Abstract:
A sensor for scanning a surface with an oscillating cantilever ( 12 ), made from piezoelectric material that is suitable for a transverse oscillation of the free end of a beam, holding an electrically conductive probe tip ( 14 ) on the free end of the beam in transverse direction, a first deflection electrode ( 26 A,  26 B) and an inversely phased second electrode ( 28 A,  28 B,  28 C) being provided to collect charges that are separated within the space of the deflection electrodes ( 34, 36 ). The cantilever ( 12 ) is provided with at least one electrode ( 30 ) in addition to the deflection electrodes ( 26 A,  26 B,  28 A,  28 B,  28 C) that provides electrical contact to the tip ( 14 ), the at least one additional electrode being located in a region on the deflecting beam where the surface charge density due to the strain caused by beam deflection ( 34, 36 ) is smaller than in the region where the deflection electrodes are located.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to a sensor for noncontact scanning of a surface with an oscillating beam made from a piezoelectric material, wherein the beam is designed for a transverse vibration of a free end of the beam, with an electrically conductive tip extending in transverse direction at the free end of the beam, wherein the beam is provided with a first deflection electrode and a second deflection electrode, which second deflection electrode is inversely polarized with regard to the first deflection electrode in order to collect charges that are generated when the beam is deflected. Such a sensor is, in particular, suitable for combined atomic force microscopy that is a combination of atomic force microscopy with other scanning probe microscopies. One example is combined scanning tunneling and atomic force microscopy. 
     2. Description of Related Art 
     Scanning probe microscopy works by scanning a sharp tip over a surface (in x- and y-direction) while keeping the interaction force between tip and sample constant by means of a feedback circuit that controls the tip height z such that an image z(x,y) is formed. Image contrast is defined by the tip-sample interaction. Two basic methods are distinguished: imaging with repulsive and imaging with attractive interactions. When the tip approaches the sample, the force is initially attractive. Once tip and sample “touch” each other, the force becomes repulsive. Scanning tunneling microscopy relies on a similar principle, but it requires electrically conductive tips and samples. Instead of the force, a current is measured (from about 100 fA to about 1000 nA), that flows once a voltage bias is applied and the distance between tip and sample is sufficiently small (between 0.2 nm and 2 nm). 
     The force is measured by mounting the probe tip onto a cantilever spring. In quasi-static force microscopy, the static spring deflection is measured. In dynamic force microscopy, the cantilever oscillates and an observable, such as the oscillation amplitude, the frequency or the oscillation phase with respect to a sinusoidal drive signal are measured. In principle, it is possible to simultaneously measure the force (or a quantity derived from it such as the force gradient), by measuring the deflection of the cantilever or a quantity derived from the deflection as well as the tunneling current that flows between tip and sample. 
       FIG. 1  is a schematic view of a known sensor for simultaneous tunneling- and force microscopy. The sensor (stiffness k) oscillates at amplitude A. The unperturbed resonance frequency is f 0 =(k/m*) 0.5 /2π, and the frequency changes to f=((k+&lt;k ts &gt;)/m*) 0.5 /2π. The influence of a tip-sample force gradient &lt;k ts &gt; leads to a frequency shift
 
Δ f=&lt;k   ts &gt;/(2 k ) f   0 ,  (G1. 1)
 
where m* is the effective mass of the cantilever. The frequency shift can be used as a feedback signal to control the distance of a probe tip that scans the sample. When both tip and sample are electrically conductive and a bias voltage is applied, a tunneling current flows that is modulated by the oscillation and contains important information about the sample. With metallic tips and samples, the tunneling resistance of the vacuum gap is approximately given by 12.9 kΩ×exp(−2 z/100 pm). A simultaneous measurement of force and current is desirable, because that extends the applicability of scanning probe microscopy.
 
     Piezoelectric sensors, such as the qPlus Sensor (see, e.g., German Patent DE 196 33 546 C2 and F. J. Giessibl,  Applied Physics Letters  73, 3956, 1998 and F. J. Giessibl,  Applied Physics Letters  76, 1470, 2000) and the so-called needle sensor (see, e.g. K. Bartzke et al., International Journal of Optoelectronics 8, Nos. 5/6, 669-676, 1993; T. An et al. Appl. Phys. Lett. 87, 133114, 2005) are formed of a quartz beam, whose lateral deflection (qPlus) or length extension (needle sensor) is measured by means of the piezoelectric effect. The quartz beam is covered by two pairs of electrodes (qPlus) or two single electrodes (needle sensor), that collect charges for a constant deflection and generate an alternating current when oscillating. 
     The qPlus sensor  10  shown schematically in  FIG. 2  utilizes the beam deflection, where a deflectable beam  12  with a tip  14  is mounted to a base part in rest. The piezoelectric effect transforms mechanical strain caused by deflection to surface charges that are collected by the electrodes that cover the quartz beam. When the beam is deflected upwards as shown in  FIG. 2 , the upper half of the beam is subject to tensile strain, the lower half to compressive strain. 
     The emergence of a surface charge density σ el  with the presence of a mechanical stress σ mech  is due to the piezoelectric effect, where the surface charge density is given by:
 
σ el   =d   12 σ mech .  (eq. 1)
 
     The prefactor d 12  is the piezoelectric coupling constant with a typical value of about 2.3 pC/m for quartz. The mechanical strain leads to surface charges, that are collected by electrodes and transferred to an amplifier. The geometric arrangement of the electrodes is chosen such that a maximal charge is delivered for a given bending symmetry in order to obtain a maximal signal-to-noise ratio in deflection measurement. The basically sinusoidal deflection transforms into a basically sinusoidal alternating current. 
     When intending to measure the tunneling current in parallel, the electrically conductive tip needs to be connected to the outside. Prior art (F. J. Giessibl,  Applied Physics Letters  76, 1470, 2000) utilizes one electrode of the quartz beam to guide the tunneling bias voltage to the tip. The tunneling current is collected at the sample. One disadvantage of this arrangement is that the tunneling current needs to be collected at the sample and deflection signal and a galvanic separation between deflection signal and tunneling current is not feasible. The sample needs to be electrically isolated from the body of the scanning probe microscope. This is a clear disadvantage, in particular in low-temperature microscopes, because the sample should be thermally connected well to the cooling bath to allow for low sample temperatures. As stated by the Wiedemann-Franz law, a good electrical connection ensures a good thermal connection and vice versa. In addition, the sample and the sample holder are generally much larger than the tunneling tip, therefore they have a larger electrical capacity with respect to ground (typically tens of pico-Farads). Large capacity to ground has the disadvantage of limiting the bandwidth of the tunneling current measurement and increasing its noise figure. 
     German Patent Application DE 195 13 529 A1 relates to a needle sensor, that contains a drive electrode on opposite faces of the beam to drive the beam into resonant vibration. One of the faces contains an additional electrode that connects to the tip to enable tunneling current measurement. 
     SUMMARY OF THE INVENTION 
     It is an object of the invention to create a sensor that is suitable for scanning force and scanning tunneling microscopy and avoids the above-mentioned disadvantages and is simple and cost effective in manufacturing, allows for a high spatial resolution in the atomic regime and is reliable in operation. 
     According to the invention, this object is achieved by a sensor for noncontact scanning of a surface having an oscillating beam made from a piezoelectric material, wherein the beam is designed for transverse vibration of a free end of the beam, with an electrically conductive tip extending in a transverse direction at the free end of the beam, wherein the beam is provided with a first deflection electrode and a second deflection electrode, the second deflection electrode being inversely polarized with respect to the first deflection electrode in order to collect charges that are generated when the beam is deflected, wherein the beam is provided with at least one additional electrode that connects the tip electrically, and wherein the additional electrode is located in an area where a density of surface charges generated by deflection of the beam is lower than in a vicinity of the deflection electrodes. 
     The invention is beneficial in that, by the beam containing one or more electrodes in addition to the deflection electrodes, additional functions can be implemented. For example, the tip can be contacted electrically to allow for a measurement of the tunneling current. The supplemental electrode is located in a region on the beam that contains a lower surface charge density during deflection to ensure small cross talk between deflection measurement and tunneling current, to enable a galvanic separation between deflection signal and tunneling current and to enable grounding of the sample; furthermore, the supplemental electrode sensor can be mounted on the sensor in an easy and reliable fashion, simplifying the manufacturing process of the sensor. This further enables high bandwidth and low noise measurements of the tunneling current. The sensor be applied not only in combined scanning tunneling and scanning force microscopy, but also in force microscopy combined with thermometry, in force microscopy combined with highly localized writing of magnetic information and in force microscopy combined with magnetometry. 
     These and further objects, features and advantages of the present invention will become apparent from the following description when taken in connection with the accompanying drawings which, for purposes of illustration only, show several embodiments in accordance with the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic view of a known sensor for simultaneous scanning tunneling and scanning force microscopy, 
         FIG. 2  is a schematic perspective view of a known qPlus-sensor; 
         FIG. 3  is a schematic view of one embodiment of the sensor according to the invention; 
         FIGS. 4A-C  are schematic cross-sectional views of the sensor shown in  FIG. 3  taken along line A-A with one ( FIG. 4A ), two ( FIG. 4B ) and four supplemental electrodes ( FIG. 4C ); and 
         FIGS. 5A-C  are views of the sensor according to the invention shown in  FIG. 3  with a schematic representation of an example of an electric wiring diagram with a combined force and tunneling current sensor ( FIG. 5A ), a version with integrated tip heating enabling the generation of locally highly confined magnetic fields ( FIG. 5B ), a version with a combined force and temperature sensor ( FIG. 5C ) and a version with a combined force and Hall sensor to measure magnetic fields ( FIG. 5D ). 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 2  shows an example of the invented sensor  10 , that contains an oscillating beam made from piezoelectric material, holding an electrically connected tip  14  at its free end that points in a transverse direction. Beam  12  is one prong of a U-shaped tuning fork configuration, while beam  16  serves to mount the sensor  10  to a scanning unit (see,  FIG. 5 ) that scans the sensor  10  across a surface  20  of a sample  22 . Unit  18  contains a driver  24  that drives beam  12  and its free end with tip  14  into transverse oscillations (see, arrow  15 ). 
     The cross-section of beam  12  is rectangular, according to  FIG. 4 , and the two horizontal sides hold a first part  26 A and a second part  26 B of one of the two deflection electrodes, i.e., the two electrode sections  26 A,  26 B together constitute the first deflection electrode (in the following, we denote those side faces of beam  12  as vertical, that align with the direction of oscillation, e.g., that are parallel to the plane of vibration, while we denote those side faces of beam  12  as horizontal, that are aligned perpendicular to the oscillation, i.e., perpendicular to the plane of vibration). Both vertical faces contain a first part  28 A and a second part  28 B and  28 C of a second deflection electrode that has an oscillation phase opposite to the first deflection electrode. The second part of the second deflection electrode is split in two parts  28 B and  28 C, leaving enough room between parts  28 A and  28 B to allow for a supplemental electrode  30 A that can be used to carry the tunneling current. The tunneling current supplemental electrode  30 A extends in the center of at least one of the two vertical faces of beam  12  in an axial direction (deflection electrode  28 C could also be split into electrodes  28 C and  28 D, similar to electrodes  28 A and  28 B, to allow space for an additional supplemental electrode  30 B; see,  FIG. 4B ). Additionally, supplemental electrodes  30 A and  30 B could be split up additionally to provide four supplemental electrodes  30 A, B, C and D as shown in  FIG. 4C . 
     In the example shown in  FIG. 3 , the supplemental electrode  30  has a wider part  32  in an area close to the tip  14  of the lateral face than further away from tip  14 , where the supplemental electrode is located between deflection electrodes  28 B,  28 C. The parts of the deflection electrode  28 B,  28 C (as well as part  28 A of the second deflection electrode  28  and parts  26 A,  26 B of the first deflection electrode  26 ) do not extend to the area close to the tip  14 , where the vertical extension of the tunneling current electrode  30  is increased. 
     The tunneling current supplemental electrode  30  does not extend across the horizontal faces of the beam where the two parts  26 A,  26 B of the first deflection electrode  26  are located, except for the area  33  close to the tip  14 . Because the tip  14  is located on the top horizontal face, the tunneling current electrode  30  needs to extend on the horizontal face close to the tip. 
     The two parts  26 A,  26 B of the first deflection electrode  26  preferentially extend across the complete area of the two horizontal faces of beam  12  (except, as said above, in the area close to the tip), where parts  28 A,  28 B and  28 C of the second deflection electrode  28  preferentially extend at least across the edges of both vertical faces of beam  12  (in the examples shown in  FIGS. 4A-4C , part  28 A of the second deflection electrode extends, in general, completely over that vertical face of beam  12  where the tunneling current electrode  30  is not located, except as stated above within the area close to the tip  33 ). In the example according to  FIG. 3 , the first deflection electrode  26 A,  26 B extends in an axial direction along the two vertical faces of beam  12 , except at least for the part covered by the tunneling current electrode  30 . 
     The area  33  on beam  12  close to the tip  14 , where the tunneling current electrode  30  makes contact to the tip  14  that is kept clear of the two deflection electrodes, typically does not cover more than 25% of the length of beam  12 . In the dynamic deflection of the beam, the part of the beam that is close to the fixing point (i.e., the right part in  FIGS. 3 and 5 ) is subject to the greatest mechanical strain. Therefore, it is sufficient for the deflection electrodes to cover the first 75% of the length of the beam referenced from the fixing point. 
       FIGS. 4A-4C  illustrate the reason for the arrangement of  26 A,  26 B,  28 A,  28 B,  28 C and  30 . When beam  12  bends in a transverse direction up or down, the surface charges arise, in particular, on the two side faces; in the example of  FIGS. 4A-4C , positive charges  34  pile up on the side faces, while negative charges pile up at the edges and at the two horizontal faces. The positive charges  34  are collected by the first deflection electrode, i.e., from parts  26 A,  26 B, while the negative charges are collected by electrodes  28 A- 28 C. The area that is covered by the tunneling current electrode is only subject to a much lower surface charge density than within the area of the deflection electrodes  26 ,  28 . Preferentially, the tunneling electrode is positioned in an area where the surface strains, and thus the charge density, is not more than 10% of the area where the maximal charge density occurs. 
       FIG. 5A  shows an example for the wiring of sensor  10 , where the sample  20  is at ground potential. The tunneling current electrode is connected to input  1  of a current-to-voltage converter  38 , its input  2  is connected to the tunneling bias voltage V Tunnel  and its output generates a voltage that is proportional to the tunneling current plus the tunneling voltage. By subtracting the tunneling bias voltage from that signal with a differential amplifier, a signal is produced that increases with decreasing distance between tip  14  and sample surface  22  of sample  20 . 
     The signal that is taken from the first deflection electrode  26 A,  26 B is fed into the input and the signal that is taken from the second deflection electrode  28 A,  28 B,  28 C respectively are fed into current-to-voltage amplifiers  40 ,  42 . The outputs of amplifiers  40 ,  42  are connected to a differential amplifier  44  that delivers an output voltage V detection  which is, by means of the information provided by the deflection of beam  12  and the charge generation in deflection electrodes  26 A,  26 B,  28 A,  28 B,  28 C, a measure of the distance between tip  14  and sample surface  22 . 
     The voltages V tunneling current  and V deflection  establish the parameters measured by sensor  10  that are typically measured with vertical adjustment of the Tipp  14  and the sample surface  22  respectively and are fed into unit  24 . 
     In the example shown in  FIG. 5A , the sample  20  is at ground potential. Alternatively, the sample  20  can be connected to V Tunnel . The tunneling current electrode  30  could be fixed to tunneling potential and the tunneling current could be taken from the sample  20  by means of a current-to-voltage converter. 
     It is also possible to ground one of the deflection electrodes or to set one of them at another fixed potential and to source the current from one of the deflection electrodes. Generally, the invention allows great flexibility in arranging the signal paths. 
     In the example shown in  FIG. 5B , the sensor is supplied with two supplemental electrodes  30 A,  30 B, as shown in cross section  FIG. 4B  (although the electrodes are located on opposite faces of the beam as shown in  FIG. 4B , the schematic side view from  FIG. 5B  displays both electrodes  30 A,  30  B to display the electrical connection scheme). The tip  14  consists of two wires  14 A and  14 B that are connected at their ends. By means of a voltage source  46  and a switch  48 , a current can be fed through tip wires that heat the tip and can thus clean the tip. Also, due to Ampere&#39;s law, a current passed through the wire generates a magnetic field. By using a very small wire diameter of only a few nanometers (such as a carbon nanotube), even small currents can produce significant magnetic fields. After heating the tip  14 , at least one of the electrodes  30 A,  30 B is used for current measurements. 
       FIG. 5C  displays a different wiring scheme of the sensor with two additional electrodes (although the electrodes are located on opposite sides of the beam as shown in  FIG. 4B , the schematic side view  FIG. 5C  displays electrodes  30 A,  30 B to illustrate the wiring scheme). The tip is also a thermocouple, where tip wires  14 A,  14 B are made of different materials, e.g., chromium and nickel. Thus, a thermocouple is created where the thermal voltage is sensed through electrodes  30 A,  30 B and is amplified via differential amplifier  50  to a thermal voltage. 
       FIG. 5D  shows an example, where all four additional electrodes shown in  FIG. 4C  are utilized (although the electrodes are located on opposite sides of the beam as shown in  FIG. 4C , the schematic side view  FIG. 5D  displays all four electrodes  30 A,  30 B,  30 C and  30 D to illustrate the wiring scheme). The tip is connected by the four electrodes  30 A- 30 D, enabling a Hall geometry as a tip. Power source  46  drives a current via electrodes  30 B,  30 D. When the tip is immersed into a magnetic field, a Hall voltage develops perpendicular to the current flow that can be sensed through electrodes  30 A,  30 C and is amplified by means of a differential amplifier. Thus, magnetic fields can be measured at very high spatial resolution. 
     While various embodiments in accordance with the present invention have been shown and described, it is understood that the invention is not limited thereto, and is susceptible to numerous changes and modifications as known to those skilled in the art. Therefore, this invention is not limited to the details shown and described herein, and includes all such changes and modifications as encompassed by the scope of the appended claims.