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

Abstract

This document relates to a bore (20) of an atomic force microscope comprising: a substrate (21), generally planar, having at least one groove (22) comprising at least a first (23) and at least a second (24) facing surfaces, the surfaces (23, 24) of the groove (22) having isotropic properties and 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 in pairs. Abstract figure: Figure 5

Description

Title of the invention: Caliper, method for manufacturing a caliper and method for calibrating an atomic force microscope. Technical field

[0001] The present disclosure relates to the field of atomic force microscopes and more specifically to calibration processes, the manufacture of a gauge and gauges. Prior art

[0002] The Atomic Force Microscope, also called AFM, is an indispensable tool for characterizing surfaces at the nanoscale for all major classes of materials, including metallic alloys, plastics and polymers, ceramics, and even biological materials, in various environments.

[0003] As illustrated in [Fig. 1], the general principle of AFM is based on measuring the interaction forces between a surface of a sample 1 to be studied and a tip 2, one end of which is approximated as a sphere, at the apex of said tip. The measurement of the interaction forces is based on determining the deflection of a microcantilever 3 on which said tip 2 is mounted. This deflection is evaluated by means of the deviation of a laser beam 4 reflected at the end of said microcantilever 3. A photodiode dial 5, also called a PhotoSensitive Detector or PSD 5, allows the position of the reflected laser beam to be estimated. This PSD 5 dial has horizontal x-axis and vertical y-axis 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 microcantilever 3.

[0004] To obtain a topographic image, a servo system 6 maintains the deflection of the microcantilever 3, measured by the PSD dial 5, constant during the scanning of the sample 1 by said tip 2. The sample 1 rests on a sample holder 7, and piezoelectric actuators 8 or ceramics are located under this sample holder or at 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, in the best case, reach atomic resolution. In parallel with topographic imaging modes, a multitude of AFM modes have been developed that quantitatively measure a whole series of properties such as adhesion, magnetic, electrostatic, and frictional forces, and electrical or thermal conductivity with very high resolution.

[0005] In particular, the measurement of friction forces by AFM contributes to a better understanding of the elementary phenomena responsible for friction. One of the main difficulties encountered in this field for quantitative measurements is the calibration of friction forces. This calibration consists of determining a conversion factor that allows the voltages measured in volts by the PSD to be converted into a friction force value measured in Newtons.

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

[0007] Determining a CLFM conversion factor for LFM signals expressed in volts, to convert them to Newtons, is done using a calibration procedure. For high-quality calibration, it is essential that the scanned areas be as large and 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 due to the necessarily significant local variations in slope at this scale. It is therefore very difficult to manufacture a high-quality caliper perfectly suited to this method. The use of an unsuitable caliper is a major source of error and uncertainty in determining the conversion factor, particularly related to the tolerances in 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 microcantilever 3 used and the position of the laser beam 4 on the microcantilever 3. Consequently, the calibration procedure must be quick and as simple as possible. Moreover, given the very high resolution of force measurements achievable by an AFM, an error in the conversion factor will significantly degrade the accuracy of the measured value.

[0009] The most commonly 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 with two slopes of different angles θ1 and θ2, each of these slopes having two different friction coefficients denoted π and π2. In the case of the method Wedge, a system of three equations with three unknowns (qB q2 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 motion 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 5 dial. 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 sweep direction Trace 11 or Retrace 12, the forces applied N and L on the microlever 3 are different, as are the forces Fx and Fz.

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

[0012] [Math.l] F^ = Lcos8 + N sine (1)

[0013] [Math.2] F? = N cos8- L sinG (2)

[0014] where F? and F~ are along the X and Z axes defined according to [Fig.3], of the force F during a Trace 11 sweep 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] Fx = - L cosine + N sin(3)

[0017] [Math.4] F^= N cos3 + L sine (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 at the contact. In Atomic Force Microscopy in lateral force mode, the force along the Z axis is systematically maintained constant during scanning by a servo system; thus F^ - F- = F7 — Cst-

[0019] For the remainder, 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 q can be assimilated to the coefficient of friction which is dimensionless.

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

[0021] [Math.5] Fx p+tan8 / A Fz — 1- fiianff

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

[0023] [Math.6] Fx -fi+tanô Fz — 1+ pianS ( o)

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

[0025] [Math.7] Fr~ Fr NFx=-^= fiFzCA (7)

[0026] [Math.8] Ff+ F? Yfx = tan6FzCà (8)

[0027] The parameters CA and C2 are then factors respectively equal to:

[0028] [Math.9] f1--LtîSfAL zg X VA“ 1-fPtariW

[0029] [Math. 10] —OA LfFtatM \n7

[0030] Equations (7) and (8) show that, to a first approximation, the half-difference and half-sum of the force components along the X-axis are respectively proportional to the friction coefficient and the slope approximated by the tangent of the angle 0. In the case of an ideal AFM, the signal represented by the LFM voltage, hereafter denoted 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 deflection and torsion exerted simultaneously during the sweep, and the value of VLFM 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 sensitivity to deflection related to the vertical force. Consequently, a slight misalignment of the laser spot with the photodiode or on the tip can lead to a major contribution of the normal force compared to the lateral force. It is therefore important to be able to eliminate the sensitivity of the LFM signal to deflection during calibration.

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

[0033] [Math. 11] ^LFM~ ^LFM^x+ CctFz+ Cq (11)

[0034] where CLFm [V / N] is the LFM conversion factor which converts the lateral force expressed in newtons into a 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] ^LFM~ (12)

[0037] [Math. 13] ^lfm~ tan6.Fz.CL.C+ 'z + Q

[0038] where ALFM and SLFM are respectively half the difference of the LFM signal and half the 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] The gauge is engraved with a pattern having two slopes with different angles 0i and 02, each of these slopes having two different coefficients of friction denoted pi and p2. In this case, it is possible to express the difference SLFMi-SLFM2 where SLFMi and SLFM2 are respectively the half-difference related to the slope 0i according to relation (14) and 02 according to relation (15) as follows:

[0040] [Math. 14] LFM1~

[0041] [Math. 15] ^LFMÎ~ f1^'z£lfm (15)

[0042] [Math. 16] ^lfm\~ ^LFM2~ {tan^C^- tanQ^CS2).C LF^ ^lé)

[0043] We subsequently obtain a system of three equations with three unknowns (pi, p2 and CLFM) which can be solved mathematically 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] ^LFM1 Z' Z' / ÜFZ ~

[0045] [Math. 18] d&LFMl (1 ol aA2“ 9FZ - [ / $1

[0046] [Math. 19] = (tond fa- tanQ^C^ (w)

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

[0048] Thus, the first difficulty lies in the precise registration of the signal values ​​constituting the Trace and Retrace images, respectively. This registration is not easy due to the intrinsic nonlinearities of the piezoelectric ceramics involved in the actuators responsible for the scanning. As a result, the AFM images are distorted and horizontally shifted relative to each other. In other words, the horizontal position of each image element is not perfectly known. Consequently, images used to measure the ALFM and SLFM parameters at each point are partially erroneous, sometimes significantly so. Theoretically, it is possible to register the topographic images to improve the images needed 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, allowing for more precise access to the gauge slopes. However, AFMs with such displacement sensors remain in the minority and generate images that are more or less noisy.

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

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

[0051] Finally, existing gauge preparation methods are costly, complex, imprecise, and environmentally unfriendly. For example, 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 with poorly defined usable face heights, since the etching kinetics are temperature-dependent. 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] This disclosure improves the situation.

[0053] A caliber of an atomic force microscope is proposed comprising: - a substrate, having 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 in pairs.

[0054] By isotropic properties, it is understood that there is an invariant proportionality characteristic between a normal charge and a friction force, regardless of the direction of displacement and the thickness of the material being engraved.

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

[0056] Since the angles are symmetrical and equal in pairs, average values ​​of the slopes relative to each of these angles can be calculated on the two surfaces of the furrow. This allows us to obtain an average statistical value across the entire population of elements constituting a topographic image of the slope, thereby reducing the uncertainty in the average slope value and consequently improving the accuracy of the underlying calibration. Indeed, the slope angle is a crucial parameter to determine in order to accurately evaluate a conversion factor using the calibration process.

[0057] This caliper also makes it possible to detect a faulty adjustment of the AFM used and / or a defect in the microlever used, which is not possible with prior art calipers. The latter have different angles and coefficients of friction, so that the half-difference of the LFM signal is not systematically constant. The caliper thus improves the reliability and accuracy of the AFM calibration process by eliminating the uncertainty introduced by a faulty microlever adjustment, caliper inclination, and / or the use of a defective microlever.

[0058] By opting for a symmetrical caliber comprising symmetrical angles equal in pairs 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 increases the accuracy of determining a CLFM conversion factor. This CLFM conversion factor is based on determining the tangent of said angle. Thus, the smaller this angle, the more accurate the determination of its tangent.

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

[0062] Said groove may be straight 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, can be constant or variable.

[0064] The variable depth allows for compatibility between the caliber, different types of microlevers, and different types of tips. Indeed, a groove with variable depth allows adaptation to several lever geometries, particularly their height and the size of the tip, which is generally approximated as a sphere at the apex. At this point, the apex can have a highly 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 nanometers to a few micrometers. These variable dimensions of the apex radius can prevent the tip from entering the groove, making imaging of the groove surfaces impossible.

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

[0066] A significant depth, typically on the order of 10 µm, allows for large groove areas and thus improves the accuracy of the calibration, since the statistical determination of the slope angle of the groove areas will be more precise the larger the measurement areas. Furthermore, a significant depth also allows for 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 significant depth also facilitates visualization with the naked eye, and therefore the identification of the gauge groove.

[0067] A shallow depth, typically on the order of 1000 nm, eliminates the risk that the low-height tips will not reach the bottom of the groove due to prohibitive contact between the microlever and the gauge.

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

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

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

[0071] This semi-circular geometry has the advantage of providing variable slopes along its contour, with the same angle value opposite each other. Thus, the conversion factor required for calibration can be determined from several angles, allowing for greater accuracy through statistical analysis. The semi-circular geometry of the groove also has the advantage of being completely independent of the alignment of an indenter's engraving tip.

[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 The friction coefficients 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 this is not the case experimentally, it means that there is either a misalignment of the sample with respect to the cantilever, or some other problem. In the case of the conventional 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 gauge can be less than 10 nm, preferably less than 1 nm, for a topographic image of the substrate of 1 itm2. As an example, this substrate roughness can be defined by a mean square roughness.

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

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

[0078] Fused silica, by virtue of its method of obtaining it, has the advantage of being an amorphous silica with a very high purity, in addition to being rigid and hard as well as resistant to corrosion and chemically inert.

[0079] The fused silica also exhibits a low coefficient of thermal expansion (0.5.10-6 K 1 to 0.6.10-6 K1) and a very low surface roughness without necessarily having to resort to 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. Moreover, fused silica has silanol groups on its surface, which allow for the easy grafting of chemical molecules and thus modify the nature of the chemical functionalities on the surface.

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

[0082] This method for manufacturing a gauge is simple, quick, and easy to implement, and much less expensive than existing gauge manufacturing methods. Indeed, the groove is simply made using an indenter, nanoindenter, or any other suitable device, all commercially available. The indenter can be a micro- or nano-indenter.

[0083] The use of an indenter technique is by no means obvious to a person skilled in the art. Indeed, these devices appear too simple in their implementation, not technologically advanced enough considering the dimensions of the grooves generated, of on 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 for such a technique.

[0084] This method for manufacturing a gauge allows for great flexibility in achieving specific geometries adapted for calibration, particularly for specific AFM tip geometries. Thus, this method for manufacturing a gauge makes it possible to create grooves of varying lengths, with constant depths or gradients, and reproducible in large numbers within the limits of the substrate size used to create the gauge.

[0085] This method of manufacturing a gauge is much simpler to implement and more environmentally friendly. Indeed, the prior art Varenberg gauge requires applying a chemical treatment while controlling parameters such as temperature, the choice of solute, and its concentration. The gauge proposed by Tocha requires a certain degree of skill to select the correct parameters of the focused ion beam in order 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 process is essentially dictated by the cost of the substrate supporting the groove or any other coating supporting the engraving.

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

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

[0089] It is preferable to use indenters whose geometry allows for very shallow slopes to be obtained when creating the groove. Indenters with a Vickers, Knoop, cubic, spherical, conical or Berkovich type point are the most suitable.

[0090] A method is proposed for determining a coefficient of friction of the substrate or of a thin film on said substrate of the aforementioned type, comprising the steps of: a. align a microlever so that an X-axis of a microlever is aligned and centered with a principal axis along a direction of an apex of a groove in a scratched substrate, b. to produce topographic images and LFM images formed during an outward pass, called LFM Trace, and a return pass, called LFM Retrace, perpendicular to the furrow and centered on the furrow produced, c. calculate the slopes of the furrow sides from the topographic images obtained, d. Calculate the average of the sum and 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 caliber flanks, 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 solving 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 support 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 include, between steps d) and e), the successive steps of: - calculate an average value of the difference between the values ​​of the LFM Trace and LFM Retrace signals respectively for different support forces, and calculate the slope between the average value of the difference between 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 respectively LFM Trace and LFM Retrace on an upward part for different support forces, called the average upward value, and on a downward part, called the average downward value, of said groove and calculate the slope coefficient between the difference between the average upward value and the average downward value on the one hand and the support force on the other hand, and make the ratio between the two slope coefficients obtained.

[0094] A calibration method for 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 consisting 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 gauge 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 uncertainties related to the calibration of the normal force and the piezoelectric actuator used to obtain the topographic and LFM images. In fact, these images allow us to determine the angle of the gauge's slope. Furthermore, the actuator calibration allows us to quantify the normal load applied to the contact, thus ensuring the invariance of the LFM images.

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

[0097] [Math.20] r —_l (20) ^LFM~ fiC\

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

[0099] Other features, details and advantages will become apparent upon reading the detailed description below, and upon analysis of the accompanying drawings, on which: Fig. 1

[0100] [Fig.l] [Fig.l] 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 gauge according to the prior art. Fig. 3

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

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

[0104] [Fig.5] [Fig.5] shows a diagram of the generic profile of a groove of a gauge according to the invention, seen from 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 straight furrow with a gradient of width and / or depth, B a curvilinear furrow and 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 an engraving point of an indenter with spherical geometry. Fig. 8

[0107] [Fig.8] [Fig.8] shows different possibilities of arrangement of grooves of a caliber according to the invention with in A, V-shaped grooves, in B V-shaped grooves but not identical, 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. 11] [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), the angles 0 of the slopes of the groove surfaces of the gauge Fig. 12

[0111] [Fig. 12] [Fig. 12] Figure 12 represents a histogram of the slope image, with the number of measurement points on the y-axis and the topographic slope on the x-axis. Fig. 13

[0112] [Fig. 13] [Fig. 13] represents a histogram of the sum of the LFM Trace and LFM Retrace images (solid line curve) and a histogram of the difference of the LFM Trace and LFM Retrace images (dotted line 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 sum and difference mentioned on the abscissa. Fig. 14

[0113] [Fig. 14] [Fig. 14] shows a curve of the average value of the difference between Trace and Retrace images as a function of the support 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 flanks of the groove in the sense of equation 20 and as a function of the support force. Description of the implementation methods

[0115] As illustrated in [Fig. 5], a 20-gauge atomic force microscope is proposed comprising: - a substrate 21 generally flat, comprising at least one groove 22 including at least a first 23 and at least a second 24 surfaces 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 by two.

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

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

[0118] As illustrated in [Fig. 6], said groove 22 can be straight 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 have a plurality of grooves 22 parallel to each other. The substrate may have a plurality of grooves arranged side by side in the form of a grid. Such a grid of grooves is visible to the naked eye and facilitates the identification of the grooves on the gauge substrate.

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

[0121] The grooves 22 can extend longitudinally along a straight 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 pm.

[0122] The furrows 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 furrow surfaces 22.

[0123] The maximum depth P illustrated in [Fig.4], i.e. 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] The surface width of the groove can be constant or variable along this groove. By surface width, we mean 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 straight with a gradient of surface width.

[0126] As illustrated in [Fig. 7], a cross-section of the groove 22 can have a 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 the same angle value for a given height h, h' opposite each other. Thus, the determination of a CLFM conversion factor necessary for calibrating said AFM can be performed from several angles, thereby allowing for greater accuracy through statistical analysis. This therefore requires maintaining h = h'. The semi-circular geometry of groove 22 also has the advantage of being completely independent of the alignment of an indenter's engraving tip.

[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 verify, by means of 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 can comprise a plurality of V-shaped grooves 22 of identical angles for a given groove 22, but of variable 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] with the addition of a groove of conical or semi-circular geometry. These grooves 22 can be arranged side by side and separated by a flat 28 whose width can be between 50 and 100 pm. This width of the flat 28 allows the AFM actuator to remain within its linearity range in terms of scanning. This configuration also improves calibration accuracy by determining a CFLm conversion factor in a single step from the angles of the V-groove, which has at least two different angles, and by verifying the parallelism of the gauge with respect to a lower face 29 of the substrate 21.

[0131] A roughness (generally the root mean square roughness) of the substrate 21 measured by an AFM can be less than 10 nm, preferably less than 1 nm, for a topographic image of the substrate of 1 pm². The substrate 21 can have an upper face 30 and a lower face 29 that are as parallel as possible. A substrate 21 with a specular-type surface can be ideal with respect to calibration accuracy.

[0132] The upper face 30 of the substrate 21 may have an essentially flat area. Such an area, which may have very low surface roughness, is advantageous because it allows for precise and easy calibration of the normal forces.

[0133] In certain specific cases, the substrate 21 can be treated to be antireflective in order to attenuate reflections on the upper surface 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 with very low surface reflectance is advantageous because it can attenuate or even eliminate interference phenomena. This is beneficial for measuring the deflection or twist of a microcantilever 3 using a PSD dial 5 of an AFM. Indeed, interference can reduce the accuracy of optical AFM measurements.

[0134] The substrate 21 may comprise an amorphous material, preferably 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 "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 "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 high-hardness substrate 21 is advantageous because it can reduce the risk of damage to the gauge, in particular the risk of the gauge being scratched during handling. Such substrate hardness also improves its resistance to wear during calibration.

[0136] The substrate 21 may have the highest possible Young's modulus, preferably greater than 30 GPa, and 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 modulus and compressive strength values ​​cover the entire family of glasses, which is a family of isotropic, inexpensive materials and therefore preferred for the manufacture of said caliber.

[0137] The substrate 21 can have the lowest possible coefficient of thermal expansion. Such a thermal expansion characteristic is advantageous because it avoids local expansion of the substrate 21, particularly when a laser beam from the AFM is reflected off the substrate 21, even though this laser beam is of low power, preferably less than 1 mW.

[0138] The degree of purity of the substrate material 21 can 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 yield a structurally well-defined material with a homogeneous and constant coefficient of friction.

[0139] A method for manufacturing a 20-gauge AFM atomic force microscope is proposed, comprising the steps of: - apply a normal load to a contact between an indenter or a nanoindenter and said substrate (21) to be scratched, - to move 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, - optionally, coat the groove (22) with a thin layer made of 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 can be configured to reach 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.

[0142] As illustrated in [Fig.9], the indenter may include at least one point of the following types: 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 physical vapor deposition (PVD) and / or chemical vapor deposition (CVD) and / or sputtering, with a film of thickness between 1 nm and 1 µm, preferably less than 1 µm, of a material exhibiting isotropic properties in terms of coefficient of friction. These types of deposition technologies allow for the use of other materials to create the groove while still achieving the desired characteristics.

[0144] A method is proposed for determining a coefficient of friction of the substrate or of a thin film on said substrate of the aforementioned type, comprising the steps: a. align a microlever so that an X-axis of the microlever is aligned with a principal axis along a direction of an apex of a groove in a scratched substrate, b. to produce topographic images and LFM Trace images formed during an outward journey and LFM Retrace images formed during a return journey perpendicular to the furrow and centered on the furrow, c. calculate the slopes of the furrow sides from the topographic images obtained, d. calculate the average of the sum and difference of the signal values ​​of the LFM images formed during a forward pass (values ​​called LFM Trace) and a return pass (values ​​called LFM Retrace) for each point of the LFM Trace and LFM Retrace images on 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 made with at least two different support 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 striated substrate 21.

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

[0148] A calibration method for 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 consisting 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 gauge 20 of the aforementioned type.

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

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

[0151] or again:

[0152] CAi=CA2=CA, CZi=Cz2=Cz, with CA and Cz two parameters respectively related to the half-difference and the half-sum of the force components along the X axis. CAi and CA2 are the two prior art parameters associated with the two angles 0i and 02. Similarly, Czi and Cz2 are the two prior art parameters 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] LFM = (17)

[0155] [Math.22] ^LFM2~ ^LFM1~ (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] „ _ FF 11 û'i aA~ ÔFZ ~ R^A^LFM \1^ )

[0158] [Math.24] = = / A A Wz z LFM \ /

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

[0160] [Math.25] R - 2. tanO,^ (21, a)

[0161] Or again:

[0162] [Math.25] R = (21',

[0163] First, the angle θ is thus determined experimentally from the Trace and Retrace topographic images. The respective coefficients θ and α are determined experimentally from the half-sums and half-differences of the LFM images. With θ, α ≠ 0, the value of R is determined from relation (21',a). The friction coefficient θ can also be calculated from equation (21',b). Indeed, θ is a solution of the quadratic equation (21',b) which has two solutions, θA and θB.

[0164] [Math.26] - ^(t+tafiA'y-A.R2 (22')

[0165] [Math.27] l+f««2(9+ l+taififf / AF2 f*B~ ÏR (23')

[0166] The usable solution is easily identified because p is generally less than 1 for most of the 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 are acquired. of a sample at the center of the gauge groove, for at least two different Fz forces, typically for five different Fz forces. The topographic slope image is then calculated. Image (a) in [Fig. 10] represents a topographic image. Image (b) in [Fig. 10] represents an LFM Trace image. Image (c) in [Fig. 10] represents an LFM Retrace image. Graph (d) in [Fig. 10] represents a topographic profile. Graph (e) in [Fig. 10] illustrates LFM Trace 40 and Retrace 41 signal profiles, with the LFM signal in mV on the y-axis and the displacement in pm on the x-axis.

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

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

[0171] The coefficients and can be determined respectively (Equations 19' and 20') from the representation of the ALFM and SLFM parameters as a function of the load Fz applied to the contact (Equations 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 in nN. The slope of each curve allows the ratio R (Equation 21',a) to be calculated, followed by the coefficient of friction p (Equation 21',b).

[0172] In view of the foregoing considerations, the CLfm conversion factor can then be calculated from the following formula:

[0173] [Math.28] ^LFM ~ (20)

[0174] with: p: the dimensionless coefficient of friction of the substrate; aA: a slope 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 the LFM Trace image, and a return scan, called the LFM Retrace image. CA: a dimensionless parameter depending on tan0 and p.

Claims

Demands

1. Caliber (20) of an atomic force microscope comprising: - a substrate (21), having at least one groove (22) comprising at least a first (23) and at least a second (24) surfaces facing each other, the surfaces (23,24) of the groove (22) having isotropic mechanical 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 being equal in pairs, the surface width of said groove (22) being variable along said groove.

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

3. Caliber according to any one of the preceding claims, wherein said groove (22) is straight or curvilinear in a plane of a surface of the substrate.

4. Caliber according to any one of the preceding claims, wherein 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, wherein the maximum depth (P) of the groove is between 10 nm and 20 pm, preferably between 100 nm and 10 pm.

6. Caliper according to any one of the preceding claims, wherein a cross-section of the groove (22) is of semi-circular geometry.

7. Caliber according to any one of claims 1 to 5, wherein a cross-section of the groove (22) has a V-shape.

8. Calibrate according to any one of the preceding claims, wherein 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.

9. Caliber according to any one of the preceding claims, wherein the substrate (21) comprises an amorphous material, preferably a fused silica.

10. A method for manufacturing a gauge (20), according to any one of claims 1 to 9, 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 support 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.

11. A method for manufacturing a gauge according to claim 10, wherein the applied support 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 pm.

12. Method of manufacturing a gauge according to claim 10 or 12, wherein the indenter comprises at least one point of the type: Berkovich, Vickers, cube-wedge, Knoop, sphere and cone.

13. A method for determining a coefficient of friction of the substrate or of a thin film on said substrate of the gauge according to any one of claims 1 to 9, comprising the steps of: a. aligning a microlever so that an X-axis of a microlever is aligned and centered with a principal axis along a direction of an apex of a groove in a scored substrate, the principal axis being the longitudinal axis of the microlever, b. producing topographic images and LFM images formed during a forward pass, called LFM Trace, and a return pass, called LFM Retrace, perpendicular to the groove and centered on the produced groove, c. calculating slopes of the groove flanks from the topographic images produced, d. calculate the average of the sum and difference of the values ​​of the signals respectively LFM Trace and LFM Retrace measured for each point of the LFM Trace and LFM Retrace images of the sides of the gauge, e. calculate the coefficient of friction.

14. A method for determining a coefficient of friction according to claim 13, wherein, in step b), the topographic images and the LFM images are made with at least two different support 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).

15. A method for determining a coefficient of friction according to claim 13 or 14, comprising, between steps d) and e), further, the successive steps of: - calculating an average value of the difference between the values ​​of the LFM Trace and LFM Retrace signals respectively for different support forces, and calculating the slope between the average value of the difference between the values ​​of the LFM Trace and LFM Retrace signals respectively and the support force; - calculating an average value of the sum of the values ​​of the LFM Trace and LFM Retrace signals respectively over an upward section for different support forces, referred to as the average upward value, and over a downward section, referred to as the average downward value, of said groove, and calculating the slope between the difference between the average upward and downward values ​​on the one hand and the support force on the other hand, and calculating the ratio between the two slopes obtained.

16. Method for calibrating an AFM microscope comprising the steps of the method for determining a coefficient of friction according to any one of claims 13 to 15 further comprising a step consisting 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 (22) of the gauge (20) according to any one of claims 1 to 10.

17. A method for calibrating an AFM microscope according to claim 16, wherein the CLFM conversion factor is calculated from the following formula: [Math. 29] C - (20) ,uC\ with: : the dimensionless friction coefficient of the substrate; “a ; a slope determined from the variation of the ALFM parameter with respect to the applied support force F, ALFM representing a difference image between a forward scan, called the LFM Trace image, and a return scan, called the LFM Retrace image. C& ; a dimensionless parameter depending on tanO and p.

Images