Caliber, method of manufacturing a caliber and method of calibrating an atomic force microscope

Abstract

The present document relates to a gauge (20) of an atomic force microscope comprising: a generally planar substrate (21), comprising at least one groove (22) comprising at least a first (23) and at least a second (24) surface facing each other, the surfaces (23, 24) of the groove (22) having isotropic properties and having a homogeneous and identical coefficient of friction, said groove (22) having at least two slopes (25, 26) formed respectively by a first angle (θ) between the first face and the normal (27) to the substrate (21), and a second angle (θ) formed between the second face and the normal (27) to the substrate (21), the two angles (θ) being symmetrical with respect to the normal and the absolute values of said angles being equal two by two. Abstract figure: Figure 5

Description

Title of the invention: Caliber, method of manufacturing a caliber and method of calibrating an atomic force microscope Technical field

[0001] The present disclosure relates to the field of atomic force microscopes and more specifically to methods of calibration, manufacturing of a caliber and calibers. Prior art

[0002] The Atomic Force Microscope, also called AFM, is an essential tool for characterizing surfaces at the nanometric scale for all major classes of materials, including metal alloys, plastics and polymers, ceramics, and even biological materials, and this in different environments.

[0003] As illustrated in [Fig.l], the general principle of AFM is based on a measurement of the interaction forces between a surface of a sample 1 to be studied and a tip 2, one end of which is assimilated to a sphere, at the apex of said tip. The measurement of the interaction forces is based on the determination of the deflection of a microlever 3 on which said tip 2 is mounted. This deflection is evaluated thanks to the deflection of a laser beam 4 reflected at the end of said microlever 3. A photodiode dial 5, also called PhotoSensitive Detector or PSD 5, makes it possible to estimate a position of the reflected laser beam. This PSD 5 dial has horizontal x and vertical y axes graduated in Volts. The value of the position of the laser spot measured in Volts along the y axis, also called the 'A-B' signal, is directly related to the value of the vertical deflection of the microlever 3.

[0004] To obtain a topographic image, a servo system 6 makes it possible to maintain constant the deflection of the microlever 3 measured by the PSD dial 5, during the scanning of the sample 1 by said tip 2. The sample 1 rests on a sample holder 7 and actuators 8 or piezoelectric ceramics are located under this sample holder or at the level of the tip support and are connected to the servo system 6. The resolution of the topographic images is generally limited by the radius of curvature of the tip, typically between 2 and 40 nm, i.e. a resolution of a few nm and can reach, in the best case, atomic resolution. In parallel with the topographic imaging modes, a multitude of AFM modes quantitatively measuring a whole series of properties such as adhesion, magnetic, electrostatic, friction forces, electrical or thermal conductivity with a very high resolution, has been developed.

[0005] In particular, the measurement of friction forces by AFM contributes to a better understanding of the elementary phenomena responsible for friction. To carry out quantitative measurements, one of the main difficulties encountered in this field is the calibration of friction forces. This calibration consists of determining a conversion factor to convert the voltages measured in Volts measured by the PSD into a friction force value measured in Newtons.

[0006] In operation, an interaction force of direction normal to the plane defined by the X and Y axes of the microlever 3 generates a vertical deflection of the microlever 3 measured by a vertical deflection of the laser beam 4 reflected at the end of the microlever 3 on the PSD dial 5, also called the 'A-B' signal along the y axis. In addition, the friction forces generate a torsion of the microlever 3 which is measured by a lateral deflection along the x axis, called the LFM signal for "Lateral Force Microscopy", of the same laser beam 4 reflected by the microlever 3 on the same PSD dial 5. This lateral deflection directly associated with the torsion of the lever induced by the friction forces between the tip and the sample during scanning is expressed in Volts.

[0007] The determination of a conversion factor CLfm of the LFM signals expressed in Volts, to translate them into Newtons, is done using a calibration procedure. For a quality calibration, it is essential that the scanned surfaces are as large and as homogeneous as possible in terms of slopes and friction coefficients. This condition is difficult to achieve due to local heterogeneities in chemical composition but especially local variations in slope which are necessarily significant at this scale. It is therefore very difficult to manufacture a quality caliber perfectly adapted to this method. The use of an unsuitable caliber is a major source of error and uncertainty in the determination of the conversion factor, particularly linked to the tolerances for determining the slopes and the friction coefficients associated with the different zones.

[0008] Furthermore, this procedure must be carried out systematically before and after each measurement and under in-situ conditions because the conversion factor depends on the type of microlever 3 used and the position of the laser beam 4 on the microlever 3. Consequently, the calibration procedure must be rapid and as simple as possible. Furthermore, given the very high resolution of the force measurements accessible by an AFM, an error in the conversion factor will significantly deteriorate the accuracy of the value of a measured quantity.

[0009] The most widely used method for calibrating the LFM signal is the Wedge method. As illustrated in [Fig.2], this method uses a gauge 9 consisting of a pattern 10 having two slopes of different angles 0i and 02, each of these slopes having two different friction coefficients denoted pi and p2. In the case of the Wedge method, a system of three equations with three unknowns (pi, p2 and CLfm) must be solved mathematically, implying perfect knowledge of 0i and 02.

[0010] Thus, according to the Wedge method, the tip 2 is moved in a linear back and forth movement, along the same axis in a first direction called Trace 11 illustrated in [Fig.3] and in a second opposite direction called Retrace 12 illustrated in [Fig.4]. The sliding of the tip 2 in contact with the sample 1 generates an overall force F which can be decomposed into a component normal to the plane of the sample, namely the normal force N and a component in the plane of the sample, namely, the friction force L. This overall force F is decomposed along the X and Z axes respectively, into a force Fx and Fz. These two quantities are measured by the PSD dial 5. As a reminder, an LFM signal is associated with the torsion of the microlever 3 generated by the force Fx and an 'A-B' signal is associated with the deflection of the microlever 3 generated by the force Fz.Depending on the slope relative to angle 0 and the scanning direction Trace 11 or Retrace 12, the forces applied N and L on the microlever 3 are different, as well as the forces Fx and Fz.

[0011] More precisely, according to the Trace 11 direction, we obtain:

[0012] [Math.l] F^LcosO+N sinB (1)

[0013] [Math.2] F^ = N cosü - L sinO (2)

[0014] where p? and pT are along the X and Z axes defined according to [Fig.3], of the force F during a Trace 11 scan and 0 is the angle between the X axis and the local slope of sample 1.

[0015] For the Retrace 12 direction, we have:

[0016] [Math.3] F^ - LcosB + N sin3 (3)

[0017] [Math.4] Ff = N cosB + L sinB (4)

[0018] It follows from these relationships that the forces applied to the microlever 3 along the X and Z axes are combinations of the normal force and the friction force applied to the contact. In Atomic Force Microscopy in lateral force mode, the force along the Z axis is systematically kept constant during scanning by a servo system; thus p{ — p^ — P„ — Qç / -

[0019] For the following, it is advantageous to rewrite relations (1), (2), (3) and (4) by considering the parameter p defined as being the ratio between the friction force L and the normal force N according to figures 3 and 4. This parameter p is similar to the coefficient of friction which is dimensionless.

[0020] Thus, relations (1) and (2) become:

[0021] [Math.5] Fx [4+tanO / AF; 1- litanü y

[0022] Similarly, from relations (3) and (4), we obtain:

[0023] [Math.6] = / s 1+ fâanff ' '

[0024] We define a half-difference AFX and a half-sum SFX of the horizontal forces obtained during a Trace 11 and Retrace 12 scan by the following relations:

[0025] [Math.7] AF x — —— [iFZCA ( 7 )

[0026] [Math. 8] ^Fx = ^1= tandFzCA (8)

[0027] The parameters CA and Cz are then factors respectively equal to:

[0028] [Math.9] __Ï-Ftan2 0 / qx A 1- / j2-tan20 \ /

[0029] [Math. 10] (10)

[0030] Equations (7) and (8) show that, as a first approximation, the half-difference and the half-sum of the components of the force along the X axis are respectively proportional to the coefficient of friction and to the slope assimilated to the tangent of the angle 0. In the case of an ideal AFM, the signal represented by the LFM voltage, subsequently noted VLFm and measured by the PSD 5 dial, is proportional to the lateral force applied to the tip. In practice, there is always a "dependence" or coupling between the lateral and vertical deflections of the microlever. In other words, the microlever undergoes both a deflection and a torsion exerted simultaneously during scanning, and the VLFM value measured by the PSD 5 dial results from a combination of the two deformations of the microlever.

[0031] In practice, the angular sensitivity related to the lateral force is much lower than the deflection sensitivity related to the vertical force. Therefore, a small misalignment of the laser spot with the photodiode or on the tip can lead to a major contribution of the normal force with respect to the lateral force. It is therefore important to be able to overcome the sensitivity of the LFM signal to deflection during calibration.

[0032] To take into account the dependence, the VLFM voltage can be expressed as follows:

[0033] [Math. 11] VLFM = ClfuFx + c„fz+ c„ (11)

[0034] where CLFM [V / N] is the LFM conversion factor which converts the lateral force expressed in newtons into voltage expressed in volts; CCt is the factor associated with the aforementioned dependence or coupling and Co is associated with the shift or offset of the LFM signal.

[0035] By combining relations 7, 8 and 11, we obtain:

[0036] [Math. 12] A LFM = (12)

[0037] [Math. 13] XLFM = + Cct.Fz + Co (13)

[0038] where ALFM and SLFM are respectively a half difference of the LFM signal and a half sum of the LFM signal. ALFM and SLFM are obtained respectively by subtracting and adding the measured values ​​of the LFM signals, obtained during each of the Trace and Retrace scans.

[0039] On the caliber is engraved a pattern having two slopes of different angles 0i and 02, each of these slopes having two different coefficients of friction noted pi and p2. In this case, it is possible to express the difference SLFMi-SLFM2 where SLFM1 and SLFM2 are respectively the half-difference related to the slope 0i according to the relation (14) and 02 according to the relation (15) as follows:

[0040] [Math. 14] &LFMÏ~ (1^)

[0041] [Math. 15] ^LFM2~ IF-F^A?^lfm (iS)

[0042] [Math. 16] £lFM\~ ^LFM2~ (tanG^C^- tCinG^CX2)-Clfm-F,

[0043] We then obtain a system of three equations with three unknowns (pi, p2 and C LFM) which can be solved mathematically and provided that 0i and 02 are perfectly determined. Thus, the evolution of these parameters with the vertical force can be expressed by:

[0044] [Math. 17] UA1 “ dF, “ F f^àr^LFM (1

[0045] [Math. 18] ttA2= dF\~ ~ LFM (1$)

[0046] [Math. 19] = (tan6,CFr tane,.CF^.C (19^ dF, i il ^2,2 / LFM yy

[0047] Although the 'wedge' method is interesting in its principle and simplicity, it nevertheless presents practical difficulties.

[0048] Thus, the first difficulty lies in the precise recalibration of the values ​​of the signals constituting the images, respectively, Trace and Retrace. This recalibration is not easy due to the intrinsic non-linearities of the piezoelectric ceramics involved in the actuators responsible for scanning. Thus, the AFM images are distorted and horizontally shifted relative to each other. In other words, a horizontal position of each element of the image is not known perfectly. Consequently, images allowing the ALFM and SLFM parameters to be measured at each point are partially erroneous, sometimes significantly so. The topographic images can theoretically be recalibrated to improve the images necessary for calculating ALFM and SLFM, but such a procedure requires recording four images simultaneously: topographic images, LFM images, Trace scan images and Retrace scan images.This is not possible for some AFMs. AFMs equipped with displacement sensors can also be used, which allows for more precise access to the caliber slopes. However, AFMs equipped with such displacement sensors remain in the minority and generate more or less noisy images.

[0049] On the other hand, the method requires knowing precisely an overall slope of the caliber. This is calculated by deriving the profile of a topographic image of said caliber, but this derivative will be very noisy, and therefore unreliable, if it is itself calculated from a noisy topographic image. Usually, calibers with only two types of slopes are used. In a publication by Ogletree et al., a SrTiO3 caliber having crystal planes of type (103) and (101) is implemented. However, the usable surface of these slopes and therefore the exploitable area for calibration remains limited and between 5 and 20 nm. The caliber obtained therefore has two types of facets corresponding to the crystallographic planes (101) and (103). These two types of facets are typically 10 to 100 nm wide and are inclined 14° and 12.5° respectively relative to the crystallographic plane (305).The inclination angles of the said gauge are therefore non-symmetrical. In the method improved by Varenberg et al., they use a commercial silicon gauge obtained by chemical etching with slopes along the (111) and (100) planes. Although they have a usable height of 1 pm, the preparation methods for these gauges only allow the obtaining of a single angle of high value, with 0 = 54°44'.

[0050] In addition, the previously mentioned calibers have slopes and coefficients of different friction. Consequently, the calculation parameters CA and Cz, corresponding respectively to the dimensionless factor of half-difference of the components of the force along the X axis and to the dimensionless factor of half-sum of the components of the force along the X axis, are not constant. It is therefore necessary to precisely calculate the slopes and the coefficients of friction of the faces of said gauge. Assuming that the slopes are known, three parameters are to be determined, and there is no real means of verifying whether the calculated slope values ​​are exact, in particular due to the possible inclination of the gauge relative to the microlever.

[0051] Finally, the methods for preparing existing gauges are expensive, complex, imprecise and not very environmentally friendly. Thus, the gauge of Ogletree et al. is obtained after chemical polishing with annealing under a regulated oxygen flow at 1100°C for 20 hours. The gauge of Varenberg et al. is also obtained by chemical etching but the manufacturing procedure produces gauges whose usable heights of the gauge faces are not well defined, given that the etching kinetics depend on the temperature. Finally, the gauges of Tocha et al. are obtained from a localized ion beam, but this technique is particularly difficult to implement and above all very expensive. Summary

[0052] The present disclosure improves the situation.

[0053] There is provided a caliber of an atomic force microscope comprising: - a substrate, comprising at least one groove comprising at least a first surface and at least a second surface facing each other, the surfaces of the groove having isotropic properties and having a homogeneous and identical coefficient of friction, - said groove having at least two slopes formed respectively by a first angle between the first face and the normal to the substrate, and a second angle formed between the second face and the normal to the substrate, the two angles being symmetrical with respect to said normal and the absolute values ​​of said angles being equal two by two.

[0054] By isotropic properties, it is meant that there is an invariant proportionality characteristic between a normal load and a friction force, whatever the direction of movement and the thickness of the material being engraved.

[0055] The substrate may be a flat or curved substrate.

[0056] Since the angles are symmetrical and equal two by two, it is possible to calculate average values ​​of the slopes relative to each of these angles on the two surfaces of the furrow. This makes it possible to obtain an average statistical value over the entire population of elements constituting a topographic image of the slope, and thus to reduce the uncertainty on the average value of the slope and consequently to improve the accuracy of the underlying calibration. Indeed, the angle of the slopes is an essential parameter to determine in order to accurately evaluate a conversion factor by the calibration process.

[0057] The present gauge also makes it possible to detect a defective adjustment of the AFM used and / or a defect on the microlever used, which is not possible with the gauges of the prior art. The latter have different angles and coefficients of friction, so that the half-difference of the LFM signal is not systematically constant. The gauge thus makes it possible to improve the reliability and precision of the calibration method of an AFM, by overcoming the uncertainty introduced by a defective adjustment of the microlever, the inclination of the gauge and / or by the use of a defective microlever.

[0058] By opting for a symmetrical caliber comprising symmetrical and equal angles two by two and a homogeneous and identical coefficient of friction, the problem is reduced to two equations with two unknowns whereas in the prior art at least three parameters must be determined.

[0059] Each angle may be less than 20°, preferably less than 10°.

[0060] Such an angle value makes it possible to increase the precision of the determination of a conversion factor CLfm- This conversion factor CLfm is in fact based on the determination of the tangent of said angle. Thus, the smaller this angle, the more the precision on the determination of its tangent is improved.

[0061] At the same time, this angle must be high enough to generate a good quality signal measurable by the AFM.

[0062] Said groove may be rectilinear or curvilinear in a plane of a surface of the substrate.

[0063] The maximum depth, i.e., a maximum distance between a surface of the substrate and an apex of the groove, may be constant or variable.

[0064] The possible variability of the depth allows compatibility between the caliber, different types of microlevers and different types of tips. Indeed, a groove with variable depth makes it possible to adapt to several lever geometries, in particular to their height and to the size of the tip generally assimilated to a sphere at the apex. At this level, the apex can have a very variable radius of curvature depending on the probes chosen by the user. Thus, the radius of curvature of the apex can vary from a few nm to a few micrometers. These variable dimensions of the radius of the apex can prevent the tip from entering the groove such that imaging of the surfaces of the groove would be impossible.

[0065] The maximum depth of the groove can be between 10 nm and 20 qm, preferably between 100 nm and 10 qm.

[0066] A large depth, typically of the order of 10 qm, makes it possible to obtain extended groove surfaces and thus to improve the precision of the calibration to be carried out. since the statistical determination of the angle of the slopes of the groove surfaces will be all the more precise as the surfaces allowing the measurement are large. In addition, a great depth also makes it possible to obtain sufficient groove widths for optimal penetration of the tip, the apex of which cannot be neglected. These two considerations constitute an advantage over existing methods. A great depth also makes it easier to visualize with the naked eye, and therefore to locate the groove of the gauge.

[0067] A low depth, typically of the order of 1000 nm, makes it possible to eliminate the risk that the low height tips do not reach the bottom of the groove due to prohibitive contact between the microlever and the gauge.

[0068] A surface width of the groove may be constant or variable along this groove.

[0069] The surface width of the groove may be between 1 μm and 20 μm, preferably from 2 to 8 μm or from 4 to 6 μm.

[0070] A cross-section of the groove may be of semi-circular geometry.

[0071] This semi-circular geometry has the advantage of providing variable slopes along the contour of the semi-circular geometry, with an angle of the same value opposite. Thus, the determination of a conversion factor necessary for calibration can be carried out from several angles and thus allow better precision thanks to a statistical analysis. The semi-circular geometry of the groove also has the advantage of being rigorously independent of the alignment of an engraving tip of an indenter.

[0072] A cross-section of the groove may have a V-shape.

[0073] In the case of a gauge with a V-shaped groove, the slope and the coefficient of friction are identical on both sides. Thus, the number of equations and unknowns to be determined is reduced to two.

[0074] The difference between the LFM Trace signal and the LFM Retrace signal must be identical on both sides of the groove. If experimentally this is not the case, this means that there is either a misalignment of the sample relative to the cantilever or another problem. In the case of the classic Wedge method, a small misalignment cannot be clearly detected and risks leading to significant errors in the calculation of a conversion factor necessary for calibration.

[0075] A roughness of the substrate constituting the caliber may be less than 10 nm, preferably less than 1 nm, for a topographic image of the substrate of 1 pm2. For example, this roughness of the substrate may be defined by a mean square roughness.

[0076] The substrate may comprise an amorphous material, preferably a fused silica.

[0077] Such a substrate comprising an amorphous material is advantageous because, compared to a crystalline material, this can make it possible to overcome possible variations in the coefficient of friction depending on the crystalline planes of the material.

[0078] Fused silica, due to its production process, has the advantage of being an amorphous silica with very high purity, in addition to being rigid and hard as well as resistant to corrosion and chemically inert.

[0079] Fused silica also has a low coefficient of thermal expansion (0.5.10-6 K 1 to 0.6.10-6 K1) and very low surface roughness without necessarily requiring polishing, which is explained by its high temperature production process.

[0080] Furthermore, fused silica is a chemically homogeneous material which leads to homogeneity of the surface properties of the opposite sides of the groove. This implies that the coefficient of friction associated with each of the opposite sides of the groove is identical and constant. Furthermore, fused silica has silanol groups on the surface which make it possible to easily graft chemical molecules and thus modify the nature of the chemical functions on the surface.

[0081] A method of manufacturing a gauge of the aforementioned type of an atomic force microscope is provided, comprising the steps of: - applying a normal load to a contact between an indenter and said substrate to be scratched, - moving said indenter in a relative and controlled manner on a surface plane of the substrate by applying a constant, increasing or increasing support force so as to form a groove symmetrical with respect to the normal to said substrate, - possibly, coat the furrow with a thin layer formed from a homogeneous and isotropic material.

[0082] This method of manufacturing a caliber is simple, fast, as is its implementation, and much less expensive than the methods of producing existing calibers. Indeed, the groove is made simply using an indenter, nanoindenter or any other suitable device, available commercially. The indenter can be a micro or nano-indenter.

[0083] The use of an indenter technique is in no way obvious to those skilled in the art. Indeed, these devices appear too simple in their implementation, not technological enough in view of the dimensions of the grooves generated, of the order of a micrometer. They are also tainted by the following prejudices: imprecision of mechanical machines, other techniques are considered more suitable for engraving, choice of substrate too specific with respect to such a technique.

[0084] This method of manufacturing a caliber allows very great flexibility to achieve specific and adapted geometries for calibration and in particular for specific AFM tip geometries. Thus, this process of manufacturing a caliber makes it possible to produce grooves of different lengths, with constant depths or presenting gradients, and reproducible in large numbers within the limit of the size of the substrate used to constitute the caliber.

[0085] This method of manufacturing a caliber is much simpler in its implementation and more environmentally friendly. Indeed, the Varenberg caliber of the prior art assumes the application of a chemical treatment by controlling parameters such as the temperature, the choice of the solute agent and its concentration. The caliber proposed by Tocha assumes a certain dexterity to choose the right settings for the focused ion beam to obtain by etching the silicon a perfectly defined groove with the desired geometry.

[0086] This method of manufacturing a caliber is also economical and rapid. In fact, the cost of this manufacturing method is essentially dictated by that of the substrate supporting the groove or any other coating supporting the engraving.

[0087] The applied bearing force may be configured to achieve a depth, i.e. a maximum distance between a surface of a substrate and an apex of the formed groove, of between 0 and 20qm.

[0088] The indenter may comprise at least one tip of the following types: Berkovich, Vickers, coincube, Knoop, sphere and cone.

[0089] It is preferable to use indenters to make the groove, the geometry of which allows for very low slopes to be obtained. Indenters with a Vickers, Knoop, cubic, spherical, conical or Berkovich type tip are the most suitable.

[0090] A method is proposed for determining a coefficient of friction of the substrate or of a thin layer on said substrate of the aforementioned type comprising the steps of: a. aligning a microlever such that an X axis of a microlever is aligned and centered with a principal axis along a direction of an apex of a groove of a scratched substrate, b. produce topographic images and LFM images formed during an outward journey, called LFM Trace, and a return journey, called LFM Retrace, perpendicular to the furrow and centered on the furrow produced, c. calculate the slopes of the sides of the furrow from the topographic images produced, d. calculate the average of the sum and the difference of the values ​​of the LFM Trace and LFM Retrace signals respectively measured for each point of the LFM Trace and LFM retrace images of the sides of the caliber, e. calculate the coefficient of friction.

[0091] Determining the conversion factor is reduced to simply solving a system of two equations with two unknowns. The prior art required a resolution involving three parameters, each dependent on an evaluation with its own error.

[0092] In step b), the topographic images and the LFM images can be produced with at least two different pressing forces with a scanning direction perpendicular to the main axis, said topographic images and said LFM images being centered on the groove of a scratched substrate.

[0093] The method for determining a coefficient of friction may comprise, between step d) and e), the successive steps consisting of: - calculate an average value of the difference in the values ​​of the LFM Trace and LFM Retrace signals respectively for different support forces, and calculate the direction coefficient between the average value of the difference in the values ​​of the LFM Trace and LFM Retrace signals respectively and the support force, - calculate an average value of the sum of the values ​​of the signals LFM Trace and LFM Retrace respectively on a rising part for different support forces, called the rising average value, and on a falling part, called the falling average value, of said groove and calculate the direction coefficient between the difference between the rising average value and the falling average value on the one hand and the support force on the other hand, and make the ratio between the two direction coefficients obtained.

[0094] A method for calibrating an AFM microscope is proposed comprising the steps of the method for determining a coefficient of friction of the aforementioned type further comprising a step of determining a conversion factor CLFM in Volt / N from said coefficient of friction and the value of the angle of the slope of the groove of the caliber of the aforementioned type.

[0095] The calibration method is more reliable than existing methods, particularly with regard to the accuracy of the determination of the CLFM conversion factor. The experimental uncertainties on the CLFM conversion factor are mainly limited to the uncertainties linked to the calibration of the normal force and the piezoelectric actuator used to obtain the topographic and LFM images. In fact, these images make it possible to go back to the angle of the slope of the gauge. Furthermore, the calibration of the actuator makes it possible to quantify the normal load applied to the contact, to obtain the LFM images while guaranteeing its invariance.

[0096] The conversion factor CLFm can be calculated from the following formula:

[0097] [Math.20] ^=^(20)

[0098] with: : a dimensionless coefficient of friction of the substrate, °a: a director coefficient determined from the variation of the ALFM parameter in relation to the applied support force F, ALFM representing a difference image between a forward scan, called an LFM Trace image, and a return scan, called an LFM Retrace image, ; a dimensionless parameter depending on tanO and p. Brief description of the drawings

[0099] Other characteristics, details and advantages will appear on reading the detailed description below, and on analyzing the attached drawings, in which: Fig.l

[0100] [Fig. 1][Fig. 1] shows a schematic diagram of an atomic force microscope (AFM). Fig. 2

[0101] [Fig.2][Fig.2] shows a diagram of the generic profile of a groove of a caliber according to prior art. Fig. 3

[0102] [Fig.3][Fig.3] shows a diagram of the forces applied to a microlever during a Trace sweep. Fig. 4

[0103] [Fig.4][Fig.4] shows a diagram of the forces applied to a microlever during a Trace sweep. Fig. 5

[0104] [Fig.5][Fig.5] shows a diagram of the generic profile of a groove of a caliber according to the invention, view of a cross-section of the groove of said gauge. Fig. 6

[0105] [Fig.6][Fig.6] shows schematic examples of grooves of a gauge with in A a rectilinear furrow with a gradient of width and / or depth, in B a curvilinear furrow and in C an aligned network of parallel furrows. Fig. 7

[0106] [Fig.7][Fig.7] shows a semi-circular groove according to the invention obtained using a engraving tip of a spherical geometry indenter. Fig. 8

[0107] [Fig.8][Fig.8] shows different possibilities of arrangement of grooves of a gauge according to the invention with in A, V-shaped grooves, in B V-shaped but not identical grooves, in C, a semi-circular groove coupled with non-identical V-shaped grooves. Fig. 9

[0108] [Fig.9][Fig.9] shows indenter tip geometries. Fig. 10

[0109] [Fig. 10] [Fig. 10] shows in A a topographic image, in B an LFM Trace image, in C an LFM Retrace image, in D a topographic profile and in E LFM signal profiles associated with a Trace and Retrace scan. Fig. 11

[0110] [Fig. 1 l][Fig. 11] shows in (a) a slope image, in (b) and (c) respectively the SLFM and ALFM images obtained from images (b) and (c) of [Fig. 10], and in (d), angles 0 of the slopes of the surfaces of the groove of the gauge Fig. 12

[0111] [Fig. 12][Fig. 12] [Fig. 12] represents a histogram of the slope image with a number of measurement points on the ordinate and a topographic slope on the abscissa. Fig. 13

[0112] [Fig. 13][Fig. 13] represents a histogram of the sum of the LFM Trace and LFM Retrace images (solid curve) and a histogram of the difference of the LFM Trace and LFM Retrace images (dotted curve), the different values ​​being calculated for an identical location on the image with a number of measurement points on the ordinate and the value of the different sums and differences mentioned on the abscissa. Fig. 14

[0113] [Fig. 14][Fig. 14] shows a curve of the average value of the difference of the Trace and Retrace images as a function of the pressure force. Fig. 15

[0114] [Fig. 15][Fig. 15] shows a curve of the average value of the difference of the sum images Trace and Retrace each of the sides of the groove in the sense of equation 20 and as a function of the support force. Description of the embodiments

[0115] As illustrated in [Fig.5], there is provided a 20 gauge of an atomic force microscope comprising: - a generally flat substrate 21, comprising at least one groove 22 comprising at least one first 23 and at least one second 24 surface facing each other, the surfaces 23, 24 of the groove 22 having isotropic properties and having a homogeneous and identical coefficient of friction, - said groove 22 having at least two slopes 25, 26 formed respectively by a first angle 0 between the first face and the normal 27 to the substrate 21, and a second angle 0 formed between the second face and the normal 27 to the substrate 21, the angles 0 being symmetrical and the absolute value of these said angles equal two to two.

[0116] The grooves of the gauge can be aligned along the X axis of the microlever or at an angle relative to said X axis in the XY plane, for example 45°. This makes it possible to modify the angle 0 and to carry out calibrations in different conditions making it possible to test the robustness of the calibration.

[0117] Each angle 0 can be less than 20°, preferably less than 10°.

[0118] As illustrated in [Fig.6], said groove 22 can be rectilinear as in (A) or curvilinear in a plane of a surface of the substrate as in (B).

[0119] As illustrated in (C) of [Fig.6], the substrate 21 may comprise a plurality of grooves 22 parallel to each other. The substrate may comprise a plurality of grooves arranged next to each other in the form of a network. Such a network of grooves is visible to the naked eye, and facilitates the location of the grooves on the substrate of the gauge.

[0120] The substrate 21 may comprise a plurality of rows of grooves 22 arranged side by side in the direction of extension of the grooves.

[0121] The grooves 22 may extend longitudinally along a rectilinear path and be arranged side by side, so as to form at least one row of parallel grooves. The distance between two adjacent grooves within the same arrangement is for example equal to 100 μm.

[0122] The grooves 22 may be identical or have different characteristics, for example in terms of length and / or depth and / or width and / or slope of the groove surfaces 22.

[0123] The maximum depth P illustrated in [Fig.4], that is to say a maximum distance between a surface of the substrate and an apex of the groove 22, can be constant or variable.

[0124] The maximum depth P of the groove 22 can be between 10 nm and 20 pm, preferably between 100 nm and 10 pm.

[0125] A surface width of the groove may be constant or variable along this groove. By surface width is meant the greatest distance between surfaces 23, 24 of the groove 22 along a cross-section of this groove 22. Thus, the groove shown in view (A) of [Fig.6] is rectilinear with a surface width gradient.

[0126] As illustrated in [Fig.7], a cross-section of the groove 22 may be of semi-circular geometry. This semi-circular geometry has the advantage of providing variable slopes 25a, 25b, 26a, 26b along the contour of the semi-circular shape, with an angle of the same value for a given height h, h' opposite. Thus, the determination of a conversion factor CLfm necessary for the calibration of said AFM can be carried out from several angles and thus allow better precision thanks to a statistical analysis. This therefore assumes maintaining h=h'. The semi-circular geometry of the groove 22 also has the advantage of being rigorously independent of the alignment of an engraving tip of an indenter.

[0127] As illustrated in [Fig.5], a cross-section of the groove 22 may have a V-shape.

[0128] As illustrated in (A) of [Fig.8], the gauge 20 may comprise a juxtaposition of a plurality of V-shaped grooves 22, with identical angles 0, arranged side by side and spaced apart by a flat 28. This flat 28 has a width of less than 10 μm. Such an arrangement makes it possible to check, using the flat 28, the parallelism of the gauge 20 with respect to a horizontal plane.

[0129] As illustrated in (B) of [Fig.8], the gauge 20 may comprise a plurality of V-shaped grooves 22 of identical angles for a given groove 22, but of varying angles from one groove 22 to another.

[0130] As illustrated in (C) of [Fig.8], the gauge can combine the configurations shown in (B) of [Fig.8] to which a groove of conical or semi-circular geometry is added. These grooves 22 can be arranged side by side and spaced apart by a flat 28 whose width can be between 50 and 100 pm. This width of flat 28 makes it possible to remain within the linearity range of the AFM actuator in terms of scanning. This configuration also makes it possible to improve the accuracy of the calibration by determining a conversion factor CFLm in a single step from the angles of the V-shaped groove having at least two different angles and to verify the parallelism of said gauge with respect to a lower face 29 of the substrate 21.

[0131] A roughness (generally the mean square roughness) of the substrate 21 measured by an AFM may be less than 10 nm, preferably less than 1 nm, for a topographic image of the substrate of 1 pm2. The substrate 21 may comprise an upper face 30 and the lower face 29 as parallel as possible. A substrate 21 with a specular type surface may constitute an ideal with regard to calibration precision.

[0132] The upper face 30 of the substrate 21 may comprise an essentially flat area. Such an area, which may have very low surface roughness, is advantageous, since such an area leads to precise and easy calibration of the normal forces.

[0133] In certain particular cases, the substrate 21 may be treated for antireflection in order to attenuate reflections on the upper face of the substrate, for example reflections of wavelengths between 400 and 1000 nm and / or 600 and 1050 nm and / or 750 and 1550 nm. A substrate 21 which may have a very low surface reflectance is advantageous because it can make it possible to attenuate or even eliminate interference phenomena. This constitutes an advantage for the measurement of the deflection or torsion of a microlever 3 by a PSD dial 5 of an AFM. Indeed, interference can reduce the accuracy of the AFM optical measurement.

[0134] The substrate 21 may comprise an amorphous material, preferably a fused silica. This fused silica may be, for example, the reference “HPFS 7979, 7980 and 8655 Fused silica » marketed by Corning.

[0135] The density of the substrate 21 may be between 2.10 and 2.30 g / cm3, preferably 2.20 g / cm3. The so-called “Knoop” hardness of said substrate 21 may be greater than or equal to 500, preferably greater than or equal to 600 and even more preferably 600. The so-called “Mohs” hardness of said substrate 21 may be greater than or equal to 6, preferably greater than or equal to 7, preferably 7. Such a substrate 21 of high hardness is advantageous because it can reduce the risk of deterioration of the caliber, in particular the risk that the caliber may be scratched during handling. Such a substrate hardness also makes it possible to improve its resistance to wear during calibration.

[0136] The substrate 21 may have the highest possible Young's modulus, preferably greater than 30 GPa, even more preferably between 60 GPa and 80 GPa. The substrate 21 may have a compressive strength between 0.9 and 1.3 GPa. Indeed, these values ​​of moduli and compressive strength cover the entire family of glasses which is a family of isotropic material, inexpensive and therefore preferred for the manufacture of said caliber.

[0137] The substrate 21 may have the lowest possible coefficient of thermal expansion. Such a thermal expansion characteristic is advantageous because it makes it possible to avoid local expansion of the substrate 21, in particular when a laser beam from the AFM is reflected on the substrate 21, although this laser beam is of low power, preferably less than 1 mW.

[0138] The degree of purity of the material of the substrate 21 may be as high as possible, preferably between 97% and 99.9% by weight of amorphous silica. A high purity substrate 21 is advantageous because it can make it possible to obtain a structurally well-defined material with a homogeneous and constant coefficient of friction.

[0139] A method of manufacturing a 20 gauge AFM atomic force microscope is provided comprising the steps of: - applying a normal load to a contact between an indenter or a na-noindenter and said substrate (21) to be scratched, - moving said indenter in a relative and controlled manner on a surface plane of the substrate so as to form a groove (22) symmetrical with respect to the normal to said substrate (21) at constant or increasing force, - possibly, coating the groove (22) with a thin layer formed from a homogeneous and isotropic material.

[0140] One of the faces of the indenter tip can be moved face forward, except in the case of spherical and conical geometries.

[0141] The applied normal load may be configured to achieve a depth, i.e., a maximum distance between a surface of a substrate and an apex of the groove 22 formed, between 0 and 20 pm.

[0142] As illustrated in [Fig.9], the indenter may comprise at least one tip of the following type: Vickers in (A), Berkovich in (B), wedge-cube in (C), Knoop in (D), sphere in (E) and cone in (F).

[0143] The groove 22 can be coated using conventional deposition technologies such as vapor deposition of material generated by a physical PVD (Physical Vapor Deposition) process and / or vapor deposition of material generated by a chemical CVD (Chemical Vapor Deposition) process and / or sputtering, with a film with a thickness of between 1 nm and 10 nm, preferably less than 10 nm, of material having isotropic properties in terms of coefficient of friction. Thanks to this type of deposition technology, it is possible to envisage other materials for producing said groove while having the desired characteristics.

[0144] A method is proposed for determining a coefficient of friction of the substrate or of a thin layer on said substrate of the aforementioned type comprising the steps: a. aligning a microlever so that an X axis of a microlever is aligned with a main axis along a direction of an apex of a groove of a scratched substrate, b. produce topographic images and LFM Trace images formed during an outward journey and LFM Retrace images formed during a return perpendicular to the furrow and centered on the furrow, c. calculate the slopes of the sides of the furrow from the topographic images produced, d. calculate the average of the sum and the difference of the signal values ​​respectively of the LFM images formed during an outward journey, values ​​called LFM Trace, and of a return journey, values ​​called LFM Retrace for each point of the LFM Trace and LFM Retrace images of the sides of the gauge, in the groove produced, e. calculate the coefficient of friction.

[0145] By main axis we mean the longitudinal axis of the microlever.

[0146] In step b), the topographic images and the LFM images can be produced with at least two different pressing forces with a rapid scanning direction perpendicular to the main axis, said topographic images and said LFM images being centered on the groove 22 of a scratched substrate 21.

[0147] The method for determining a coefficient of friction may comprise, between step d) and e), the successive steps consisting of: - calculate an average value of the difference in the values ​​of the signals LFM Trace and LFM Retrace respectively for different support forces, and calculate the direction coefficient between the average of the difference in the values of the signals respectively LFM Trace and LFM Retrace and the support force - calculate the average of the sum of the values ​​of the signals respectively LFM Trace and LFM Retrace on a rising part for different support forces, called the rising average value, and on a falling part, called the falling average value, of said groove and calculate the direction coefficient between the difference between the rising average value and the falling average value and the support force, and make the ratio between the two direction coefficients obtained.

[0148] A method for calibrating an AFM microscope is proposed comprising the steps of the method for determining a coefficient of friction of the aforementioned type and further comprising a step of determining a conversion factor CLFM in Volt / Newton from said coefficient of friction and the value of the angle of the slope of the groove 22 of the caliber 20 of the aforementioned type.

[0149] From a mathematical point of view, considering the geometry of the caliber of the invention, we therefore advantageously have:

[0150] -01=02=0 and pi=p2=p, with 0 the slope angle of said groove 22 and q the coefficient of friction of the substrate 21.

[0151] or again:

[0152] Cai=Ca2=Ca, C2i=C22=C2, with CA and C2 two parameters linked respectively to the half-difference and the half-sum of the components of the force along the X axis. CAi and CA2 are the two parameters of the prior art associated with the two angles 0i and 02. Similarly, C2i and Cz2 are the two parameters of the prior art associated with the two angles 0i and 02.

[0153] Thus relations (14), (15) and (16) of the prior art are simplified and become:

[0154] [Math.21] ^CA].Clfm (17)

[0155] [Math.22] ^LFM2~ ^anO.C£.Clfm-F (18')

[0156] From equations (17') and (18'), the evolution of the two parameters involved as a function of the vertical force, Fz, is then directly described with:

[0157] [Math.23] «A ~ = ^CACLFM (19)

[0158] [Math.24] a. = = 2,tane.Cv.C (20) “ or s LFM V /

[0159] It is useful to consider the following ratio R:

[0160] [Math.25] R = 2.tan3.^ (21', a)

[0161] Or again:

[0162] [Math.25] R = (2t, b)

[0163] First, the angle 0 is thus determined experimentally from the topographic images Trace and Retrace. The respective coefficients, aA and ^ are determined experimentally from the half-sums and half-differences of the LFM images. With 0, az, the value of R is determined from the relation (21',a). The friction coefficient p can also be calculated from the equation (21',b). Indeed, p is a solution of the quadratic equation (21',b) having two solutions, pA and pB

[0164] [Math.26] l+tan20 - J ( l+tan20) "A.R2 Ra~ 57 (22')

[0165] [Math.27] l+ran20+ -J ( ]+tan20y~4J^ 57 (23')

[0166] The exploitable solution is easily identified because p is generally less than 1 for most materials used as standards.

[0167] Knowing the consistent value of p, generally given by equation (22'), the conversion factor in newton / volt, CLfm, is thus calculated.

[0168] Thus, in a first step of the calibration process as illustrated in [Fig. 10], the topographic images and the LFM Trace and LFM Retrace images of a sample are produced at the center of the gauge groove, this for at least two different Fz forces, typically for five different Fz forces. The image of the topographic slopes is then calculated. Image (a) of [Fig. 10] represents a topographic image. Image (b) of [Fig. 10] represents an LFM Trace image. Image (c) of [Fig. 10] represents an LFM Retrace image. Graph (d) of [Fig. 10] represents a topographic profile. Graph (e) of [Fig. 10] illustrates LFM Trace 40 and Retrace 41 signal profiles with the LFM signal in mV on the ordinate and the displacement in pm on the abscissa.

[0169] In this step of the calibration process illustrated in [Fig.l 1], the SLFM sum and ALFM difference images can be obtained by calculation. According to the expected results, the images can be similar to the slope image and the images may not exhibit contrast depending on the slope. Image (a) in [Fig. 11] represents a slope image. Images (b) and (c) in [Fig. 11] illustrate the SLFM and ALFM images obtained from the images in images (b) and (c) in [Fig.10] respectively. Graph (d) in [Fig.11] represents angles 0 of the slopes of the gauge groove surfaces.

[0170] For each application of a normal contact load, Fz, the histograms of the slope, sum and difference images can be calculated. [Fig. 12] illustrates a representation of the slope image while [Fig. 13] illustrates an LFM sum representation 43, i.e. summing the LFM Trace and LFM Retrace values ​​for the same position on the image, as well as an LFM difference image 44, i.e. realizing the difference between the LFM Trace values ​​and the LFM Retrace values ​​for the same position on the image. An adjustment of the different Gaussians corresponding to the different slopes of the sample can be carried out so as to define the center of each of them.

[0171] The coefficients and a£ can be respectively determined (relations 19' and 20') from the representation of the ALFM and SLFM parameters as a function of the load F z applied to the contact (relations 17' and 18'). Thus, [Fig. 14] is a representation of the ALFM parameter as a function of the normal force in nN and [Fig. 15] is a representation of the SLFM parameter as a function of the normal force nN. The slope coefficient of each of the curves makes it possible to calculate the ratio R (relation 21',a) then the friction coefficient p (relation 21',b).

[0172] Taking into account the above considerations, the CLFM conversion factor can then be calculated from the following formula:

[0173] [Math.28] (20)

[0174] with: p: the dimensionless coefficient of friction of the substrate; aA: a director coefficient determined from the variation of the ALFM parameter with respect to the applied normal force F, ALFM representing a difference image between a forward scan, called LFM Trace image, and a return scan, called LFM Retrace image, CA: a dimensionless parameter depending on tanO and p.

Claims

Claims

1. Caliber (20) of an atomic force microscope comprising: - a substrate (21), comprising at least one groove (22) comprising at least a first (23) and at least a second (24) surface facing each other, the surfaces (23, 24) of the groove (22) having isotropic properties and having a homogeneous and identical coefficient of friction, - said groove (22) having at least two slopes (25, 26) formed respectively by a first angle (0) between the first face and the normal (27) to the substrate (21), and a second angle (0) formed between the second face and the normal (27) to the substrate (21), the two angles (0) being symmetrical with respect to said normal and the absolute values ​​of said angles equal two by two.

2. Caliber according to claim 1, in which each angle (0) is less than 20°, preferably less than 10°.

3. A gauge according to any preceding claim, wherein said groove (22) is rectilinear or curvilinear in a plane of a surface of the substrate.

4. Caliber according to one of the preceding claims, in which the maximum depth (P), i.e. a maximum distance between a surface of the substrate and an apex of the groove, is constant or variable.

5. Caliber according to claim 4, in which the maximum depth (P) of the groove is between 10 nm and 20 pm, preferably between 100 nm and 10 pm.

6. Caliber according to one of the preceding claims, in which a surface width of the groove (22) is constant or variable along this groove.

7. Caliber according to one of the preceding claims, in which a cross section of the groove (22) is of semi-circular geometry.

8. A gauge according to any one of claims 1 to 6, wherein a cross-section of the groove (22) has a V-shape.

9. Caliber according to one of the preceding claims, in which a roughness of the substrate (21) is less than 10 nm, preferably less than 1 nm, for a topographic image of the substrate of 1 pm2.

10. Caliber according to one of the preceding claims, in which the substrate (21) comprises an amorphous material, preferably a fused silica.

11. Method for manufacturing a gauge (20), according to one of claims 1 to 10, of an atomic force microscope comprising the steps of: - applying a normal load to a contact between an indenter and said substrate (21) to be scratched, - moving said indenter in a relative and controlled manner on a surface plane of the substrate by applying a constant, increasing or decreasing bearing force so as to form a groove (22) symmetrical with respect to the normal to said substrate (21) - optionally, coating the groove (22) with a thin layer formed of a homogeneous and isotropic material.

12. A method of manufacturing a gauge according to claim 11, wherein the applied pressing force is configured to achieve a depth, i.e. a maximum distance between a surface of a substrate and an apex of the groove (22) formed, of between 0 and 20 qm.

13. A method of manufacturing a gauge according to claim 11 or 12, wherein the indenter comprises at least one tip of the type: Berkovich, Vickers, wedge-cube, Knoop, sphere and cone.

14. Method for determining a coefficient of friction of the substrate or of a thin layer on said substrate of the gauge according to one of claims 1 to 10, comprising the steps of: a. aligning a microlever so that an X axis of a microlever is aligned and centered with a main axis along a direction of an apex of a groove of a scratched substrate, b. producing topographic images and LFM images formed during an outward movement, called LFM Trace, and a return movement, called LFM Retrace, perpendicular to the groove and centered on the groove produced, c. calculating slopes of the sides of the groove from the topographic images produced, d. calculating the average of the sum and the difference of the values ​​of the signals respectively LFM Trace and LFM Trace measured for each point of the LFM Trace and LFM retrace images of the caliber flanks, e. calculate the coefficient of friction.

15. Method for determining a coefficient of friction according to claim 14, wherein, in step b), the topographic images and the LFM images are produced with at least two different bearing forces with a scanning direction perpendicular to the main axis, said topographic images and said LFM images being centered on the groove (22) of a scratched substrate (21).

16. Method for determining a coefficient of friction according to claim 14 or 15, further comprising, between step d) and e), the successive steps of: - calculating an average value of the difference in the values ​​of the signals LFM Trace and LFM Retrace respectively for different bearing forces, and calculating the direction coefficient between the average value of the difference in the values ​​of the signals LFM Trace and LFM Retrace respectively and the bearing force. - calculating an average value of the sum of the values ​​of the signals LFM Trace and LFM Retrace respectively on a rising part for different bearing forces, called the rising average value, and on a falling part, called the falling average value, of said groove and calculating the direction coefficient between the difference between the rising and falling average value on the one hand and the bearing force on the other hand, and calculating the ratio between the two direction coefficients obtained.

17. Method for calibrating an AFM microscope comprising the steps of the method for determining a coefficient of friction according to one of claims 14 to 16 further comprising a step consisting of: - determining a CLFM conversion factor in Volt / N from said coefficient of friction and the value of the angle of the slope of the groove (22) of the gauge (20) according to one of claims 1 to 10.

18. A method of calibrating an AFM microscope according to claim 17, wherein the CLFM conversion factor is calculated from the following formula: [Math. 29] (20) with : : the dimensionless coefficient of friction of the substrate; ; a director coefficient determined from the variation of the ALFM parameter in relation to the applied support force F,, ALFM representing a difference image between a forward scan, called an LFM Trace image, and a return scan, called an LFM Retrace image. CA; a dimensionless parameter depending on tanO and p.

Images