fig2 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 , fig5 ) 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 fig4 , 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 , fig4 b ). 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 fig4 c . in the example shown in fig3 , 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 fig4 a - 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 fig3 , 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 fig3 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 . fig4 a - 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 fig4 a - 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 . fig5 a 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 deflectoin 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 fig5 a , 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 fig5 b , the sensor is supplied with two supplemental electrodes 30 a , 30 b , as shown in cross section fig4 b ( although the electrodes are located on opposite faces of the beam as shown in fig4 b , the schematic side view from fig5 b 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 . fig5 c 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 fig4 b , the schematic side view fig5 c 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 . fig5 d shows an example , where all four additional electrodes shown in fig4 c are utilized ( although the electrodes are located on opposite sides of the beam as shown in fig4 c , the schematic side view fig5 d 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 .