DE102018105756B3 - Cantilever for a scanning probe microscope and atomic force microscope - Google Patents

Abstract

The invention relates to a cantilever (14) for a scanning probe microscope, in particular an atomic force microscope (10), comprising (a) a base body (20) having a body portion (44) at a free end (E) an attachment portion (46) for Attaching to the scanning probe microscope, and at the opposite end has a head portion (32), and (b) a tip (34) for scanning an object to be examined, which extends away from the head portion (32). According to the invention, (c) the base body (20) has a neck portion (42) adjoining the body portion (44) and adjoining the head portion (32) and having a neck portion torsional rigidity and (i ) the neck portion torsional stiffness is at most one-tenth of a body portion torsional rigidity of the body portion (44).

Description

The invention relates to a cantilever for a scanning probe microscope, in particular an atomic force microscope, comprising (a) a base body having a body portion having a mounting portion for attachment to the scanning probe microscope at a free end and a head portion at the other end and (b) a tip for rasterizing the examination object extending away from the head portion. In particular, the cantilever is a cantilever for an atomic force microscope.

Such cantilevers are used to interact in a scanning probe microscope, in particular an atomic force microscope, with a surface of the object to be examined. Since the objects that can be manufactured technically have become steadily smaller in recent years, there is a desire to capture ever-smaller structures and forces by means of an atomic force microscope. However, it has been found that the measurement accuracy of existing atomic force microscopes becomes smaller the thinner the tip of the cantilever is for the structures to be measured. With smaller structure sizes in nanotechnology, a thin tip is preferable.

From the US 6,223,591 B1 For example, a cantilever is known for a scanning probe microscope, which has a plate-like extension, so that a torsional vibration can be detected particularly easily. A facilitated lateral deflection and isotropic stiffness ratio, as it is necessary for the nanometrology, can not be achieved with it.

From the US 7,137,291 B2 For example, a scanning probe microscope is known, the drive unit of which is designed to oscillate the cantilever so that it oscillates in a resonant fashion using carbon nanotube tips. In such a cantilever, the tip deviates from lateral forces, but this leads to a strong deformation of the tip and a low detectable signal.

From the US 2008/0087820 A1 For example, a cantilever is known that has two lateral notches to reduce torsional stiffness. In addition, a regulation ensures that the torsion does not assume too large values.

From the US 2011/0041224 A1 is known a cantilever, which has a flap-like structure between the base body and the head portion, which is connected via thin webs respectively with the base body and the head portion. This lowers the torsional rigidity only a small amount, but has the advantage that it can be deduced from the movement of this section on the movement of the tip.

From the US 2008/0128385 A1 is known a cantilever, which has a recess transverse to the longitudinal direction, so that the flexural rigidity is reduced. The recess also leads to a slight reduction in torsional rigidity. Such a cantilever is only partially suitable for nanostructured surfaces.

From the publication "Microfabricated torsion levers optimized for low force and high-frequency operation in fluids" by Beyder and Sachs, Ultramicroscopy 106 (2006) 838-846 discloses a cantilever in which a probe hangs between a tuning fork-shaped structure.

The invention is based on the object to reduce disadvantages in the prior art.

The invention solves the problem by a generic cantilever in which the main body has a neck portion adjoining the body portion and adjoining the head portion and having a neck portion torsional stiffness, said neck portion torsional stiffness being at most one tenth of a body portion torsional stiffness. Torsional stiffness of the fuselage section corresponds.

In other words, the main body with the neck portion has a weakening, which reduces the torsional stiffness. The tip can therefore be deflected much easier laterally compared to known Kantilevern.

The invention is based on the finding that it is particularly favorable when the tip recedes in a direction which corresponds as well as possible to the normal direction on the surface of the test object at the touch point. In known cantilevers, the torsional stiffness of the cantilever is very high in comparison to the flexural rigidity. This causes the tip to be pushed in a direction deviating from the normal direction when it comes into contact with the surface to be measured in normal directions. This leads to the misinterpretation of the measured contour. For example, if the tip comes into contact with the surface to be examined at a 45 ° angle, the tip can hardly move sideways. For example, if the tip comes in contact with the surface to be examined at a 90 ° angle, only a very small torsional signal can be detected, since the bending stiffness of the soft tip is much smaller than the torsional rigidity of the cantilever. A deflection is so significant in the field of Tip, by bending this, instead. This is not detectable and leads to measurement errors. By contrast, in the case of the cantilever according to the invention, the torsional stiffness is so small that the head section can twist and a sufficient torsion signal can be detected. In addition, the position of the neck portion near the tip results in a greater bending angle per deflection of the tip. These improvements result in larger measurement signals and a lower measurement error.

In the context of the present description, the basic body is understood as meaning that part of the cantilever which does not belong to the apex. In other words, the cantilever is composed of the main body and the tip. The tip is that portion of the cantilever whose free end is adapted to interact with the surface of the specimen.

By the feature that a body portion, a head portion and the neck portion exist, it is specifically understood that at least three distinguishable portions exist in which the specified criterion of torsional rigidity is satisfied. In other words, it is possible, but not necessary, for the corresponding sections to be already visible by being different in their cross-sections or materials.

According to a preferred embodiment, the neck portion torsional rigidity corresponds to at most one tenth of the head portion torsional rigidity of the head or torso portion torsional rigidity of the trunk. In this case, there are two torsionally rigid portions, namely the body portion and the head portion, which are connected by a torsionally soft neck portion. In particular, the body portion passes directly into the neck portion and the neck portion immediately merges into the head portion. However, it is also conceivable that the cantilever has two or more neck sections. All that matters is that the three sections, with the exception of the fuselage section, exist at least once. However, it is particularly favorable if exactly one head section, exactly one neck section and exactly one body section exist.

In the following, it is assumed that the tip extends along a z-direction away from the head portion and that the body portion extends along a y-direction. The x-direction results from these definitions in that the resulting coordinate system is a legal system.

In this coordinate system, the inverse stiffness of the cantilever may be related to movement of the tip relative to the attachment portion through an overall inverse stiffness matrix C to be discribed. The inverse stiffness of the tip with respect to movement of the tip relative to the head may be due to a tip inverse stiffness matrix C _s to be discribed. The inverse stiffness of the head portion with respect to movement of the head portion relative to the attachment portion is due to a head inverse stiffness matrix C _c writable.

A first peak stiffness ratio in the form of a quotient of the first diagonal element c _s11 the peak inverse stiffness matrix C _s as a counter and the first diagonal element c _c11 the head inverse stiffness matrix C _c denominator is at most 50, preferably at most 20. In other words, the inverse stiffness of the head with respect to a movement relative to the attachment portion is significantly torsionsweicher than conventional Kantilevern. This allows the head portion to respond to a force at the tip with increased deflection, which deflection motion can be detected.

Preferably, a second peak stiffness value is in the form of a quotient of the second diagonal element c _s22 the peak inverse stiffness matrix C _s as counter and the second diagonal element c _c22 the head inverse stiffness matrix C _c as denominator not more than 50, preferably not more than 20.

It is favorable if a first transverse inverse stiffness value I ₁₁ in the form of a quotient of the first diagonal element c ₁₁ the total inverse stiffness matrix C as a counter and the third diagonal element c ₃₃ of C as denominator is at most 4 or at least 0.25. Alternatively and additionally, there is a second transverse inverse stiffness value I ₂₂ in the form of the quotient of the second diagonal element c ₂₂ as a counter and the third diagonal element c ₃₃ the total inverse stiffness matrix C as denominator at most 4 or at least 0.25. In this way, a high isotropy of the stiffnesses with improved measuring sensitivity results in comparison to Kantilevern from the prior art, which has the advantages discussed above.

The non-diagonal elements of the total inverse stiffness matrix C are preferably at most 4 times the third diagonal element c ₃₃ this matrix. Preferably, at least two, in particular four, preferably six of the non-diagonal elements are equal to zero. It is favorable if the non-diagonal elements of the total inverse stiffness matrix C are at most 1 times the third diagonal element c ₃₃ amount of this matrix. This reduces crosstalk.

The mass of the head portion and the tip, and the neck portion bending stiffness and neck portion torsional stiffness are preferably selected such that a first natural frequency of the cantilever is at least 1000 hertz. If the first natural frequency is too small, the mass of the head section must be reduced. Alternatively, flexural stiffness and / or torsional rigidity may be increased as long as the above requirement for the ratio of torsional stiffnesses between the neck portion and the remaining portions is maintained.

A nominal inverse stiffness is preferably between 100 m / N and 0.01 m / N.

Preferably, the tip is widened. A flared tip is known by the term "flared tip". A flared tip means that the free end of the tip has a larger diameter than spaced from the free end. Such probe tips are particularly advantageous when it should also be touched on the side. In this case, the reduced torsional rigidity of the cantilever according to the invention is particularly advantageous.

According to the invention, an atomic force microscope with a fastening device and a cantilever according to the invention, which is attached to its attachment portion by means of the fastening device.

Such an atomic force microscope preferably has a first drive and a second drive and a drive unit which is designed to drive the drives. Preferably, the drive unit is configured so that the tip is movable in a first oscillation direction and a second oscillation direction, wherein the second oscillation direction is transverse to the first oscillation direction. It is particularly favorable if the drives and the drive unit are designed to move the head section in a rotational oscillation movement relative to the body section and / or attachment section. Preferably, the drives and the drive unit are designed so that the neck portion performs a torsional vibration.

The atomic force microscope preferably also includes a detection unit for detecting an at least two-dimensional, preferably three-dimensional deflection of the head portion relative to the body portion.

• 1a eine dreidimensionale Ansicht eines erfindungsgemäßen Rasterkraftmikroskops,
• 1b ein Kräftediagramm zur Erläuterung der Kräfte, die auf die Spitze beim Kontakt mit einer Oberfläche des zu untersuchenden Objekts wirken,
• 2 eine erste Ausführungsform eines erfindungsgemäßen Kantilevers, der an einer Befestigungsvorrichtung des Rasterkraftmikroskops gemäß 1 befestigt ist,
• 3 in den 3a bis 3d weitere Ausführungsformen erfindungsgemäßer Kantilever und
• 4 in den 4a bis 4c weitere Ausführungsformen erfindungsgemäßer Kantilever und
• 5 in den 5a bis 5b weitere Ausführungsformen erfindungsgemäßer Kantilever.

In the following the invention will be explained in more detail with reference to the accompanying drawings. It shows

• 1a a three-dimensional view of an atomic force microscope according to the invention,
• 1b a force diagram for explaining the forces acting on the tip when in contact with a surface of the object to be examined,
• 2 a first embodiment of a cantilever according to the invention, the at a mounting device of the atomic force microscope according to 1 is attached,
• 3 in the 3a to 3d Further embodiments of cantilevers according to the invention and
• 4 in the 4a to 4c Further embodiments of cantilevers according to the invention and
• 5 in the 5a to 5b Further embodiments of cantilever according to the invention.

1a shows a schematic view of an atomic force microscope according to the invention 10 , which is a schematically drawn fastening device 12 , by means of a cantilever 14 is attached.

The atomic force microscope 10 includes a drive unit 16 that with a first drive 18.1 and a second drive 18.2 connected is. In the present case are the drives 18.1 . 18.2 designed as piezoelectric elements, with a base body 20 of the cantilever 14 are connected. But it is also possible that the drives 18.1 . 18.2 and possibly other existing drives are possible, as well as drives only in mechanical contact with the cantilever 14 and not, as in the present case, which is a preferred embodiment, fixed to the cantilever 14 are connected.

The atomic force microscope 10 also has a position indicator 22 that is a light source 24 , for example in the form of a laser diode, and a detector 26 includes. The light source 24 sends a beam of light 28 from, the, for example by means of an optics 30 , on a head section 32 of the cantilever 14 is directed. Moves a tip 34 of the cantilever 14 , so moves the head section 32 corresponding. The light beam 28 is at the head section 32 reflected, so that a reflected light beam 28 ' arises on the detector 26 falls. From the position of the reflected light beam 28 ' on the detector 26 can on the position of the top 34 be closed in a given coordinate system. Other readout techniques, for example interferometric, piezoelectric or other, are conceivable.

The summit 34 is for scanning a surface 36 of a test object 38 educated. The examinee 38 is on one xy table 40 arranged and can be moved by this at least in the x and y direction. It is also possible that the xy table 40 in the z-direction is movable.

The drive unit 16 is with the drive 18.1 . 18.2 as well as with the detector 26 connected. The type of control of the drives 18.1 . 18.2 is known from the prior art and is therefore not further explained.

(vgl. Formel 1) nicht in Richtung der Kraftspitze $\overrightarrow{F}$

verläuft. 1b shows schematically the forces acting on the tip 34 when touching the surface 36 Act. It can be seen that a horizontal force component F _H from the probing force F _top arises. This, together with a normally acting one, can lead to a stick-slip effect that falsifies the measurement results, for example by the resulting deflection $\mathrm{\Delta }\overrightarrow{s}$

(see formula 1) not in the direction of the force peak $\overrightarrow{F}$

runs.

2 shows a cantilever according to the invention with a main body, in addition to the head portion 32 a neck section 42 and a body section 44 Has. The body section has at its free end e that is, at the end, the neck portion 42 opposite, a mounting portion 46 with which it can be attached to an atomic force microscope. At the head section 32 is the top 34 arranged, which is widened in the present case. Such a tip is referred to in English as "flared tip".

Acts on the top 34 the probing force F _top This leads to an elastic deformation of the entire cantilever 14 ,

beschrieben. Es gilt $$\mathrm{\Delta }\overrightarrow{F}=C^{-1}\mathrm{\Delta }\overrightarrow{s}=:\mathbf{K}\mathrm{\Delta }\overrightarrow{s}$$

A movement of the top 34 relative to the attachment portion of the cantilever 14 is determined by the total inverse stiffness matrix C $$\mathrm{\Delta }\overrightarrow{s}=\left(\begin{array}{l}\mathrm{\Delta }x\\ \mathrm{\Delta }y\\ \mathrm{\Delta }z\end{array}\right)=\left(\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right)\left(\begin{array}{l}\mathrm{\Delta }{F}_x\\ \mathrm{\Delta }{F}_y\\ \mathrm{\Delta }{F}_z\end{array}\right)=C\mathrm{\Delta }\overrightarrow{F}$$

described. It applies $$\mathrm{\Delta }\overrightarrow{F}=C^{-1}\mathrm{\Delta }\overrightarrow{s}=:\mathbf{K}\mathrm{\Delta }\overrightarrow{s}$$

K is the inverse of the total inverse stiffness matrix C and is called the stiffness matrix.

beschrieben.A movement of the tip relative to the head section 32 is through a peak inverse stiffness matrix C _s $$C_S=\left(\begin{array}{ccc}{c}_{s\mathrm{,\; 11}}& c_{s12}& c_{s13}\\ c_{s\mathrm{,\; 21}}& c_{s\mathrm{,\; 22}}& c_{s\mathrm{,\; 23}}\\ c_{s\mathrm{,\; 31}}& c_{s\mathrm{,\; 32}}& c_{s\mathrm{,\; 33}}\end{array}\right)$$

described.

beschrieben, (C =C_c + C_s).A movement of the head section 32 relative to the attachment section 46 is determined by a head inverse stiffness matrix C _c $$C_C=\left(\begin{array}{ccc}{c}_{c\mathrm{,\; 11}}& c_{c12}& c_{c13}\\ c_{c\mathrm{,\; 21}}& c_{c\mathrm{,\; 22}}& c_{c\mathrm{,\; 23}}\\ c_{c\mathrm{,\; 31}}& c_{c\mathrm{,\; 32}}& c_{c\mathrm{,\; 33}}\end{array}\right)$$

described, (C = C _c + C _s ).

A mass m ₃₂ of the head is between m ₃₂ = 0.5 picogram to 100 micrograms. A length L _ges is between 4 microns and 300 microns, L _eff is between 4 microns and 300 microns. A width w ₄₄ of the fuselage section 44 is preferably between 2 microns and 200 microns, a width ₄₂ of the neck section 42 which is a preferred embodiment, is at most one tenth of the width w ₄₄ of the fuselage section and is in this case between 0.03 microns and 10 microns.

A thickness t ₄₄ of the fuselage section is between 0.01 microns and 10 microns, a thickness ₄₂ of the neck is between 0.01 microns or 10 microns.

It has been found that a neck length L ₄₂ = L ₁ -L _{2 is} 0.1 microns to 60 microns. A length L ₃₂ the head portion is preferably at least three times the neck length L ₄₂ and in the present case is between 2 microns and 200 microns. A width w ₃₂ of the head is 2 microns to 200 microns, a mean nominal diameter of the tip 34 is between 3 nanometers and 5 microns. A top length L ₃₄ is between 0.01 microns and 300 microns. The head section 32 can take a lead 48 have, so the top 34 at its free end may have a distance of L _tip = 0.5 microns to 350 microns.

For example, the cantilever 14 designed to absorb a force up to 100 nanoneewton, whereby forces in the range between 1 and 10 nanoneewton can be measured with a relative accuracy of 5%.

A natural frequency of the cantilever, d. H. the frequency with which it oscillates in its fundamental mode is above one kilohertz, for example at 1.5 kilohertz.

From the total inverse stiffness matrix C and the peak inverse stiffness matrix C _s and the head inverse stiffness matrix C _c the following characteristic values result. A first peak _{stiffness ratio} I _s11 = c _{s, 11} / c _{c, 11} is I _s1 = 5. The transverse inverse stiffness values are in the present case I ₁₁ = 1.2 and I ₂₂ = 1.5, where the c _{s, 11} = c _{s, is 22} . The non-diagonal elements c ₁₂ . c ₁₃ . c ₂₁ . c ₃₁ are in the present case all less than a twentieth of c ₃₃ , in which c ₂₃ and c ₃₂ less than 0.65 times the third diagonal element c ₃₃ are.

3a shows a second embodiment of a cantilever according to the invention 14 in which the top 34 not expanded.

3b shows a second embodiment of a cantilever according to the invention 14 in which the neck section through two incisions 50.1 . 50.2 is formed.

3c shows a further embodiment of a cantilever according to the invention, in which the neck portion 42 as in the embodiment according to 3a is formed by a thin web, wherein the web in the embodiment according to 3c biconcave is formed.

3d shows a further embodiment of a cantilever according to the invention 14 with more than one neck section ( 42 ).

4a shows a further embodiment in which, as in 3b the head section 42 through cuts 50.1 . 50.2 is defined.

4 shows in 4a a cantilever according to the invention 14 , at the neck section 42 is formed by a range of significantly reduced thicknesses. cuts 50.1 . 50.2 cause only the neck section 42 with the reduced thickness, the connection between the head section 32 with the fuselage section 44 forms.

4b shows a further embodiment of a cantilever according to the invention 14 in which in addition to the neck section 42.1 as he for 4a is described, a second neck portion 42.2 is available.

4c shows a cantilever according to the invention according to the second aspect of the invention. This has no body section, but the torsional stiffness is significantly lower than in Kantilevern according to the prior art.

5a shows a cantilever according to the invention 14 with a neck section 42 passing through the recess 52 in the main body 20 is effected. In the present case, the recess 52 with aspiration 54.1 . 54.2 stiffened.

5b shows a further view of a cantilever according to the invention 14 with reduced torsional rigidity.

LIST OF REFERENCE NUMBERS

10

Atomic Force Microscope

12

fastening device

14

cantilever

16

control unit

18

drive

20

body

22

position knife

24

light source

26

detector

28

beam of light

30

optics

32

header

34

top

36

surface

38

examinee

40

x-y table

42

neck section

44

fuselage section

46

attachment section

48

head Start

50

incision

52

recess

54

strut

F _H

Horizontal force

F _top

contact force

e

free end

m

Dimensions

L _ges

Length of the cantilever

W

width

L

length

T

thickness

Claims (9)

Cantilever (14) for a scanning probe microscope, in particular an atomic force microscope (10), having (a) a base body (20), which a body portion (44) having a mounting portion (46) for attachment to the scanning probe microscope at a free end (E), and having a head portion (32) at the opposite end, and (b) a tip (34) for scanning an object under inspection extending from the head portion (32), characterized in that (c) the base body (20) has a neck portion (42), which adjoins the body portion (44) and to which the head portion (32) and that has a neck portion torsional rigidity and that (d) the neck portion torsional stiffness is at most one tenth of a body portion torsional rigidity of the body portion (44). Kantilever (14) after Claim 1 , characterized in that the neck portion torsional rigidity corresponds to at most one tenth of a head portion torsional stiffness of the head portion (32), without a tip. A cantilever (14) according to any one of the preceding claims, characterized in that (a) the tip (34) extends along a z-direction away from the head portion (32) and the body portion (44) extends along a y-direction (b ) an inverse stiffness of the cantilever (14) with respect to a movement of the tip (34) relative to the attachment portion (46) is described by an overall inverse stiffness matrix (C), (c) an inverse stiffness of the tip (34) with respect to movement of the free one Tip end (34) is writable relative to the head portion (32) by a tip inverse stiffness matrix (C _s ), (d) an inverse stiffness of the head portion (32) relative to movement of the head portion (32) relative to the attachment portion (46) a head inverse stiffness matrix (C _c ) is writable; and (e) a first peak _stiffness ratio (I _s1 = c _{s, 11} / c _c11 ) in the form of a quotient of the first diagonal _element (c _{s, 11} ) of the spit zen inverse stiffness matrix (C _s ) as a numerator and the first diagonal _element (c _c11 ) of the head inverse stiffness matrix (C _c ) as a denominator is at most 50. Cantilever according to one of the preceding claims, characterized in that a second peak _stiffness ratio (I _s2 = c _{s, 22} / c _c22 ) in the form of a quotient of the second diagonal element (c _{s, 22} ) of the peak inverse stiffness matrix (C _s ) as a counter and the second diagonal _element (c _c22 ) of the head inverse stiffness matrix (C _c ) as a denominator is at most 50. Cantilever (14) according to one of the preceding claims, characterized in that (a) a first transverse inverse stiffness value (I ₁₁ ) in the form of a quotient (I ₁₁ = c ₁₁ / C33) from the first diagonal element (c ₁₁ ) of the total Inverse stiffness matrix (C) as a numerator and the third diagonal element (c ₃₃ ) of the total inverse stiffness matrix (C) denominator is at most 4 and / or at least 0.25 and / or (b) a second transverse inverse stiffness value (I ₂₂ ) in shape a quotient (I ₂₂ = c ₂₂ / C33) from the second diagonal element (c ₂₂ ) of the total inverse stiffness matrix (C) as a numerator and the third diagonal element (c ₃₃ ) of the total inverse stiffness matrix (C) as denominator at most 4 and / or at least 0.25. A cantilever (14) according to any one of the preceding claims, characterized in that (a) the total inverse stiffness matrix (C) has non-diagonal elements (c ₁₂ , c ₁₃ , c ₂₁ , c ₃₁ , c ₂₃ , c ₃₂ ) which are smaller are four times the third diagonal element (c ₃₃ ) of the total inverse stiffness matrix (C), in particular zero, and / or (b) the peak inverse stiffness matrix (C _s ) non-diagonal elements (c _{s, 12} , c _{s, 13} , c _{s, 21} , c _{s, 31} , Cs, 23, Cs, 32) having at most one twentieth of the minimum of the diagonal elements (c _s11 , c _s22 , c _s33 ) of the peak inverse stiffness matrix (C _s ), especially zero, are. Atomic force microscope (10) with (A) a fastening device (12) and (B) a cantilever (14) according to any one of the preceding claims, which is fixed at its attachment portion (46) by means of the fastening device (12). Atomic force microscope (10) according to Claim 7 , characterized by (a) a first drive (18.1), (b) a second drive (18.2) and (c) a drive unit (16) which is configured such that the tip (34) in a first oscillation direction and a second Oscillation direction, which is transverse to the first direction of oscillation, is movable. Atomic force microscope (10) according to Claim 7 or 8th characterized in that the one drive unit (16) is adapted to move the head portion in a rotational oscillatory motion relative to the body portion (44).

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