about 44.0 μm and is more preferably about 10 μm. This description of scrub marks assumes Al or Cu contact pads. 
       FIG. 24  shows a close up view of a probe tip in contact with a contact pad. More specifically, probe tip  2306  makes contact with contact pad  2320  on a circuit (or device)  2402 . Note that the view of  FIG. 24  (and of  FIGS. 25 and 26 ) differs from the view of  FIGS. 23   a - b  by a 90 degree rotation about the Z-axis. Thus moving left or right on  FIGS. 24-26  corresponds to moving into or out of the page of  FIG. 23 . 
       FIG. 25  shows an alternative embodiment of the invention, where probe tip  2306  includes multiple layers (one of which is shown as  2502  and another of which is shown as  2504 ). Such a multilayer probe configuration provides several advantages. First, as shown on  FIG. 25 , one of the layers ( 2504  in this example) can extend past the others, thereby defining a “skate” having a width (i.e., y extent) substantially less than the width of probe tip  2306 . Reducing the probe contact area can enhance scrub motion performance, because the force per unit area is thereby increased. However, decreasing the width of the entire probe can undesirably allow the probe to deflect in the y direction. A probe tip with a skate, as shown in  FIG. 25 , allows most of the probe to have a y-thickness sufficient to render y-deflection negligible, while also desirably reducing the contact area. 
     A further advantage of the multi-layer skate configuration of  FIG. 25  is that only the skate layer (i.e., layer  2504 ) should be a material selected for suitability as a tip contacting material. The remaining layers (e.g.,  2502 ) can be selected to optimize the overall probe performance without regard for their suitability as tip materials, since they never actually make contact with contact pad  2320 . 
       FIG. 26  shows a dual-skate configuration, where probe tip  2306  includes two skates  2602  and  2604 . This dual skate configuration is suitable for probing a contact pad  2320  having a dimple  2606  at its center. Such a dimple is characteristic of contact pads formed by metal plating (e.g. as in flip-chip wafers). Typical dimple dimensions are about 10 μm diameter on a contact pad having a 110 μm diameter, with the size of the dimple depending on the pitch of the contact pads. A single skate configuration as in  FIG. 25  will undesirably require a choice between probing at the dimple location (which can degrade the electrical contact made by the probe), or off-center probing (which can be difficult to align). Probing at the dimple can also cause high mechanical stress on the probe if the probe tip gets caught by the dimple. In contrast, the dual-skate approach of  FIG. 26  avoids probing the dimple, but still has the probe tip centered on the contact, thereby simplifying automatic probe alignment. 
       FIGS. 27   a - b  show results from an embodiment of the invention. More specifically,  FIG. 27   a  is a photograph of a probe tip and  FIG. 27   b  is a picture of the probe tip of  FIG. 27   a  after 1,000,000 probing cycles according to the invention. The probe of this example is a multi-layer single-skate configuration, as in  FIG. 25 .  FIG. 27   b  shows no significant degradation of the probe tip, either by wear or by accumulation of debris. 
       FIGS. 28   a - d  are photographs of a probe array suitable for practicing the invention. Such arrays are often required in practice, since many circuits being tested have a large number of contact pads which must be probed. For probe arrays, it is important that each probe deform in a uniform and predictable manner when the contact force is applied, to prevent probe-to-probe contact resulting from probe deflection. Thus it is preferred for the probe configuration of  FIGS. 23   a - b  to only deform in the X-Z plane responsive to the contact force, as also indicated above in connection with probe tip skates. 
       FIG. 30  shows a probe  3000  according to an embodiment of the invention. A shank  3002  defines a probe axis  3016 . A curved knee section  3004  is connected to shank  3002  and includes an upper knee section  3006  and a lower knee section  3008 . A probe tip  3012  is connected to an end of knee section  3004  opposite from the shank. Upper knee section  3006  extends outward from shank  3002  and reaches a knee point  3010  of maximum separation from probe axis  3016 , thereby defining a lateral knee offset  3018  from the probe axis. Lower knee section  3008  extends from knee point  3010  toward probe axis  3016  and to a tip location  3014 , thereby defining a lateral tip offset  3020  from the probe axis. 
     A probe plane includes and is thereby defined by probe axis  3016  and knee point  3010 . In this example, the plane of  FIG. 30  is the probe plane. A thickness of upper knee section  3006  in the probe plane varies along the length of the upper knee section according to a thickness function h(z), where z is position along the probe. The upper knee section includes a reduced thickness section, as described above. More specifically, h(z) has a local minimum located between shank  3002  and knee point  3010 , as shown in the example of  FIG. 30 . 
     Suitable materials for shank  3002 , knee section  3004  and probe tip  3012  are well known in the art, and any such materials can be employed in practicing the invention. Suitable tip materials are electrically conductive and wear-resistant, and include Rh and Cr. Known probe fabrication methods are applicable for fabricating embodiments of the invention. These methods include, but are not limited to, standard multi-layer metal deposition techniques such as plating, sputtering, photolithographic techniques and microelectromechanical systems (MEMS) techniques. No unusual fabrication difficulties due to the reduced thickness section arise in fabricating probes according to the invention. 
     Preferably, h(z) varies smoothly (i.e., h(z) is preferably continuous with a continuous first derivative) to avoid stress concentration at discontinuities and/or sharp corners of h(z). It is also preferred for the minimum probe thickness (i.e., the local minimum of h(z)) to have a value between about 0.5 h nom  and about 0.95 h nom , where h nom  is a nominal in-plane probe thickness. In some cases (e.g., as on  FIG. 30 ), lower probe section  3008  has a roughly constant thickness h 1 , and in such cases, h nom  can equal h 1 . In other cases, the nominal probe thickness h nom  can be taken to be the maximum value of h(z) (i.e., the maximum thickness of the upper knee section). In either of these two cases, the nominal in-plane probe thickness h nom  is typically between about 25 μm and about 55 μm, although the invention can also be practiced outside of this thickness range. 
     Preferably, h(z) varies smoothly along the entire length of upper knee section  3006 , in order to minimize stress concentration for a given minimum thickness. It is also preferred for the probe thickness perpendicular to the probe plane to be somewhat higher than the nominal in-plane probe thickness, so that deformation of the probe is easiest in the probe plane. More specifically, the out of plane thickness is preferably between about 1.1 h nom  and about 1.5 h nom . 
     For a configuration with a small knee offset and large tip offset one can expect a longer scrub length. For a configuration with large knee offset and small tip offset, a shorter scrub length is expected. Preferred probe design approaches depend on the friction between probe and contact pad. For large contact friction, probe designs that generate larger horizontal reaction force typically produced with larger scrub length are preferred. For smoother, less frictional contact pad surfaces, probe designs producing a shorter scrub length are preferred. 
     Preferably, the reduced thickness section is in the upper knee section as shown and described above, although the invention can also be practiced by having the reduced thickness section anywhere along the length of knee section  3004 . Placing the reduced thickness section in the upper knee section tends to decrease scrub motion without appreciably decreasing the contact force, while placing the reduced thickness section in the lower knee section (e.g., as shown on  FIG. 37 ) tends to decrease both scrub motion and contact force. More specifically, a negative tip offset probe having an upper knee section reduced thickness section tends to rotate toward the knee during deflection, thereby decreasing scrub motion. A probe having a lower knee section reduced thickness section tends to have increased flexibility (which reduces contact force). This reduced horizontal scrubbing force decreases the scrub motion. Probes having multiple reduced thickness sections can also be employed (e.g., one being in the upper knee section and the other being in the lower knee section) in practicing the invention. 
     As described above, the invention is applicable to probes having a positive tip offset, a negative tip offset, or no tip offset. The example of  FIG. 30  shows a probe having a negative tip offset. Here probe axis  3016  is between knee point  3010  and tip location  3014 .  FIG. 31  shows an embodiment of the invention having no tip offset. Here tip location  3014  is substantially on probe axis  3016 .  FIG. 32  shows an embodiment of the invention having a positive tip offset. Here tip location  3014  is between probe axis  3016  and knee point  3010 . For the probe of  FIG. 32 , the knee section does not cross the probe axis. 
     Reduced thickness sections of probes according to the invention can be regarded as resulting from removing material from the left and/or right sides of a smooth, constant-thickness probe profile. For example,  FIG. 33  shows an embodiment of the invention where the reduced thickness section is formed by variation of a right probe boundary f 2 (z).  FIG. 34  shows an embodiment of the invention where the reduced thickness section is formed by variation of a left probe boundary f i (z).  FIG. 30  shows an embodiment of the invention where the reduced thickness section is formed by variation of both a left probe boundary f i (z) and a right probe boundary f 2 (z). 
     In the preceding examples, lower knee section  3008  has a roughly constant in-plane thickness. The detailed shape of lower knee section  3008  is not critical in practicing the invention, and any other lower knee section shape can also be employed in practicing the invention. For example,  FIG. 35  shows an embodiment of the invention having a tapered lower knee section  3008 . More specifically, the in-plane thickness of lower knee section  3008  decreases monotonically along the length of the lower knee section from knee point  3010  to the tip location  3014 . 
     Operation of the invention can be appreciated in connection with  FIGS. 36   a - b , which show an embodiment of the invention in an initial contact configuration and an operating contact configuration respectively. On  FIG. 36   a  a probe according to the invention makes initial contact with a contact pad  3604 . It is convenient to describe the initial contact point between the probe and contact pad  3604  in terms of an initial contact offset  3608  defined with respect to probe axis  3016 . In operation, the arrangement of  FIG. 36   a  is vertically compressed (e.g., by moving contact pad  3604  up by a vertical deflection  3606 ). Under this compression, the probe elastically deforms as schematically shown on  FIG. 36   b . As a result of this deformation, the probe tip moves relative to contact pad  3604 . Typically this relative motion includes a translation (i.e., operating contact offset  3608 ′ being different from initial contact offset  3608 ) and a rocking motion of the probe tip relative to the contact pad surface. The rocking motion can be appreciated by noting the different orientations of a tip axis  3602  on  FIGS. 36   a  and  36   b . The scrub mark length is the difference between offset  3608  and offset  3608 ′. 
     In one example, a reference probe (probe A) having a nominal in-plane probe thickness of 52 μm and a negative tip offset (as shown on  FIG. 30 ), provided a 25 μm scrub length on an Al surface for 75 μm vertical deflection. A probe according to the invention (probe B) had the same shape as the reference probe, except that the upper knee section of probe B smoothly varied to provide a local minimum thickness of 33 μm in the upper knee section. This local minimum was located about halfway between the knee point and the shank. The thickness variation of the upper knee section was distributed over the entire length of the upper knee section. Probe B provided a 10 μm scrub length on the same Al surface used for testing probe A. For both probes A and B, the contact force was about the same (2 grams per 25 μm vertical deflection).