Abstract:
A levitated XY stage with a mechanism to disable the bearing element to allow the physical elements of the stage to come into contact with one another and “Coulomb weld” together, thereby eliminating drift. Preferably, the XY position shift of the stage that results from disabling the bearing is measured, and feed-forward communication to, for example, the AFM scanner is used to enable an offset and remove the error.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention is directed to a method and apparatus for minimizing the effects of drift on small scale metrology measurements, and more particularly, to a method and apparatus of correcting for a position shift from a tip-sample target location such as that which occurs during lock down of an air bearing stage used in a scanning probe microscope. 
     2. Description of Related Art 
     Several probe-based instruments monitor the interaction between a cantilever-based probe and a sample to obtain information concerning one or more characteristics of the sample. Such measurements are often made on the nanoscale so positioning between the probe and sample is a challenge and often leads to corrupted data. Known systems lack the desired precision and, moreover, are susceptible to factors that compromise the ability to obtain reliable data. 
     Scanning probe microscopes (SPMs), such as the atomic force microscope (AFM), are devices which typically use a sharp tip to make a local measurement of one or more properties of a sample. More particularly, SPMs typically characterize the surfaces of such small-scale sample features by monitoring the interaction between the sample and the tip of the associated probe assembly. By providing relative scanning movement between the tip and the sample, surface characteristic data and other sample-dependent data can be acquired over a particular region of the sample, and a corresponding map of the sample can be generated. 
     The atomic force microscope is a very popular type of SPM. The probe of the typical AFM includes a very small cantilever which is fixed to a support at its base and has a sharp probe tip attached to the opposite, free end. The probe tip is brought very near to or into direct or intermittent contact with a surface of the sample to be examined, and the deflection of the cantilever in response to the probe tip&#39;s interaction with the sample is measured with an extremely sensitive deflection detector, often an optical lever system such as described in Hansma et al. U.S. Pat. No. RE 34,489, or some other deflection detector such as an arrangement of strain gauges, capacitance sensors, etc. AFMs can obtain resolution down to the atomic level on a wide variety of insulating or conductive surfaces in air, liquid or vacuum. Because of their resolution and versatility, AFMs are important measurement devices in many diverse fields ranging from semiconductor manufacturing to biological research. 
     Preferably, the probe is scanned over a surface using a high-resolution three axis scanner acting on the sample support and/or the probe. The instrument is thus capable of creating relative motion between the probe and the sample while measuring the topography or some other property of the sample as described, for example, in Hansma et al. supra; Elings et al. U.S. Pat. No. 5,266,801; and Elings et al. U.S. Pat. No. 5,412,980. 
     AFMs can be designed to operate in a variety of modes, including contact mode and oscillating flexural mode. In an oscillation “flexural mode” of operation the cantilever oscillates generally about a fixed end. One flexure mode of operation is the so-called TappingMode™ AFM operation (TappingMode™ is a trademark of the present assignee). In a TappingMode™ AFM, the tip is oscillated flexurally at or near a resonant frequency of the cantilever of the probe. When the tip is in intermittent or proximate contact with the sample surface, the oscillation amplitude is determined by tip/surface interactions. Typically, amplitude, phase or frequency of this oscillation is kept constant during scanning using feedback signals, which are generated in response to tip-sample interaction. These feedback signals are then collected, stored, and used as data to characterize the sample. When measuring semiconductor samples, such as the trench capacitors discussed herein, a particular version of this oscillating mode known as deep trench (DT) mode, which employs a unique and costly tip, is used. 
     As metrology applications demand greater and greater throughput, and as the desirability of using SPM in a wide variety of applications requiring sub-micron measurements continues to grow, improvements to data acquisition using SPM have become necessary. Wafer analysis in the semiconductor industry is one key application. In general, chip makers want to measure structures (e.g., lines, vias, trenches, etc.) having critical dimensions (CDs) that are 90 nm and below. When analyzing these structures at such small scale, the corresponding measurements require uniformity control and must be able to accommodate high volume production environments. In this regard, one advancement has been in the area of automated AFMs which greatly improve the number of samples that may be imaged in a certain time frame by minimizing expert user tasks during operation. Instruments for performing automated wafer measurements are varied but AFM offers a unique solution by providing, for example, the ability to perform high-resolution multi-dimension (e.g., 3-D) imaging. Some instruments, like the Dimension X automated AFM offered by Veeco Instruments, have proven 200 mm and 300 mm automation platforms. 
     More particularly, two performance metrics to be considered when evaluating instruments used to make such measurements include throughput and repeatability. Throughput, in this case, typically is the number of wafers that may be imaged per unit time, and repeatability is the variation in results obtained from repeated measurements made on the same object under substantially identical conditions. These measurements most often must be proved prior to the tool being useful. A third issue concerns reproducibility, which is the variation that results when making the same measurement under different conditions. Reproducibility is important in that it determines whether the technique can accommodate condition variations when both positioning the wafer and focusing the optics. When considering these metrics, known systems have significant limitations. 
     One problem, for instance, is that repeatability, precision and accuracy can be severely compromised due to drift in the stage supporting the sample. Drift can occur during various phases of making AFM measurements, including during both set-up and operation. Notably, drift in this context is measured in nanometers/second. For conventional mechanical stages used in scanning probe microscopy, one to five nanometers/second of continuous drift is common. Clearly, if either the position of the tip or the position of the sample experiences drift before or during the measurement, an inaccurate measurement will be obtained. Drift affects the measurement in at least two ways, one being that repeating probe-sample positioning at a selected location on a line of the sample to be imaged, an important metric as understood in the art, is a challenge. Proving repeatability of the tool when drift is present can be nearly impossible. This becomes particularly challenging in view of the fact that there is enough variability in the line width that, if the tool is off by some fraction of the tip diameter when repeating the line measurement, a different measurement will be obtained. 
     The other primary reason data can be compromised by drift concerns line width variability. This problem is directly related to a metric that is monitored in semiconductor fabrication known as linewidth roughness (LWR), a measure of the variability of the width of the line itself. 
     With current SPM systems, as a line of a sample is scanned at a number of different places, different measurements of line width are obtained depending on the LWR. This is illustrated in  FIG. 1 .  FIG. 1  illustrates a single line  10  having a width varying in what is shown as the vertical or “Y” direction. Line width roughness or LWR is essentially the deviation from the average of the independent widths, W 1 , W 2 , W 3 , etc. Depending upon the location at which the tip contacts the sample, different data will result. In the context of drift, the apparent width of line  10  will be expanded if drift occurs in a direction of scanning, and narrowed when drift is opposite the direction of scanning. As a result, a component of LWR will be introduced that is not due to the line itself but to drift. In many cases, this is the largest impact on the data due to drift, even more so than position repeatability along the line, since it is used to construct sample surface images. 
     Notably, it is only with the recent advancements in the resolution of scanning probe microscopy that LWR can even be measured and accounted for using SPM. In many known systems, users would not know that a different measurement was being conducted because the data would be essentially the same, requiring semiconductor manufacturers to use tools such as an SEM, and its attendant drawbacks, as understood in the art, to perform such measurements. 
     Known attempted solutions to the problem of controlling drift of AFM sample stages include providing an air bearing stage with a lock-down scheme, such as a vacuum lock down stage. However, even though such stages can be effective in minimizing the effects of drift, none of these systems correct for the position error that occurs during the lock down operation. 
     More particularly, current air-bearing stage technology allows for precise translation and a final position lock during which the air bearing is de-activated, most typically by applying a magnetic or vacuum force. However, the tradeoff with the benefits of an air-bearing stage (e.g., minimal adverse effects due to drift, fine positioning substantially free of counteracting forces, etc.) is that the lock down operation contributes to a final position error. When lock down of the stage occurs at a commanded or target position (using vacuum or magnetic force, or even gravity, for instance), Coulomb welding between the two pieces of the stage occurs so that the whole system responds like a solid piece of material. This often causes at least a micron or two of position shift of the stage. Moreover, the stage will oftentimes tilt during lock down, further compromising the precise positioning required for the applications contemplated by the preferred embodiments. 
     As a result, what was desired in the field of making atomic force microscope (AFM) measurements, particularly in the semiconductor industry, was an improved stage and corresponding method that minimizes positioning errors (e.g., due to stage lock down and drift), including improving position repeatability and reproducibility along AFM scan lines, as well as achieving a linewidth roughness (LWR) repeatability that yields increased throughput for high volume applications, such as semiconductor wafer measurement. 
     SUMMARY OF THE INVENTION 
     The preferred embodiments overcome the above-noted drawbacks of known systems by providing an air bearing, hydrostatic bearing, or magnetic bearing XY stage with a mechanism to disable the bearing element to allow the physical elements of the stage to come into contact with one another and “Coulomb weld” together, thereby eliminating drift. Preferably, the XY position shift of the stage that results from disabling the bearing is measured. A look up table can be used to calibrate the stage or the error can be recorded by position encoders during operation. Feed-forward communication to, for example, the AFM scanner may be used to enable an offset and reduce or even remove the error. Correction of the XY position shift may be achieved using the measured position shift to alter the relative position between the probe and sample, for example, by actuating the AFM scanner. 
     According to a first aspect of the preferred embodiment, a method includes commanding a stage of a scanning probe microscope to move to a position, and locking the stage at the position. The method thereafter compensates for a stage position shift that occurs, for example, during the locking step. 
     In another aspect of this embodiment, the stage is a levitated stage, preferably one of a hydrostatic, magnetic and an air bearing stage. Moreover, the compensating step includes actuating a second stage. 
     In a further aspect of this embodiment, the method includes measuring the stage position shift and creating a look-up table including stage position shift versus commanded stage position. In this case, the compensating step utilizes the look-up table. 
     According to yet another aspect of this embodiment, the compensating step includes actuating a second stage based on the measured stage shift. 
     In a still further aspect of this embodiment, the compensating step includes modifying the commanded position based on the measuring step and locking the stage in the modified commanded position. 
     According to another aspect of this preferred embodiment, the measuring step is performed using at least one of a light-based position sensor, a capacitance sensor, a Linear Variable Differential Transformer (LVDT) and a non-contact inductive sensor. 
     According to a still further aspect of this embodiment, the locking step includes actively locking the stage in place. 
     In another aspect of this embodiment, the method includes performing a survey scan of less than 10 microns in length, preferably less than 8 microns, and more preferably less than 5 microns thus extending tip life and increasing throughput over known systems. 
     According to another aspect of this embodiment, the drift is less than about 0.5 nm/sec., preferably less than about 0.2 nm/sec. Most preferably, the drift is less than about 0.1 nm/sec. 
     According to a still further aspect of this embodiment, the method includes making a measurement of a sample property at a rate exceeding 125 sites per hour. 
     In another embodiment of the present invention, a method includes commanding a stage of a scanning probe microscope to move to a position, locking the stage in place, and measuring a sample property of a sample at a rate exceeding 125 sites per hour for samples that are 200 mm and 300 mm semiconductor wafers. 
     According to another aspect of this preferred embodiment, a scanning probe microscope (SPM) comprises a probe, a stage that is selectively movable to provide relative motion between the probe and a sample, a locking mechanism that selectively locks the stage in place and a control system that commands the stage to move to a position. The control system controls the SPM to compensate for a stage position shift, for example, a shift that occurs during locking of the stage. 
     In another aspect of this preferred embodiment, the control system compensates for the stage position shift by measuring the stage position shift. 
     In yet another aspect of this embodiment, the stage position shift is measured in real time. 
     According to a still further aspect of this embodiment, the stage position shift is measured during a calibration process to create a calibration factor and is implemented during SPM operation using the calibration factor. 
     These and other objects, features, and advantages of the invention will become apparent to those skilled in the art from the following detailed description and the accompanying drawings. It should be understood, however, that the detailed description and specific examples, while indicating preferred embodiments of the present invention, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the present invention without departing from the spirit thereof, and the invention includes all such modifications. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A preferred exemplary embodiment of the invention is illustrated in the accompanying drawings in which like reference numerals represent like parts throughout, and in which: 
         FIG. 1  is a schematic top plan view of a line to be imaged for an AFM illustrating linewidth roughness (LWR); 
         FIG. 2  is a schematic block diagram of an atomic force microscope, appropriately labeled “Prior Art”; 
         FIG. 3A  is a schematic front elevation view of an atomic force microscope (AFM) for imaging a sample disposed on a fluid-bearing stage; 
         FIG. 3B  is a schematic front elevation view of the AFM and stage of  FIG. 3A , illustrating “lock down” at a location of interest; 
         FIG. 4  is a block diagram of an AFM according to a preferred embodiment, including drift compensation control apparatus; 
         FIG. 5  is a flow diagram illustrating a drift compensation method according to one embodiment; 
         FIG. 6  is a flow diagram illustrating a drift compensation method according to an alternate embodiment; 
         FIG. 7  is a schematic front elevation view of a stage incorporating a short range position sensor to measure position shift; 
         FIG. 8  is a schematic front elevation view of an alternate position sensor including a laser interferometer; and 
         FIG. 9  is a schematic top view of a sample illustrating the dimensions of a survey scan and a corresponding image scan. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A scanning probe microscope, such as an atomic force microscope (AFM) operates by providing relative scanning movement between a measuring probe and a sample while measuring one or more properties of the sample. A typical AFM system is shown schematically in  FIG. 2 . An AFM  11  employing a probe device  12  including a probe  14  having a cantilever  15  is coupled to an oscillating actuator or drive  16  that is used to drive probe  14  to oscillate, in this case, at or near the probe&#39;s resonant frequency. Commonly, an electronic signal is applied from an AC signal source  18  under control of an AFM controller  20  to cause actuator  16  to drive the probe  14  to oscillate, preferably at a free oscillation amplitude AO. Probe  14  is typically actuated to move toward and away from sample  22  using a suitable actuator or scanner  24  controlled via feedback by controller  20 . The actuator  16  may be coupled to the scanner  24  and probe  14  or may be formed integrally with the cantilever  15  of probe  14  as part of a self-actuated cantilever/probe. 
     Scanner  24  may be a single XYZ actuator that moves either the sample or probe. Alternatively, the scanner may be divided into separate components, for example an XY scanner moving the sample and a Z actuator moving the probe. Any permutation of probe and sample motion that generates relative motion between the probe and sample will suffice. Scanners usually contain piezoelectric actuators, but can also be constructed from other actuator mechanisms, including electrostrictive, magnetostrictive, thermomechanical, electrostatic and magnetic actuators. Recently AFMs have been constructed using micro machined scanners employing MEMS (Micro Electronic Mechanical Systems) technology. 
     One or more probes may be loaded into the AFM and the AFM may be equipped to select one of several loaded probes. Typically, the selected probe  14  is oscillated and brought into interaction with sample  22  as sample characteristics are monitored by detecting changes in one or more characteristics of the oscillation of probe  14 , as described above. In this regard, a deflection detection apparatus  17  is typically employed to direct a beam towards the backside of probe  14 , the beam then being reflected towards a detector  26 , such as a four quadrant photodetector. As the beam translates across detector  26 , appropriate signals are transmitted to controller  20 , which processes the signals to determine changes in the oscillation of probe  14 . Commonly, controller  20  generates control signals to maintain a constant force between the tip and sample, typically to maintain a setpoint characteristic of the oscillation of probe  14 . For example, controller  20  is often used to maintain the oscillation amplitude at a setpoint value, As, to insure a generally constant force between the tip and sample. Alternatively, a setpoint phase or frequency may be used. 
     Commonly, scanner  24  is a piezoelectric actuator possibly in combination with mechanical flexures that is used to generate relative motion between the measuring probe and the sample surface. A piezoelectric actuator is a device that moves in one or more directions when voltages are applied. As mentioned previously, many other actuator technologies may be employed, keeping in mind the scanner comprises one or more actuators that move in response to a control signal. Actuators may be coupled to the probe, the sample, or both. Most typically, an actuator assembly is provided in the form of an XY actuator that drives the probe or sample in a horizontal, or XY plane and a Z actuator that moves the probe or sample in a vertical or Z direction. 
     As noted previously, positioning between the probe and sample when analyzing different regions of a sample is critical to the AFM&#39;s ability to provide acceptable high quality data. Drift can severely compromise this goal, as can lock-down shift for levitated stages. The preferred embodiments overcome the limitations of prior arrangements in this regard. 
     Turning to  FIG. 3A , a SPM system  50  according to a preferred embodiment includes a levitated stage, preferably an air bearing stage  52  (e.g., an XY stage) having a stage carriage  54  registered to an XY stage base  56  using a guide rail  58  that mates with a corresponding opening  60  of carriage  54 . Notably, such a stage  52  is able to provide highly precise positioning and thus is particularly useful for metrology tools such as SPMs that perform sub-micron measurements. A sample  62  to be scanned is supported by carriage  52  and may be for example, an eight inch semiconductor wafer. In this case, carriage  52  can be manipulated in two orthogonal directions to position sample  62  at a location of interest. Though the illustration in  FIG. 3A  shows single axis translation of carriage  54 , this is shown for the purposes of illustration only, and actuation of the sample can be performed in multiple directions with an appropriately configured stage. Moreover, although preferably used to actuate the sample, stage  52  can be used to actuate an SPM probe, or some combination thereof. And though an air-bearing stage is shown, a hydrostatic or magnetic, or ultrasonic bearing stage, or the like, could be employed. 
     Between carriage  54  and base  56  is a gap  66  that accommodates a fluid such as air that acts as a bearing during stage carriage translation. Once sample  62  is located, stage  52  can be locked down by removing the air bearing in gap  66 , hence “Coulomb welding” the surfaces as described previously and ultimately minimizing drift of sample  62  from the target location. 
     Adjacent to and in this case above stage  52  is an AFM head  70  mounted to a reference structure  72 , head  70  including a probe  74  having a tip  76  adapted to interact with sample  62 . AFM  70  preferably includes an XYZ actuator (not shown in  FIG. 3A ), such as a piezoelectric tube or assembly of one or more piezoelectric stacks and mechanical flexures, that is able to translate the probe in three orthogonal directions. Reference structure  72  is a superstructure made of a suitable material (low coefficient of thermal expansion, etc.) such as Invar® designed to minimize the effects of adverse environmental phenomena such as drift and vibration, and thus maximize the AFM&#39;s ability to obtain high quality data. 
     In operation, when a location of interest is identified, a command signal, provided either automatically or manually entered by the AFM operator, instructs the stage carriage  54  to correspondingly position sample  62  for imaging by the AFM. Once located as shown in  FIG. 3A , carriage  54  is locked down to base  56  with an appropriate command signal. This is illustrated in  FIG. 3B . Notably, lock down can be an active or a passive operation. Actively locking the stage down typically involves pulling the stage  54  using applied force, for example, generated by a vacuum, piezoelectric, pneumatic, or a magnetic device, or any similar actuator capable of applying a positive locking force. Passively locking down the stage, on the other hand, may involve removing the bearing, allowing gravity to operate thereon, or using some compliant device, for example a spring or a flexure. 
     In  FIG. 3B , as carriage  54  is locked down to base  56 , a position shift results which is illustrated as a shift “S” of stage  52 . As noted previously, shift “S” can be microns long and thus significantly compromise the ability to obtain reliable data when imaging the features of interest. Moreover, once the lock down command is executed, carriage  54  and base  56  lock to one another as described previously, resulting in stage  52  behaving as a solid unitary structure and locking the shift between AFM  70  and stage  52 . As a result, to overcome the adverse affects of this shift on position repeatability and measured LWR, for instance, the preferred embodiments operate to adjust the relative position of AFM probe  74  and sample  62  and does so based on a measured position shift, as described in further detail below. 
       FIG. 4  illustrates a preferred embodiment of an SPM system  100  including a control system  101  coupled to stage  52  and an SPM  102  such as AFM head  70 . SPM  102  is coupled to an SPM controller  104  that implements commands via a computer  106 . For example, the commands may be provided automatically (e.g., a pre-set data acquisition program) or manually by an operator. A stage controller  108  is also provided to position carriage ( 54  in  FIGS. 3A &amp; 3B ) of air-bearing stage  52  at a target location in response to appropriate signals, typically to focus on a feature or region of interest. As noted above, based on a measured/predicted position shift, the relative position between the probe of SPM  102  and the sample is adjusted to compensate, for example, the position shift that occurs during lockdown at the target location, illustrated in  FIG. 3B . In this regard, computer  106  is used to instruct controller  104  to actuate, for example, a scanner of SPM  102  an amount “P,” as shown in  FIG. 3B , to compensate for the position shift. Alternatively, a separate fine position actuator (see  FIG. 7  and discussion below, for instance) can be provided to translate stage  52  and thus compensate for the offset caused by lock down shift. Notably, the compensation described herein is often referred to with respect to cor ecting position shift caused by lock-down of the air-bearing stage; however, the preferred embodiments can operate to compensate any position shift caused by any source including, for example, position shifts more generally such as those due to drift. 
     A correction algorithm  120  of the preferred embodiment is illustrated in  FIG. 5 . Initially, after a start-up and initialization step in Block  122 , a command is sent via computer  106  to stage controller  108  in Block  124  that causes carriage  54  of stage  52  to move to a target position, preferably in response to user input. Then, carriage  54  is locked down with respect to base  52  in Block  126 , as described above. 
     In Block  128 , the stage position shift caused by lockdown or otherwise, is determined. The shift may be measured at that time, or, if the shift was measured previously, a look-up table may be summoned to identify an expected shift of the stage associated with the target location. Alternatively, rather than measuring the position shift (real time or during a calibration procedure), the position shift can be determined using a program developed for the stage in which the stage position shift is modeled by an equation derived based on the known characteristics or behavior of the stage. 
     In the case in which the stage is calibrated, the look-up table may be developed by calibrating the stage at the location of the manufacturer. In this regard, the manufacturer preferably actuates the stage to an array of x, y locations and then measures the actual stage position shift at each location using, for example, a sensor such as an optical linear encoder. A look-up table of compensation or calibration factors (e.g., offsets associated with each scan position) is then developed for each of the (x, y) locations. 
     When a command is sent to actuate carriage  54  to a particular location (x, y), the look-up table can then be used to identify an expected position shift which is compensated by correcting tip-sample positioning prior to conducting an imaging operation. In the case shown in  FIG. 5 , the position shift identified in Block  128  is used to set a stage offset in Block  130 . Notably, the apparatus may employ a second stage, such as a separate fine position actuator to move either the probe or the stage ( 52  in  FIGS. 3A and 3B ) according to the offset associated with the target location after it has been locked down. The fine position actuator could be a piezoelectric-based flexure, for instance. 
     Alternatively, the second stage can be the scanning actuator. In that case, the compensation is preferably implemented using the offset to correspondingly translate the center of the scan by an amount corresponding to the offset, the scan center typically set upon start-up, as understood in the art. Once the stage position shift has been compensated, measurements of the sample can proceed in Block  132 . 
     Note that many AFM scans already contain an offset from the center of the scanning actuator&#39;s range. In this case it is not necessary to perform a second offsetting step. Instead it is sufficient to mathematically add the desired scan offset plus the offset to compensate for the stage shift. The total offset is then applied to the scanning actuator to simultaneously accomplish the scan offset and the compensation step. 
     Turning to  FIG. 6 , an alternative shift compensation algorithm  140  is illustrated. In this case, the shift corresponding to each scan position (x, y) is mapped to create a look-up table in Block  142 . Once the user selects a feature of interest, a location is determined, typically by performing a survey scan and a pattern recognition operation (see  FIG. 9  and discussion below) to identify a stage target position in Block  144 . The target position is then modified to accommodate the expected shift associated with that target position using the shift or offset values stored in the look-up table generated in Block  142 . Thereafter, in Block  148 , the stage can be moved to the corrected target position determined in Block  146 . With the target position corrected, the stage can then be locked down for sample measurement by the AFM in Block  150 . Notably, the modified target position is determined so that, when the stage is locked down and a corresponding shift occurs, the modification to the target position accounts for the shift. 
     According to the additional, and optional, steps of algorithm  140 , once the stage is locked down, the AFM, and more particularly, a position sensor (see below), may be used in Block  152  to measure the actual shift. In Block  154 , that measured shift is compared to a selected tolerance. A tolerance in the range of 10 nm-100 nm is typically acceptable. In the event that the measured shift is within the tolerance range, the sample may be measured in Block  156 . If, however, the shift is not within the accepted tolerance, the operator is notified with an appropriate alert in Block  158 , preferably prompting the operator with specific data to allow the user to decide whether to go forward with sample measurement. 
     Turing to  FIG. 7 , a stage  160  equipped to measure position is shown. Stage  160  includes a stage carriage  54 ′ supporting, in this case, a sample  62 ′ and a stage base  56 ′ having a center rail  58 ′ upon which carriage  54 ′ is guided. As carriage  54 ′ is locked down to base  56 ′, passively or actively, an offset “O” results due to the lockdown operation. As a result, and as described in connection with the algorithms illustrated in  FIGS. 5 and 6 , the amount of this position shift can be measured with an appropriate sensor  168  mounted to carriage  54 ′. As a result, translation of carriage  54 ′ relative to base  56 ′ coupled to reference structure  72 ′ can be measured. The stage position shift can then be utilized by the algorithms of the preferred embodiments to compensate for the shift by enabling a corresponding offset so as to maximize the integrity of the data obtained, including improving repeatability and accuracy of LWR measurement. 
     Sensor  168  may be a light-based position sensor such as an interferometer, a laser triangulation sensor, a linear optical encoder or the like. Alternatively, sensor  168  could be a capacitance sensor, a linear variable differential transformer (LVDT), a non-contact inductive sensor, or any other sensor suitable for high precision measurements. In this regard, combinations of two or more sensors may also be employed. Turning to  FIG. 8 , a stage  170  equipped with a laser interferometer is shown as still another example. 
     Stage  170  of this embodiment includes a stage carriage  54 ″ and a stage base  56 ″ having a guide rail  58 ″ that mates with a corresponding opening  60 ″ of carriage  54 ″ to guide carriage  54 ″ with respect to base  56 ″. A light-based position sensor  172  including a laser interferometer  174  is provided to measure the position of stage  170 . More particularly, stage carriage  54 ″ includes an opening  176  to accommodate one or more light beams “B” emitted by laser interferometer  174  towards center rail  58 ″ which is fixed. In operation, as the moving stage or carriage  54 ″ translates, the beams “B” transmitted by laser interferometer  174  contact center rail  58 ″, which is equipped with a reflective element  178 , and return to the laser interferometer for determination of the amount of translation (depending on phase of the laser light, for example), as understood in the art. The moving stage or carriage  54 ″ defines a reference surface  180  for making the measurements with the sensor relative to the fixed center rail  58 ″. Note,  FIG. 8  is provided to illustrate an example of a sensor and it is contemplated that other sensors readily adaptable to SPM tools are within the scope of the preferred embodiments. 
     Notably, improving accuracy and repeatability of tip-sample positioning not only facilitates producing high integrity image data, but also operates to improve speed of SPM operation and tip life longevity. For instance, one advantage of the preferred embodiments is that, often times, a survey scan such as that illustrated in  FIG. 9  and described above, is performed to identify a region of interest before a final scan is conducted on a target feature. As shown in  FIG. 9 , a sample  180  including an array of features  182  to be imaged includes a feature of interest  184  that must be identified. In some cases, a survey scan  186  of sample  180  is performed to identify the features  182 . This is done with a relatively coarse scan which is able to identify the features  182 , with the feature of interest  184  and its associated target location capable of being identified, for example, by conducting a pattern recognition operation on the coarse data. In this way, feature of interest  184  is identified prior to performing a comprehensive scan of the entire sample or even a subregion thereof. Moreover, as a result, the survey scan operates to prolong tip life and minimize the time spent generating a detailed image of portions of the sample of less interest, including those areas outside the target location. 
     In known systems with low position precision, lock down shift, and its associated uncertain positioning, typically requires survey scans to be large to identify the feature of interest. As a result, such systems see significant wear of the tip prior to any data being obtained. This is a significant issue given that the probes used by most AFMs can be very expensive, each costing as much as a thousand dollars or more. Therefore, minimizing the size of the survey scan or the need to do a survey scan at all is a significant benefit to increased precision, repeatability, throughput, and sustaining tip life. 
     Overall, with the precision, repeatability and accuracy provided by the present apparatus and methods, features of interest can be readily identified and tip-sample position reliably located. As a result, the size of the corresponding survey scan can be reduced significantly, and in some cases, the survey scan can be eliminated. Moreover, by minimizing or eliminating the survey scan, additional throughput benefits are achieved. For example, conventional AFMs are able to obtain topographical images of samples at about approximately 125 sites per hour on 200 mm and 300 mm wafers. With the improved position accuracy provided by the present preferred embodiments, throughput can be increased significantly. In view of the high throughput requirements of most semiconductor fabrication facilities, the preferred embodiments provide significant advantages when making such measurements. 
     More specifically, a discussion of CD precision and drift follows. Typically, high precision air bearing stages can achieve positioning accuracy of less than +/−0.5 micron over 300 mm range of travel. The addition of a lock down mechanism can degrade the accuracy by as much as +/−1.5 μm, resulting in a total accuracy of greater than about +/−2 μm. As a result, survey scans of greater than 5 μm may be required With the preferred embodiments, up to about a 4× reduction in survey scan size and corresponding survey scan time can be realized by mitigating accuracy degradation due to lock down or parking shift. Exemplary benefits include increased throughput and reduced tip wear, with the magnitude of improvement dependent on the particular application. Moreover, by being to perform survey scans of less than about five (5) microns in length, the present invention provides improvements with respect to repeatability including the ability to more easily and accurately identify a feature in a repeated pattern of the sample. 
     Simulations show that reduction of drift from 1 nm/sec to 0.1 nm/sec can improve CD measurement precision by 4× for typical tip radius and line shape. Reduction of drift in this fashion facilitates achieving the parameters of the ITRS roadmap for CD precision. (See Table 1) 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 ITRS requirements 
               
             
          
           
               
                   
                 Year 
               
             
          
           
               
                   
                 2007 
                 2008 
                 2009 
                 2010 
                 2011 
                 2012 
                 2013 
               
               
                   
                   
               
             
          
           
               
                 Node (Half-pitch 
                   
                  65 nm 
                  57 nm 
                  50 nm 
                  45 nm 
                 40 nm 
                  35 nm 
                  32 nm 
               
               
                 LWR (3σ) 
                   
                 2.8 
                 2.6 
                 2.2 
                 2   
                 1.8 
                 1.6  
                 1.4  
               
             
          
           
               
                 CD Precision 
                 Isolated 
                 0.4 nm 
                 0.4 nm 
                 0.4 nm 
                 0.3 nm 
                   
                 0.3 nm 
                 0.2 nm 
               
               
                   
                 Lines 
               
               
                   
                 Dense 
                 1.6 nm 
                 1.4 nm 
                 1.2 nm 
                 1.1 nm 
                   
                 0.9 nm 
                 0.8 nm 
               
               
                   
                 Lines 
               
               
                   
                 LWR 
                 0.4 
                 0.4 
                 0.3 
                 0.29 
                   
                 0.22 
                 0.21 
               
               
                   
               
             
          
         
       
     
     In particular, line width roughness (LWR) measurement precision is an metric of particular interest. Line width roughness (LWR) precision is influenced by drift perpendicular to the measured line, as shown in  FIG. 1 . Given a component of drift having a magnitude ν d  perpendicular to the measured line, the impact on line width can be analyzed. If the line takes δt seconds to traverse, the apparent width of the line will be increased by δx pos  when scanning in the same direction as the drift, and decreased by δx neg  when scanning in the reverse direction, as follows,
 
δx pos =ν d δt  (Equation 1)
 
δx neg =−ν d δt  (Equation 2)
 
This results in an additional LWR component equal to about 2 ν d  δt. Since the drift bias is uncorrelated with the true LWR of the line, the measured LWR (3 σ), LWR meas , is given by,
 
 LWR   2   meas   =LWR   2 +(2ν d   δt)   2   (Equation 3)
 
ΔLWR=2ν d δt  (Equation 4)
 
And given the ITRS requirements of Table 1, the LWR precision desired for the 32 nm node is 0.21 nm. Assuming δt=0.5 sec.,
 
2ν d δt&lt;0.21 nm  (Equation 5)
 
ν d &lt;0.21 nm/s  (Equation 6)
 
     For the lock down air bearing stage of the preferred embodiments, this amount of drift can be readily maintained, with the preferred amount of drift being held to about 0.1 nm/s. By comparison, the best drift rates of about 1 nm/s achieved using known mechanical stages result in a LWR error of about 1 nm, and thus exceed the ITRS requirement by close to 5×. 
     Overall, using the present levitated stage shown and described herein, stage drift is minimized, preferably exhibiting no more than about 0.5 nm of drift per second. And more preferably, stage drift is kept to no more than about 0.1 nm/sec, well within the range of CD precision for the 32 nm node of the ITRS roadmap. In addition, when making measurements with SPMs using the stage of preferred embodiments, RMS noise is preferably no more than about 1 nm for operating bandwidths of about 1 kHz. In this way, the above performance metrics, including, for example, the capability of measuring forty wafers per hour, can be achieved while maintaining data integrity. 
     Although the best mode contemplated by the inventors of carrying out the present invention is disclosed above, practice of the present invention is not limited thereto. It will be manifested various additions, modifications and rearrangements of the features of the present invention may be made without deviating from the spirit and scope of the underlying inventive concept.