WO2008037427A1 - Procédé et dispositif pour l'analyse résolue localement des propriétés élastiques d'un échantillon au moyen d'un microscope à force atomique - Google Patents

Procédé et dispositif pour l'analyse résolue localement des propriétés élastiques d'un échantillon au moyen d'un microscope à force atomique Download PDF

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Publication number
WO2008037427A1
WO2008037427A1 PCT/EP2007/008324 EP2007008324W WO2008037427A1 WO 2008037427 A1 WO2008037427 A1 WO 2008037427A1 EP 2007008324 W EP2007008324 W EP 2007008324W WO 2008037427 A1 WO2008037427 A1 WO 2008037427A1
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Prior art keywords
sample
afm
tip
contact
force
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PCT/EP2007/008324
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German (de)
English (en)
Inventor
Tilman E. SCHÄFFER
Felix Danckwerts
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Westfälische Wilhelms-Universität Münster
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Publication of WO2008037427A1 publication Critical patent/WO2008037427A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
    • G01Q60/00—Particular types of SPM [Scanning Probe Microscopy] or microscopes; Essential components thereof
    • G01Q60/24—AFM [Atomic Force Microscopy] or apparatus therefor, e.g. AFM probes
    • G01Q60/26—Friction force microscopy
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
    • G01Q20/00—Monitoring the movement or position of the probe
    • G01Q20/02—Monitoring the movement or position of the probe by optical means

Definitions

  • the present invention relates to a method and a device for the spatially resolved examination of the elastic properties of a sample with an atomic force microscope (hereinafter referred to as AFM, Atomic Force Microscope).
  • AFM Atomic Force Microscope
  • the AFM was developed in 1986 by Gerd Binnig, Calvin Quate and Christoph Gerber and is used for the mechanical scanning of surfaces on the nanometer scale.
  • the AFM has a beam, sometimes referred to as a leaf spring or cantilever, which is attached at one end to a beam holder that can be adjusted by piezo actuator elements relative to a sample.
  • beam is not intended to imply any limitation on its form.
  • prior art triangular cantilevers are used, which are also referred to as "bars" in the context of the present specification.
  • At the free end of the beam is a point or needle that is perpendicular to the beam and facing the sample.
  • the tip is scanned over the sample.
  • the plane in which the sample is located is usually called the X-Y plane.
  • the distance between the tip and the sample is modulated by a relative movement in the Z direction.
  • the beam bends depending on the pressing force. The bending of the beam is in turn detected by the deflection of a laser beam reflected from the beam.
  • contact mode An important mode of operation of the AFM is the so-called contact mode.
  • contact mode the tip and sample are always in contact while the tip is scanned over the sample.
  • the deflection of the beam as described above is observed by the deflection of a laser beam reflected by this.
  • the first is the so-called constant-force mode, in which the bending of the beam and thus the force that the beam exerts on the probe over the tip is kept constant via a control loop during the screening.
  • the relative movement between the AFM and The sample required to keep the force constant is recorded.
  • the Z-component corresponds to the relative movement of the height of the sample at a point which is characterized by the associated coordinates X and Y.
  • the second sub-mode is the so-called constant-altitude mode.
  • Constant Height mode the Z position of the AFM (more precisely, the holder of the bar) is kept constant in the X and Y directions when it is scanned. In this movement, the beam is bent more or less in dependence on the height of the sample, so that it can be concluded from the deflection of the reflected laser beam on the height of the sample.
  • the piezo actuator will cause the beam to vibrate in the Z direction at a frequency that is at or near the resonant frequency of the beam when it is not interacting with the sample.
  • the average tip-sample distance is chosen so that the tip only touches the sample for a small fraction of the oscillation cycle of the beam. This significantly reduces lateral forces during scanning compared to the contact mode, which is especially important when examining soft samples that may be deformed or damaged in contact mode.
  • the amplitude of the oscillation is strongly dependent on the distance between the rest position of the beam and the sample. Therefore, the topography can be determined in a similar manner as in the contact mode, except that the amplitude of the vibration is substituted for the bending of the beam.
  • This angle causes the tip to slide toward the free end thereof upon contact of the specimen in the longitudinal direction of the beam and to slide toward the beam retainer as the tip is removed from the specimen in the longitudinal direction of the AFM beam.
  • the sliding friction thereby causes the beam when contacting the tip with the sample undergoes a kink or Buckelverformung (so-called "Bückling") and during the removal of the tip of the sample stronger or at least otherwise bent, as it would be the case with a smooth surface ,
  • AFMs have been used in the prior art to measure individual components of local contact stiffness.
  • Contact stiffness refers to the force required per unit displacement required to compress or deform an elastic contact in a particular direction.
  • the contact stiffness is thus essentially the "spring constant" of the contact.
  • the contact stiffness of a contact between the tip and the sample in the Z direction is given by dF / dz, where F is the force with which the tip is pressed into the sample, and z is the elastic penetration depth.
  • This contact stiffness in the vertical direction thus depends on the Young's modulus (or its vertical component) of the sample.
  • the contact stiffness initially only reflects this property indirectly, since the size of the contact stiffness naturally includes the shape of the tip, the size of the contact surface, etc., as well as the Young's modulus.
  • Contact stiffnesses in the vertical, ie Z-direction were measured in different ways with the aid of an AFM. For example, in Yuekan Jiao and Tilman E.
  • lateral contact stiffnesses were measured in the prior art, ie contact stiffness in the sample plane in a direction transverse to the longitudinal axis of the AFM beam. Such measurements are in Carpick RW, Ogletree DF and Salmeron M., Appl. Phy. Lett. 70 (12), 24 March 1997, "Lateral stiffhess: A new nanomechanical measurement for the determination of shear strength with friction force microscopy "and Ca ⁇ ick RW and Eriksson MA, MRS BULLETIN / JuIy 2004,” Measurements of In-Plane Material Properties with Scanning Probe Microscopy "using a suitable model for tip-to-tip interaction and sample may be closed by the lateral contact stiffness on the lateral shear modulus component.
  • the present invention is therefore based on the object of specifying a method and a device for the spatially resolved examination of the elastic properties of a sample with the aid of an AFM. This object is achieved by a method having the features of claim 1 and by a device according to claim 20. Advantageous developments are specified in the dependent claims.
  • the method according to the invention comprises the following steps:
  • a moving an AFM tip to a position above a sample point on the sample B Approaching the AFM tip to the sample site and determining a component of the
  • the physical parameters associated with the contact stiffness may be the Young's modulus for the direction vertical to the sample surface (Z-direction) and two shear modulus components in the sample plane.
  • the AFM tip is approximated to the sample along the first direction so as to depress the sample, with movement of the AFM tip with respect to the sample fixed coordinate system and a force acting on the tip. to be recorded.
  • the "sample-fixed coordinate system” is a reference system which is stationary, for example, with respect to the center of gravity of the sample or with respect to a sample holder.
  • the relative motion of the AFM tip with respect to the sample-fixed coordinate system is indicative of the deformation of a portion of the sample in contact with the tip.
  • the contact rigidity in the first direction can be calculated from the force acting on the AFM tip and the movement of the AFM tip relative to the sample-fixed coordinate system.
  • step B the AFM tip is brought into contact with the sample at the sample site, and the relative movement between the beam holder and the sample is superimposed on a vibration along the first direction. This allows a measurement of the contact stiffness in the first direction in the above-described Isocompliance Force Modulation mode.
  • the height of the sample is determined at the respective sample point.
  • the method according to this development in addition to a "map" of the elasticity properties of the sample at the same time also determines the topography of the sample. This allows the sample to be characterized very widely in a single run of the process.
  • step C and / or in step D the AFM tip is moved along the second or third direction, wherein the movement of the AFM tip with respect to the sample-fixed coordinate system and a force acting on the AFM tip, to be recorded.
  • the contact stiffness in the second and / or third direction can then be determined from the force-movement curve obtained, as will be explained in more detail below with reference to an exemplary embodiment. Further, steps C and D may be performed several times in succession.
  • the AFM during the steps C and D along the first direction with respect to the sample is adjusted so that a predetermined penetration depth of the AFM tip into the sample and / or a predetermined force in the first direction results, which acts on the top.
  • a force in the vertical direction leads, in a known manner, to bending of the AFM beam, which can be detected optically with the aid of a reflected laser beam.
  • a force transverse to the longitudinal direction of the beam results in a torsion of the beam about its longitudinal axis, that is to say a deformation which is substantially perpendicular to the deformation of the bending of the beam. Therefore, the signals resulting from these two deformations are substantially decoupled.
  • the AFM tip is moved so little in steps B and C that it adheres to the sample during the movement. This means that the movement is carried out only in the static friction region, but not in the sliding friction region. This has the advantage, among other things, that all three components of the contact stiffness are actually recorded at the exact same sample site.
  • the sample and the AFM can be adjusted relative to each other by piezoelectric elements, it is understood that this relative movement is not identical to the relative movement of the AFM tip relative to the sample-fixed coordinate system, since the AFM beam which lies between the beam holder and the top can deform.
  • the device In order to determine the location of the AFM tip with respect to the sample-fixed coordinate system, the device must first be calibrated in a certain way. In an advantageous development, this is done by a curve of the force is determined as a function of the relative position of the sample and holding the AFM beam and compared with a corresponding curve, which was obtained with a reference sample whose contact stiffness, the contact stiffness of the sample essential, in particular exceeds by more than five times. This will be explained below with reference to an embodiment. Alternatively, a reference sample with a well-known contact stiffness can be used.
  • the force acting on the tip is determined from the signal from at least one detector that receives laser light reflected at a first location from the AFM beam.
  • a second laser is provided, whose beam is directed to a second position of the AFM beam, which is offset from the first position in the longitudinal direction of the AFM beam, and a second sensor is provided, that of the second location reflected laser light receives.
  • the shape of the bar can be determined.
  • its shape can be determined very accurately by the measurements of the two detectors. This makes it possible in particular to calculate the three-dimensional movement of the AFM tip. In particular, this allows a decoupling of the measurement of the vertical component of the contact stiffness and the horizontal component of the contact stiffness in the longitudinal direction of the AFM beam.
  • the first direction can be perpendicular to the sample plane. Alternatively, however, the first direction may also be parallel to the AFM tip, which, as described above, typically deviates by 10 ° to 20 ° from the normal to the sample plane. If the first direction is parallel to the tip of the AFM, there will be no horizontal forces in the longitudinal direction of the AFM beam when the tip hits the sample. This facilitates the interpretation of the measured signals.
  • the second direction corresponds to the longitudinal direction and the third direction corresponds to the transverse direction of the AFM beam.
  • step D which in this case corresponds to the measurement of the contact stiffness in the direction transverse to the AFM beam
  • the AFM beam is set in torsional resonance while the AFM tip is in contact with the sample.
  • the corresponding component of the contact stiffness can then be determined from a change in the resonant frequency and / or the amplitude and / or the phase of the torsional vibration as compared to the case where the AFM tip is removed from the sample.
  • Fig. 1 is a schematic representation of an infinitesimal volume element and its voltage components
  • FIG. 5 is a perspective view of a sample, an AFM beam and an AFM
  • Fig. 6 shows a schematic perspective view of the deformation of a sample and a
  • AFM beams as a result of a vertical force
  • FIG. 7 schematically shows the deformation of a sample and an AFM beam due to a horizontal force transverse to the longitudinal direction of the AFM beam
  • Fig. 8 schematically shows a force-displacement curve for the approach of an AFM tip to a very stiff sample (solid line) and to a compliant sample (dashed line);
  • Linear elasticity of a body means that there is a linear relationship between tension and strain, and that deformation of a body occurs instantaneously with its load and remains constant until the body is relieved, whereupon it assumes its initial shape. This is true for many solids at not too high voltages and not too fast loading and unloading processes.
  • FIG. 1 an infinitesimal cube-shaped volume element of a condensed matter is shown.
  • P 1 , P 2 and P 3 designate the forces per unit area acting on the three cube faces shown.
  • the forces Pi, P 2 and P 3 are vectors whose components are denoted as follows:
  • the following also describes the six independent components of the technical elongation, which differ somewhat from the tensor components of elongation, but are easier to work with because they simplify the relationship between stress and strain versus tensor rotation.
  • the absolute Displacement or rotation of a volume element is not relevant. We are only interested in the displacement of one point relative to neighboring points.
  • the first three components of the technical voltage xx e, designated ⁇ yy, e z2, representing the relative expansion or compression of the infinitesimal volume element of Fig. 1 schematically in the spatial directions X, Y, Z, as shown in Fig. 3 for the Case e yy is shown.
  • the second three components e yz , e zx and e xy of the technical strain represent the shear strains of the infinitesimal volume element of FIG. 1 in the planes YZ, ZX and XY, of which the component e xy is shown by way of example in FIG.
  • the generalized Hooke's law states that there is a linear relationship between stress and strain, i. It is assumed that each of the six independent stress components is linearly related to the six components of the technical strain, and vice versa. To simplify the notation, we replace the indices as follows: xx by 1, yy by 2, zz by 3, yz by 4, xz by 5, and xy by 6.
  • the generalized Hook's law can then be written as follows:
  • p, q 1, 2, ... 6, and it is summed according to the Einstein'schen sum convention over identical indices.
  • the 36 constants c pq are called stiffness constants, while the 36 constants s pq are called compliance or compliance constants.
  • Gk ffk / e k .
  • the six independent stress components and the 36 compliance constants s pq are known at a particular point in a body, one can calculate the six components of the technical strain and thus the deformation of the infinitesimal volume sweep element that surrounds that point by plotting the values in the above generalized Hook's law will be used. If you have the six independent of voltage components and some of the six components of the technical strain, some of the compliance constants can be determined, such as the Young's modulus Ej mentioned above or the shear modulus G k . Since the matrix s pq is symmetric, there are a maximum of 21 independent compliance constants. In the case of an isotropic material, there are only two independent compliance constants.
  • FIG. 4 shows a device 10 for the spatially resolved examination of the elastic properties of a sample 12.
  • the apparatus 10 includes an AFM 14 having an AFM beam or cantilever 16 supported on a beam holder 18. At the free end of the beam 16, a tip 20 is attached.
  • the beam 16 is at an angle of about 10 ° to the plane of the sample 12.
  • the tip 20 is perpendicular to the beam 16 and thus also at an angle of about 10 ° to the normal to the sample plane.
  • the sample 12 lies in the XY plane, and this plane is also referred to as a horizontal plane.
  • the vertical direction is called the Z direction.
  • the Y direction corresponds to the direction of the longitudinal axis of the beam 16, i. more precisely, the direction of projection of the longitudinal axis of the beam 16 onto the sample plane.
  • the beam holder 18 is attached to a Z-piezo element 22, with which it can be moved in the Z direction.
  • the Z piezo element 22 is connected to an XY scanner 24, with which the beam holder 18 can be moved together with the beam 16 and the tip 20 in the X and Y directions.
  • the Z piezo element 22 and the XY scanner 24 are connected via signal lines 26 to a control device 28, which controls the said elements. Furthermore, the apparatus 10 comprises a first laser 30, the beam of which is focused on a first point 32 of the beam 16, which is located near the free end of the beam 16. From this first point 32, the laser beam is reflected and detected by a detector 34, which is formed in the illustrated embodiment by a four-quadrant optical position sensor.
  • a second laser 36 is provided, whose light is focused on a second position 38 on the beam 16, which lies in the middle third of the beam 16. From this second At point 38, the light from the second laser 36 is reflected to a second detector 40, which is also formed by a four-quadrant optical position sensor.
  • the detectors 34 and 40 are also connected via signal lines 26 to the control unit 28.
  • an output device 42 which may, for example, be a screen, is connected to the control unit 28 via a signal line 26.
  • a step A the AFM tip 20 is moved to a position above a sample point on the sample 12 to be examined. This movement is done with the XY scanner 24, which is controlled by the control unit 28 in a suitable manner.
  • step B the bar holder 18 is lowered by actuation of the Z piezo element 22 by a distance ⁇ z c .
  • FIG. 5 shows an enlarged section of the sample 12 of the beam 16 and the tip 20.
  • the tip 20 comes in contact with the sample 12, and it presses the sample at the sample point, as shown schematically in Fig. 6.
  • the Z-directional distance traversing the tip 20 between the first contact with the surface of the sample 12 and the depressed position shown in Fig. 6 is referred to as ⁇ z.
  • a force .DELTA.F Z is required, which is shown in Fig. 6 by a force arrow.
  • This force .DELTA.F Z leads to a bending of the beam 16 and thus a deflection of the beams from the laser 30 and 36, which is detected at the detectors 34 and 40th Based on the signals of the detectors 34 and 40, the control unit 28 can calculate the force .DELTA.F 2 .
  • step B the height d.z of the sample 12 is measured.
  • step C the Z position of the beam holder 18 is adjusted so that the tip 20 is pressed against the surface of the sample 12 with a predetermined force. Then, the beam holder 18 is reciprocated by means of the XY scanner 24 in the Y direction by deflection - ⁇ y c and + .DELTA.y c , wherein the movement of the tip 20 relative to the sample 12 and the change of the force .DELTA.F y on the tip 20 acts, is measured.
  • ⁇ y describes a displacement relative to a sample-fixed coordinate system which, for example, is stationary relative to the center of gravity of the sample or a sample holder (not shown). Because the sample 12 itself moves to the sample site by static friction in common with the tip 20. Also in the step C, the movement of the tip Dy are recorded relative to the sample-fixed coordinate system and the force .DELTA.F y, and out of them as described above, the Y component the contact stiffness k contact ⁇ calculated.
  • step D the bar holder 18 is moved back and forth in the X direction with the aid of the XY scanner 24.
  • the movement ⁇ x of the tip relative to the sample-fixed coordinate system and the force ⁇ F X acting on the tip 20 in the X direction are recorded.
  • the contact stiffness in the X direction, kcontatc.x is then calculated from ⁇ F X and ⁇ x.
  • FIG. 7 shows a snapshot during method step D, in which the elongation of the sample 12 in the X direction at the contact point can be seen.
  • the force .DELTA.F X passes in the X direction to a torsion of the bar 16.
  • the deflection of the laser light resulting from the torsion of the bar 16 is, therefore, perpendicular to the deflection, which is characterized by a Bending of the beam 16 as a result of the force .DELTA.F Z results. Therefore, one can distinguish between ⁇ F X and ⁇ F Z and measure both forces with a single four-quadrant detector 34.
  • the situation is more difficult in the measurement of the contact stiffness in the Y direction in step C.
  • the force ⁇ F y leads, in particular, to humping of the beam 16, and the corresponding light signal can not initially be distinguished from a light signal due to a force ⁇ F Z.
  • the tip 20 is moved to a defined Z position at the beginning of step C, for example in accordance with a predetermined force ⁇ F Z (or a predetermined penetration depth ⁇ z)
  • the subsequent changes in the signals of the reflected laser light may be due to movement due to deflection be returned in the Y direction, in particular on a humpback of the beam 16.
  • the second laser detector pair 36, 40 is also provided.
  • displacement of the beam holder 18 in a spatial direction results not only in movement of the tip (when in contact with the sample) in this spatial direction, but also in a generally much smaller movement into others Spaces can lead.
  • an adjustment of the beam holder by .DELTA.y c in addition to a movement of the tip by .DELTA.Y in the Y direction also lead to a movement by .DELTA.x and .DELTA.z in the other two spatial directions. Using two lasers, these movements can be measured.
  • Steps C and D are repeated several times, i. the tip is moved back and forth crosswise several times.
  • steps A to D are then repeated for a large number of sample points, for example for a blanket grid of the sample.
  • the three components of the contact rigidity are output to the output device 42 together with the height of the sample.
  • a topographical map of the sample and three maps showing the respective component of the contact stiffness can then be output.
  • they can also be calculated and output using a suitable model of the Young's modulus E 3 and the shear moduli G 4 and G 5 , as defined above, which are characteristic of the shape the tip is 20 independent material properties.
  • Fig. 8 two curves of the force .DELTA.F Z over the deflection of the Z-piezo element 14 when approaching the tip 20 to the sample 12 are shown.
  • the solid curve shows measurement results obtained with an "infinitely" stiff sample.
  • the "infinitely” stiff sample is a sample that is at least much harder than the sample at which the Elasticity measurements should be performed.
  • the dashed line corresponds to the measurement results of the actual sample to be examined.
  • the dashed line in Fig. 8 shows the force-displacement curve for a compliant sample.
  • the dashed curve was shifted so that the contact point is at the same z-value Zh as in the solid reference curve.
  • the dashed curve for Z values increases sharply as Z h , not quite as strong as the solid curve.
  • FIG. 9 shows a friction cycle for the X-direction, which may occur, for example, in the above-mentioned step D.
  • the movement ⁇ x c of the beam holder 18 in the X direction and the ordinate the change of the force ⁇ F X in the X direction are shown on the abscissa.
  • the beam holder 18 is in a home position in which no force acts on the tip 20 in the X direction.
  • portion A of the cycle the beam holder 18 is moved in the positive X direction, and with it, to a lesser extent, the tip 20, which is in contact with the surface of the sample 12, entrains and thereby stretches.
  • the bar 16 is rotated as shown in Fig.
  • the adhesive sections A, C and E can be used to determine the contact stiffness.
  • the sliding sections B, D and F can be used to study the friction properties of the sample.
  • the tip wears during the friction portions of the friction cycle that the sample may be damaged, and that different adhesive portions such as the adhesive portions C and E in which the contact rigidities can be measured are not accurately related to the same sample site ,
  • the movements .DELTA.y c and .DELTA.x c in the above process steps C and D can be kept so small that it does not come to a sliding movement, but that the tip is continuously in contact with the sample 12 at the sample site.
  • process steps B, C and D can all be performed at one and the same location of the sample 12 without the contact between the tip 20 and the sample 12 occurring during or between the steps will be annulled.
  • the spatial resolution of the measurement of the elastic properties becomes extremely high.
  • step B the dependence of the contact stiffness on the frequency or speed with which the force curves are recorded in steps B, C and D in order to investigate the viscoelastic behavior of the sample surface.
  • the radius of the tip 20 could be increased to investigate how the sample is to have larger static or dynamic. Friction forces respond.
  • step B the AFM tip could be brought into contact with the sample 12 at the sample site and the relative movement between the beam holder 18 and the sample 12 could be superimposed with a Z-directional vibration.
  • the AFM could be operated in the Isocompliance Force Modulation mode described above by keeping constant the amount of change in the bending angle of the beam during each cycle to determine the Z component of the contact stiffness.
  • an oscillation in the X, Y and / or Z direction could be superimposed. The vibration can be generated by movement of the beam or sample.
  • the beam 16 may be torsionally resonated in step D while the tip 20 is in contact with the sample 12.
  • the contact stiffness k CO ntact, x in the X direction can then be determined from a change in the resonance frequency, the amplitude of the torsional vibration and / or the phase as compared to the case in which the tip 20 is removed from the sample 12.
  • Control unit first laser first reflection point first detector second laser second reflection point second detector

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Abstract

L'invention concerne un procédé pour l'analyse résolue localement des propriétés élastiques d'un échantillon, ledit procédé comprenant les étapes suivantes: A) déplacement d'une pointe (20) d'un microscope à force atomique (AFM) dans une position située au-dessus d'un emplacement d'échantillon (12); B) rapprochement de la pointe (20) d'AFM vers l'emplacement d'échantillon et détermination d'un composant de la rigidité de contact dans un premier sens, déviant de la verticale du plan d'échantillon de 20° maximum; C) détermination de la rigidité de contact sur l'emplacement d'échantillon dans un deuxième sens parallèle au plan d'échantillon; et D) détermination d'un composant de la rigidité de contact sur l'emplacement d'échantillon dans un troisième sens parallèle au plan d'échantillon mais différent du deuxième sens. Les étapes A à D sont répétées pour une pluralité d'emplacements d'échantillons et la rigidité de contact et/ou les variables physiques sont indiquées pour chaque emplacement d'échantillon.
PCT/EP2007/008324 2006-09-27 2007-09-25 Procédé et dispositif pour l'analyse résolue localement des propriétés élastiques d'un échantillon au moyen d'un microscope à force atomique WO2008037427A1 (fr)

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