Patent Publication Number: US-6337478-B1

Title: Electrostatic force detector with cantilever and shield for an electrostatic force microscope

Description:
CROSS REFERENCE TO A RELATED APPLICATION 
     Applicants hereby claim priority based on Provisional Application No. 60/107,400 filed Nov. 6, 1998 and entitled “Electrostatic Force Detector With Cantilever And Shield For An Electrostatic Force Microscope” which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Hard copies with higher spatial resolution and better quality full color pictures are always expected in electrophotography technology. The photoreceptor is a key device to acquire the high quality hard copies. While on the one hand it is required to make a precise measurement of charge distribution on a photoreceptor drum, on the other hand the spatial resolution of currently available apparatus is fairly low. Charge distribution measurement with a very high spatial resolution is required both in electrophotography and in semiconductor research. It would be desirable to realize a measurement system which enables the charge distribution measurement to have a spatial resolution less than 10 μm in diameter with utilizing the electrostatic force. Laser printers may already have the spatial resolution of 600 dpi or higher, which indicates that each pixel has approximately 21 μm in diameter. Studies have been made relating to the scanning electrostatic force microscope, however, the theoretical aspects of those studies were only extended to the analysis of a parallel plate model and no further discussion was made relating how the detector needle would affect the charge distribution measurement. 
     A cantilever shaped sensor is normally used for atomic force microscopes, electrostatic force microscopes and similar critical dimension measurement instruments. The cantilever for those applications always consists of a needle or tip detector part and an arm part. If an electrostatic force appears at the needle part, other electrostatic force which is caused by the same electrostatic field appears at the arm part which should generate measurement error. It would, therefore, be highly desirable to shield the arm part to prevent the electrostatic force from appearing on the arm part, so that the accuracy of the measurement can be improved. 
     SUMMARY OF INVENTION 
     The present invention provides an electrostatic force microscope for measuring electrostatic force of a sample under test including a detector comprising a cantilever arm having a tip formation at one end and located so that electrostatic force is induced at the tip due to electrostatic charge on the sample under test, an optical system for transforming bending of the cantilever arm due to electrostatic force induced at the tip into an electrical signal containing a frequency component of the electrostatic force induced at the detector tip, means for applying bias voltage to the detector, means for detecting the frequency component of the electrostatic force induced at the detector tip so that a measurement of electrostatic force on the sample under test can be obtained, and an electrostatic shield operatively associated with the cantilever arm. The shield is located between the cantilever arm and the sample under test, in particular in close spaced relation to the arm. The cantilever arm and the shield are maintained at the same electrical potential so that lines of electrostatic force are terminated at the shield. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING FIGURES 
     FIG. 1 is a schematic diagram of an electrostatic force microscope according to the present invention; 
     FIG. 2 is a diagrammatic view of a parallel plane model; 
     FIG. 3 is a diagrammatic view illustrating the mesh for the FEM calculation; 
     FIGS. 4-6 are graphs illustrating aspects of the present invention; 
     FIG. 7 is table providing comparison data illustrating sensibility of the cantilever in the detector of the present invention; 
     FIG. 8 is a diagrammatic view illustrating the mesh for the finite element calculation; 
     FIG. 9 is a graph illustrating another aspect of the present invention; 
     FIGS. 10A-10C are diagrammatic views illustrating different shaped detectors according to the present invention; 
     FIG. 11 is a diagrammatic perspective view illustrating a systematic head of an electrostatic force microscope according to the present invention; and 
     FIG. 12 is a diagrammatic view illustrating the shield according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT 
     A representative configuration of an electrostatic microscope to which the present invention is applicable is shown is FIG.  1 . The system consists of a fine detector with cantilever generally designated  10  and comprising an arm  12  and a needle or tip  14 , an optical system  20  comprising laser  22  and photodetector  24 , a detection circuit  30 , a sample  40  under test operatively associated with an actuator  44  such as a piezoelectric driver which, in turn, is operatively associated with a scanner  48  for the actuator  44 , a processor  50  connected to the output of detection circuit  30 , a controllable source  60  of direct voltage, a feedback circuit  70  having an input connected to the output of detection circuit  30  and an output connected in controlling relation to d.c. source  60 , and an a.c. source  80 . The sample  40  under test is connected between d.c. source  60  and an electrical ground or reference. The combination of d.c. source  60  and a.c. source  80  is connected to detector arm  12  and to detection circuit  30 . 
     Electrostatic force is induced at the tip  14  of the detector due to a charge on the surface  40  under test. The electrostatic force gives a bend to the cantilever of which one of the two ends is fixed to the solid body of transducer  90 . The bending amount is transduced as electrical signal with the optical-lever method. An external bias voltage which consists of DC and AC is applied via conductor  92  to the detector to distinguish the polarity of the charge. The bias voltage V t  is given by equation (1) below. Then, the detector receives the vibration force which contains the frequency components of ω and  2 x ω. If the relation between the tip of the detector and the metal substrate is considered as a parallel plane model as shown in FIG. 2, the following equations (2) and (3) give the information of ω and  2 x ω components from the electrostatic force which appears on the probe tip. 
     
       
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     In the foregoing equations, V t  is the external bias voltage, ρ is the density of the charge distribution, ∈ is the dielectric constant of the sample under test, d o  is the distance between the detector tip and the surface under test, d is the distance between the detector tip and the metal substrate and S is the area of the plate respectively. If ∈ and d o  were known, one could obtain ρ by detecting F ω  (ωcomponent of electrostatic force), or by measuring V DC , which is given to the detector as a feedback to let F ω  become zero. If d o  is zero, it means that the surface under test is a solid metal. F 2ω  gives the information of roughness on the surface under test with controlling d to make F 2ω  constant. Since one has to measure the charge distribution on the dielectric film  100 , the condition of d o =0 is not realistic, therefore one has to measure F 2ω  directly. 
     To obtain the electrostatic force which is induced between the detector and surface charge under test, firstly one has to calculate the electrostatic voltage distribution which appears in the space between the surface under test and the detector due to a charge on the surface under test. For the sake of obtaining the voltage distribution, the Poisson&#39;s equation is solved: 
     
       
         ∇ 2 V=−ρ/∈ o   (4) 
       
     
     where V is the voltage to be obtained from this calculation, ρ is the density of the charge distribution, and ∈ o   is the dielectric constant of vacuum. One can visualize the electrostatic voltage with a computer enhancement of the numerical data. The Finite Element Method, a software for UNIX work station designed by Nihom Soken (Japan Research Institute, Limited), is used for the computer enhancement. 
     Secondly one determines the electrostatic field distribution around the detector and the surface under the test by utilizing the above mentioned voltage distribution. Thirdly one calculates the electrostatic force which is induced between the detector and the charge on surface the under test from data obtained through the previous two steps. 
     The electrostatic force on three different shaped detectors has been calculated. In one detector the tip  110  has a pillar shape as shown in FIG. 10A of which the diameter at the tip is 20 μm and the length of the tip is 50 μm , and in another detector the tip  112  has a cone shape as shown in FIG. 10B of which the diameter at the cantilever is 20 μm with a hemisphere  113  on the tip which has a diameter of 5 μm . One other detector has a tip  114  with perfect or right conical shape as shown in FIG. 10C of which the diameter at the cantilever is 20 μm and the height is 10 μm. A mesh configuration  120  for the FEM calculation for the pillar type detector is shown in FIG.  3 . Finer calculation has been given to the area where it is close to the tip of the detector. The calculation tends to be broader in the area where it is relatively far away from the detector. The calculation is made based upon the conditions that: 
     1) The surface under test comprises a metal substrate and a layer of dielectric film having a thickness of 15 μm-25 μm of which the relative dielectric constant is 3. 
     2) The detector is located above the surface under test. The distance between the detector tip and the metal substrate is 30 μm . 
     3) A charge of 1fC (1×10−15C) is located below the detector on the surface under test. 
     Each calculation of electrostatic force has been given for the three different shape detectors. Upon the calculations the thickness of dielectric film was changed from 15 μm to 25 μm . The results from these calculations furnish information on how the shape difference of detectors may influence the charge detection. 
     The calculated values in FIGS. 4-6 show the perpendicular component of the electrostatic force which is generated on the detector to the surface under test. It can be confirmed that the detector having wider area at the tip, which is in parallel with the surface under test, can generate larger electrostatic force. The result indicates that sensitivity should be sacrificed if higher spatial resolution is demanded or vise versa. Then, the shape of the detector is always subject to the consideration in accordance with the spatial resolution required. It is confirmed that the wider the area of the detector tip which sees surface under test, the larger the electrostatic force which will be detected. 
     For a conventional parallel plate model, the charge amount on surface under test is acquired through first obtaining a capacitance with using electrostatic force on the detector, then acquiring the charge amount by using the capacitance used as a constant for the mathematical formula (2) hereinabove. What has been done is to obtain the equivalent area as the parallel plate model for the pillar shaped detector at d o =20[μm], then the change of the electrostatic force of the parallel plate model in reference to the change of d o  is plotted with dot line FIG.  4 . The actual area of this parallel plate model is 282[μm] 2 . In particular, referring to FIG. 4, curve  130  is for the pillar type detector designated  110  in FIG. 10A, curve  132  is for the cone with hemisphere tip type  112  of FIG. 10B, curve  134  is for the cone type  114  of FIG.  10 C and curve  136  is for the parallel plate model. It is found that the results from even the pillar model detector, which is very close to the parallel plate model in shape out of three different models, were different from the results of parallel plate model. 
     The error between the parallel plate model and the new calculation increases when the distance between the detector to surface under test (d−d o ) decreases, and when the distance reaches d o =25[μm], 50% of error has to be anticipated. This result indicates that the equivalent area in area parallel plane model on the actual detector changes whenever the film thickness of dielectric material (surface under test) changes. 
     In order to consider the film thickness measurement with using  2 xω component, it is necessary to either, obtain the equivalent area in the parallel model at several different places in accordance with the difference of the film thickness, or analyze the actual electrostatic force appearing on the detector directly. The error in conjunction with the change of film thickness with d o =20[μm] as a reference is shown in FIG.  5 . In particular, curve  140  is for the pillar type detector designated  110  in FIG. 10A, curve  142  is for the cone with hemisphere tip type  112  of FIG. 10B, and curve  144  is for the cone type  114  of FIG.  10 C. One is able to see the error of −50% to 250% in accordance with the film thickness of 20[μm]±5[μm], especially that the error is increasing when the detector gets closer to the surface under test. Therefore, the results suggest that the accurate charge amount cannot be obtained with parallel a plate model if the surface under test is not perfectly flat. To suppress the error less than 10% it is necessary to make the film thickness measurement with the resolution of 0.1 to 0.5[μm]. 
     If the dielectric constant is not infinite and the bottom of the surface under test is flat, the film thickness can be measured with the following method. Firstly, the detector tip is allowed to touch the bottom part of the surface under test so that the reference point is calibrated. Then the position of the detector is moved upward using the combination of piezo element  44  and scanner  48  shown in FIG.  1  and the position of the detector is set at that high point. The excursion amount of the detector is detected by measuring the voltage change at the piezo element. Then, one calculates each F 2ω  component for the various film thickness of the dielectric film at a fixed distance between the detector tip and surface under test in advance so that the calculated results can be used as the parameter for the film thickness measurement. Therefore it is possible to obtain the film thickness from the measurement data and calculation results. 
     The electrostatic force to the detector (F 2ω  component) is calculated in conjunction with the film thickness change. An AC bias voltage of 10V is applied to the detector. The results are reported in FIG.  6 . In particular, curve  150  is for the pillar type detector designated  110  in FIG. 10A, curve  152  is for the cone with hemisphere tip type  112  of FIG. 10B, and curve  154  is for the cone type  114  of FIG.  10 C. The least electrostatic force was expected from the small conical shaped detector model. Approximately 12[pN] of electrostatic force difference due to the film thickness change of 0.5 [μm] could be detected, and the detectable electrostatic force due to film thickness change is greater than the resolution of conventional Atomic Force Microscopes (AFM) in force detection. This confirmed on the calculation basis that the measurement of d o  with a resolution of 0.5 [μm] should be accomplished with using the light leverage. 
     Based upon the above calculation results, several detectors are manufactured which are attached to each cantilever of which tip are a few to 10 [μm] in diameter. The material chosen for the detectors is nickel foil of which spring constant is in the range of a few to 10 mN/m. The physical dimensions and spring constant of the detector and cantilever which have been manufactured and those characteristics of the of the commercially available Atomic Force Microscope (AFM) detectors with cantilever are shown the table of in FIG.  7 . As mentioned, the spring constant of the cantilevers which are manufactured is chosen almost identical to the spring constant of conventional AFM cantilevers. There can be obtained the detector of which tip diameter is less that 5 [μm]. The electrostatic charge measurement resolution of less than 1[fC]c, which may generate a few [pN] of electrostatic force on the detector tip, should be accomplished with a spatial resolution of 10 [μm]. Secondly, the electrostatic force appeared on the detector was calculated as per the calculation method shown in FIG.  4 . The calculation model and the results are shown in FIGS. 8 and 9 respectively. In particular, a mesh configuration  160  for the FEM calculation is shown in FIG. 8, and curves  162  and  164  in FIG. 9 are for the F ω  and F 2   ω  components, respectively. However, it should be noted that the calculation was merely given for the one quarter part of the actual three dimension model with using the symmetric nature of the calculation model due to the limitation on the memory storage capacity of the computer system, the detector needle being relatively long so that it was necessary to calculate large number of elements and nodes on the FEM. 
     From these calculation results, it was found that the detection error in every [μm] for the film having a 20 [μm] was 19.5%/μm, and to reduce the detection error to less than 10%/um it is necessary to give a film thickness measurement with a resolution of less than 0.5[μm]. If a VAC=15V was applied to the detector, F 2ω  changed with a ratio of 1 pN/μm due to the AC field. Therefore the film thickness measurement can be accomplished with a resolution of 0.5[μm]. Under the foregoing bias condition for the measurement, the field strength at the detector tip was 5.8×10 6 [V/m]. This field strength is low enough as compared to the field strength of 10 9 [V/m] where corona discharge is supposed to begin, so that no corona generation is anticipated. Therefore, it is possible to measure both film thickness and charge amount on a sample under test using the detector of the present invention. On top of that, the erroneous reading of charge amount due to the change of film thickness can be reduced to less than 10%. 
     The schematic diagram of the systematic head in FIG. 11 further illustrates the electrostatic force microscope described hereinabove. Detector  170  has a tip  172  on one end of the cantilever arm  174 , and the other end of arm  174  is fixed to a body  176  operatively associated with a controller  178  for the cantilever angle and a micrometer head. A laser head  180  provides a beam  182  which is focused by line  184  onto detector  170 . A mirror  186  directs the reflected beam  188  to a cylindrical lens  190  which concentrates the beam onto a photodetector  192 . The surface  194  under test is on a piezo actuator  196  operatively associated with an X-Y stage  198 . 
     With the method and apparatus as described hereinabove, scanning in a relatively large area, for example, several 100 cm 2 , is provided with relatively high spatial resolution and a precise measurement of charge distribution. The influence of the shape of the detector tip or needle is taken into account, and a correction is provided for the influence of the change in dielectric film thickness on the sample under test. Analyzing the electrostatic force on the detector using the finite element method previously described provides an estimate of the influence due to the shape of the detector and the change in film thickness. For measuring a precise amount of charge distribution if it is necessary to make the film thickness measurement. Error is calculated in accordance with film thickness, and the film thickness measurement method is carried out by detecting F 2W . 
     The electrostatic force detector with cantilever described hereinabove has been designed and manufactured so that electrostatic charge can be detected on a dielectric film which is located on a conductive surface. It has been ascertained that by the method of knowing electrostatic charge amount on a certain thickness of film d o  through obtaining electrostatic force, the electrostatic force is changed in accordance with the change of the film thickness d o  because the equivalent detector tip area which sees the surface under test changes due to the change of d o . A few concrete samples have been shown as well. The absolute amount of error which is generated by the change of film thickness has been calculated to prove that knowing absolute amount of electrostatic charge on a film can not be accomplished without compensating the data through knowing the dielectric film thickness change. A film thickness measurement method has been proposed with detecting F 2w  component out of applied AC bias voltage and confirmed that the error could be reduced less than 10% theoretically due to the change of film thickness d o . A detector with cantilever was made out of nickel foil. The electrostatic force appeared on the detector was calculated to confirm the possibility of the electrostatic charge detection with less than 1 fC sensitivity and a spatial resolution of 10 [μm]. From these results, a simultaneous measurement of both electrostatic charge and film thickness of sample under test can be accomplished so that one can expect the measurement of absolute amount of electrostatic charge on a sample under test. 
     In the electrostatic force detector described hereinabove, when an electrostatic force appears at or applies to the detector tip  14  or needle portion, additional electrostatic force caused by the same electrostatic field appears at the arm portion  12  of detector which can cause a measurement error and reduce the spatial resolution. In accordance with the present invention, the cantilever arm portion of the detector is shielded to prevent the electrostatic force from appearing on the arm portion so that accuracy of the measurement can be improved. Referring to FIG. 12, there is shown a detector  200  of an atomic force microscope or an electrostatic force microscope. Detector  200 , like detector  10  shown in FIG. 1, includes a cantilever arm  202  and a needle or tip  204 . Needle  204  can have various shapes and sizes, and in the detector  200  of the present invention needle  204  has a length greater than that of known detectors of this type. The illustrative shape of needle  204  shown in FIG. 12 is a pillar with a hemisphere on the end. In accordance with the present invention, an electrostatic shield  210  is operatively associated with cantilever arm  202  of detector  200 . Shield  210  is of metal, in the form of an elongated strip, and is located between cantilever arm  202  and the sample under test (not shown in FIG. 12) and in closely spaced relation to arm  202 . The length of shield  210  preferably is the same as that of arm  202 , at least sufficient to shield the portion of the length of arm  202  exposed to the sample under test. In the arrangement illustrated in FIG. 12, the width of shield  210  is greater than the width of arm  202 . However, shield  210  can have any width desired, typically at least about the same as the width of arm  202 . 
     The cantilever arm  202  and shield  210  need to be maintained as an equal electrical potential, then the lines of electric force are terminated at the shield  210  and the force on the arm part  202  by the electrostatic field which has to be generated when the shield  210  is not deployed at the cantilever  202  is neglected. This is represented diagrammatically in FIG. 12 by the source  216  of electrical potential applied to both arm  202  and shield  210 . Other arrangements can of course be employed to keep arm  202  and shield  210  at the same electrical potential. 
     A mathematical analysis can demonstrate how effective the shield is functioning to reduce the effect of the electrostatic force. It has been confirmed that the force which appeared on the arm part  202  in reference with force which appeared on the needle  204  was 42%, whereas the force which appeared on the arm part  202  in reference with the force which appeared on the needle  204  became 0.15% after the shield  210  was deployed and the effect of the force which appeared on the arm part  202  became mostly negligible. 
     It is therefore apparent that the present invention accomplishes its intended objectives. While an embodiment of the present invention has been described in detail, that is done for the purpose of illustration, not limitation.