Computer-implemented method and apparatus for processing a sample using a nanomanipulator

Abstract

The disclosure provides a method for landing a tip (106) of a probe (1106) of a nanomanipulator (104) on a sample (102, 1102), in particular in vacuum, the probe (1106) comprising a cantilever (108) and the tip (106) attached thereto, the nanomanipulator (104) further comprising an excitation unit (1110), the probe (1106) being mechanically coupled with the excitation unit (1110), the method including the following steps: - oscillating the probe (1106) by providing a resonant driving signal (1010) to the excitation unit (1110) while the tip (106) is not in contact with the sample (102); - reducing a first distance in a z-direction between the tip (106) and the sample (102) during a first approach phase until at least one first stop condition of a first set of stop conditions is met, wherein the first set of stop conditions comprises detecting a shift in the frequency of the resonant driving signal (1010) used during the first approach phase; and - terminating the first approach phase when the at least one first stop condition of the first set of stop conditions is met, and deactivating the resonant driving signal (1010).

Description

[0001]Carl Zeiss SMT GmbH 1 COMPUTER-IMPLEMENTED METHOD AND APPARATUS FOR PROCESSING A SAMPLE USING A NANOMANIPULATOR The present invention relates to a computer-implemented method and an appa- ratus for processing a sample using a nanomanipulator. The content of the priority application DE 102023129682.5 is incorporated in full by reference. Microlithography is used for producing microstructured components, such as for example integrated circuits. The microlithography process is carried out using a lithography apparatus comprising an illumination system and a projection sys- tem. The image of a mask (reticle) illuminated by means of the illumination sys- tem is projected here by means of the projection system onto a substrate, for ex- ample a silicon wafer, which is coated with a light-sensitive layer (photoresist) and arranged in the image plane of the projection system, in order to transfer the mask structure to the light-sensitive coating of the substrate. The mask (i.e. lithography mask) is used for a multiplicity of exposures, for which reason it is very important that the mask be free of defects and contaminations. Therefore, lithography masks are examined in regard to defects and contamina- tions at great expense. Attempts are then made to repair identified defects or to remove contaminations. The defects and contaminations may be extremely small and have sizes of the order of a few nanometers. Therefore, removing them re- quires apparatuses with very high spatial resolution. The contaminations are for example extremely small particles which have depos- ited on the mask from the surroundings. Such contaminations occur to an in- creased extent, for example, if the mask is transferred between different pro- cessing apparatuses. The particles are of a very diverse nature and have different Carl Zeiss SMT GmbH 2 sizes and / or shapes. They may for example be metal particles, in particular tin, but ceramic particles, polymer particles and further carbon compounds may also occur. The particles are typically adsorbed on the mask surface, that is to say that there are no strong chemical bonds, such as atomic bonds, between the parti- cle material and the mask surface. A particle will leave the mask surface if applied attractive forces (e.g. Coulomb forces and van der Waals forces) for removing the particle are greater than at- tractive forces (e.g. Coulomb forces and van der Waals forces) of the mask sur- face. Depending on what kind of interaction there is between the particle and the mask surface, an activation energy may be necessary to break the existing bond to the mask surface. Processing apparatuses are known which can remove individual particles from a surface in a targeted manner. For example, nanomanipulators, such as for exam- ple atomic force microscopes, are used for this purpose. In this case, a particle is picked up by a measuring tip (measuring and manipulator tip) of the nanomanip- ulator and, adhering to the measuring tip, is removed from the mask surface. Particle removal is usually supported by imaging methods (e.g., image recording by means of a scanning electron microscope and / or a scanning ion microscope) and requires manipulations by a user on nanometer scales. In this case, small er- rors on the part of a user may easily result in damage or destruction of the meas- uring tip of the nanomanipulator or of the sample. Moreover, the processing re- quires high attentiveness on the part of the user, as a result of which fatigue phe- nomena lead to an increased risk of errors on the part of the user. Furthermore, processing the sample, in particular removing particles from the sample, is made more difficult by the fact that the precise position of the apex of the measuring tip is unknown. In particular, the apex of the measuring tip is the point and / or region of the measuring tip which makes initial contact with the Carl Zeiss SMT GmbH 3 sample or a particle on the sample when the measuring tip approaches the sam- ple and / or particle. As a rule, the actual apex of the measuring tip cannot be seen in an image (e.g. a scanning electron microscope image and / or scanning ion mi- croscope image) of the sample with the measuring tip, and so a lateral position of the apex cannot be derived from such an image on its own. Furthermore, a height position of the apex of the measuring tip (i.e. a distance from the sample) is gen- erally not known accurately either on account of a deflection of a cantilever to which the measuring tip is secured. Against this background, an object of the present invention is to improve the pro- cessing of a sample using a nanomanipulator. Accordingly, a method for landing a tip of a probe of a nanomanipulator on a sample, in particular in vacuum, is proposed. The probe comprises a cantilever and the tip attached thereto. The nanomanipulator further comprises an excita- tion unit, the probe being mechanically coupled with the excitation unit. The method includes the following steps: - oscillating the probe by providing a resonant driving signal to the excita- tion unit while the tip is not in contact with the sample; - reducing a first distance in a z-direction between the tip and the sample during a first approach phase until at least one first stop condition of a first set of stop conditions is met, wherein the first set of stop conditions comprises detecting a shift in the frequency of the resonant driving signal used during the first ap- proach phase; and / or - terminating the first approach phase when the at least one first stop condi- tion of the first set of stop conditions is met, and deactivating the resonant driv- ing signal. Carl Zeiss SMT GmbH 4 This method may be used on its own or in combination with one or more of the other methods disclosed below. Optionally, the method further comprises: further reducing the first distance dur- ing a second approach phase until at least one second stop condition of a second set of stop conditions is met, wherein the second set of stop conditions comprises detecting a deflection of the cantilever; and terminating the second approach phase at a contact position when the at least one second stop condition of the sec- ond set of stop conditions is met Optionally, the location of at least one of the probe or the sample are controlled in the z-direction using a combination of a coarse drive and a fine drive. Optionally, the method further comprising performing a third approach phase, comprising: increasing the first distance by operating the fine drive to move the tip from the contact position to a partially retracted position; and reducing or in- creasing the first distance by operating the coarse drive based on a second dis- tance in the z-direction between the contact position and the partially retracted position; and reducing the first distance by operating the fine drive to return the tip to the contact position or to a predefined position at third distance in the z-di- rection from the contact position. Optionally, the method further comprises determining at least one parameter of a resonance characteristic of the probe while the tip is not in contact with the sample, the at least one parameter comprising at least one of a resonance fre- quency of the probe, a Q-value of the probe, and a phase angle between the reso- nant driving signal and a detected deflection signal associated with the oscilla- tion of the probe. Carl Zeiss SMT GmbH 5 Optionally, the first set of stop conditions comprises at least one of the following conditions: - a frequency control signal (e.g. dF) indicative of shift in the frequency of the resonant driving signal exceeding a first threshold value; - a frequency control signal (e.g. dF) indicative of shift in the frequency of the resonant driving signal lying below a second threshold value; - an amplitude feedback signal (e.g. A) used for amplitude control of the res- onant driving signal exceeding a third threshold value; - an amplitude feedback signal (e.g. A) used for amplitude control of the res- onant driving signal lying below a fourth threshold value; - a phase signal indicative of a relationship between the resonant driving signal and a detected oscillation of the probe exceeding a fifth threshold value and / or lying below a sixth threshold value; and / or - a driving speed in the z-direction exceeding a seventh threshold value and / or lying below an eighth threshold value. Optionally, landing the probe is aborted in the first approach phase when at least one of the following conditions are met: the frequency control signal lies below the second threshold value; the amplitude feedback signal exceeds the third threshold value; the phase signal exceeds the fifth threshold value and / or lies be- low the sixth threshold value; and / or the driving speed exceeds the seventh threshold value and / or lies below the eighth threshold value. Optionally, the second set of stop conditions used in the second approach phase further comprises: - a first deflection signal (e.g., DFL) indicative of a deflection of the probe in the z-direction exceeding a first ninth threshold value; - a second deflection signal (e.g., LAT) indicative of a lateral deflection of the probe exceeding a tenth threshold value; Carl Zeiss SMT GmbH 6 - a sum signal (e.g., SUM) indicative of a combined deflection of the probe exceeding an eleventh threshold value; and / or - a driving speed in the z-direction exceeding a twelfth threshold value and / or lying below a thirteenth threshold value. Optionally, landing the probe is aborted in the second approach phase when at least one of the following conditions are met: the driving speed exceeds the twelfth threshold value and / or lies below the thirteenth threshold value. According to another embodiment, an apparatus is provided. The apparatus com- prises: a sample stage for holding a sample; a nanomanipulator comprising a po- sitioning unit and an excitation unit, the positioning unit being configured to move a probe comprising a cantilever and a tip attached thereto, the excitation unit being configured to oscillate the probe based on a driving signal; a cantilever deflection detection system configured for detecting deflections of the cantilever; a control loop circuitry configured to track a signal relationship between an oscil- lation of the cantilever detected by the cantilever detection system and a driving signal provided to the excitation unit; and at least one control unit. The at least one control unit is configured to perform the following steps: driving, using the excitation unit, the probe using a resonant driving signal provided by the control loop circuitry while the tip is not in contact with the sample; reducing, by the po- sitioning unit, a first distance in a z-direction between the tip and the sample during a first approach phase until at least one first stop condition of a first set of stop conditions is met, wherein the first set of stop conditions comprises detecting a shift in the frequency of the resonant driving signal used during the first ap- proach phase; and terminating the first approach phase when the at least one first stop condition of the first set of stop conditions is met by deactivating the resonant driving signal. Carl Zeiss SMT GmbH 7 Optionally, the control loop circuitry comprises: a frequency control system con- figured to provide a first output signal based on a phase of a detected oscillation of the cantilever and a phase setpoint; and an amplitude control system config- ured to provide a second output signal based on an amplitude of the detected os- cillation of the cantilever and an amplitude setpoint; and a multiplier configured to multiply the first output signal provided by the frequency control system with the second output signal provided by the amplitude control system and to provide the multiplied signal as resonant driving signal to the excitation unit. Optionally, the frequency control system comprises a phase detector for providing a phase signal, an integrator for providing a frequency control signal, and a con- trollable oscillator for providing an oscillator output signal. Optionally, the amplitude control system comprises an amplitude detector for providing an amplitude signal, and a PI controller for providing an amplitude feedback signal. According to another aspect, a computer-implemented method for processing a sample using a nanomanipulator is proposed. The nanomanipulator comprises a measuring tip for processing the sample and a positioning unit for moving the measuring tip. Furthermore, the sample is arranged on a sample stage. An x-di- rection and a y-direction of the nanomanipulator are each arranged parallel to a main extension plane of the sample and / or sample stage and perpendicular to one another. The method comprises the following steps: 1a) controlling the positioning unit to move the measuring tip in the y-direc- tion such that an apex of the measuring tip is in contact with a surface of a test region of the sample stage or sample, and the measuring tip leaves a first track on the surface, Carl Zeiss SMT GmbH 8 1b) controlling the positioning unit to move the measuring tip in the x-direc- tion such that the apex of the measuring tip is in contact with the surface, and the measuring tip leaves a second track on the surface, 1c) controlling an image recording device to record at least one image of the test region in each case, the first and the second track being at least partially captured accordingly therein, and 1d) ascertaining an x-position of the apex of the measuring tip in relation to the x-direction on the basis of the first track captured in the at least one image and ascertaining a y-position of the apex of the measuring tip in relation to the y- direction on the basis of the second track captured in the at least one image. Using the method, it is possible to ascertain the x- and y-position of the actual apex of the measuring tip, even if only the apparent apex of the measuring tip is visible in the captured and received image. In particular, the actual apex of the measuring tip might not be visible in the image because it is concealed in relation to a line-of-sight of the image recording device. In particular, the apex of the measuring tip is the point and / or region of the measuring tip which makes initial contact with the sample or a particle on the sample when the measuring tip approaches the sample and / or particle. For exam- ple, the apex of the measuring tip is a lowest point and / or region of the measur- ing tip in relation to a z-direction of the nanomanipulator. In particular, the measuring tip of the nanomanipulator is configured to contact a surface of the sample at its apex. In particular, the z-direction of the nanomanipulator is ar- ranged perpendicular to the x- and the y-direction. In particular, the z-direction of the nanomanipulator corresponds to a vertical direction of the nanomanipula- tor or its direction of gravity. In particular, the x- and y-directions of the nanomanipulator are any desired di- rections which are each arranged parallel to the main extension plane of the Carl Zeiss SMT GmbH 9 sample and / or sample stage (e.g. a surface of the sample stage for arrangement of the sample) and perpendicular to one another. For example, the x-, y- and z-directions of the nanomanipulator can correspond to x-, y- and z-directions of the positioning unit of the nanomanipulator. For example, the sample is a lithography mask with structures (e.g., absorber structures). The structures have for example a structure size in the range of 10 nm - 10 µm. The structures are arranged for example in a structure pattern for producing a specific type of semiconductor chip. The sample can be for exam- ple a transmissive lithography mask for DUV lithography (DUV: "deep ultravio- let", operating light wavelengths in the range of 30 – 250 nm) or a reflective li- thography mask for EUV lithography (EUV: "extreme ultraviolet", operating light wavelengths in the range of 1 – 30 nm, in particular 13.5 nm). The sample can also be a microelectronic component, such as for example an inte- grated circuit, in particular a CPU (CPU: "central processing unit"), GPU (GPU: "graphics processing unit"), a RAM memory (RAM: "random access memory"), a flash memory and suchlike. The nanomanipulator and / or a superordinate apparatus comprising the nanoma- nipulator comprise(s) for example a sample stage device having a mount, a sam- ple stage for arrangement of the sample and movably arranged on the mount, and a further positioning unit for moving the sample stage relative to the mount. The sample stage can be moved for example with the aid of the further position- ing unit in the x-direction and the y-direction (i.e. laterally) and / or in the z-direc- tion (vertical direction or direction of gravity). The sample stage can for example also be mounted rotatably on the mount, such that it can be rotated about the x-, y- and / or z-direction with the aid of the further positioning unit. The sample stage comprises in particular a surface for arrangement of the sample. Carl Zeiss SMT GmbH 10 The measuring tip is in particular a tip configured for measurement and manipu- lation (measuring and manipulator tip). The nanomanipulator comprises a cantilever, for example, on which the measur- ing tip is arranged and / or secured. The cantilever and the measuring tip can also have a monolithic design. The term cantilever also appears in the German text as "Cantilever". The measuring tip has for example a length in the range of 0.5 µm – 1 mm and a diameter in the range of 20 nm – 1 µm. In particular, the measuring tip can taper towards its free end. For example, the measuring tip consists of a material including carbon, silicon, one or more noble metals, tungsten, platinum, iridium and / or a platinum-iridium alloy. The measuring tip makes it possible to move to individual positions on the sample surface in a targeted manner, in particular even if the sample has struc- tures having a high aspect ratio. The aspect ratio may be defined for example as the ratio of width to height of a structure. An example of a structure having a high aspect ratio of 1:10 is a narrow, deep trench which for example is 1 µm wide and 10 µm deep. For example, when expressed as a Mohs harness, the measuring tip has a hard- ness of 7 or more, 8 or more and / or 9 or more. The Mohs hardness is a hardness based on the Mohs scale developed by Friedrich Mohs. The nanomanipulator comprises the positioning unit, on which the cantilever is mounted movably and which enables the cantilever to be moved in the three spa- tial directions x, y and z relative to the positioning unit (translational movement in the three spatial directions). The three spatial directions span in particular a three-dimensional space. The positioning unit is secured for example to a housing Carl Zeiss SMT GmbH 11 of the nanomanipulator and / or a superordinate apparatus comprising the nano- manipulator. The cantilever has in particular an elongate shape with a longitudinal axis. Fur- thermore, the cantilever is secured to the positioning unit movably at a first end in relation to its longitudinal axis. With the aid of the positioning unit, a position of the first end of the cantilever (also called base point or base end of the cantile- ver) can thus be set in the three spatial directions x, y and z. Moreover, the canti- lever has the measuring tip at a second end (free end) in relation to its longitudi- nal axis. If the measuring tip comes into the vicinity of the sample surface, an interaction occurs between the measuring tip and the sample surface. The interaction may be based on direct contact, on a van der Waals interaction or further physical in- teractions, and mixtures thereof. By way of the measuring tip being moved (ras- ter-scanned) over the sample surface, a three-dimensional image of the sample surface can be captured. In this case, for example, for each raster-scan position the distance between the measuring tip and the sample surface is kept constant by means of a closed-loop control circuit and a position of a microactuator for set- ting the distance is captured. In particular, the particle is a foreign body, such as dust or dirt, which has depos- ited on the sample surface. It may also be said that the particle is adsorbed on the sample surface. Particles absorbed on the sample surface may have different constitutions and different shapes. For example, the size of the particles ranges from 3 nm – 50 µm. Such a particle can for example be located on the sample surface by means of op- tical analysis methods and approached by the measuring tip in a targeted man- ner. In order to pick up the particle with the measuring tip, the particle must be Carl Zeiss SMT GmbH 12 detached from the sample surface. That means that the forces acting between the sample surface and the particle must be overcome. The strength with which the particle is bound to the sample surface depends both on the shape and constitu- tion of the particle and on the constitution of the sample surface, in particular the surface energy thereof. The greater the surface energy of the surface, the more strongly the particle is adsorbed. To pick up the particle with the measuring tip, the measuring tip is for example brought into contact with the particle. If attractive forces of the measuring tip are greater than attractive forces of the sample surface, the particle will be able to be detached from the sample surface and can be picked up by the measuring tip. It may be helpful to first use the measuring tip to displace the particle on the sample surface in order to break existing bonds between particle and sample sur- face. It is thereby possible for example to reduce the binding energy of the parti- cle in relation to binding to the surface. Furthermore, for example a contact area between the measuring tip and the particle can be increased as a result. If the contact area between the particle and the measuring tip becomes larger, the probability that the particle will adhere to the measuring tip and be able to be de- tached from the sample surface increases. After the particle has been picked up by the measuring tip, the particle must be removed again from the measuring tip in order to be able to continue to use the measuring tip. The particle should in this case in particular be deposited at a po- sition on the sample surface at which it is not a disturbance, or on a separate deposition unit. The nanomanipulator can be part of a superordinate apparatus for processing the sample, the apparatus comprising the nanomanipulator. Carl Zeiss SMT GmbH 13 The superordinate apparatus for processing the sample can for example also com- prise a control apparatus for performing the proposed method. For example, the control apparatus controls the positioning unit in step 1a) to move the measuring tip in the y-direction in order to write the first track in the y-direction. For exam- ple, the control apparatus controls the positioning unit in step 1b) to move the measuring tip in the x-direction in order to write the second track in the x-direc- tion. For example, the control apparatus controls the image recording device in step 1c) to record at least one image of the test region in each case. For example, the control apparatus receives the recorded images from the image recording de- vice. For example, the control apparatus accordingly ascertains in step 1d) the x- position and the y-position of the apex of the measuring tip on the basis of the first and the second track captured in the images. Moreover, the superordinate apparatus for processing the sample can for exam- ple also comprise an image recording device, e.g. a scanning electron microscope and / or a scanning ion microscope, for recording images of the sample. In particular, the test region of the sample stage or sample, into the material of which the first and the second track are written, is a region of the sample stage or sample in which the tracks are not bothersome. For example, a test region of the sample is a region that is not required when the sample is used (e.g. as a mask in lithography). For example, the sample comprises a substrate, a capping layer and / or structures (e.g. absorber structures) made of a material with a first hardness. Furthermore, the test region of the sample stage or sample for example comprises a material with a second hardness, which is less than the first hardness. The first and sec- ond hardness each denote a mechanical resistance which the respective material exhibits against mechanical penetration by the apex of the measuring tip. Carl Zeiss SMT GmbH 14 For example, the first and the second track are each tracks, for example engraved tracks and / or scratched tracks, written into a material of the test region by the apex of the measuring tip. For example, the first and the second track each have depressions relative to a surface of the test region before the first and the second track are applied. The first track is arranged parallel to the y-direction in partic- ular, and the second track is arranged parallel to the x-direction in particular. Following step 1a) in particular, steps 1c) and 1d) are initially carried out for the first track only. In this case, the image recording device is controlled in step 1c) to record at least one image of the test region, the first track being at least par- tially captured therein. Following step 1b), steps 1c) and 1d) are carried out again, only for the second track in this case. In this case, the image recording de- vice is controlled in step 1c) to record at least one image of the test region, the second track being at least partially captured therein. For example, in a first arrangement variant, the first and the second track can be created on the surface of the test region, in such a way that the first and the sec- ond track are arranged on the surface at a distance from one another and without contact with one another. In other words, the first and the second track are not contiguous in this case. For example, in a second arrangement variant, the first and the second track can also be created on the surface of the test region, in such a way that the first and the second track intersect (e.g. intersect at right angles). For example, in a third arrangement variant, the first and the second track – in addition to the two tracks intersecting or instead of the two tracks intersecting – can be portions of a contiguous overall track. Carl Zeiss SMT GmbH 15 Moreover, the apex of the measuring tip can for example be removed from the surface of the test region between the creation of the first track and the creation of the second track in one, more and / or all of the three aforementioned arrange- ment variants. For example, the image recording device is a scanning electron microscope and / or a scanning ion microscope. Furthermore, the x-position and the y-position of the apex of the measuring tip is ascertained in this case on the basis of at least one scanning electron microscope image or scanning ion microscope image received from the scanning electron microscope or scanning ion microscope. According to an embodiment, the nanomanipulator comprises a cantilever having a base end and a free end, wherein the measuring tip is arranged at the free end of the cantilever, and, at its base end, the cantilever is secured to the positioning unit so as to be movable. Moreover, the positioning unit is controlled to move the base end of the cantilever such that the measuring tip is moved. For example, the positioning unit is controlled by the control apparatus. In par- ticular, the positioning unit is controlled to move the base end of the cantilever such that the measuring tip is moved as well. According to a further embodiment, the x-position and the y-position of the apex of the measuring tip are ascertained by accordingly fitting a respective straight line to the first and the second track captured in the image. Fitting the respective straight line is performed by the control apparatus, for ex- ample. For example, the respective straight line is fitted by a computer-assisted approximation method, in which a respective linear function is fitted to the first track captured in the image or to the second track captured in the image. Carl Zeiss SMT GmbH 16 According to a further embodiment, the measuring tip is at least partially cap- tured in the at least one image, wherein a lateral position of an apparent apex of the measuring tip in the at least one image deviates from a lateral position of an actual apex of the measuring tip in the at least one image, and the lateral posi- tion of the actual apex of the measuring tip is ascertained relative to the lateral position of the apparent apex of the measuring tip in the at least one image. An offset between the x- and y-position of the actual apex of the measuring tip (not visible in the image) and the x- and y-position of the apparent apex of the measuring tip (visible in the image) can be ascertained with knowledge of the lat- eral position (i.e. the x- and y-position) of the actual apex of the measuring tip relative to the lateral position (i.e. the x- and y-position) of the apparent apex of the measuring tip in the at least one image. Since this x- and y-offset generally does not change for a specific measuring tip, the x- and y-position of the actual apex of the measuring tip can easily be ascertained with the aid of the ascer- tained x- and y-offset based on any desired image of the measuring tip, recorded in particular along the same line-of-sight. Accurate knowledge of the x- and y-position of the actual apex of the measuring tip used to process a sample enables more accurate processing of the sample. For example, a particle on the sample can be removed in more targeted fashion and better with the aid of the measuring tip as a result. In particular, the image is a two-dimensional image. According to a further embodiment, the lateral position of the actual apex of the measuring tip is ascertained relative to a lateral position of the base end of the cantilever. Carl Zeiss SMT GmbH 17 As a result, the contact point between the actual apex of the measuring tip and the surface of the sample can be ascertained at any time when the measuring tip is visible in the image. According to another aspect, a method for landing a probe or processing a sample comprises: capturing a first image of a surface of the sample, the first image com- prising a least one section not obscured by the tip; generating a second image, the second image comprising as least one section obscured by the tip and at least one mark arranged in the obscured section, indicating a position of at least one hid- den element; and displaying the second image on a user interface to an operator of the nanomanipulator during manipulation of the sample. This method may be used on its own or in combination with one or more of the other methods dis- closed above or below. Optionally, the at least one mark comprises at least one of the following: a con- tact point indicator indicating a position of a contact point of the tip with the sample; a structure indicator indicating an edge or an area of a surface feature or a particle located on the surface of the sample; and a tip indicator indicating an outline of the tip, wherein the tip is replaced in the second image by a corre- sponding section of the surface of the sample obtained from the first image. According to a further embodiment, the nanomanipulator comprises a deflection detection device for detecting a z-deflection of the free end of the cantilever in a z- direction which is arranged perpendicular to the x- and the y-direction and which points away from the sample. In addition, the method includes: 6a) controlling the positioning unit to move the base end of the cantilever in the negative z-direction such that a z-distance in relation to the z-direction is re- duced between the base end of the cantilever and the sample, and the measuring tip is made to approach the sample in a test region of the sample, Carl Zeiss SMT GmbH 18 6b) repeatedly receiving, from the deflection detection device, an extent of the z-deflection of the free end of the cantilever depending on the z-distance of the base end of the cantilever from the sample, 6c) ascertaining an approach curve which contains the extent of the z-deflec- tion of the free end of the cantilever as a function of the z-distance of the base end of the cantilever from the sample, 6d) receiving at least one image of the sample, the test region being at least partially captured therein, 6e) ascertaining whether the sample is damaged in the test region using the at least one received image as a basis, and 6f) storing a minimal z-deflection and / or a minimal z-distance of the ap- proach curve as a safe z-deflection of the free end of the cantilever or as a safe z- distance of the base end of the cantilever from the sample should the sample be ascertained as being undamaged in the test region. As a result, it is possible to ascertain a safe deflection of the free end of the canti- lever and hence a safe minimal distance of the apex of the measuring tip from the sample in the z-direction even though the precise z-position of the apex of the measuring tip is generally unknown. In this case, the nanomanipulator is used as a force sensor in particular, and force distance spectroscopy is performed. For example, the x-, y- and z-position of the base end of the cantilever is known accurately relative to the positioning unit. In particular, the x-, y- and z-position of the base end of the cantilever can be set by controlling the positioning unit. Consequently, current values of the x-, y- and z-position of the base end of the cantilever relative to the positioning unit can be provided by the positioning unit, for example. In particular, the z-position of the base end of the cantilever can thus be provided by the positioning unit, and hence it is known accurately. Carl Zeiss SMT GmbH 19 Nevertheless, the precise z-position of the apex of the measuring tip might be un- known on account of the changing deflection of the free end of the cantilever and on account of a possible bending of the measuring tip relative to the cantilever. The deflection of the free end of the cantilever in the z-direction is caused by forces that act between the measuring tip and the sample. The deflection of the free end of the cantilever in the z-direction is moreover proportional to a spring constant of the cantilever. In particular, the cantilever bends to different extents during the scanning of the sample according to the forces acting between measur- ing tip and sample. An extent of this bending or deflection of the free end of the cantilever in the z-direction can be detected with the aid of the deflection detec- tion device. The nanomanipulator and / or a superordinate apparatus comprising the nanomanipulator comprise(s) such a deflection detection device, for example. For example, the deflection detection device is a light pointer device. The light pointer device comprises for example a laser source and a position-sensitive pho- todetector. A laser beam emitted by the laser source is directed at the free end of the cantilever and reflected from there in an undeflected position of the cantile- ver into the centre of the position-sensitive photodetector. The photodetector is subdivided for example into four regions: "top left", "top right", "bottom left" and "bottom right". If the bending (deflection) of the cantilever changes, then the re- flected laser spot shifts on the photodetector as in the case of the light pointer. By measuring the intensities in the four regions of the photodetector, it is possible to determine vertical and horizontal bending signals which are proportional to the normal force and respectively to lateral forces. Moreover, bending (i.e., an elastic deformation) of the measuring tip relative to the cantilever can occur as a result of interaction of the measuring tip with the sample (e.g. as a result of a lateral movement of the measuring tip upon contact between the measuring tip and the sample). An extent of this bending of the Carl Zeiss SMT GmbH 20 measuring tip relative to the cantilever can be ascertained by means of image processing in recorded images (e.g., scanning electron microscope images, scan- ning ion microscope images) of the measuring tip. For example, the x- and y-position of the base end of the cantilever is kept con- stant in step 6a). In particular, the test region of the sample is a region in which damage to the sample is not bothersome. For example, the test region of the sample is a region that is not required when the sample is used (e.g. as a mask in lithography). For example, damage to the test region includes dented material in the test re- gion. For example, the safe deflection is stored in a storage device of the nanomanipu- lator. For example, before controlling the positioning unit to move the measuring tip in the negative z-direction, the method includes: controlling the positioning unit to move the measuring tip laterally (i.e. in the x- and / or y-direction) into the test region of the sample, wherein the x- and the y-position of the base end of the cantilever are kept constant during the subsequent controlling of the positioning unit to move the measuring tip in the negative z-direction. For example, after ascertaining the approach curve, the method includes control- ling the positioning unit to move the measuring tip in the positive z-direction by a predetermined z-distance (withdrawing the measuring tip from the sample by the predetermined z-distance). Carl Zeiss SMT GmbH 21 For example, steps 6a) to 6f) are carried out by the control apparatus. In embodiments, the positioning unit is controlled in step 6a) to move the base end of the cantilever in the negative z-direction such that the measuring tip in the test region of the sample is made to approach the sample up to a final z-dis- tance in relation to the z-direction. Furthermore, a plurality of approach curves are ascertained on the basis of in each case different final z-distances of the measuring tip from the sample in relation to the z-direction and mutually offset x- and / or y-positions of the measuring tip. Moreover, in a manner assigned to each ascertained approach curve, at least one image of the sample in which the test region is at least partially captured is received. Whether the sample in the test region is damaged is then ascertained for each received image. Moreover, a minimal deflection (and hence a minimal distance) of the approach curve which is based on the smallest final z-distance of the measuring tip from the sample for which the sample is established as not being damaged in the test region on the basis of the corresponding image is stored as a safe deflection of the free end of the cantilever. According to a further embodiment: a plurality of approach curves are ascertained on the basis of a plurality of in each case different test regions which differ from one another in terms of a type of material of the test region, at least one image is received, in which the plurality of test regions are at least partially captured, whether the sample is damaged in the respective test region is ascertained for each ascertained approach curve on the basis of the at least one received im- age, and a minimal z-deflection and / or a minimal z-distance of the respective ap- proach curve is stored in a manner dependent on the corresponding material of the respective test region as a safe z-deflection of the free end of the cantilever or Carl Zeiss SMT GmbH 22 as a safe z-distance of the base end of the cantilever from the sample should the sample be ascertained as being undamaged in the respective test region. For example, in a manner assigned to each ascertained approach curve, at least one image in which the respective test region is at least partially captured is re- ceived. Alternatively, two, more or all test regions are imaged in the image detail of an image. The different test regions which differ from one another in terms of a type of a material of the test region for example contain a material that corresponds to a material of structures (e.g. absorber structures) of the sample, a material that corresponds to a material of a substrate of the sample and a material that corre- sponds to a capping layer, covering layer and / or protective layer (e.g. capping layer of an EUV mask) of the sample. According to a further embodiment, the nanomanipulator preferably comprises a sample stage device having a mount, a sample stage arranged movably on the mount and a further positioning unit for moving the sample stage relative to the mount. Moreover, the method includes: 8a) controlling the positioning unit to move the measuring tip in the negative z-direction such that the measuring tip is brought into contact with the sample, and 8b) controlling the positioning unit and / or the further positioning unit to move the measuring tip and / or the sample arranged on the sample stage such that the measuring tip and the sample are brought to a predetermined dis- tance from one another. As a result – starting from contact between the measuring tip and the sample (e.g. a surface of the sample) – the measuring tip can be removed from the sam- ple by the predetermined distance. Hence, a predetermined fixed working Carl Zeiss SMT GmbH 23 distance can advantageously be applied between the measuring tip and the sam- ple (i.e. in the z-direction). The fixedly predetermined working distance improves the reproducibility of image recordings (e.g. made by a scanning electron micro- scope and / or a scanning ion microscope) of the sample, in which the measuring tip is at least partially captured. Image-monitored processing processes can be improved as a result. For example, the image-monitored processing processes re- late to manipulation processes with the aid of the measuring tip (e.g. a displace- ment of particles on the sample and / or removal of particles from the sample) and / or particle beam-induced processes (e.g. electron beam-induced processes and / or ion beam-induced processes), e.g. etching processes and deposition pro- cesses. Moreover, the predetermined distance can be chosen such that a drift movement of the measuring tip relative to the sample does not lead to sample damage, e.g. damage to the structures of the sample. A drift movement of the measuring tip relative to the sample may arise due to thermal drifts (e.g. heating up of the measuring tip and / or of the cantilever) or charging processes of the sample sur- face on account of processing with a particle beam (e.g. imaging by a scanning electron microscope). This increases a force between measuring tip and sample, leading to the drift movement. So-called “subsequent creeping” of the measuring tip when moving to a specific position on the sample is also known. In a first variant, the predetermined distance between the measuring tip and the sample can be set by controlling the positioning unit to move the base end of the cantilever, and hence the measuring tip, away from the sample. Alternatively, the predetermined distance between the measuring tip and the sample can be set in a second variant by controlling the further positioning unit of the sample stage device to move the sample stage, and hence the sample arranged on the sample stage, away from the measuring tip in the negative z-direction. Carl Zeiss SMT GmbH 24 For example, steps 8a) and 8b) are carried out by the control apparatus. In embodiments, the nanomanipulator comprises a deflection detection device (e.g. a light pointer device) for detecting a deflection of the free end of the cantile- ver in a z-direction, which is arranged perpendicular to the x- and the y-direction. Moreover, an extent of the deflection of the free end of the cantilever in the z-di- rection is received by the deflection detection device in step 8a). Furthermore, the positioning unit is controlled in step 8a) to move the base end of the cantilever in the negative z-direction such that the measuring tip is made to approach the sample until the received extent of the deflection corresponds to a predetermined extent of the deflection. In particular, the predetermined extent of the deflection corresponds to contact between the measuring tip and the sample (e.g. the sur- face of the sample). According to a further embodiment, the method includes: 9a) providing a removal trajectory for removing a particle arranged on the sample, wherein the removal trajectory lies in an xy-plane that is spanned by the x- and the y-direction and intersects an xy-position of the particle, 9b) controlling the positioning unit to position the measuring tip at a first predetermined z-distance from the sample in relation to the z-direction, 9c) controlling the positioning unit to laterally move the measuring tip along the ascertained removal trajectory and at the first predetermined z-distance from the sample, 9d) controlling the positioning unit to move the measuring tip away from the sample in the positive z-direction, 9e) ascertaining as to whether the particle adheres to the measuring tip, and 9f) repeating steps 9b) to 9e) for one or more further predetermined z-dis- tances which are increasingly smaller than the first predetermined z-distance, until the particle is ascertained as adhering to the measuring tip, Carl Zeiss SMT GmbH 25 wherein steps 9b) to 9f) are carried out fully automatically. The removal of particles from the sample requires nanometer-scale manipula- tions in particular. The proposed particle removal process allows a particle to be removed from the sample in fully automated fashion, i.e. without the action of a user. In particular, a predetermined removal trajectory is applied, which is a path and / or trajectory along which the measurement tip is moved in order to make contact with the particle. One could also say that the removal trajectory is an access path of the measuring tip for making contact with the particle. In par- ticular, the predetermined removal trajectory (which is arranged in an xy-plane in particular) can be successively traversed in fully automated fashion by the measuring tip at different z-distances from the sample. In that case, a z-distance between the measuring tip and the sample is progressively and incrementally re- duced. This allows the measuring tip to make contact with the particle as far down as possible (i.e. as close as possible to the sample surface) without damag- ing the measuring tip and / or the sample. In particular, the incremental reduction in the z-distance between the measuring tip and the sample is advantageous in that physical contact between the measuring tip and / or the sample is prevented to the greatest possible extent, and it is hence possible to avoid damage to the measuring tip and / or the sample. For example, a user merely needs to start the particle removal process – e.g. by means of a human-machine interface (HMI). For example, the human-machine interface comprises a keyboard, a mouse pointer, joystick, game controller, touchscreen or the like. Steps 9b) to 9f) are carried out in fully automated fashion by starting the particle removal process. In particular, starting the particle re- moval process causes the measuring tip to be moved in fully automated fashion at the various z-distances, initially in the lateral direction along the removal tra- jectory (step 9c) and then in the positive z-direction away from the sample (step 9d), until the particle adheres to the measuring tip. Carl Zeiss SMT GmbH 26 For example, the first predetermined z-distance is 50 nm, 40 nm or 30 nm. For example, the one or more further predetermined z-distances are 5 nm, 10 nm or 15 nm smaller than an immediately preceding z-distance (i.e. than the first or the further predetermined z-distance). Purely by way of example, the first predeter- mined z-distance is 50 nm, a second predetermined z-distance is 40 nm, a third predetermined z-distance is 30 nm, a fourth predetermined z-distance is 20 nm and a fifth predetermined z-distance is 10 nm. Step 9f) is not carried out should the particle already be ascertained as adhering to the measuring tip at the first z-distance in step 9e). A lateral movement of the measuring tip is a movement of the measurement tip in the x- and / or y-direction (in other words in the xy-plane) in particular. For ex- ample, the measuring tip is moved only in the x-direction, only in the y-direction or simultaneously in the x- and the y-direction. The x- and the y-position of the particle accordingly are positions in relation to the x- and the y-direction. For example, the removal trajectory is a linear removal trajectory. For example, steps 9a) to 9f) are carried out by the control apparatus. In embodiments, ascertaining the removal trajectory includes: receiving an image of at least one part of the sample, wherein the particle arranged on the sample surface is captured in the image, ascertaining, on the basis of the received image, the removal trajectory for removing the particle. Carl Zeiss SMT GmbH 27 In embodiments, a linear removal trajectory for the particle to remove the parti- cle is ascertained in such a way that the removal trajectory intersects the parti- cle, a length of the removal trajectory is longer than a size of the particle and the removal trajectory is free of structures of the sample. In embodiments, a linear removal trajectory for the particle to remove the particle is ascertained in such a way that on one side of the particle the removal trajectory projects beyond the particle by double the size of the particle. Additionally or in- stead, the removal trajectory is ascertained for example in such a way that on the other side of the particle the removal trajectory projects beyond the particle by one and a half times a diameter of the measuring tip. In embodiments, the method includes: automatically monitoring one or more pa- rameters, for example a deflection of the free end of the cantilever in the z-direc- tion, a twist of the free end of the cantilever around the x-direction, and / or a bending of the measuring tip relative to the cantilever. Further, the positioning unit is controlled to stop a lateral movement of the measuring tip and / or to with- draw the measuring tip in relation to the sample (i.e. in the positive z-direction) should the current state of the one or more parameters be ascertained as outside of a permitted region. For example, in step 9b), the positioning unit is controlled in such a way that the measuring tip (i.e. the apex of the measuring tip) is positioned in relation to the x- and y-direction on a point on the removal trajectory. According to a further embodiment, step 9c) includes: controlling the positioning unit to laterally move the measuring tip along the ascertained removal trajectory in steps of a first predetermined lateral dis- tance and preferably in steps of one or more further predetermined lateral Carl Zeiss SMT GmbH 28 distances, which are increasingly greater than the first predetermined lateral distance. As a result of progressively increasing the increment during the lateral move- ment of the measuring tip, it is possible to laterally apply a progressively greater force in order to attempt to break a particle free. However, since this harbors the risk of damaging the sample and / or the measuring tip at the same time, the lat- eral distance is only increased incrementally. This can ensure that the amount of force applied is only as much as is required to detach the particle. For example, the first predetermined lateral distance is 10 nm, 20 nm or 30 nm. The one or more further predetermined lateral distances are 30 nm, 40 nm, 50 nm, 60 nm and / or 70 nm, for example. According to a further embodiment, the method includes: 9a') controlling the positioning unit to position the measuring tip on a sur- face of the sample adjacent to a particle on the surface, wherein a base point of the cantilever is situated in relation to the z-direction at a first predetermined z- distance from the sample, 9b') controlling the positioning unit to laterally move the measuring tip in order to detach the particle from the surface, 9c') ascertaining whether the particle has moved on the surface, and 9d') repeating steps 9a') to 9c') for one or more further predetermined z-dis- tances which are between the base point of the cantilever and the sample and which are increasingly smaller than the first predetermined z-distance, until the particle is ascertained as having moved on the surface, wherein steps 9a') to 9d') are carried out fully automatically. By repeating steps 9a') to 9c') for progressively smaller z-distances between the base point of the cantilever and the sample, an incrementally increasing force is Carl Zeiss SMT GmbH 29 applied to the measuring tip, and hence to the particle, until the particle has de- tached from the surface. As a result, the amount of force applied can be only as much as is required to detach the particle from the surface. At the same time, an unnecessarily high exertion of force is avoided, whereby damage to the measur- ing tip and / or the sample can be prevented. According to a further embodiment, the method includes: 12a) controlling the positioning unit to laterally move the measuring tip in the direction of a particle arranged on the sample, 12b) ascertaining as to whether the particle adheres to the measuring tip, and 12c) controlling the positioning unit to move the measuring tip away from the sample in the positive z-direction and / or to move the measuring tip along a curved trajectory, which in the region of the particle curves from an initially lat- eral movement into a movement in the positive z-direction, should the particle be ascertained as adhering to the measuring tip, wherein steps 12a) to 12c) are performed fully automatically. As a result, a move and lift process of the measuring tip, as may be required for picking a particle up from the sample surface, can be carried out fully automati- cally. In particular, it is possible to fully automatically ascertain whether the par- ticle adheres to the measuring tip. Furthermore, should the particle be confirmed as adhering to the measuring tip, the measuring tip is moved away from the sam- ple in the positive z-direction (step 12c) and hence the particle is lifted from the sample surface; this is implemented fully automatically. For example, steps 12a) and 12b) are repeated simultaneously and / or repeatedly. For example, steps 12a) to 12c) are carried out by the control apparatus. Carl Zeiss SMT GmbH 30 In step 12a), the positioning unit is controlled, in particular to linearly laterally move the measuring tip in the direction of the particle arranged on the sample and / or to move the measuring tip along the curved trajectory. According to a further embodiment, the method includes: controlling the positioning unit to move the measuring tip in the lateral di- rection and / or in the positive z-direction in order to pick up a particle arranged on the sample using the measuring tip, ascertaining as to whether the particle adheres to the measuring tip on the basis of: an extent of a lateral deflection of the cantilever received from a de- flection detection device, a plurality of received images of at least one part of the sample, the images capturing the particle, and a change in the brightness of the particle and / or a change in the contrast of the particle relative to the measuring tip in the plurality of images, as ascertained by means of image processing, a plurality of images of at least one part of the sample, the images being received from an image recording device and capturing the particle, and a migration of the particle out of a fixedly set focus of the image recording device, as ascertained by means of image processing of the plurality of images, and / or information that is received from an image recording device which records images of at least one part of the sample, in which the particle is cap- tured, with an autofocus setting focused on the particle and that relates to an ex- tent of an automatic adjustment of the autofocus focused on the particle, the ad- justment being greater than a predetermined threshold value. As a result, whether the particle adheres to the measuring tip can be ascertained according to one, more or all of four different variants (first to fourth variants). In particular, as a result it is possible in each case to for example fully automati- cally ascertain whether the particle adheres to the measuring tip. Carl Zeiss SMT GmbH 31 For example, the particle can be moved laterally by means of the measuring tip until an indication for an adherence according to one or more of the first to fourth variants is ascertained. Thereupon, the measuring tip can be moved in the posi- tive z-direction (i.e. lifted), wherein a check is carried out with the aid of one or more of the first to fourth variants as to whether the particle is lifted off together with the measuring tip (i.e. remains adhering to the measuring tip) or not (i.e. detaches from the measuring tip again). For example, the control apparatus receives the extent of the deflection detected by the deflection detection device. For example, the control apparatus receives the one or more images recorded by the image recording device. For example, in accordance with one, more or all of the four different variants, the control appa- ratus ascertains whether the particle adheres to the measuring tip. In the first variant, whether the particle adheres to the measuring tip is ascer- tained on the basis of an extent of the deflection of the cantilever in the lateral di- rection, which is received from the deflection detection device. The extent of the deflection of the cantilever in the lateral direction can for example be ascertained on the basis of an extent of a twist of the cantilever. For example, the measuring tip is ascertained as having contact with the particle should the extent of the de- flection of the cantilever in the lateral direction be greater than a predetermined threshold value. In the second variant, whether the particle adheres to the measuring tip is ascer- tained on the basis of a change in the brightness and / or a change in the contrast of the particle in images (e.g. electron microscope images and / or ion microscope images) of the particle. For example, at least one part of the measuring tip is also captured in the plurality of received images of the sample, in addition to the par- ticle. For example, the change in the brightness of the particle is a change of a Carl Zeiss SMT GmbH 32 brightness of the particle relative to a brightness of the measuring tip in the im- ages. For example, the change in the contrast of the particle is a change of a con- trast between the particle and the measuring tip in the images. For example, in comparison with the case in which the particle does not adhere to the measuring tip, the brightness of the particle increases when the particle adheres to the measuring tip. For example, adherence of the particle to the measuring tip leads to electric charging of the particle, whereby the particle becomes brighter in the image. For example, a detachment of the particle from the measuring tip leads to the parti- cle becoming darker again in the image. In the third variant, the particle adhering to the measuring tip and consequently being lifted (moved in the positive z-direction) together with the measuring tip is ascertained on the basis of a migration of the particle out of a fixedly set focus of the image recording device. In particular, what is ascertained here on the basis of the images is that the particle initially is in a focus of the image recording device (i.e. the focus is adjusted to the particle), and the particle no longer is in the focus of the image recording device in later images. In the fourth variant, the images of the particle are recorded using an autofocus setting that is focused on the particle. Furthermore, what follows from an auto- matic adjustment by more than the predetermined threshold value of the autofo- cus focused on the particle is that a z-position of the particle has changed signifi- cantly, and this indicates a lifting of the particle together with the measuring tip (in the positive z-direction). In the fourth variant, it is possible to optionally ascertain whether the autofocus adjusted to the particle changes in accordance with a movement of the measuring tip in the positive z-direction. The movement of the measuring tip in the positive Carl Zeiss SMT GmbH 33 z-direction is for example ascertained with the aid of position data relating to the base end of the cantilever, which are received by the positioning unit. According to a further embodiment, the nanomanipulator comprises a sample stage device having a mount, a sample stage arranged on the mount so as to be laterally movable and a further positioning unit for laterally moving the sample stage relative to the mount in the x- and the y-direction. Furthermore, the method includes: 14a) controlling the positioning unit to position the measuring tip in a lateral initial position, preset in the positioning unit, in relation to the x- and the y-direction, 14b) receiving at least one image of the sample in which a particle arranged on the sample is captured, 14c) ascertaining, on the basis of image processing, a lateral position of the particle captured in the at least one image, and 14d) controlling the further positioning unit to laterally move the sample stage with the sample, in such a way that the lateral position of the parti- cle corresponds to the lateral initial position of the measuring tip in relation to the x- and the y-direction, and steps 14a) to 14d) are carried out fully automatically. As a result, the measuring tip can initially be brought into its preset initial posi- tion. Moreover, the particle to be processed can be arranged below the measuring tip, i.e. at the same x- and y-position as the measuring tip. This facilitates pro- cessing of the particle using the measuring tip. For example, the measuring tip has only a small limited lateral range (e.g. ±20 µm in the x- and the y-direction) within which it can be displaced. Therefore, it is advantageous to fully automatically arrange the particle below the measur- ing tip at the same x- and y-coordinates as the measuring tip, and at the same time arrange the measuring tip at its origin position. As a result, there is Carl Zeiss SMT GmbH 34 sufficient space around the particle in the x- and the y-direction for displacing the measuring tip in such a way that the particle can be picked up by the measuring tip. Especially if a plurality of particles arranged on the sample are too far apart to be reached by the measuring tip by only moving the measuring tip, it is advan- tageous to automatically displace the sample stage accordingly. Fully automatically arranging the particle below the measuring tip at the same x- and y-coordinates as the measuring tip and simultaneously arranging the measuring tip at its origin position is therefore also advantageous because the particle is in the field of view of the image recording device as a result. The initial position of the measuring tip in relation to the x- and the y-direction, preset in the positioning unit, is for example an origin position of the measuring tip, which is preset in the positioning unit. The initial position or origin position for example corresponds to an origin of the coordinate system of the positioning unit (x=0, y=0). For example, steps 14a) to 14d) are carried out by the control apparatus. In embodiments, the method includes: controlling an image recording device to record one or more first images of at least one part of the sample, in which the measuring tip is at least partially captured, ascertaining, on the basis of image processing, a position of the measuring tip (lateral position, x- and / or y-position, e.g. position of the apparent apex of the measuring tip) in the one or more first images, and controlling the image recording device to record one or more further images of at least one part of the sample in which the measuring tip captured in the first image(s) is arranged at a predetermined position in the image (e.g. in an image centre). Carl Zeiss SMT GmbH 35 As a result, the measuring tip, in the course of repeated recording of images, can be automatically kept at a predetermined position in the one or more further im- ages (e.g. in an image center) (referred to as: tip tracking). For example, a lateral position (i.e. an x- and / or y-position) of the measuring tip is ascertained on the basis of image processing of the first image or the first im- ages. For example, a position (e.g. lateral position or x- and / or y-position) of the appar- ent apex of the measuring tip is ascertained on the basis of image processing of the first image or the first images. Furthermore, the image recording device, for example, is controlled to record one or more further images of at least one part of the sample in which the apex of the measuring tip captured in the first image(s) is arranged at a predetermined position in the image (e.g. in an image center). According to a further aspect, a computer-implemented method for processing a sample using a nanomanipulator is proposed. The nanomanipulator comprises a measuring tip for processing the sample and a positioning unit for moving the measuring tip. Furthermore, the sample is arranged on a sample stage. An x-di- rection and a y-direction of the nanomanipulator are each arranged parallel to a main extension plane of the sample and / or sample stage and perpendicular to one another. The sample has a nanostructure on its surface for the purpose of ascer- taining an actual apex of the measuring tip. The method comprises the following steps: 15a) controlling the positioning unit to laterally move the measuring tip from lateral initial coordinates to the lateral end coordinates in order to scan the nanostructure and create raster-scan data, 15b) ascertaining nanostructure coordinates of a highest point of the nanostructure in the raster-scan data, Carl Zeiss SMT GmbH 36 15c) ascertaining a first lateral distance between the nanostructure coordi- nates and the lateral end coordinates, 15d) recording at least one image of the sample in which the measuring tip and the nanostructure are at least partially captured, wherein the measuring tip is situated at the lateral end coordinates, 15e) ascertaining a second distance of an apparent apex of the measuring tip from the nanostructure, and 15f) ascertaining a position of an actual apex of the measuring tip on the ba- sis of a difference between the first and the second distance. As a result, it is possible to ascertain a position (e.g. x- and y-position) of the ac- tual apex of the measuring tip, even if only the apparent apex of the measuring tip is visible in the recorded and received image. In particular, the actual apex of the measuring tip might not be visible in the image because it is concealed in re- lation to a line-of-sight of the image recording device. The nanostructure for ascertaining the actual apex of the measuring tip for ex- ample has a lateral dimension of 30 nm or less, 20 nm or less, 10 nm or less and / or 5 nm or less. The nanostructure for ascertaining the actual apex of the measuring tip for ex- ample has a spherical shape, hemispherical shape and / or spherical surface. Alter- natively, the nanostructure for ascertaining the actual apex of the measuring tip might for example also have a tip, in particular a tip that tapers in a direction go- ing away from the sample surface. According to a further aspect, a computer program product is proposed, compris- ing instructions which, upon execution of the program by at least one computer, cause the latter to carry out one of the methods described above. Carl Zeiss SMT GmbH 37 A computer program product, such as e.g. a computer program means, can be provided or supplied for example as a storage medium, such as e.g. a memory card, a USB stick, a CD-ROM, a DVD, or else in the form of a downloadable file from a server in a network and / or from a cloud-based source. For example, in a wireless communications network, this can be effected by transferring an appro- priate file with the computer program product or the computer program means. According to a further aspect, an apparatus for processing a sample is proposed. The apparatus comprises: a nanomanipulator having a measuring tip for processing the sample and a positioning unit for moving the measuring tip, a sample stage for arrangement of the sample, wherein an x-direction and a y-direction of the nanomanipulator are each arranged parallel to a main exten- sion plane of the sample and / or sample stage and perpendicular to one another, and a control apparatus configured to carry out the method described above. The main extension plane of the sample and / or sample stage is for example an xy-plane spanned by the x-direction and the y-direction. The apparatus for processing a sample for example comprises a sample stage de- vice having a mount, wherein the sample stage is arranged movably on the mount. Moreover, the sample stage device comprises e.g. a further positioning unit for moving the sample stage relative to the mount. The sample stage can be moved for example with the aid of the further positioning unit in the x-direction and the y-direction (i.e. laterally) and / or in the z-direction (vertical direction). The sample stage can for example also be mounted rotatably on the mount, such that it can be rotated about the x-, y- and / or z-direction with the aid of the fur- ther positioning unit. The sample stage comprises in particular a surface for ar- rangement of the sample. Carl Zeiss SMT GmbH 38 The respective unit, for example the control apparatus, can be implemented in terms of hardware technology and / or else software technology. In the case of an implementation in terms of hardware technology, the respective unit can be em- bodied as an apparatus or as part of an apparatus, for example as a computer or as a microprocessor. In the case of an implementation in terms of software tech- nology, the respective unit can be embodied as a computer program product, as a function, as a routine, as part of a program code or as an executable object. “A(n)” should not necessarily be understood as a restriction to exactly one ele- ment in the present case. Rather, a plurality of elements, such as for example two, three or more, can also be provided. Nor should any other numeral used here be understood to the effect that there is a restriction to exactly the stated number of elements. Rather, unless indicated otherwise, numerical deviations upwards and downwards are possible. The numbering of features in the claims, for exam- ple 1a, 1b, 6a, 6b, etc. does not imply any order, neither within one claim nor in the combination of a plurality of claims. For example, unless indicated otherwise, step 6b can be implemented before step 6a. Also, "first", "second", etc. is used only to distinguish elements from one another. For example, a "third" (or any other) element does not required a "first" or "second" (or any other) element to be pre- sent in the claim. Also, the "second" or "third" (or any other) element may be re- named as the "first" (or any other) element. The embodiments and features described for one or more method aspects apply correspondingly to the proposed apparatus aspects, and vice versa. Also, the above method aspects and / or the above apparatus aspects may be combined with each other. Further possible implementations of the invention also comprise non-explicitly mentioned combinations of features or embodiments described previously or Carl Zeiss SMT GmbH 39 hereinafter with regard to the exemplary embodiments. In this case, a person skilled in the art will also add individual aspects as improvements or supplemen- tations to the respective basic form of the invention. Further advantageous configurations and aspects of the invention are the subject matter of the dependent claims and also of the exemplary embodiments of the in- vention that are described below. The invention is explained in detail hereinafter on the basis of preferred embodiments with reference to the accompanying fig- ures. Fig.1 shows an apparatus for analyzing and / or processing a sample, according to one embodiment; Fig.2 shows an enlarged portion of the apparatus from Fig.1 together with a light pointer device, according to one embodiment; Fig.3 shows an image of a portion of a sample to be processed by the apparatus from Fig.1, according to one embodiment; Fig.4 shows a cross section from Fig.3 along the line IV-IV; Fig.5 shows an enlarged view of a measuring tip of the apparatus from Fig.1, ac- cording to one embodiment; Fig.6 shows an image of a portion of a sample and the measuring tip from Fig.5, according to one embodiment; Fig.7 shows a view similar to Fig.6, wherein the measuring tip has left a first track in a test region of the sample, according to one embodiment; Carl Zeiss SMT GmbH 40 Fig.8 shows a view similar to Fig.7, wherein a first straight line has been fitted to the first track, according to one embodiment; Fig.9 shows a view similar to Fig.8, wherein the measuring tip has left a second track in a test region of the sample, and a second straight line has been fitted to the second track, according to one embodiment; Fig.10 shows an approach curve, which plots a deflection of a free end of a canti- lever of the apparatus from Fig.1 as a function of a distance of a base end of the cantilever, according to one embodiment; Fig.11 shows an image of a portion of a sample with three test regions, according to one embodiment; Fig.12 shows a view similar to Fig.10, wherein three approach curves are shown for the three test regions in Fig.11, according to one embodiment; Fig.13 elucidates automatic positioning of the measuring tip in a predetermined working distance from a sample, according to one embodiment; Fig.14 elucidates a fully automatic iterative particle removal process, according to one embodiment; Fig.15a shows different lateral distances which are applied during the fully auto- matic iterative particle removal process from Fig.14, according to one embodi- ment; Fig.15b shows different z-distances which are applied during the fully automatic iterative particle removal process from Fig.14, according to one embodiment; Carl Zeiss SMT GmbH 41 Figs 16a to 16c elucidate a further fully automatic iterative particle removal pro- cess, according to one embodiment; Fig.17 elucidates a first variant of a process in which a check is carried out as to whether a particle adheres to the measuring tip, according to one embodiment; Fig.18 elucidates a second variant of a process in which a check is carried out as to whether a particle adheres to the measuring tip, according to one embodiment; Fig.19 shows a change in the brightness of a particle adhering to a measuring tip within the second variant of the process from Fig.18, according to one embodi- ment; Fig.20 elucidates a third variant of a process in which a check is carried out as to whether a particle adheres to the measuring tip, according to one embodiment; Fig.21 elucidates a fourth variant of a process in which a check is carried out as to whether a particle adheres to the measuring tip, according to one embodiment; Fig.22 shows a flowchart of a computer-implemented method for processing a sample using the apparatus from Fig.1, according to one embodiment; Fig.23 shows a flowchart of a computer-implemented method for processing a sample using the apparatus from Fig.1, according to a further embodiment; Fig.24 shows a flowchart of a computer-implemented method for processing a sample using the apparatus from Fig.1, according to a further embodiment; Fig.25 shows a flowchart of a computer-implemented method for processing a sample using the apparatus from Fig.1, according to a further embodiment; Carl Zeiss SMT GmbH 42 Fig.26 elucidates a computer-implemented method for ascertaining an actual apex of a measuring tip, according to one embodiment, wherein Fig.26 shows a sample having a nanostructure for ascertaining the actual apex of the measuring tip and the measuring tip; Fig.27 shows a recorded image, in which the sample having the nanostructure and the measuring tip from Fig.26 are captured, according to one embodiment; Fig.28 elucidates a further embodiment of a nanostructure for ascertaining the actual apex of the measuring tip; Fig.29 shows a flowchart of a computer-implemented method for processing a sample using the apparatus from Fig.1, according to a further embodiment; Fig.30 shows a schematic diagram of a system for detecting a frequency shift of a driving signal, according to a further embodiment; Fig.31 shows a schematic diagram of a beam deflection system; Fig.32 shows resonance curves of a probe in vacuum and air, respectively; Fig.33 illustrates a method for detecting an interaction between a probe and a sample based on tracking an amplitude signal; Fig.34 illustrates a method for detecting an interaction between a probe and a sample based on tracking a frequency signal, according to a further embodiment; Carl Zeiss SMT GmbH 43 Fig.35 shows a flowchart of a computer-implemented method for landing a probe of a nanomanipulator on a sample using the system from Fig.30, according to one embodiment; and Fig.36 shows different images provided by an apparatus for aiding a user during particle removal. Unless indicated otherwise, elements that are identical or functionally identical have been provided with the same reference signs in the figures. Furthermore, it should be noted that the illustrations in the figures are not necessarily true to scale. Figure 1 schematically shows one exemplary embodiment of an apparatus 100 for analyzing and / or processing a sample 102 with the aid of an atomic force micro- scope 104 as one example of a nanomanipulator. The atomic force microscope 104 comprises a measuring tip 106 for analyzing and / or processing the sample 102. The measuring tip 106 is arranged on a cantilever 108 secured movably to a posi- tioning unit 110 (movement unit). In particular, the cantilever 108 comprises a first end 112 (base end 112), at which the cantilever 108 is movably secured to the positioning unit 110. Furthermore, the cantilever 108 comprises a second end 114 (free end 114), at which the measuring tip 106 is arranged. With the aid of the positioning unit 110, the measuring tip 106 can be moved in three spatial di- rections x, y, z (translational movement in x-, y- and z-directions). Movements in the x- and / or y-direction are referred to as lateral movements herein. Herein, movements in the z-direction are referred to as an approach of the sample 102 by the measuring tip 106 (negative z-direction) and a removal / away movement of the measuring tip 106 from the sample 102 (positive z-direction). The apparatus 100 comprises a housing 116 which can be evacuated to a residual gas pressure of 10-5– 10-9mbar for example by means of a vacuum pump 118. Carl Zeiss SMT GmbH 44 The atomic force microscope 104 is arranged in the housing 116. Furthermore, a sample stage 120 for holding the sample 102 is provided. The sample stage 120 is preferably held by the housing 116 by means of a mount 122. The sample stage 120 can furthermore comprise a further positioning unit 124 (not illustrated indi- vidually), by means of which the sample stage 120 is displaceable relative to the mount 122 in the three spatial directions x, y and z, for example, and is rotatable about at least one axis (e.g. an axis arranged parallel to the z-direction in Fig.1), for example. Reference sign 126 denotes a sample stage device which comprises the sample stage 120, the mount 122 and the further positioning unit 124. Moreover, a particle beam column (corpuscular beam column) 128, for example, is arranged in the housing 116. The particle beam column 128 is configured to pro- vide a particle beam 130. The particle beam column 128 can be designed in par- ticular as a particle beam microscope and can be used to monitor processing of the sample 102 using the measuring tip 106. For example, the particle beam column 128 is an electron column 128, which is configured to provide an electron beam 130. In particular, the electron column 128 can be designed as an electron microscope. By way of example, the particle beam column 128 is described as electron column 128 below. However, the particle beam column 128 could also be an ion column (not shown) in other examples, which is configured to provide an ion beam. In conjunction with a process gas providing unit 134, the electron column 128 can additionally be used for conducting particle beam-induced processing processes on the sample 102. For this purpose, for example, a process gas 136 is supplied by means of the process gas providing unit 134, and is irradiated by the particle beam 130. Carl Zeiss SMT GmbH 45 A particle 132 (Fig.3) adhering on a sample surface 138 (Fig.2) of the sample 102 can be picked up with the measuring tip 106. For this purpose, the measur- ing tip 106 is correspondingly moved for example by means of the positioning unit 110. For assistance, the sample stage 120 can also be displaced by means of its further positioning unit 124. The picking up of the particle 132 by the measur- ing tip 106 is monitored live in particular with the electron microscope 128. Afterwards, the measuring tip 106 is moved by means of the positioning unit 110 to a repository unit (shown), where the particle 132 is transferred from the meas- uring tip 106 to the repository unit. Fig.1 additionally shows a control apparatus 140 for controlling the atomic force microscope 104 (e.g. the positioning unit 110), the sample stage 120 or the fur- ther positioning unit 124, the electron microscope 128 and / or the process gas providing unit 134. A human-machine interface 142 can be provided as part of the control apparatus 140 or in a manner connected to the control apparatus 140 in wired or wireless fashion for data transfer. The human-machine interface 142 comprises for example a display device 144, a loudspeaker (not shown), a key- board 146, a mouse pointer 148, a joystick, a game controller (not shown) or the like. As shown in Fig.2, the atomic force microscope 104 can for example comprise a deflection detection device 150 (e.g. a light pointer device 150) for detecting an ex- tent of the deflection D of the free end 114 of the cantilever 108 in the z-direction. In particular, the z-direction is arranged perpendicular to the sample 102 or to a main extension plane E (xy-plane in Fig.3) of the sample 102 and / or of the sam- ple stage (120). The deflection D of the free end 114 of the cantilever 108 in the z- direction is caused by forces acting between the measuring tip 106 and the sam- ple 102 and is proportional to a spring constant of the cantilever 108. A force Carl Zeiss SMT GmbH 46 acting on the cantilever 108 in the z-direction can thus be ascertained by detect- ing the deflection D. The light pointer device 150 can also be used for detecting an extent of a rotation R of the free end 114 of the cantilever 108 about the x-direction. A rotation R (twist R; see Fig.2) of the free end 114 of the cantilever 108 about the x-direction can be caused by lateral forces that act between the measuring tip 106 and the sample 102. The light pointer device 150 comprises for example a laser source 152 and a posi- tion-sensitive photodetector 154. A laser beam 156 emitted by the laser source 152 is directed at the free end 114 of the cantilever 108 and reflected from there onto the photodetector 154. The photodetector 154 comprises for example four photosensitive regions ul, ur, bl and br. In an undeflected position of the cantile- ver 108, the laser beam 156, 158 is reflected into the center of the photodetector 154, as shown in Fig.2. However, if the cantilever 108 is deflected in a positive or negative z-direction (deflection D), then the reflected laser beam 158 migrates on the photodetector 154 as in the case of a light pointer. By measuring the received intensities in the four regions ul, ur, bl and br of the photodetector 154, it is pos- sible to determine vertical and horizontal deflection signals (bending signals) of the cantilever 108. The deflection signals are proportional to forces acting on the cantilever 108 in the z-direction (normal force) and also to lateral forces acting in the x-direction or y-direction. For example, a bending B (Fig.2) of the measuring tip 106 relative to the cantile- ver 108 can also be ascertained in the method. In particular, interaction of the measuring tip 106 with the sample 102 can result in a bending B (i.e. an elastic deformation) of the measuring tip 106 relative to the cantilever 108. For example, the measuring tip 106 may bend on account of a lateral movement of the measur- ing tip 106 (in the x- and / or y-direction in Fig.2) while the measuring tip 106 is Carl Zeiss SMT GmbH 47 simultaneously in contact with the sample 102. An extent of this bending B of the measuring tip 106 can be ascertained by means of image processing in recorded images 160 of the measuring tip 106. The illustrated apparatus 100 (Figs 1, 2) comprises a number of optional ele- ments which do not necessarily have to be present. These are in particular the housing 116, the vacuum pump 118, the sample stage device 126, the electron column 128 (or an ion column), the process gas providing unit 134, the human- machine interface 142 and the deflection detection device 150. Fig.3 shows an image 160 (e.g. a scanning electron microscope image 160, for short: SEM image 160) of a portion of an exemplary sample 102. Fig.4 shows the portion of the sample 102 shown as image 160 in Fig.3 in a cross-sectional view along line IV-IV in Fig.3. The sample 102 comprises for example structures 162 (e.g. absorber structures 152) with intervening trenches 164. H denotes height of the structures 162. Moreover, an exemplary particle 132 is shown on the sample 102, which particle lies in one of the trenches 164 at the edge of one of the ab- sorber structures 162 and needs to be removed. The reference sign 166 in Figs 3 and 4 denotes a substrate of the sample 102. Removing particles 132 with the aid of the atomic force microscope 104 requires a manipulation of the measuring tip 106 with an accuracy of the order of magni- tude of nanometers. It may be necessary here to move to a particle 132 many times with the measuring tip 106 controlled by a user and to track the procedure in the SEM images 160 until finally adhering of the particle 132 to the measuring tip 106 is achieved and the particle 132 can be removed from the sample 102. Furthermore, processing the sample 102, in particular removing particles 132 from the sample 102, is made more difficult by the fact that the precise position of an apex 168 (Fig.2) of the measuring tip 106 is generally unknown. In Carl Zeiss SMT GmbH 48 particular, the apex 168 of the measuring tip 106 is the point and / or region of the measuring tip 106 which makes initial contact with the sample 102 or a particle 132 on the sample 102 when the measuring tip 106 approaches the sample 102 and / or particle 132. On account of the geometry of the measuring tip 106, the ac- tual apex 168 of the measuring tip 106 might not be visible in the SEM images 160, and so the accurate x- and y-position x1, y1 (Fig.5) of the actual apex 168 cannot be ascertained from an SEM image 160 alone. Fig.5 elucidates a measuring tip 106 with a geometry in which the apex 168 is arranged in such a way that the apex 168 is concealed in relation to a line-of- sight S of the scanning electron microscope 128. Consequently, the actual apex 168 will not be visible in an SEM image 260 (Fig.6). Instead, a point 170 (Fig.5) of the measuring tip 106 will appear in the SEM image 260 as an apparent apex 170. In the example of Fig.6, the actual apex 168 is at a lateral position x1, y1, and the apparent apex 170 is at a lateral position x2, y2. In the example of Fig.6, the y-position y1 of the actual apex corresponds to the y-position y2 of the appar- ent apex 170. However, the x-position x1 of the actual apex 168 is displaced from the x-position x2 of the apparent apex 170 by a distance Δx. A computer-implemented method for processing a sample 102 using an atomic force microscope 104 is described below with reference to Figures 1 to 25. In a first step S1 of the method, the positioning unit 110 is controlled to move the measuring tip 106 in the y-direction such that the apex 168 of the measuring tip 106 is in contact with a surface 172 of the sample stage 120 or a surface 174 of the sample 102 in a test region 176 of the sample stage 120 or sample 102, and the measuring tip 106 leaves a first track 178 (e.g. a scratched track 178) on the surface 172, 174. In particular, the first track 178 is arranged parallel to the y- direction. A test region 176 of the sample 102 is shown in Fig.6 by way of exam- ple. However, the method can also be used for a test region (not shown here) of Carl Zeiss SMT GmbH 49 the sample stage 120 in other examples. As elucidated in Fig.7, the apex 168 of the measuring tip 106 thus is scratched in the y-direction along the surface 172, 174 of the test region 176 in step S1. In a second step S2 of the method, the image recording device 128 is controlled to record at least one image 260' of the test region 176, the first track 178 being at least partially captured therein (Fig.7). In a third step S3 of the method, an x-position x1 of the apex 168 of the measur- ing tip 106 is ascertained in relation to the x-direction on the basis of the first track 178 captured in the image 260'. For example, as shown in Fig.8, a straight line 180 is fitted to the first track 178. Thereupon, the x-position x1 of the actual apex 168 of the measuring tip 106 is ascertained as the x-position xG of the straight line 180. For example, the x-position x1 of the actual apex 168 is ascer- tained relative to the x-position x2 of the apparent apex 170 of the measuring tip 106, e.g. as an x-offset Δx. In a fourth step S4 of the method, the positioning unit 110 is controlled to move the measuring tip 106 in the x-direction such that the apex 168 of the measuring tip 106 is in contact with the surface 174 of the sample 102 (or with the surface 172 of the sample stage 120 in other examples) in the test region 176, and the measuring tip 106 leaves a second track 182 (e.g. a scratched track 182) on the surface 174. In particular, the second track 182 is arranged parallel to the x-di- rection. As elucidated in Fig.9, the apex 168 of the measuring tip 106 thus is scratched in the x-direction along the surface 174 of the test region 176 in step S4. In a fifth step S5 of the method, the image recording device 128 is controlled to record at least one further image 260" of the test region 176, the second track 182 being at least partially captured therein (Fig.9). Carl Zeiss SMT GmbH 50 In a sixth step S6 of the method, a y-position y1' of the apex 168 of the measuring tip 106 is ascertained in relation to the y-direction on the basis of the second track 182 captured in the image 260" (Fig.9). For example, as shown in Fig.9, a straight line 184 is fitted to the second track 182. Thereupon, the y-position y1' of the actual apex 168 of the measuring tip 106 is ascertained as the y-position yG of the straight line 184. For example, the y-position y1' of the actual apex 168 is as- certained relative to the y-position y2' of the apparent apex 170 of the measuring tip 106, e.g. as a y-offset Δy. In the example shown in Figs 6 to 9, the y-position y1, y1' of the actual apex 168 corresponds to the y-position y2, y2' of the apparent apex 170 of the measuring tip 106, and so the y-offset Δy is equal to zero. Thus, by way of steps S1 to S6, it is possible to ascertain the precise x- and y-po- sition x1, y1 (x1', y1') of the actual apex 168 of the measuring tip 106 (e.g. relative to the apparent apex 170), even though only the apparent apex 170 of the meas- uring tip is visible in the SEM images 260, 260', 260". Within the scope of the proposed method, it is optionally also possible to ascer- tain an approach curve 186 (Fig.10) in relation to a deflection D (Fig.2) of the cantilever 108 when the measuring tip 106 approaches the sample 102 in a man- ner parallel to the z-direction. In particular, attractive and / or repulsive forces act on the free end 114 of the cantilever 108 in a manner dependent on the z-position Pz of the base end 112 of the cantilever 108, and the said forces attract the free end 114 of the cantilever 108 to the sample 102 or repulse the said free end there- from. For the approach curve 186 (Fig.10) in relation to the deflection D of the free end 114 of the cantilever 108, consideration is given here only to a distance range in relation to the z-direction in which only repulsive forces act on the free end 114 of the cantilever 108 and / or in which a repulsive force is greater than an attractive force. Carl Zeiss SMT GmbH 51 With the aid of the approach curve 186, it is possible to ascertain a safe deflection DS (Fig.10) of the free end 114 of the cantilever 108 in the z-direction, for which the sample 102 is not damaged by the measuring tip 106. The safe deflection DS of the free end 114 of the cantilever 108 corresponds in particular to a safe mini- mal z-distance ASof the base end 112 of the cantilever 108 from the sample 102 (i.e. in the z-direction). Ascertaining the approach curve 186 is advantageous be- cause the precise z-position z1 of the apex 168 (Fig.5) of the measuring tip 106 is generally unknown. In particular, although the z-position Pz of the base end 112 of the cantilever 108 is set and provided by the positioning unit 110, the precise z-position z1 of the apex 168 of the measuring tip 106 is generally not known on account of the changing deflection D of the free end 114 of the cantilever 108 and on account of a possible bending B of the measuring tip 106 relative to the canti- lever 108. In a first step S1' of the method, the positioning unit 110 is controlled to move the base end 112 of the cantilever 108 in the negative z-direction. As a result, a z-dis- tance A (Fig.5) between the base end 112 of the cantilever 108 and the sample 102 is reduced, and the measuring tip 106 is made to approach the sample 302 in a test region 188 (Fig.11) of the sample 302. In particular, the test region 188 is arranged outside of and / or at a distance from structures 362, 364 (e.g. absorber structures) of the sample 302. In a second step S2' of the method, the deflection detection device 150 (e.g. the light pointer device 150, Fig.2) repeatedly receives information regarding an ex- tent D1, D2, D3(Fig.10) of the z-deflection D of the free end 114 of the cantilever 108 as a function of a set z-position Pz of the base end 112 of the cantilever 108 (i.e. as a function of the z-distance A, A1, A2, A3 of the base end 112 of the cantile- ver 108 from the sample 302; see Figs 5 and 10). In particular, step S2' is per- formed simultaneously with step S1'. Expressed differently, during the displace- ment of the measuring tip 106 in the negative z-direction (i.e. while the Carl Zeiss SMT GmbH 52 measuring tip 106 approaches the sample 302), the deflection detection device 150 simultaneously or repeatedly measures the z-deflection D of the free end 114 of the cantilever 108. In the example of Fig.10, the base end 112 of the cantilever 108 is made to approach the sample 102 up to a distance A3, at which a force that brings about a deflection D3acts on the free end 114 of the cantilever. In particu- lar, the distance A in Fig.10 reduces from left to right, and so A3 is smaller than A2, and A2 is smaller than A1. An approach curve 186 (Fig.10) is ascertained in a third step S3' of the method. The approach curve 186 specifies the extent D1, D2, D3 of the deflection D of the free end 114 of the cantilever 108 as a function of the distance A, A1, A2, A3of the z-position Pz of the base end 112 of the cantilever 108 from the sample 302. As shown in Fig.10, the deflection D of the cantilever 108 becomes ever smaller, the closer the base end 112 of the cantilever 108 – and hence also the measuring tip 106 – is made to approach the sample 102, 302. In other words, the repulsive force acting on the measuring tip 106 becomes ever smaller, the closer the meas- uring tip 106 is made to approach the sample 102. One could also say that the atomic force microscope 104 is used as a force sensor in the process, and that a force distance spectroscopy is performed. In a fourth step S4' of the method, at least one image 360 of the sample 302 is re- ceived, the test region 188 being at least partially captured therein (Fig.11). In a fifth step S5' of the method, whether the sample 302 has been damaged in the test region 188 is ascertained on the basis of the at least one received image 360. By way of example, the test region 188 (i.e. a material 190 of the test region 188) was not damaged by the measuring tip 106 in Fig.11. In a sixth step S6' of the method, a minimal z-deflection D3 and / or a minimal z- distance A3 of the approach curve 186 ascertained in step S3' is ascertained as a Carl Zeiss SMT GmbH 53 safe z-deflection D3, DS of the free end 114 of the cantilever 108 or as a safe z-dis- tance A3, AS of the base end 112 of the cantilever 108 from the sample 102 should the sample 302 be ascertained as being undamaged in the test region 188 in step S5'. Optionally, a plurality of approach curves 186, 186', 186" (Fig.12) are ascertained on the basis of in each case different test regions 188, 188', 188" (Fig.11) in this method. The test regions 188, 188', 188" differ from one another, in particular by way of a type of a material 190, 190', 190" of the respective test region 188, 188', 188". Thereupon, at least one image 360 is recorded using an image recording de- vice 128, the plurality of test regions 188, 188', 188" being at least partially cap- tured therein. Also, at least one image 360 can be recorded for each test region 188, 188', 188". For each ascertained approach curve 186, 186', 186", there subse- quently is an ascertainment as to whether the sample 302 is damaged in the re- spective test region 188, 188', 188" using the at least one received image 360 as a basis. In the example of Fig.11, the respective material 190, 190' of the test re- gions 188, 188' was not damaged by the measuring tip 106. Merely by way of ex- ample, an impression 200 left by the measuring tip 106 is elucidated for the test region 188" as an example of damage to the material 190" of the test region 188". By way of example, no damage to the sample 302 was consequently ascertained for the test regions 188, 188'. Furthermore, damage to the sample 302 was ascer- tained by way of example for the test region 188". Next, a safe deflection DS, DS' (Fig.12) of the respective approach curve 186, 186' is stored as a function of the corresponding material 190, 190' of the respective test region 188, 188' should the sample 302 be ascertained as being undamaged in the respective test region 188, 188'. In the proposed method, the measuring tip 106 can optionally also be positioned automatically at a suitable predetermined working distance Δz2 from the sample 402, as elucidated in Fig.13. In particular, provision can be made for the Carl Zeiss SMT GmbH 54 positioning unit 110 to initially be controlled to move the measuring tip 106 in the negative z-direction such that the measuring tip 106 is brought into contact with the sample 102 (left-hand drawing in Fig.13). Here, a distance Δz1 between the measuring tip 106 and the sample 402 is equal to zero (Δz1=0). Next, provi- sion can be made for a predetermined working distance Δz2to be set between the measuring tip 106 and the sample 402 using the contact between the measuring tip 106 and the sample 402 as a starting point. To this end, the positioning unit 110 can be controlled to move the measuring tip 106 in the direction of the sam- ple 402 and / or the further positioning unit 124 (Fig.1) can be controlled to move the sample 402 arranged on the sample stage 120 in the direction of the measur- ing tip 106. In particular, the positioning unit 110 and / or the further positioning unit 124 is controlled in such a way that the measuring tip 106 and the sample 402 are brought to the predetermined distance Δz2 from one another (right-hand drawing in Fig.13). As a result of setting the predetermined working distance Δz2, image recordings (e.g. using the scanning electron microscope 128, Fig.1) of the sample 402, the measuring tip 106 being at least partially captured therein, can be compared with one another in an improved fashion. Hence image-monitored processing pro- cess, such as manipulation processes with the aid of the measuring tip 106 (e.g. a displacement and / or removal of particles 132 on the sample 102, 402) for exam- ple, can be monitored better. Optionally, a fully automatic iterative process for removing particles 532 can be provided in the proposed method, as illustrated in Fig.14. This substantially sim- plifies the removal of particles 532. In a first step S1" of the iterative particle removal process, a removal trajectory T (e.g. a linear removal trajectory T) for removing a particle 532 arranged on the sample 502 is provided. In particular, the removal trajectory T lies in an xy-plane Carl Zeiss SMT GmbH 55 E (Fig.3) that is spanned by the x- and the y-direction and intersects an xy-posi- tion (xP, yP; Fig.3) of the particle 132, 532. For illustrative reasons, the particle 532 has been drawn excessively large relative to the measuring tip 106 in Fig.14. However, in reality, the particle 532 in Fig.14 (and in other figures) can be much smaller in relation to the measuring tip 106. In a second step S2" of the iterative particle removal process, the positioning unit 110 is fully automatically controlled to position the measuring tip 106 at a first predetermined z-distance Δz3 (e.g. Δz3 = 50 nm) from the sample 502 in relation to the z-direction. In a third step S3" of the iterative particle removal process, the positioning unit 110 is fully automatically controlled to laterally move 204 (i.e. in the x- and / or the y-direction) the measuring tip 106 along the ascertained removal trajectory T. In particular, in the process the measuring tip 106 is kept from the sample 502 at the first predetermined z-distance Δz3 set in step S2". In the example of Fig.14, the movement of the measuring tip 103 in step S3" is in the x-direction only. However, in other examples the movement of the measuring tip 103 in step S3" can also be implemented in the x- and the y-direction or in the y-direction only. Optionally, in method step S3", the measuring tip 106 is moved incrementally in individual steps 208 of a predetermined lateral distance Δl1(e.g. Δl1= 20 nm). Method step S3" can also be carried out multiple times for lateral distances Δl1, Δl2 that are different in each case, as elucidated in Fig.15a. In this case, the lat- eral distances Δl1, Δl2increase with increasing number of repetitions (e.g. Δl1= 20 nm and Δl2 = 50 nm). In a fourth step S4" of the iterative particle removal process, the positioning unit 110 is fully automatically controlled to move 206 (Fig.14) the measuring tip 106 away from the sample 502 in the positive z-direction. Carl Zeiss SMT GmbH 56 In a fifth step S5" of the iterative particle removal process, whether the particle 532 adheres to the measuring tip 106 is ascertained fully automatically. In a sixth step S6" of the iterative particle removal step, steps S2" to S5" are repeated fully automatically for one or more further prede- termined z-distances Δz4, Δz5, Δz6, Δz7, as elucidated in Fig.15b. The further pre- determined z-distances Δz4, Δz5, Δz6, Δz7are in particular progressively smaller than the first predetermined z-distance Δz3 (e.g. Δz4 = 40 nm, Δz5 = 30 nm, Δz6 = 20 nm, Δz7 = 10 nm). In particular, steps S2" to S5" are fully automatically re- peated for progressively smaller z-distances Δz4, Δz5, Δz6, Δz7until the particle 532 is ascertained as adhering to the measuring tip 106. Optionally, a further fully automatic iterative process for removing particles 532 can be provided in the proposed method, as illustrated in Figs 16a to 16c. In a first step of the method, the positioning unit 110 is controlled to position the measuring tip 106 on a surface 538 of the sample 502 and adjacent to a particle 532 on the surface 538 of the sample 502. In so doing, a base point 112 of the can- tilever 108 is situated in relation to the z-direction at a first predetermined z-dis- tance z8from the sample 502. In the second step of the method, the positioning unit 110 is controlled to later- ally move the measuring tip 106 (i.e. in the x- and / or y-direction) in order to de- tach the particle 532 from the surface 538. Whether the particle 532 is or has moved on the surface 538 (i.e. changed its posi- tion on the surface 538 from an initial position in the first step) is ascertained in a third step of the method. Carl Zeiss SMT GmbH 57 For example, the third step is performed with the aid of an image recording de- vice 128 (Fig.1). For example, an image which captures the particle 532 is rec- orded by the image recording device 128 in both the first step and the third step. In a fourth step of the method, the first to third steps are repeated for one or more further predetermined z-distances z9, z10 (Figs 16b, 16c) between the base point 112 of the cantilever 108 and the sample 502. In particular, the further pre- determined z-distances z9, z10are progressively smaller than the first predeter- mined z-distance z8. As a result, an incrementally increasing force is exerted on the measuring tip 106 and hence on the particle 532. As evident from Figs 16b and 16c, the cantilever 108 bends progressively in the process. The first to third steps are repeated for the one or more further predetermined z-distances z9, z10between the base point 112 of the cantilever 108 and the sample 502 until the particle 532 on the surface 538 is ascertained as having moved. In particular, the first to fourth steps are carried out fully automatically. By repeating the steps of the method for progressively smaller z-distances z8, z9, z10 between the base point 112 of the cantilever 108 and the sample 502, it is pos- sible to apply to the measuring tip 106 only precisely the force required to detach the particle 532 from the surface 538, without causing damage to the measuring tip 106 and / or the sample 538. Optionally, a fully automatic move and lift process can be provided for the meas- uring tip 106 in the proposed method, as illustrated in Fig.17. To this end, the positioning unit 110 is initially controlled to laterally move 210 (Fig.17) the measuring tip 106 in the direction of a particle 632 arranged on the sample 602. Whether the particle 632 adheres to the measuring tip is ascertained next. The adherence of the particle 632 to the measuring tip 106 can be checked on the ba- sis of various methods as described below. Should the particle 632 be ascertained Carl Zeiss SMT GmbH 58 as adhering to the measuring tip 106, the positioning unit 110 is controlled to perform a lift movement 212, 214 of the measuring tip 106. As evident in the cen- tre of Fig.17, the lift movement 212, 214 can be a movement 212 of the measur- ing tip 106 in the positive z-direction only in a first variant. Furthermore, the lift movement 212, 214 can be a movement 214 of the measuring tip 106 along a curved trajectory 215 in a second variant, the said trajectory curving in the re- gion of the particle 632 from an initially lateral movement into a movement in the positive z-direction. Hence a move and lift process 210, 212, 214 of the meas- uring tip 106, as might be required to pick up a particle 632 from the sample sur- face, can be carried out fully automatically, including a check as to whether the particle 632 adheres to the measuring tip 106. Optionally, an (e.g. fully automatic) check as to whether a particle 632 (Fig.17) adheres to the measuring tip 106 might be provided in the proposed method. To this end, the positioning unit 110 (e.g. as shown in Fig.14 and / or Fig.17) is con- trolled to move the measuring tip 106 laterally and / or in the positive z-direction in order to pick up a particle 632 arranged on the sample 602 using the measur- ing tip 106. Thereupon, whether the particle 632 adheres to the measuring tip 106 is ascertained in accordance with one or more of the following four variants. In the first variant, whether the particle 632 adheres to the measuring tip 106 is ascertained on the basis of an extent of a lateral deflection of the cantilever 108 (i.e. in the x- and / or y-direction), which is received from the deflection detection device 150 (Fig.2). For example, the lateral deflection of the cantilever 108 can be ascertained with the aid of the light pointer device 150. In particular, lateral forces acting between the measuring tip 106 and the sample 102 can cause a rotation R of the free end 114 of the cantilever 108 about the x-direction. Carl Zeiss SMT GmbH 59 Hence, the lateral deflection of the cantilever 108 can be ascertained with the aid of the light pointer device 150, for example by detecting the extent of the rotation R of the free end 114 of the cantilever 108 about the x-direction. In the second variant, whether the particle 732, 732' adheres to the measuring tip 106 is ascertained on the basis of a change in the brightness ΔB and / or a change in the contrast of the particle 732 in images 760, 760' of the particle 732, 732' (e.g. in electron microscope images and / or ion microscope images), as illus- trated in Figs 18 and 19. At least one part of the measuring tip 106 is also cap- tured in the plurality of received images 760, 760' of the sample 702, in addition to the particle 732, 732'. The particle 732 does not yet adhere to the measuring tip 106 in the image 760 (Fig.18). By contrast, a brightness B2 of the particle 732' in the further image 760' (Fig.19) has increased significantly in comparison with a brightness B1 of the particle 732 in image 760 (i.e. the particle 732' in im- age 760' is brighter than the particle 732 in image 760). In particular, the change in brightness ΔB arises from the difference in the brightnesses B1 and B2. In other words, a contrast between the particle 732' and the measuring tip 106 in Fig.19 is greater than a contrast between the particle 732 and the measuring tip 106 in Fig.18. This is an indication of electric charging of the particle 732' in Fig. 19 on account of adhering, and hence of the particle 732' adhering to the measur- ing tip 106 in Fig.19. In a third variant, the particle 832' adhering to the measuring tip 106 is ascer- tained on the basis of a migration of the particle 832, 832' out of a fixedly set fo- cus of the image recording device 128, as illustrated in Fig.20. This is because this is an indication of the particle 832' being lifted together with the measuring tip 106. In particular, what is ascertained here on the basis of the images 860, 860' is that the particle 832 initially (image 860, to the left in Fig.20) is situated in a focus of the image recording device 128, and the particle 832' is no longer Carl Zeiss SMT GmbH 60 situated in the focus of the image recording device 128 in later images 860' (to the right in Fig.20). In the fourth variant, the images 160 (Fig.3) of the particle 132 are recorded us- ing the image recording device 128 with an autofocus setting that is focused on the particle 132. Furthermore, what follows from an automatic adjustment ΔF (Fig.21) by more than the predetermined threshold value ΔFS of the autofocus fo- cused on the particle 132 is that a z-position Pz of the particle 132 has changed significantly, and this indicates a lifting of the particle 132 together with the measuring tip 106 (in the positive z-direction). Fig.21 illustrates a change ΔF in the autofocus. An automatic adjustment ΔF1which is greater than the threshold value ΔFScan for example be interpreted as an indication for a movement of the particle 132 in a manner corresponding to an adhering to the measuring tip 106. Optionally, a fully automatic centration of the measuring tip 106 and sample stage 120 can be provided in the proposed method. In particular, the atomic force microscope 104 comprises the sample stage device 126 having the mount 122, the sample stage 120 arranged on the mount 122 so as to be laterally movable and the further positioning unit 124 for laterally moving the sample stage 120 rela- tive to the mount 120 in the x- and the y-direction. The sample stage 120 can for example also be mounted rotatably on the mount 122, such that it can be rotated about the x-, y- and / or z-direction with the aid of the further positioning unit 124. In a first step S1''' of the method, the positioning unit 110 is controlled to fully automatically position the measuring tip 106 in an initial position Px0, Py0(e.g. at x = 0 and y = 0), preset in the positioning unit 110, in relation to the x- and the y-direction. In a second step S2''' of the method, at least one image 160 of the sample 102 in which a particle 132 arranged on the sample 102 is captured is recorded. Carl Zeiss SMT GmbH 61 In a third step S3''' of the method, a lateral position xP, yP (Fig.3) of the particle 132 captured in the at least one image 160 is ascertained by means of image pro- cessing. In a fourth step S4''' of the method, the further positioning unit 124 is controlled to laterally move the sample stage 120 relative to the mount 122, in such a way that the lateral position xP, yPof the particle 132 corresponds to the initial posi- tion Px0, Py0 of the measuring tip 106 in relation to the x- and the y-direction. Using the described methods, the x-, y- and / or z-positions of the apex 168 of the measuring tip 106 can be ascertained more accurately, and so the sample 102 can be processed more precisely using the measuring tip 106. Moreover, the required nanometer-scale manipulations with the measuring tip 106 can be facilitated and / or automated in various ways. Figures 26 to 28 illustrate a further computer-implemented method for pro- cessing a sample 102 using a nanomanipulator 104 (Fig.1). The nanomanipula- tor 104 comprises a measuring tip 106 for processing the sample 102 and a posi- tioning unit 124 for moving the measuring tip 106. Only the measuring tip 106 of the nanomanipulator 104 is visible in Fig.26; with regards to other components of the nanomanipulator 104, for example the positioning unit 124, a sample stage 120 on which the sample 102 is arranged and an image recording unit 128, refer- ence is made to Fig.1 and the description thereof. An x-direction and a y-direc- tion of the nanomanipulator 104 are each arranged parallel to a main extension plane E of the sample 102 and / or sample stage 120 and perpendicular to one an- other. The sample 120 has a nanostructure 900 on its surface 902 for the purpose of ascertaining an actual apex 904 of the measuring tip 106. Carl Zeiss SMT GmbH 62 In a first step S1"" of the method, the positioning unit 124 is controlled to later- ally (in the x- and / or y-direction) move the measuring tip 106 from lateral initial coordinates xA to lateral end coordinates xE in order to scan the nanostructure 900. Raster-scan data 906 are created in the process. By way of example and for illustrative reasons, a respective x-coordinate is speci- fied as lateral initial coordinate xA and as lateral end coordinate xE in Fig.26. However, the lateral initial coordinates and lateral end coordinates can each have an x- and / or y-coordinate as positional specification. In a second step S2"" of the method, nanostructure coordinates xN of a highest point 908, 910 of the nanostructure 900 are ascertained in the raster-scan data 906. In Fig.26, an x-coordinate is also specified as nanostructure coordinate xN. How- ever, the nanostructure coordinate xNmight also have an x- and / or y-coordinate as positional specification. In the third step S3"" of the method, a first lateral distance C1 is ascertained be- tween the nanostructure coordinates xN and the lateral end coordinates xE. In a fourth step S4"" of the method, at least one image 912 (Fig.27) of the sample 102 is recorded, the measuring tip 106 and the nanostructure 900 being at least partially captured therein. In this case, an actual apex 904 (which is not visible in the image 912) of the measuring tip 106 is situated at the lateral end coordi- nates xE. An apparent apex 914 of the measuring tip 106 which is visible in the image 912 is also shown in Fig.27. In a fifth step S5"" of the method, a second distance C2 is ascertained in the im- age 912 (e.g. by image analysis) between the apparent apex 914 of the measuring tip 106 and the nanostructure 900 (e.g. the nanostructure coordinate xN). Carl Zeiss SMT GmbH 63 In a sixth step S6"" of the method, a lateral position xE, x'E of the actual apex 904 of the measuring tip 106 is ascertained on the basis of a difference between the first and second distance C1, C2. For example, a third distance C3 is ascertained between the apparent apex 914 and the actual apex 904 of the measuring tip 106 by virtue of the second distance C2 being subtracted from the first distance C1. A position xE, x'Eof the actual apex 904 of the measuring tip 106, which is not visible in the image 912, can nevertheless be ascertained in this way. The nanostructure 900 for ascertaining the actual apex 904 of the measuring tip 106 for example has a lateral dimension G (Fig.26) of 30 nm or less, 20 nm or less, 10 nm or less and / or 5 nm or less. In the example of Figs 26, 27, the nanostructure 900 for ascertaining the actual apex 904 of the measuring tip 106 has a spherical shape and / or a spherical sur- face. As shown in Fig.28, however, a nanostructure 916 for ascertaining the actual apex 904 of the measuring tip 106 might also for example have a tip 918, which for example tapers in a direction going away from the sample surface 902. According to a further embodiment, systems, apparatuses and methods for land- ing a probe of a nanomanipulator 104 on a sample 102 are provided and de- scribed below. The apparatus may be similar to the apparatuses described above with respect to Figs.1 and 2. Accordingly, components and details described above may also be present in or applicable to the systems described below, unless stated differently. The disclosed method may be implemented at least in part on a computing system, for example the control apparatus 140 described above. Carl Zeiss SMT GmbH 64 Fig.30 shows a schematic diagram of a system 1000 for detecting a frequency shift of a driving signal. The system 1000 comprises a cantilever deflection sys- tem 1001 (e.g., a beam deflection system 1100 as described below), a frequency control system 1002, and an amplitude control system 1003. The frequency con- trol system 1002 comprises a phase detector 1004, a first feedback unit 1005 (e.g., an integrator), and a controllable oscillator 1006 (e.g., a voltage controlled oscilla- tor or numerically controlled oscillator). The amplitude control system 1003 com- prises an amplitude detector 1007 (e.g., a root mean square detector), and a sec- ond feedback unit 1008 (e.g. a proportional-integral (PI) controller). A first output signal provided by the frequency control system 1002, and a second output signal provided by the amplitude control system 1003 are combined by a multiplier 1009 to provide a driving signal to an excitation unit of the cantilever deflection sys- tem 1001 (i.e., an excitation signal, such as A sin (2πf t), where A is the second output signal corresponding to the amplitude provided by the amplitude control system 1003, and sin (2πf t) is the first output signal provided by frequency con- trol system 1002, wherein f is the current operating frequency of the controllable oscillator 1006 and t is the time). The excitation unit 1110 may comprise an exci- tation piezo as shown in Fig.31 or a similar actuator converting the electrical driving signal into a mechanical vibration, thereby leading to a forced oscillation of a cantilever 108 attached thereto. The oscillation of the cantilever 108 or other parts of the probe attached thereto may be detected as deflection signal 1011 by a 4-quadrant photodiode 1154 as shown in Fig.31 or a similar sensor converting the mechanical oscillation back into an electrical control signal. Note that the 4- Quadrant photodiode 1154 may also provide a lateral signal 1012. However, the lateral signal is not necessary for implementing the control loop described below. The frequency control system 1002 follows a phase component of the deflection signal 1011 by forming a phase locked loop (PLL). In particular, the phase detec- tor 1004 compares the deflection signal 1011 with a current oscillator output sig- nal 1018 to output a corresponding phase signal 1013, e.g. a phase error signal. Carl Zeiss SMT GmbH 65 The first feedback unit 1005 integrates the phase signal 1013 to provide a fre- quency control signal 1014 indicative of a frequency shift (i.e., frequency shift dF) based on the integrated phase signal 1013 and a phase setpoint 1015. In resonant driving conditions, the phase angle between the excitation signal 1010 and the deflection signal 1011 should be close to 90°. However, due to delays in the pro- cessing circuitry or other imperfections, the phase setpoint may be set to a value above or below 90° as detailed further below with regard to the determination of resonance characteristics. The frequency control signal 1014 is fed to the control- lable oscillator 1006 to adjust a frequency of the oscillator output signal 1018 pro- vided by the oscillator 1006 to follow the resonance frequency of the cantilever. The amplitude control system 1003 provides an amplitude control loop. In partic- ular, the amplitude detector 1007 detects a current signal strength of the deflec- tion signal 1011 and provides a corresponding amplitude signal 1016 to the sec- ond feedback unit 1008. Based on the amplitude signal 1016 and an amplitude setpoint 1017, the second feedback unit 1008 provides an amplitude feedback sig- nal 1018 for maintaining an amplitude of the cantilever’s maximum deflection close to a desired value. Fig.31 shows a schematic diagram of an exemplary configuration of a beam de- flection system 1100 (e.g. the cantilever deflection system 1001 of the system 1000). As shown, a tip 106 (e.g., a measurement tip or a manipulation tip) is at- tached to a cantilever 108. Together, the tip 106 and the cantilever 108 form a probe 1106 for detecting or manipulation a specimen 1102 (e.g., a sample 106). The probe 1106 can be mechanically driven (e.g., excited) by an excitation unit 1110. For example, a first end of the cantilever 108 (i.e., the end 112 in Figs.1 and 2) may be attached to the piezo 1110, whereas the tip 106 may be attached to a second (e.g., opposite) end of the cantilever 108 (i.e., the end 114 in Figs.1 and 2). Light from a light source 1152, e.g. a LED or laser diode, is reflected of the second end towards a 4-quadrant photodiode 1154 to detect a deflection of the Carl Zeiss SMT GmbH 66 cantilever. Note that the use of a 4-quadrant photodiode 1154 allows the genera- tion of different control signals. In particular, a first deflection signal in a z-direc- tion, i.e. a vertical deflection value DFL, and a lateral deflection of the cantilever in the x / y direction, i.e. a lateral deflection value LAT may be determined. The lateral deflection value LAT is computed as the sum of the left two diode areas minus the sum of the right two diode areas. Similarly, the vertical deflection value DFL is computed as the sum of the upper two diode areas minus the sum of the lower two diode areas. In addition, a sum signal SUM over all four diode ar- eas may be provided. Fig.32 shows resonance curves of a probe 1106 in vacuum and air, respectively. Note that the two curves differ significantly in that the peak in vacuum is much narrower and higher than the peak of the same probe 1106 oscillating in air (shown at a magnification factor of 50x to present it in the same diagram). One of the reasons for this behavior is that the air has a damping effect on the oscilla- tion. This results in a much lower Q-value of 500 instead as 50,000 as well as a downwards shift of the resonance frequency from about 320,150 Hz to 320,000 Hz for the example probe 1106. Further note that due to the higher damping in air, an amplitude of the oscillation of the probe 1106 in air changes more quickly than the amplitude of the oscillation of the probe 1106 in vacuum (e.g., at a pres- sure at or below 10e-3mbar). Fig.33 illustrates a first method for detecting an interaction between a probe 1106 and a sample based on tracking an amplitude signal. The method shown in Fig.33 is based on detecting changes in an amplitude of an oscillation, and may therefore be referred to as AM (amplitude modulation) detection for short. In the AM detection, the cantilever 108 is excited with a fixed amplitude and a fixed frequency signal and a constant (controlled) amplitude. Curve 2 of Fig.33 shows the resonance curve without tip - sample interaction. In contrast, Curve 1 Carl Zeiss SMT GmbH 67 shows a resonance curve with repulsive tip - sample interaction to the right of curve 2, i.e. at a higher resonance frequency. In AM detection, the measured am- plitude signal is used as input for the topography feedback. Line 4 shows the os- cillation amplitude without tip - sample interaction. In contrast, line 5 shows the oscillation amplitude with repulsive tip sample interaction. The amplitude change due to tip - sample interaction always reduces the observed amplitude as the resonance frequency rises. Accordingly, an operating point for the excitation signal is selected away from the resonance frequency as shown by line 3 of Fig. 33. Fig.34 illustrates a second method for detecting an interaction between a probe 1106 and a sample based on tracking a frequency signal, according to a further embodiment of the present disclosure. The method shown in Fig.34 is based on detecting changes directly in a frequency of an oscillation, and may therefore be referred to as FM (frequency modulation) detection for short. Contrary to the AM detection method, in the FM detection method the oscillator, i.e., the cantilever 108 and / or other parts of a probe 1106 are driven (i.e., excited) at their resonance frequency. This may be implemented, as detailed above, using a PLL or similar frequency control circuit (e.g., 1002 above). In addition, an am- plitude feedback circuit (e.g., 1003 above) may be used to control an amplitude of the oscillation to stay constant. Curve 1 of Fig.34 shows a first resonance curve with repulsive tip - sample interaction. Curve 2 shows a second resonance curve without tip - sample interaction. As before, the resonance frequency is shifted up- wards when the tip 106 of the probe 1106 approaches the sample 102. In the FM detection method, a frequency shift signal dF is used as input signal for the to- pography feedback. This signal may be provided by a PLL or similar frequency control circuit as described above. Note that the use of a PLL provides a very fast response signal to variations in a resonance frequency and thus allows a better Carl Zeiss SMT GmbH 68 response to tip - sample interactions, in particular in vacuum or at reduced at- mospheric pressure. Fig.35 shows a flowchart of a, partially or fully computer-implemented, method for landing a probe 1106 of a nanomanipulator on a sample using the system from Fig.30 and the FM detection method described above, according to one em- bodiment. In a step S20, resonance characteristics of a probe 1106 are measured. This is performed in a state where the tip 106 is not in contact with or proximate to the probe. For example, the tip may be located at a significant distance from the probe 1106, i.e. at a distance between 50 to 500µm, for example 100µm, where forces (e.g. attractive or repulsive forces) acting between the tip 106 and the sam- ple 102 are negligible. For example, a frequency sweep signal may be used to de- termine a resonance frequency (i.e., a natural or harmonic frequency) of the probe 1106. In addition, other parameters, including a Q-value and a phase set- point value corresponding to a phase difference between the excitation signal and the deflection signal specific for the system 1000 may be determined. Alterna- tively, part or all of a characteristic of the probe 1106 may be provided as stored values, e.g. by a manufacturer or from a library, etc. The actual landing of the probe 1106, i.e. the approach of the tip 106 to a surface of the sample 102, may be performed in several stages and / or using correspond- ing operation modes. During a first stage or approach phase, the above FM detection may be employed to avoid an unwanted hard contact between the tip 106 and the probe 1106. The FM detection mode provides a high sensitivity for the detection of attractive or repulsive forces. During this stage, small electrostatic, attractive forces can be Carl Zeiss SMT GmbH 69 detected and analyzed. If the electrostatic force exceeds a predefined threshold, the approach may be aborted to avoid damaging the probe 1106. This operating mode may be referred to as dynamic mode of the system. In the dynamic mode, the probe 1106 is actively driven and oscillates mechanically. In other words, in the dynamic mode, the excitation signal 1010 is provided to the excitation unit 1110. In the dynamic mode, multiple parameters may be moni- tored and used to determine an approach of the tip 106 to the surface of the sam- ple 102 and / or various error conditions that may be encountered. As the system 1000, including the cantilever deflection system 1001 and the frequency control system 1002, forms a control loop for tracking the resonance frequency of the probe, this mode may also be referred to as closed loop operation, and some or all of the control signals provided by the frequency control system 1002 and the am- plitude control system 1003 may be used to monitor and / or control the first ap- proach phase (e.g., an initial phase of the landing operation). For example, in the dynamic mode, the amplitude feedback signal 1019, the phase signal 1013 and the frequency control signal 1014 derived during closed loop control from the de- flection signal 1011 may be monitored and analyzed. In addition, further system parameters, including open loop parameters, like the SUM, LAT and DFL signals provided by the sensor 1154, may also be monitored and analyzed. A vertical speed of the tip 106 may also be monitored. For example, the speed of a fine drive of a positioning unit may be monitored. In a step S21, a resonant driving signal is provided to the excitation unit 1110. Initially, the piezo exciter may be driven with a known, natural resonance fre- quency of the probe 1106 determined, for example, in step S20. Once the oscilla- tion is started, it is maintained by the control loop(s) of the system 1000 while tracking the resonance frequency of the probe 1106. In addition, at least one of the above parameters is selected to define a stop condition for the first stage of the approach. For example, an approach is halted when the difference frequency Carl Zeiss SMT GmbH 70 or frequency shift dF (e.g., frequency control signal 1014) exceeds an upper fre- quency threshold indicative of a tip – probe interaction corresponding to a repul- sive force. Alternatively or in addition, the approach may also be halted when the amplitude of the oscillation falls below a lower amplitude indicating that the os- cillation is partly blocked by the sample, i.e. parts of the probe 1106 are in con- tact with the sample. An unusually large amplitude, unusually small or large phase signal values or a negative difference frequency dF may be indicative of various error conditions, such as an uncontrolled oscillation of the cantilever, a loss of locking by the PLL or a high electrostatic charge of the probe 1106 and / or sample. In step S22, a first approach phase is performed. In the following, a control of the probe 1106 by means of a coarse and a fine drive of the positioning unit 110 is used as example for simplicity. However, in other embodiments, all or part of the relative movement may be affected by moving the sample stage 120 and or by a single-stage positioning unit 110 for moving the probe 1106. For example, a coarse and / or fine drive of the positioning unit 110 may be used concurrently or intermittently to reduce the distance in the z-direction between the tip 106 and the sample 102. As a specific example, the tip 106 may be advanced by the fine drive first. Then, if the sample is not detected within the range of the fine drive, the fine drive is returned to a minimal position, and the coarse drive is advanced by a corresponding amount. The approach continues until one of the stop criteria is met. Assuming that no error conditions are encountered, the approach should stop when a repulsive force starts to act between the tip 106 and the sample 102, resulting in a noticeable upwards shift of the resonance frequency, i.e. a dF value exceeding a predefined threshold. The tip 106 is now in proximity to the surface of the sample 102. Optionally, in a step S23, this z-position is saved. Alternatively, the tip 106 may be retracted by a small, predefined amount to avoid an unintended contact. For Carl Zeiss SMT GmbH 71 example, the control unit may retract the tip by a fixed distance, such as one or several nanometer, or by a number of steps of a digital control parameter Zfine used for control of the fine drive. Optionally, to remove a particle 132 from a surface 138 of the sample 102 or per- form other manipulations of the sample 102 or its surface 138, the system is switched into a second operating mode, referred to as static mode in the follow- ing. In the static mode, the tip 106 may approach the sample 102 even further in a second approach stage or phase, as described below. In the static mode, the probe 1106 is not actively driven. Accordingly, deflection of the cantilever is determined by attractive and repulsive forces between the probe 1106 and the specimen 1102. In other words, in the static mode, no excita- tion signal is provided to the excitation unit 1110. Similar to the above, in the static mode, multiple parameters may be monitored and used to determine an ap- proach of the tip to the surface of the sample 102 and / or various error conditions that may be encountered. As the control loop for tracking the resonance fre- quency of the probe is opened (i.e., deactivated), this mode may also be referred to as open loop operation, and only the remaining system parameters, including open loop parameters, like the SUM, LAT and DFL signals provided by the sen- sor 1154, may also be monitored and analyzed. A vertical speed of the tip 106 may also be monitored. For example, the speed of a fine drive of a positioning unit may be monitored. In a step S24, the driving signal for the probe 1106 is deactivated to stop the os- cillation of the cantilever 108. In addition, a different set of stop conditions is se- lected to control the further approach. Note that the tip 106 is already close to the surface 138 of the sample 102 at this stage. Thus, a parameter indicative of a direct contact between the tip 106 and the particle 132 or the surface 138 of the sample 102 may be used to stop the further approach. For example, a deflection Carl Zeiss SMT GmbH 72 signal, such as the vertical deflection signal DFL, of the cantilever 108 may be used directly as a stop condition the further approach. In addition, an unexpected low or high speed of the positioning unit 110 may be used as a stop condition or to indicate an error as described above. In a step S25, the further approach is performed. For example, a further ap- proach may be implemented by activating the fine drive to approach the sample surface step by step. Depending on the first stop criteria used in the first ap- proach phase, the coarse drive may also be used. The approach is stopped when at least one of the second stop criteria is met. For example, the further approach may be stopped when the tip 106 is physically in touch with the surface of the sample 102 or a particle 132 located on the surface 138, In a further, optional step S26, the position of the probe 1106 with respect to the sample 102 may be optimized in case a combination of a coarse and fine drive is used to control the approach. In this case, in order to provide a good dynamic range for the fine drive during particle or surface manipulation, a z-position of the contact position may be stored. Then, the tip 106 may be retracted by means of the fine drive. For example, the fine drive may be pulled completely away from the surface. Thereafter, the coarse drive may be controlled such that the contact position lies within the effective operating range of the fine drive. For example, the coarse drive may be moved away from or towards the surface until the stored contact position lies halfway between in minimum and a maximum range of the fine drive. In this state, the fine drive is once more used to bring the tip 106 back to the contact position. Optionally, a small negative or positive offset may be used to increase or reduce the final distance between the tip 106 and the surface. Al- ternatively or in addition, the same stop criteria may be used at this stage to pre- vent unwanted contacts with particles or the like. Carl Zeiss SMT GmbH 73 The above procedure allows a fully or at least partially automatic landing of the tip 106 on the sample surface 138 or a particle 132 previously identified, acceler- ating a preparatory phase for manipulation of the surface 138 or the particle 132. It thereby greatly simplifies the approach maneuver conventionally performed under the operator’s control. At the same time, it provides a high degree of safety due to the monitoring of relevant stopping criteria in real-time, thereby avoiding unwanted hard contacts between the tip 106 and the sample 102. Fig.36 shows different images provided by an apparatus for aiding a user during particle removal according to another embodiment. As detailed above, image recording may be provided by a scanning electron mi- croscope 128 or similar imaging device. In the described embodiment, image re- cording may be provided live, i.e. in real-time while the nanomanipulator 104 is active. This generally provides good control and feedback for the operator, e.g. during particle removal. However, in case of manipulating very small surface structures of a sample 102 or during removal of very small particles 1232, the tip 106 may obscure the vision of the operator. This is depicted in the images 1260 provided by a scanning elec- tron microscope according to Figures 36 a) and b). Note that the structure fea- tures 1292 and 1294, for example line features, as well as a particle 1232 located on a surface of the sample 102 are smaller in width or diameter than the tip 106. Moreover, as detailed above, an actual contact point 1268 (i.e. actual apex 168) of the tip 106 may not lie at its outer edge (e.g., the left point in Fig.36), but some- where underneath the tip 106. That is to say, the operator may not be able to see the part of the surface 138 actually in contact with the tip 106. Moreover, when the operator moves the tip 106 to remove the particle 1232, the particle 1232 it- self may be partially or fully obscured by the tip 106 as shown in Fig.36 b). Carl Zeiss SMT GmbH 74 In order to provide the operator with better control during manipulation, an im- proved image 1260’ may be displayed on a user interface (e.g., human-machine interface 142). In one embodiment, a first mark 1268’ is shown at the position of the contact point 1268 previously determined, for example using the method for ascertaining the apex 168 described above. When the tip 106 is moved within the field of view corresponding to the image 1260, the position of the first mark 1268’ is moved in a corresponding direction to always mark the contact point 1268 as shown in Figs.36 a) to d). In the same or another embodiment, an edge detection, contrast analysis or simi- lar image processing algorithm may be used to detect the outer edge (i.e., con- tours) or shape (i.e., area) of the structures features 1292, 1294 and / or particles 1232 before the tip 106 is moved over them, i.e., before the tip 106 obscures the structures features 1292 and 1294 and / or particles 1232. Then, when the tip 106 is moved over the structures features 1292 and 1294 and / or particles 1232, their previously detected edges or contours are indicated with special marks 1232’ and 1292’, and 1294’ as shown in Figure 36 c). Alternatively, an image of the entire surface may be store (e.g., buffered) and may be used to show the entire surface physically obscured by the tip 106 as shown in Fig.36 d) by merging a segment of a stored image taken before the tip moved over the corresponding segment with a live image. In that case, the position of the tip 106 (i.e., the area comprising the image overlay) may be shown by a third mark 1206’ as also shown in Fig.36 d). Optionally, the user may choose between the output image 1260’ according to Fig. 36 c) or the output image 1260” according to Fig.36 d). Although the present invention has been described on the basis of exemplary em- bodiments, it can be modified in various ways. Carl Zeiss SMT GmbH 75 LIST OF REFERENCE SIGNS 100 Apparatus 102 Sample 104 Nanomanipulator (atomic force microscope) 106 Measuring tip 108 Cantilever 110 Positioning unit 112 End 114 End 116 Housing 118 Pump 120 Sample stage 122 Holder 124 Positioning unit 126 Sample stage device 128 Particle column 130 Particle beam 132 Defect (particle) 134 Process gas providing unit 136 Process gas 138 Surface 140 Control apparatus 142 Human-machine interface 144 Display device 146 Keyboard 148 Mouse pointer 150 Deflection detection device 152 Laser source 154 Photodetector Carl Zeiss SMT GmbH 76 156 Laser beam 158 Laser beam 160 Image 162 Structure 164 Trench 166 Substrate 168 Actual apex 170 Apparent apex 172 Surface 174 Surface 176 Region 178 Track 180 Straight line 182 Track 184 Straight line 186, 186', 186" Approach curve 188, 188', 188" Region 190, 190', 190" Material 200 Impression 204 Movement 206 Movement 208, 208' Step 210 Movement 212 Movement 214 Movement 215 Trajectory 260, 260', 260" Image 302 Sample 360 Image 362 Structures Carl Zeiss SMT GmbH 77 364 Trenches 402 Sample 438 Surface 502 Sample 532 Particle 538 Surface 602 Sample 632 Particle 702 Sample 732, 732' Particle 760, 760' Image 802 Particle 832, 832' Particle 860, 860' Image 900 Nanostructure 902 Surface 904 Actual apex 906 Raster-scan data 908 Point 910 Point 912 Image 914 Apparent apex 916 Nanostructure 918 Tip 1000 System 1001 Cantilever deflection system 1002 Frequency control system 1003 Amplitude control system 1004 Phase detector 1005 First feedback unit Carl Zeiss SMT GmbH 78 1006 Controllable oscillator 1007 Amplitude detector 1008 Second feedback unit 1009 Multiplier 1010 Excitation signal (resonant driving signal) 1011 Deflection Signal 1012 Lateral signal 1013 Phase signal 1014 Frequency control signal (frequency shift signal) 1015 Phase setpoint 1016 Amplitude signal 1017 Amplitude setpoint 1018 Oscillator output signal 1019 Amplitude feedback signal 1100 Beam deflection system 1102 Specimen 1106 Probe 1110 Excitation unit (piezo) 1152 Light source 1154 Photodiode 1206’ Mark (tip indicator) 1232 Particle 1232’ Mark (particle indicator) 1260 Image 1260’, 1260” Image 1268 Contact point 1268’ Mark (contact point indicator) 1292, 1294 Structure feature 1292’, 1294’ Mark (structure indicator) Carl Zeiss SMT GmbH 79 A, A1, A2, A3 Distance AS, AS' Distance bl Region br Region B Bending B1, B2 Brightness C1, C2, C3 Distance D Deflection D1, D2, D3, D3" Deflection DS, DS' Deflection ΔB Change in the brightness ΔF, ΔF1Change in the focus ΔFS Threshold value Δl1, Δl2Distance Δx Distance, offset Δy Offset Δz1 - Δz9 Distance E Plane G Dimension H Height Px, Py, Pz Position Px0, Py0Position R Rotation S Line-of-sight S1-S6 Method steps S1'-S6' Method steps S1"- S6" Method steps S1'''-S4''' Method steps S1""-S6"" Method steps T Removal trajectory Carl Zeiss SMT GmbH 80 ul Region ur Region x, y, z Direction x1, x2 Position x1', x2' Position xA, xE, x'E Position xG Position xNPosition xP Position y1, y2 Position y1', y2' Position yGPosition yP Position

Claims

Carl Zeiss SMT GmbH 81 CLAIMS 1. A method for landing a tip (106) of a probe (1106) of a nanomanipulator (104) on a sample (102, 1102), in particular in vacuum, the probe (1106) compris- ing a cantilever (108) and the tip (106) attached thereto, the nanomanipulator (104) further comprising an excitation unit (1110), the probe (1106) being me- chanically coupled with the excitation unit (1110), the method including the fol- lowing steps: - oscillating the probe (1106) by providing a resonant driving signal (1010) to the excitation unit (1110) while the tip (106) is not in contact with the sample (102); - reducing a first distance in a z-direction between the tip (106) and the sam- ple (102) during a first approach phase until at least one first stop condition of a first set of stop conditions is met, wherein the first set of stop conditions com- prises detecting a shift in the frequency of the resonant driving signal (1010) used during the first approach phase; and - terminating the first approach phase when the at least one first stop condi- tion of the first set of stop conditions is met, and deactivating the resonant driv- ing signal (1010).

2. The method according to Claim 1, further comprising: - further reducing the first distance during a second approach phase until at least one second stop condition of a second set of stop conditions is met, wherein the second set of stop conditions comprises detecting a deflection of the cantilever (108); and - terminating the second approach phase at a contact position when the at least one second stop condition of the second set of stop conditions is met.

3. The method according to Claim 2, wherein the location of at least one of the probe (1106) or the sample (102) are controlled in the z-direction using aCarl Zeiss SMT GmbH 82 combination of a coarse drive and a fine drive, the method further comprising performing a third approach phase, comprising: - increasing the first distance by operating the fine drive to move the tip (106) from the contact position to a partially retracted position; and - reducing or increasing the first distance by operating the coarse drive based on a second distance in the z-direction between the contact position and the partially retracted position; and - reducing the first distance by operating the fine drive to return the tip (106) to the contact position or to a predefined position at third distance in the z- direction from the contact position.

4. The method according to any one of Claims 1 to 3, further comprising: - determining at least one parameter of a resonance characteristic of the probe (1106) while the tip (106) is not in contact with the sample (102), the at least one parameter comprising at least one of a resonance frequency of the probe (1106), a Q-value of the probe (1106), and a phase angle between the resonant driving signal (1010) and a detected deflection signal (1011) associated with the oscillation of the probe (1106).

5. The method according to any one of Claims 1 to 4, wherein the first set of stop conditions comprises at least one of the following conditions: - a frequency control signal (1014) indicative of shift in the frequency of the resonant driving signal (1010) exceeding a first threshold value; - a frequency control signal (1014) indicative of shift in the frequency of the resonant driving signal (1010) lying below a second threshold value; - an amplitude feedback signal (1019) used for amplitude control of the reso- nant driving signal (1010) exceeding a third threshold value; - an amplitude feedback signal (1019) used for amplitude control of the reso- nant driving signal (1010) lying below a fourth threshold value;Carl Zeiss SMT GmbH 83 - a phase signal (1013) indicative of a relationship between the resonant driving signal (1010) and a detected oscillation of the probe (1106) exceeding a fifth threshold value and / or lying below a sixth threshold value; and / or - a driving speed in the z-direction exceeding a seventh threshold value and / or lying below an eighth threshold value.

6. The method according to Claim 5, wherein landing the probe (1106) is aborted in the first approach phase when at least one of the following conditions are met: - the frequency control signal (1014) lies below the second threshold value; - the amplitude feedback signal (1019) exceeds the third threshold value; - the phase signal (1013) exceeds the fifth threshold value and / or lies below the sixth threshold value; and / or - the driving speed exceeds the seventh threshold value and / or lies below the eighth threshold value.

7. The method according to any one of Claims 2 to 6, wherein the second set of stop conditions further comprises: - a first deflection signal (DFL) indicative of a deflection of the probe (1106) in the z-direction exceeding a first ninth threshold value; - a second deflection signal (LAT) indicative of a lateral deflection of the probe (1106) exceeding a tenth threshold value; - a sum signal (SUM) indicative of a combined deflection of the probe (1106) exceeding an eleventh threshold value; and / or - a driving speed in the z-direction exceeding a twelfth threshold value and / or lying below a thirteenth threshold value.

8. The method according to Claim 2 and 7, wherein landing the probe (1106) is aborted in the second approach phase when at least one of the following condi- tions are met:Carl Zeiss SMT GmbH 84 - the driving speed exceeds the twelfth threshold value and / or lies below the thirteenth threshold value.

9. The method according to any one of Claims 1 to 8, further comprising: - capturing a first image (1260) of a surface (138) of the sample (102), the first image comprising a least one section not obscured by the tip (106); - generating a second image (1260’, 1260’’), the second image comprising as least one section obscured by the tip (106) and at least one mark (1206’, 1232’, 1268’, 1292’, 1294’) arranged in the obscured section, indicating a position of at least one hidden element; and - displaying the second image (1260’, 1260”) on a user interface to an opera- tor of the nanomanipulator (104) during manipulation of the sample (102).

10. The method according to claim 9, wherein the at least one mark (1206’, 1232’, 1268’, 1292’, 1294’) comprises at least one of the following: - a contact point indicator (1268’) indicating a position of a contact point (1268) of the tip (106) with the sample (102); - a structure indicator (1232’, 1292’, 1294’) indicating an edge or an area of a surface feature (1292, 1294) or a particle (1232) located on the surface (138) of the sample (102); and - a tip indicator (1206’) indicating an outline of the tip (106), wherein the tip (106) is replaced in the second image by a corresponding section of the surface (138) of the sample (102) obtained from the first image (1260).

11. An apparatus (100), comprising: - a sample stage (120) for holding a sample (102); - a nanomanipulator (104) comprising a positioning unit (110) and an excita- tion unit (1110), the positioning unit (110) being configured to move a probe (1106) comprising a cantilever (108) and a tip (106) attached thereto, theCarl Zeiss SMT GmbH 85 excitation unit (1110) being configured to oscillate the probe (1106) based on a driving signal; - a cantilever deflection detection system (1001) configured for detecting de- flections of the cantilever (108); - a control loop circuitry configured to track a signal relationship between an oscillation of the cantilever (108) detected by the cantilever detection system and a driving signal provided to the excitation unit (1110); and - at least one control unit configured to perform the following steps: - driving, using the excitation unit (1110), the probe (1106) using a resonant driving signal (1010) provided by the control loop circuitry while the tip (106) is not in contact with the sample (102); - reducing, by the positioning unit, a first distance in a z-direction between the tip (106) and the sample (102) during a first approach phase until at least one first stop condition of a first set of stop conditions is met, wherein the first set of stop conditions comprises detecting a shift in the fre- quency of the resonant driving signal (1010) used during the first approach phase; and - terminating the first approach phase when the at least one first stop condition of the first set of stop conditions is met by deactivating the resonant driving signal (1010).

12. The apparatus of claim 11, wherein the control loop circuitry comprises: - a frequency control system (1002) configured to provide a first output sig- nal based on a phase of a detected oscillation of the cantilever (108) and a phase setpoint (1015); - an amplitude control system (1003) configured to provide a second output signal based on an amplitude of the detected oscillation of the cantilever (108) and an amplitude setpoint (1017); and - a multiplier (1009) configured to multiply the first output signal provided by the frequency control system (1002) with the second output signal provided byCarl Zeiss SMT GmbH 86 the amplitude control system (1003) and to provide the multiplied signal as reso- nant driving signal (1010) to the excitation unit (1110).

13. The apparatus of claim 12, wherein the frequency control system (1002) comprises a phase detector (1004) for providing a phase signal (1013), an integra- tor (1005) for providing a frequency control signal (1014), and a controllable oscil- lator (1006) for providing an oscillator output signal (1018).

14. The apparatus of claim 12 or 13, wherein the amplitude control system (1003) comprises an amplitude detector (1007) for providing an amplitude signal (1016), and a PI controller (1008) for providing an amplitude feedback signal (1019).

15. A computer program product, comprising instructions which, upon execu- tion of the program by at least one computer, cause the computer to carry out the method according to any one of claims 1 to 11.

16. Computer-implemented method for processing a sample (102) using a nano- manipulator (104) comprising a measuring tip (106) for processing the sample (102) and a positioning unit (110) for moving the measuring tip (106), wherein the sample (102) is arranged on a sample stage (120), and an x-direction (x) and a y-direction (y) of the nanomanipulator (104) are each arranged parallel to a main extension plane (E) of the sample (102) and / or sample stage (120) and perpendic- ular to one another, the method including the following steps: 1a) controlling (S1) the positioning unit (110) to move the measuring tip (106) in the y-direction (y) such that an apex (168) of the measuring tip (106) is in contact with a surface (138, 172) of a test region (176) of the sample stage (120) or sample (102), and the measuring tip (106) leaves a first track (178) on the surface (138, 172),Carl Zeiss SMT GmbH 87 1b) controlling (S4) the positioning unit (110) to move the measuring tip (106) in the x-direction (x) such that the apex (168) of the measuring tip (106) is in contact with the surface (138, 172), and the measuring tip (106) leaves a sec- ond track (182) on the surface (138, 172), 1c) controlling (S2, S5) an image recording device (128) to record at least one image (260, 260', 260") of the test region (176) in each case, the first and the sec- ond track (178, 182) being at least partially captured accordingly therein, and 1d) ascertaining (S3, S6) an x-position (x1, x1') of the apex (168) of the meas- uring tip (106) in relation to the x-direction on the basis of the first track (178) captured in the at least one image (260') and ascertaining a y-position (y1, y1') of the apex (168) of the measuring tip (106) in relation to the y-direction on the ba- sis of the second track (182) captured in the at least one image (260").

17. Method according to Claim 16, wherein the nanomanipulator (104) com- prises a cantilever (108) having a base end (112) and a free end (114); the meas- uring tip (106) is arranged on the free end (114) of the cantilever (108); at its base end (112), the cantilever (108) is secured to the positioning unit (110) so as to be movable; and the positioning unit (110) is controlled to move the base end (112) of the cantilever (108) such that the measuring tip (106) is moved.

18. Method according to Claim 16 or 17, wherein the x-position (x1, x1') and the y-position (y1, y1') of the apex (168) of the measuring tip (106) are ascertained by accordingly fitting a respective straight line (180, 184) to the first and the second track (178, 182) captured in the image (260', 260").

19. Method according to any of Claims 16 to 18, wherein the measuring tip (106) is at least partially captured in the at least one image (260, 260', 260"), a lateral position (x2, y2) of an apparent apex (170) of the measuring tip (106) in the at least one image (260, 260', 260") deviates from a lateral position (x1, y1) of an actual apex (168) of the measuring tip (106) in the at least one image (260,Carl Zeiss SMT GmbH 88 260', 260") and the lateral position (x1, y1) of the actual apex (168) of the measur- ing tip (106) is ascertained relative to the lateral position (x2, y2) of the apparent apex (170) of the measuring tip (106) in the at least one image (260, 260', 260").

20. Method according to any of Claims 17 to 19, wherein the lateral position (x1, y1) of the actual apex (168) of the measuring tip (106) is ascertained relative to a lateral position (x2, y2) of the base end (112) of the cantilever (108).

21. Method according to any of Claims 17 to 20, wherein the nanomanipulator (104) comprises a deflection detection device (150) for detecting a deflection (D) of the free end (114) of the cantilever (108) in a z-direction (z) which is arranged perpendicular to the x- and the y-direction (x, y) and which points away from the sample (102, 302), and wherein the method includes the following steps: 6a) controlling (S1') the positioning unit (110) to move the base end (112) of the cantilever (108) in the negative z-direction (z) such that the measuring tip (106) is made to approach to the sample (302) in a test region (188) of the sample (302), 6b) repeatedly receiving (S2'), from the deflection detection device (150), an extent (D1, D2, Dmax) of the deflection (D) of the free end (114) of the cantilever (108) in the z-direction (z), depending on a z-position (Pz) of the base end (112) of the cantilever (108), 6c) ascertaining (S3') an approach curve (186) which contains the extent (D1, D2, Dmax) of the deflection (D) of the free end (114) of the cantilever (108) as a function of the z-position (Pz) of the base end (112) of the cantilever (108), 6d) receiving (S4') at least one image (360) of the sample (302), the test re- gion (188) being at least partially captured therein, 6e) ascertaining (S5') whether the sample (302) is damaged in the test re- gion (188) using the at least one received image (360) as a basis, and 6f) storing (S6') a maximum deflection the approach curve (186) asa safe maximum deflection (DS) of the free end (114) of the cantilever (108)Carl Zeiss SMT GmbH 89 should the sample (302) be ascertained as being undamaged in the test region (188).

22. Method according to Claim 21, wherein: a plurality of approach curves (186, 186', 186") are ascertained on the basis of a plurality of in each case different test regions (188, 188', 188") which differ from one another in terms of a type of material (190, 190', 190") of the respective test region (188, 188', 188"), at least one image (360) is received, in which the plurality of test regions (188, 188', 188") are at least partially captured, for each ascertained approach curve (186, 186', 186"), there is an ascertain- ment as to whether the sample (302) is damaged in the respective test region (188, 188', 188") using the at least one received image (360) as a basis, and a maximum deflection (Dmax, Dmax') of the respective approach curve (186, 186') is stored as a safe maximum deflection (DS, DS') of the free end (114) of the cantilever (108), as a function of the corresponding material (190, 190') of the re- spective test region (188, 188'), should the sample (302) be ascertained as being undamaged in the respective test region (186, 186').

23. Method according to any of Claims 16 to 22, wherein: the nanomanipulator (104) preferably comprises a sample stage device (126) having a mount (122), a sample stage (120) arranged movably on the mount (122) and a further positioning unit (124) for moving the sample stage (120) relative to the mount (122), and the method includes: 8a) controlling the positioning unit (110) to move the measuring tip (106) in the negative z-direction (z) such that the measuring tip (106) is brought into contact with the sample (402), and 8b) controlling the positioning unit (110) and / or the further position- ing unit (124) to move the measuring tip (106) and / or the sample (402) arrangedCarl Zeiss SMT GmbH 90 on the sample stage (120) such that the measuring tip (106) and the sample (402) are brought to a predetermined distance (Δz2) from one another.

24. Method according to any of Claims 16 to 23, including: 9a) providing (S1") a removal trajectory (T) for removing a particle (532) ar- ranged on the sample (502), wherein the removal trajectory (T) lies in an xy- plane (E) that is spanned by the x- and the y-direction (x, y) and intersects an x- and y-position (xP, yP) of the particle (532), 9b) controlling (S2") the positioning unit (110) to position the measuring tip (106) at a first predetermined z-distance (Δz3) from the sample (502) in relation to the z-direction (z), 9c) controlling (S3") the positioning unit (110) to laterally move the measur- ing tip (106) along the ascertained removal trajectory (T) and at the first prede- termined z-distance (Δz3) from the sample (502), and 9d) controlling (S4") the positioning unit (110) to move the measuring tip (106) away from the sample (502) in the positive z-direction (z), 9e) ascertaining (S5") as to whether the particle (532) adheres to the meas- uring tip (106), and 9f) repeating (S6") steps 9b) to 9e) for one or more further predetermined z- distances (Δz4, Δz5, Δz6, Δz7) which are increasingly smaller than the first prede- termined z-distance (Δz3), until the particle (532) is ascertained as adhering to the measuring tip (106), wherein steps 9b) to 9f) are carried out fully automatically.

25. Method according to Claim 24, wherein step 9c) includes: controlling the positioning unit (110) to laterally move the measuring tip (106) along the ascertained removal trajectory (T) in steps (208) of a first prede- termined lateral distance (Δl1) and preferably in steps (208') of one or more fur- ther predetermined lateral distances (Δl2), which are increasingly greater than the first predetermined lateral distance (Δl1).Carl Zeiss SMT GmbH 91 26. Method according to any of Claims 16 to 25, including: 12a) controlling the positioning unit (110) to laterally move (210) the meas- uring tip (106) in the direction of a particle (632) arranged on the sample (602), 12b) ascertaining as to whether the particle (632) adheres to the measuring tip (106), 12c) controlling the positioning unit (110) to move (212) the measuring tip (106) away from the sample (602) in the positive z-direction (z) and / or to move the measuring tip (106) along a curved trajectory (214), which in the region of the particle (632) curves from an initially lateral movement into a movement in the positive z-direction (z), should the particle (632) be ascertained as adhering to the measuring tip (106), wherein steps 12a) to 12c) are performed fully automatically.

27. Method according to any of Claims 17 to 26, including: controlling the positioning unit (110) to move the measuring tip (106) in the lateral direction (x, y) and / or in the positive z-direction (z) in order to pick up a particle arranged on the sample (132) using the measuring tip (106), ascertaining as to whether the particle (132) adheres to the measuring tip (106) on the basis of: an extent of a deflection of the cantilever (108) in a lateral direction (x, y) received from a deflection detection device (150), a plurality of received images (760, 760') of at least one part of the sample (702), the images capturing the particle (732, 732'), and a change in the brightness (ΔB) of the particle (732, 732') and / or a change in the contrast of the particle (732, 732') relative to the measuring tip (106) in the plurality of images (760, 760'), as ascertained by means of image processing, a plurality of images (860, 860') of at least one part of the sample (802), the images being received from an image recording device (128) and cap- turing the particle (832, 832'), and a migration of the particle (832, 832') out of aCarl Zeiss SMT GmbH 92 fixedly set focus of the image recording device (128), as ascertained by means of image processing of the plurality of images (860, 860'), and / or information that is received from an image recording device (128) which records images (160) of at least one part of the sample (102), in which the particle (132) is captured, with an autofocus setting focused on the particle (132) and that relates to an extent (ΔF1) of an automatic adjustment (ΔF) of the autofo- cus focused on the particle (132), the adjustment being greater than a predeter- mined threshold value (ΔFS).

28. Method according to any of Claims 16 to 27, wherein: the nanomanipulator (104) comprises a sample stage device (126) having a mount (122), a sample stage (120) arranged on the mount (122) so as to be later- ally movable and a further positioning unit (124) for laterally moving the sample stage (120) relative to the mount (122) in the x- and the y-direction (x, y), and the method includes: 14a) controlling (S1''') the positioning unit (110) to position the measuring tip (106) in a lateral initial position (Px0, Py0), preset in the position- ing unit (110), in relation to the x- and the y-direction (x, y), 14b) receiving (S2''') at least one image (160) of the sample (102) in which a particle (132) arranged on the sample (102) is captured, 14c) ascertaining (S3'''), on the basis of image processing, a lateral position (xP, yP) of the particle (132) captured in the at least one image (160), and 14d) controlling (S4''') the further positioning unit (124) to laterally move the sample stage (120) with the sample (102), in such a way that the lateral position (xP, yP) of the particle (132) corresponds to the lateral initial position (Px0, Py0) of the measuring tip (106) in relation to the x- and the y-direction (x, y), and steps 14a) to 14d) are carried out fully automatically.

29. Apparatus (100) for processing a sample (102), comprising:Carl Zeiss SMT GmbH 93 a nanomanipulator (104) having a measuring tip (106) for processing the sample (102) and a positioning unit (110) for moving the measuring tip (106), a sample stage (120) for arrangement of the sample (102), wherein an x-di- rection (x) and a y-direction (y) of the nanomanipulator (104) are each arranged parallel to a main extension plane (E) of the sample (102) and / or sample stage (120) and perpendicular to one another, and a control apparatus (140) configured to carry out the method according to any of Claims 16 to 28.

Images