**3. Dual‐axis FFM probes**

uses the torsion angle *θ* and vertical deflection *∆z* for detecting the friction force *F*<sup>L</sup> and load *F*V. Two deformations have to be independent of each other for accurate measurement of the friction force and load. Considering that both deformations occur at the end of the micro cantilever, they are possible to interfere with each other. The independent deformations are valid only when the deformations are small enough, which means that the friction force and load are small enough. This mechanical interference cause significant drawbacks in FFM.

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

Tip Tip

**Figure 2.** Typical types of micro cantilever for FFM. (a) I-shaped and (b) V-shaped cantilevers. The figures are viewed

The first drawback is the decrease of the measurement accuracy [5, 6]. As described in Section 2.1, in Eqs.(1) and (2),the tensionalrigidity *k*<sup>l</sup> and spring constant *k*<sup>v</sup> are assumed to be constant. However, when the friction force is large, the torsional rigidity *k*<sup>l</sup> and the spring constant *k*<sup>v</sup> depends on the load and friction force. These limit FFM applications for conventional probe. Therefore, conventional FFMs remain at the level of qualitative evaluation means in many

The second drawback is the decrease of the measurement performance. The fundamental equations, Eqs. (1) and (2) indicate that the improvement of the force sensitivity requires the decrease of the rigidity, *k*<sup>l</sup> or *k*v. In contrast, the reduction of the mechanical interference requires the high rigidity for the counterpart deformation. For example, the torsional rigidity has to be set high in order to measure the load accurately. Since the V‐shaped cantilevers are designed for a contact AFM mode, crossed cantilever structure is adopted in order to increase

Probe base Probe base

Microcantilever Microcantilever

(a) (b)

from the tip side.

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applications.

Many trials have been done in order to overcome the above drawbacks of the conventional FFM. One promising candidate is a dual‐axis probe. The mechanical interference problem in the conventional probe is caused by the fact that the probe uses the two deformations of the same part, the probe end. If the different parts of the probe deform due to the friction force and load, the mechanical interference can be reduced or eliminated. Dual‐axis probe is based on this idea. Chui et al. presented the probe that serially connected an array of cantilevers to a V‐shaped cantilever with a tip [8]. The schematic structure is shown in Figure 3. The surface of the cantilever array is set vertically to the V‐shaped cantilever one. The double cantilever array laterally deflects for the friction force and V‐shaped cantilever vertically deforms for the load. The friction force and load is obtained from these lateral and vertical deflections. Ando et al. presented the concept of another type of dual‐axis probe, where the two double cantile‐ vers that rotate by 90 degrees to each other are serially connected as shown in Figure 4 [9]. The double cantilever with its surface normal to the sample surface deflects for the friction force and another double cantilever does for the load.

The detection method for vertical deflection of the probe for conventional FFM can be applied to the dual‐axis probe whereas that forlateral one cannot because the probe does not twist and deflects laterally. In the optical lever method, which is widely used in conventional FFMs, the light does not move on the PD even if the probe deflects laterally. Therefore, the optical lever method cannot be applied to dual‐axis probes directly. Moreover, in the both dual‐axis probes, the deformation parts are serially connected as shown in Figures 3 and 4. The displacement of

the probe end is the sum of the deformations of two deformation parts such as the cantilever array and V‐shaped cantilever. This means that the deformations of the two parts cannot be determined by measuring the displacement of the probe end as can be done in conventional FFMs. In the probe that presented by Chui et al., in orderto solve this problem, they fabricated a very special type of the probe that has piezoresistive sensors both on the lateral and vertical cantilevers to detect lateral and vertical deflections. In general, the piezo resistive sensor is not easy to fabricate on the double cantilever array because their surface is normal to the base substrate. In the probe that presented by Ando et al., the solution for this problem was on a conceptual level and not demonstrated experimentally. Thus, the standard probe for the dual‐ axis FFM has not been established yet. Recently, a new type of dual‐axis probe called micro mechanical probe (MMP) has been presented [10]. This probe can overcome the significant problemofthedual‐axisprobeasmentionedabove.ThedetailsoftheMMParedescribedbelow.

**3.1. Concept of Micro Mechanical Probe (MMP)**

the friction force *F*<sup>L</sup> and load *F*<sup>V</sup> can be obtained by

conventional FFM to dual‐axis FFM.

**3.2. Mechanical design of MMP**

The structure and set‐up of MMP are schematically shown in Figure 5. This probe consists of the double cantileverforthe friction force detection and the torsion beam forthe load detection. The tip is fabricated at the end of the double cantilever. The double cantilever is supported by the torsion beam and rotates along the torsion beam when the load is applied to the tip. In this probe, the deformation parts are not connected serially as done in the dual‐axis probes that above mentioned. This can provide that both the deformations of the double cantilever and torsion beams can be measured by detecting the displacement of the probe end. By detecting the lateral deflection of the double cantilever *∆x* and the torsion angle of the torsion beam, *θ*,

> *FV* = *ktv l t*

where *k*Ld and *k*Vt are the spring constant of the double cantilever and torsional rigidity of the torsion beam, respectively. In the MMP, the lateral deflection *∆x* and the torsion angle can be measured by detecting the lateral and vertical displacements of the probe end. As described above, the lateral displacement of the dual‐axis probe cannot be detected by the optical lever method. In the MMP, the low reflection pattern called optical lever pattern is fabricated on the probe head surface. As one of the optical lever pattern, a micro roof‐shaped structure was presented [11]. The light that focused onto the roof‐shaped structure scatter whereas the light focused onto the flat surface reflects and goes to the PD forthe optical lever method. Therefore, the reflection light forms the light spot with a dark pattern on the PD. When the load is applied, the light spot on the PD moves in the vertical direction as does in conventional FFM.In contrast, when the friction force is applied, the spot does not move but the dark pattern generated by the optical lever pattern moves laterally. Therefore, the differential signal (*I*A+*I*B)‐(*I*C+*I*D) gives the vertical displacement of the probe head or the torsion angle of the torsion beam *θ* whereas (*I*A+*I*C)‐(*I*B+*I*D) gives the lateral deflection of the double cantilever *∆x*. This method for measur‐ ing the vertical and lateral displacements are the same as that in conventional FFMs as explained in Section 2.1. This indicates that the optical lever method, which is widely used in conventional FFMs, can be applied to the MMP‐based dual‐axis FFM. Therefore, the MMP can be easily installed to conventional FFM or AFM setups with FFM options and can change

Let us think about the necessary structure for the MMP [12]. In general, the needed force resolution for the friction force and load is of the order of 1 nN. The typical displacement resolution of the optical lever method is of the order of 0.1 nm. Therefore, a required spring constant of the double cantilever and torsion beam is of the order of 1 N/m. In conventional FFM probes, the typical lateral and vertical spring constants of V‐shaped cantilever is around

*FL* =*kdlΔx* (3)

*θt* (4)

Measurement of Frictional Properties on the Micro/Nanometer Scale 195

**Figure 3.** Schematic of dual-axis FFM probe with an array of double cantilevers for the friction force detection and Vshaped cantilever for the load detection.

**Figure 4.** Schematic of a dual-axis FFM probe with serially connected double cantilevers for the friction and load detections

#### **3.1. Concept of Micro Mechanical Probe (MMP)**

the probe end is the sum of the deformations of two deformation parts such as the cantilever array and V‐shaped cantilever. This means that the deformations of the two parts cannot be determined by measuring the displacement of the probe end as can be done in conventional FFMs. In the probe that presented by Chui et al., in orderto solve this problem, they fabricated a very special type of the probe that has piezoresistive sensors both on the lateral and vertical cantilevers to detect lateral and vertical deflections. In general, the piezo resistive sensor is not easy to fabricate on the double cantilever array because their surface is normal to the base substrate. In the probe that presented by Ando et al., the solution for this problem was on a conceptual level and not demonstrated experimentally. Thus, the standard probe for the dual‐ axis FFM has not been established yet. Recently, a new type of dual‐axis probe called micro mechanical probe (MMP) has been presented [10]. This probe can overcome the significant problemofthedual‐axisprobeasmentionedabove.ThedetailsoftheMMParedescribedbelow.

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

**Figure 3.** Schematic of dual-axis FFM probe with an array of double cantilevers for the friction force detection and V-

V-shaped cantilever for load detection

Double cantilever for load detection

Tip

Tip

Double cantilever

Silicon substrate

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shaped cantilever for the load detection.

Silicon substrate

detections

for friction force detection

Double cantilever

for friction force detection

**Figure 4.** Schematic of a dual-axis FFM probe with serially connected double cantilevers for the friction and load

The structure and set‐up of MMP are schematically shown in Figure 5. This probe consists of the double cantileverforthe friction force detection and the torsion beam forthe load detection. The tip is fabricated at the end of the double cantilever. The double cantilever is supported by the torsion beam and rotates along the torsion beam when the load is applied to the tip. In this probe, the deformation parts are not connected serially as done in the dual‐axis probes that above mentioned. This can provide that both the deformations of the double cantilever and torsion beams can be measured by detecting the displacement of the probe end. By detecting the lateral deflection of the double cantilever *∆x* and the torsion angle of the torsion beam, *θ*, the friction force *F*<sup>L</sup> and load *F*<sup>V</sup> can be obtained by

$$F\_L = k\_{dl} \Delta \mathbf{x} \tag{3}$$

$$F\_V = \frac{k\_{tv}}{l\_t} \Theta\_t \tag{4}$$

where *k*Ld and *k*Vt are the spring constant of the double cantilever and torsional rigidity of the torsion beam, respectively. In the MMP, the lateral deflection *∆x* and the torsion angle can be measured by detecting the lateral and vertical displacements of the probe end. As described above, the lateral displacement of the dual‐axis probe cannot be detected by the optical lever method. In the MMP, the low reflection pattern called optical lever pattern is fabricated on the probe head surface. As one of the optical lever pattern, a micro roof‐shaped structure was presented [11]. The light that focused onto the roof‐shaped structure scatter whereas the light focused onto the flat surface reflects and goes to the PD forthe optical lever method. Therefore, the reflection light forms the light spot with a dark pattern on the PD. When the load is applied, the light spot on the PD moves in the vertical direction as does in conventional FFM.In contrast, when the friction force is applied, the spot does not move but the dark pattern generated by the optical lever pattern moves laterally. Therefore, the differential signal (*I*A+*I*B)‐(*I*C+*I*D) gives the vertical displacement of the probe head or the torsion angle of the torsion beam *θ* whereas (*I*A+*I*C)‐(*I*B+*I*D) gives the lateral deflection of the double cantilever *∆x*. This method for measur‐ ing the vertical and lateral displacements are the same as that in conventional FFMs as explained in Section 2.1. This indicates that the optical lever method, which is widely used in conventional FFMs, can be applied to the MMP‐based dual‐axis FFM. Therefore, the MMP can be easily installed to conventional FFM or AFM setups with FFM options and can change conventional FFM to dual‐axis FFM.

#### **3.2. Mechanical design of MMP**

Let us think about the necessary structure for the MMP [12]. In general, the needed force resolution for the friction force and load is of the order of 1 nN. The typical displacement resolution of the optical lever method is of the order of 0.1 nm. Therefore, a required spring constant of the double cantilever and torsion beam is of the order of 1 N/m. In conventional FFM probes, the typical lateral and vertical spring constants of V‐shaped cantilever is around

**Figure 5.** Schematic of the micro mechanical probe (MMP)-based FFM. The MMP consists of a double cantilever for the friction force detection and a torsion beam for the load detection.

100 and 0.1 N/m, respectively, and the typical lateral and vertical spring constants of I‐shaped cantilever is around 100 and 1 N/m, respectively. These indicate that the friction force sensi‐ tivity is two or three order of magnitude lower than that of the load. This is because these probes are designed for AFM and the mechanical interference is reduced by sacrificing the friction sensitivity as described above.

The spring constant of the double cantilever beam in the lateral direction is given by

$$\mathcal{k}\_{dl} = 2E \frac{b\_d \hbar \, \mathrm{d}^3}{\mathrm{l}\_d^3} \tag{5}$$

*ktl* <sup>=</sup> <sup>2</sup> 3 *E bt* 3 *ht l c* 2 *l t*

**3.3. Fabrication method of MMP**

Silicon substrate

tion by the etching.

[001]

By using Eqs. (5) to (8), the spring constants are obtained as *k*dl = 4.3 N/m, *k*dv = 1.5 x 103 N/m, *k*tv = 13.1 N/m, *k*tl = 4.9 x 102 N/m when *l*<sup>d</sup> = 1200 μm, *b*<sup>d</sup> = 185 μm, *h*<sup>d</sup> = 5 μm, *l*<sup>t</sup> = 370 μm, *b*<sup>t</sup> = 70 μm, and *h*<sup>t</sup> = 20 μm. Here, *l*, *b*, and *h* denote the length, width, and thickness, respectively and the suffixes *d* and *t* mean the double cantilever and torsion beam, respectively. The pitch between the double cantilever beams is set to *w*<sup>h</sup> = 400 μm and the tip height *t* is set to 10 μm. The lateral rigidity of the torsion beam *k*tl is 100 times larger than that of the double cantilever beam *k*dl, and the vertical rigidity of the double cantilever beam *k*dv is 100 times larger than that of the torsion beam *k*tv. The probe with these dimensions can measure the lateral and vertical forces independently with a force resolution of 1 nN without the mechanical interference.

Here, the fabrication method of the MMP is described. As described in the above section, the double cantilever of the MMP requires the structure with a very high aspect ratio of around 40: 1. In the above example, a cantilever with a width of 185 μm and the thickness of 5 μm. The structure at these small dimensions is difficult to fabricate for conventional machining techniques. Moreover, the high aspect structure is not easy for even the micromachining techniques although they are suitable for fabrication of the structure on the micrometer scale. Among the current micromachining techniques, anisotropic chemical etching and deep reactive ion etching (DRIE) are candidates that can fabricate microstructure with a high aspect ratio. Although the DRIE can provide height aspect microstructure, it takes efforts to make the fabricated surface flat. In contrast, anisotropic etching can produce flat surface more easily because a crystal plane appears by etching. In the anisotropic chemical etching the shapes of structures that can be fabricated are limited to the crystal structure of the substrate whereas they are not in the DIE. The case where anisotropic etching is selected is explained below.

Etching mask

**Figure 6.** Anisotropic chemical etching through a slit-shaped opening.(a) A {100} silicon substrate. (b) Groove forma‐

(a) Slit shaped opening (b)

Groove formed by etching

W

Measurement of Frictional Properties on the Micro/Nanometer Scale 197

D

[010]

[001]

[010]

(8)

where *E* is Youngʹs modulus. the spring constant of the double cantilever beam in the vertical direction is given by

$$k\_{dv} = \frac{1}{\mathbf{2}} E \frac{b\_d^3 h\_d}{l\_d^3} \tag{6}$$

The effective spring constant of the torsion beam in the vertical direction is given by

$$k\_{tv} = 2f \frac{G b\_t h\_t^{-3}}{l\_c^2 l\_t} \tag{7}$$

where the torsion angle is converted to the vertical displacement of the probe end. The lateral spring constant of the torsion beam *k*tl is given by

$$\lambda\_{tl} = \frac{\mathcal{D}}{\mathcal{B}} E \frac{b\_t^{\;3} h\_t}{l\_c^2 l\_t} \tag{8}$$

By using Eqs. (5) to (8), the spring constants are obtained as *k*dl = 4.3 N/m, *k*dv = 1.5 x 103 N/m, *k*tv = 13.1 N/m, *k*tl = 4.9 x 102 N/m when *l*<sup>d</sup> = 1200 μm, *b*<sup>d</sup> = 185 μm, *h*<sup>d</sup> = 5 μm, *l*<sup>t</sup> = 370 μm, *b*<sup>t</sup> = 70 μm, and *h*<sup>t</sup> = 20 μm. Here, *l*, *b*, and *h* denote the length, width, and thickness, respectively and the suffixes *d* and *t* mean the double cantilever and torsion beam, respectively. The pitch between the double cantilever beams is set to *w*<sup>h</sup> = 400 μm and the tip height *t* is set to 10 μm. The lateral rigidity of the torsion beam *k*tl is 100 times larger than that of the double cantilever beam *k*dl, and the vertical rigidity of the double cantilever beam *k*dv is 100 times larger than that of the torsion beam *k*tv. The probe with these dimensions can measure the lateral and vertical forces independently with a force resolution of 1 nN without the mechanical interference.

#### **3.3. Fabrication method of MMP**

100 and 0.1 N/m, respectively, and the typical lateral and vertical spring constants of I‐shaped cantilever is around 100 and 1 N/m, respectively. These indicate that the friction force sensi‐ tivity is two or three order of magnitude lower than that of the load. This is because these probes are designed for AFM and the mechanical interference is reduced by sacrificing the

**Figure 5.** Schematic of the micro mechanical probe (MMP)-based FFM. The MMP consists of a double cantilever for

Load

B

D C

pattern image

A

Movement of optical lever

*bd hd* 3

<sup>3</sup> (5)

Sample

Tip

PD

Optical lever pattern

Laser spot

Four-segmented

<sup>3</sup> (6)

(7)

*l d*

where *E* is Youngʹs modulus. the spring constant of the double cantilever beam in the vertical

The spring constant of the double cantilever beam in the lateral direction is given by

*kdl* = 2*E*

*kdv* <sup>=</sup> <sup>1</sup> 2 *E bd* 3 *hd l d*

*ktv* = 2 *f*

spring constant of the torsion beam *k*tl is given by

The effective spring constant of the torsion beam in the vertical direction is given by

*Gbtht* 3

where the torsion angle is converted to the vertical displacement of the probe end. The lateral

*l c* 2 *l t*

friction sensitivity as described above.

Torsion beam for load detection

Silicon substrate

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Double cantilever for friction force detection

Optical lever pattern image

> Laser for optical lever

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

Friction force

the friction force detection and a torsion beam for the load detection.

direction is given by

Here, the fabrication method of the MMP is described. As described in the above section, the double cantilever of the MMP requires the structure with a very high aspect ratio of around 40: 1. In the above example, a cantilever with a width of 185 μm and the thickness of 5 μm. The structure at these small dimensions is difficult to fabricate for conventional machining techniques. Moreover, the high aspect structure is not easy for even the micromachining techniques although they are suitable for fabrication of the structure on the micrometer scale. Among the current micromachining techniques, anisotropic chemical etching and deep reactive ion etching (DRIE) are candidates that can fabricate microstructure with a high aspect ratio. Although the DRIE can provide height aspect microstructure, it takes efforts to make the fabricated surface flat. In contrast, anisotropic etching can produce flat surface more easily because a crystal plane appears by etching. In the anisotropic chemical etching the shapes of structures that can be fabricated are limited to the crystal structure of the substrate whereas they are not in the DIE. The case where anisotropic etching is selected is explained below.

**Figure 6.** Anisotropic chemical etching through a slit-shaped opening.(a) A {100} silicon substrate. (b) Groove forma‐ tion by the etching.

Anisotropic chemical etching uses that etch speed depends on the crystal orientation. Figure 6 explains how to fabricate a vertically oriented surface for the double cantilever. In single crystal silicon, the etch speed for {100} plane is higher than those of other orientation planes when aqueous solution of potassium hydrate (KOH) is used as an etchant. When a {100} silicon waferis used as a substrate, {100} plane is parallel (e. g. (100) plane) or normal (e. g. (010) plane) to the wafer surface. By KOH etching the {100} silicon wafer, (010) and (01ˉ0)planes appear and form the normal to the wafer surface with a crystallographic accuracy. First, an etching mask film, which is typically made of silicon oxide or silicon nitride for KOH etching, is formed on the wafer. The wafer is dipped in the etchant after the slit‐shaped opening is formed in the etching mask film as shown in Figure 6. The silicon substrate in this opening is exposed to the etchant and etched during the etching whereas the silicon substrate covered with the etching mask film is protected from the etchant. If we choose a silicon wafer whose crystal plane is the [001] direction and orientation flat of the lower end is 1 ˉ00 , the direction of the opening should be set to be parallel to the crystal direction of [100] or [010]. In the case shown in Fig. 6, the opening is along the [100] direction. As the progress ofthe etching,the groove is formed, whose bottom face is the (100) plane and the sidewalls are (010) and (01ˉ0) planes. When the two parallel slit‐shaped openings are formed in the etching mask, a vertically oriented thin plate is formed between the openings. By arranging the three openings so that two thin films between the three grooves remain when the substrate is fully etched, a double cantilever with a micrometer‐order thickness can be formed. Thus, the thickness of the double cantilever is determined by the slit pitch and width by the thickness of the silicon wafer. Since typical wafer thickness is around 100 to 500 μm, the double cantilever with a high aspect ratio of several tens to one is possible.

It should be noted that the dimensions of target devices are partially constrained in this fabrication method. The etch rates of the crystal plane in the bottom surface and sidewalls are equal because all the planes belong to the {100} planes. In addition, the (010) and (01ˉ0) planes are etched in the lateral direction whereas only the (100) plane is etched in the vertical direction (Figure 6). Therefore, the growth speed of the groove in the lateral direction is twice as large as that in the vertical direction. That is to say, the width is always twice as large as depth in the etched groove. In order to make the device freestanding, all the silicon substrate has to be etched. In this case, the etch depth is equal to the wafer thickness. Therefore, the width of the etched groove is larger than twice the wafer thickness. The thickness of the double cantilever is determined by the pitch of the slit‐shaped openings and the width of the etched groove, that is, the wafer thickness. When the slits are arranged in the photomask, these relations should be considered carefully. In addition, the pitch of the cantilevers of the double cantilever is larger than twice the wafer thickness due to the above reason.

An example of the fabrication method of the MMP is schematically in shown in Figure 7 [11]. The directions of the wafer plane and orientation flat are set to be (001) and (1 ˉ00), respectively. Considering the relationship between the width and depth of the groove, the wafer thickness should be selected, for example, around 200 μm. The larger wafer thickness causes the larger pitch of the cantilevers, which leads to the larger probe head that connects the cantilever. This decreases the naturalfrequency ofthe probe and reduces the robustness against environmental mechanical noises. Usually, the thickness of commercial silicon wafers has a variation of around 10 μm. Prior to the fabrication, the substrates should be uniformly etched so as to reduce the thickness variation. The fabrication processes mainly consists of three anisotropic chemical etching. The etchant is an aqueous solution of KOH for all the etchings. Silicon oxide films for etching mask can be formed by thermal oxidation method. In the first etching, the torsion beam and optical lever pattern are formed (Figure 7(a)). The optical lever pattern is

**Figure 7.** Fabrication process of the micro mechanical probe (MMP). (a) Formation of the optical lever pattern and ridge for the torsion beam. (b) Formation of the tip on the backside of the silicon substrate. (c) Formation of etching

Tip

mask for the substrate etching. (d) Free standing probe after the substrate etching.

C D C D

A B A B

Silicon oxide

A B A B

Torsion beam

(100) plane

C D C D

A B

C D

C D

A B

{100} Silicon wafer

Measurement of Frictional Properties on the Micro/Nanometer Scale 199

(010) plane

Double cantilever beam

(010) plane

(b)

Tip

A B

C D

C D

A B

(c) (d)

(a)

Ridge for torsion beam

Roofshaped optical lever pattern

Silicon oxide Slit-shaped opening

Anisotropic chemical etching uses that etch speed depends on the crystal orientation. Figure 6 explains how to fabricate a vertically oriented surface for the double cantilever. In single crystal silicon, the etch speed for {100} plane is higher than those of other orientation planes when aqueous solution of potassium hydrate (KOH) is used as an etchant. When a {100} silicon waferis used as a substrate, {100} plane is parallel (e. g. (100) plane) or normal (e. g. (010) plane) to the wafer surface. By KOH etching the {100} silicon wafer, (010) and (01ˉ0)planes appear and form the normal to the wafer surface with a crystallographic accuracy. First, an etching mask film, which is typically made of silicon oxide or silicon nitride for KOH etching, is formed on the wafer. The wafer is dipped in the etchant after the slit‐shaped opening is formed in the etching mask film as shown in Figure 6. The silicon substrate in this opening is exposed to the etchant and etched during the etching whereas the silicon substrate covered with the etching mask film is protected from the etchant. If we choose a silicon wafer whose crystal plane is the

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

be set to be parallel to the crystal direction of [100] or [010]. In the case shown in Fig. 6, the opening is along the [100] direction. As the progress ofthe etching,the groove is formed, whose bottom face is the (100) plane and the sidewalls are (010) and (01ˉ0) planes. When the two parallel slit‐shaped openings are formed in the etching mask, a vertically oriented thin plate is formed between the openings. By arranging the three openings so that two thin films between the three grooves remain when the substrate is fully etched, a double cantilever with a micrometer‐order thickness can be formed. Thus, the thickness of the double cantilever is determined by the slit pitch and width by the thickness of the silicon wafer. Since typical wafer thickness is around 100 to 500 μm, the double cantilever with a high aspect ratio of several

It should be noted that the dimensions of target devices are partially constrained in this fabrication method. The etch rates of the crystal plane in the bottom surface and sidewalls are equal because all the planes belong to the {100} planes. In addition, the (010) and (01ˉ0) planes are etched in the lateral direction whereas only the (100) plane is etched in the vertical direction (Figure 6). Therefore, the growth speed of the groove in the lateral direction is twice as large as that in the vertical direction. That is to say, the width is always twice as large as depth in the etched groove. In order to make the device freestanding, all the silicon substrate has to be etched. In this case, the etch depth is equal to the wafer thickness. Therefore, the width of the etched groove is larger than twice the wafer thickness. The thickness of the double cantilever is determined by the pitch of the slit‐shaped openings and the width of the etched groove, that is, the wafer thickness. When the slits are arranged in the photomask, these relations should be considered carefully. In addition, the pitch of the cantilevers of the double cantilever is

An example of the fabrication method of the MMP is schematically in shown in Figure 7 [11].

Considering the relationship between the width and depth of the groove, the wafer thickness should be selected, for example, around 200 μm. The larger wafer thickness causes the larger pitch of the cantilevers, which leads to the larger probe head that connects the cantilever. This decreases the naturalfrequency ofthe probe and reduces the robustness against environmental

ˉ00 , the direction of the opening should

ˉ00), respectively.

[001] direction and orientation flat of the lower end is 1

larger than twice the wafer thickness due to the above reason.

The directions of the wafer plane and orientation flat are set to be (001) and (1

tens to one is possible.

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**Figure 7.** Fabrication process of the micro mechanical probe (MMP). (a) Formation of the optical lever pattern and ridge for the torsion beam. (b) Formation of the tip on the backside of the silicon substrate. (c) Formation of etching mask for the substrate etching. (d) Free standing probe after the substrate etching.

mechanical noises. Usually, the thickness of commercial silicon wafers has a variation of around 10 μm. Prior to the fabrication, the substrates should be uniformly etched so as to reduce the thickness variation. The fabrication processes mainly consists of three anisotropic chemical etching. The etchant is an aqueous solution of KOH for all the etchings. Silicon oxide films for etching mask can be formed by thermal oxidation method. In the first etching, the torsion beam and optical lever pattern are formed (Figure 7(a)). The optical lever pattern is

formed by using the undercut etching under a rectangle‐etching mask. In the second etching, the tip at the probe end is formed (Figure 7(b)). The tip is also fabricated by undercut etching. In the third etching, the double cantilever beam is formed (Figure 7(c)). Through a slit‐shaped opening in the etching mask on the rear side ofthe wafer, the substrate silicon is etched. Finally, the freestanding double cantilever beam is formed (Figure 7(d)). The electron microscope image of a fabricated probe is shown in Figure 8. A magnified view of tip and a roof‐shaped optical lever pattern are also shown. In this example, the thickness, width and length of the double cantilever were about 8 μm, 167 μm, and 1410 μm, respectively. Using the anisotropic chemical etching, the MMP with a high aspect ratio double cantilever can be formed.

in AFMs. That is is because the calibration of the friction force in the MMP can be implemented by obtaining the relationship between the differential signal, (*I*A+*I*C)‐(*I*B+*I*D) and the lateral

Measurement of Frictional Properties on the Micro/Nanometer Scale 201

One methodofthe friction force calibration is shown in Figure 9.In this method, a stepstructure is used as a standard sample. For example, the fraction of the silicon wafer, which is glued onto the flat substrate, can be used as the step structure. The step height is set to be higherthan the double cantilever width. During the probe scanning on the substrate, the probe stops at the step structure as shown in Figure 9(a). In contrast, the probe base, which is attached to the piezo scanner, continues to move. When the optical lever system of an FFM apparatus is implemented so that it moves together with the piezo scanner or probe base, the optical lever pattern appears to move in the inversedirection although the pattern stops atthe step structure. This cause the lateral movement of the dark optical lever pattern on the PD of the optical lever system as showin in Figure 9(b). Since the lateral movement of the pattern is equal to the displacement of the probe base i. e. piezo scanner, the relationship between the signal (*I*A+*I*C)‐

**Figure 9.** Calibration of friction force with a step-structure. (a) Arrangement of the micro mechanical probe and step structure. (b) Typical relationship between the differential signal for probe lateral deflection and probe displacement.

deflection of the double cantilever.

(*I*B+*I*D) and the lateral deflection can be obtained.

**Figure 8.** Fabricated micro mechanical probe (MMP).

#### **3.4. Force calibration**

The force calibration is indispensable for quantitative FFM measurements. In the MMP, the differential signals from the four‐segmented PD, (*I*A+*I*B)‐(*I*C+*I*D) and (*I*A+*I*C)‐(*I*B+*I*D) have to be converted to the lateral deflection of the double cantilever and torsion angle of the torsion beam or vertical displacement of the probe head, respectively. After these sensitivity calibra‐ tion, the deflection and torsion angle can be converted to the friction force and load, respec‐ tively.

The latter can be implemented as is done for the calibration of the vertical deflection in usual AFMs or FFMs. Using force curve measurement, the conversion coefficient can be obtained from the relationship between the piezo displacement and differential signal (*I*A+*I*B)‐(*I*C+*I*D). In conventional FFMs, as described in Section 2.2, the calibration of the friction force is not easy because the torsion angle of the micro cantilever has to be measured. In contrast, the calibration of the friction force in the MMP is similarto usual calibration method forthe vertical deflection in AFMs. That is is because the calibration of the friction force in the MMP can be implemented by obtaining the relationship between the differential signal, (*I*A+*I*C)‐(*I*B+*I*D) and the lateral deflection of the double cantilever.

formed by using the undercut etching under a rectangle‐etching mask. In the second etching, the tip at the probe end is formed (Figure 7(b)). The tip is also fabricated by undercut etching. In the third etching, the double cantilever beam is formed (Figure 7(c)). Through a slit‐shaped opening in the etching mask on the rear side ofthe wafer, the substrate silicon is etched. Finally, the freestanding double cantilever beam is formed (Figure 7(d)). The electron microscope image of a fabricated probe is shown in Figure 8. A magnified view of tip and a roof‐shaped optical lever pattern are also shown. In this example, the thickness, width and length of the double cantilever were about 8 μm, 167 μm, and 1410 μm, respectively. Using the anisotropic

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

chemical etching, the MMP with a high aspect ratio double cantilever can be formed.

10 µm

300 µm 10 µm

The force calibration is indispensable for quantitative FFM measurements. In the MMP, the differential signals from the four‐segmented PD, (*I*A+*I*B)‐(*I*C+*I*D) and (*I*A+*I*C)‐(*I*B+*I*D) have to be converted to the lateral deflection of the double cantilever and torsion angle of the torsion beam or vertical displacement of the probe head, respectively. After these sensitivity calibra‐ tion, the deflection and torsion angle can be converted to the friction force and load, respec‐

The latter can be implemented as is done for the calibration of the vertical deflection in usual AFMs or FFMs. Using force curve measurement, the conversion coefficient can be obtained from the relationship between the piezo displacement and differential signal (*I*A+*I*B)‐(*I*C+*I*D). In conventional FFMs, as described in Section 2.2, the calibration of the friction force is not easy because the torsion angle of the micro cantilever has to be measured. In contrast, the calibration of the friction force in the MMP is similarto usual calibration method forthe vertical deflection

Roof-shaped optical lever pattern

Tip

Toision beam

Double cantilever

**Figure 8.** Fabricated micro mechanical probe (MMP).

**3.4. Force calibration**

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tively.

One methodofthe friction force calibration is shown in Figure 9.In this method, a stepstructure is used as a standard sample. For example, the fraction of the silicon wafer, which is glued onto the flat substrate, can be used as the step structure. The step height is set to be higherthan the double cantilever width. During the probe scanning on the substrate, the probe stops at the step structure as shown in Figure 9(a). In contrast, the probe base, which is attached to the piezo scanner, continues to move. When the optical lever system of an FFM apparatus is implemented so that it moves together with the piezo scanner or probe base, the optical lever pattern appears to move in the inversedirection although the pattern stops atthe step structure. This cause the lateral movement of the dark optical lever pattern on the PD of the optical lever system as showin in Figure 9(b). Since the lateral movement of the pattern is equal to the displacement of the probe base i. e. piezo scanner, the relationship between the signal (*I*A+*I*C)‐ (*I*B+*I*D) and the lateral deflection can be obtained.

**Figure 9.** Calibration of friction force with a step-structure. (a) Arrangement of the micro mechanical probe and step structure. (b) Typical relationship between the differential signal for probe lateral deflection and probe displacement.

> by the solvent, the UV‐irradiated lubricant film remains and the unirradiated lubricants not. By controlling the irradiation area with a photomask, the patterned nm‐thick lubricant film can be obtained. Here, a line and space pattern whose line width and pitch were about 5 μm and 15 μm, respectively. The lubricated region showed the lower friction whereas the disk exposed region showed higher friction. In this measurement, the contact mode was used, which means that the load was constant. Therefore, the friction force distribution shown in Figure 11 shows the distribution of the friction coefficient because the coefficient is obtained

> **Figure 11.** Example measured by a micro mechanical probe. The sample was a nanometer thick lubricant film with line-and-space-patterned by the ultra violet light radiation. The lower region is lubricant remained region and the

> Thus, the MMP can elevate FFM from the qualitative visualization method to the quantitative measurement method. In addition, the optimum conditions as a FFM probe can be selected because the MMP‐based dual‐axis FFM become free from the limitation due to the reduction of the mechanical interference. This can provide high sensitive measurement of both friction force and load, which is difficult in the conventional probe. The MMP is expected to be a

> As described above, the significant problems of the dual‐axis probe can be solved by the MMP‐ based FFM and the MMP can provide the friction properties on the nanometer scale. This is expected to open up the new field of FFM as a quantitative evaluation method. For further advancements, the various sliding speeds are expected. In the current dual‐axis probes, the sliding speed is limited to the scan speed, typically around 1 μm/s, which is determined by

standard probe for FFM by overcoming the problem of the conventional FFM probes.

25 µm

Measurement of Frictional Properties on the Micro/Nanometer Scale 203

by dividing the friction force by the load.

higher is substrate magnetic disk exposed region.

**3.6. Future directions**

**Figure 10.** Calibration of the friction force by using the probe sticking due to the static friction at the beginning of the probe scan.

In the above method, the step structure that specially prepared is used. If the probe sticks to the substrate at the beginning of the probe scan by the static frictional force, the step structure is not necessary. In many cases, at the beginning of the scan, the probe remains still on the sample substrate due to static friction although the probe base or piezo scanner moves. After the elastic force overcomes the static friction, the probe start to slide on the substrate and the friction mode changes from the static to the kinetic friction. The conversion coefficient can be obtained from the relationship between the differential signal and piezo displacement before the probe sliding as shown in Fig. 10. Although this method is easily implemented, the error is possible to occur when the sample does not stick the probe enough. Therefore, the sample for the calibration has to be carefully selected.

In the previous report [13], the conversion coefficient of signal to the deflection, where the MMP was installed to the commercial AFM setup (NanoScope, Bruker), was of the order of several mV/nm. Here, this was determined by the step structure method. From this result, the minimum detection limit of the lateral deflection was obtained as the order of 0.1 nm because the typical noise level was around 1 mV. These results indicate that sub nN force can be detected when the lateral spring constant of the double cantilever is of the order of 1 N/m,

#### **3.5. Example of MMP‐based FFM measurement**

Figure 11 shows an example of the FFM measurement. The sample was a nm‐thick‐lubricant film on a substrate. In this example, the lubricant was pepfluoropolyehter (PFPE) and the substrate was a magnetic disk. Both of the lubricant and disk are used in the lubrication of the HDDs. In addition, the lubricant film was patterned by the ultra‐violet (UV) light treatment [14]. The UV light illumination bonds the lubricant molecule onto the disk surface by photo‐ chemical reaction. If some parts of the lubricated disk is irradiated and whole disk is rinsed by the solvent, the UV‐irradiated lubricant film remains and the unirradiated lubricants not. By controlling the irradiation area with a photomask, the patterned nm‐thick lubricant film can be obtained. Here, a line and space pattern whose line width and pitch were about 5 μm and 15 μm, respectively. The lubricated region showed the lower friction whereas the disk exposed region showed higher friction. In this measurement, the contact mode was used, which means that the load was constant. Therefore, the friction force distribution shown in Figure 11 shows the distribution of the friction coefficient because the coefficient is obtained by dividing the friction force by the load.

**Figure 11.** Example measured by a micro mechanical probe. The sample was a nanometer thick lubricant film with line-and-space-patterned by the ultra violet light radiation. The lower region is lubricant remained region and the higher is substrate magnetic disk exposed region.

Thus, the MMP can elevate FFM from the qualitative visualization method to the quantitative measurement method. In addition, the optimum conditions as a FFM probe can be selected because the MMP‐based dual‐axis FFM become free from the limitation due to the reduction of the mechanical interference. This can provide high sensitive measurement of both friction force and load, which is difficult in the conventional probe. The MMP is expected to be a standard probe for FFM by overcoming the problem of the conventional FFM probes.

### **3.6. Future directions**

**Figure 10.** Calibration of the friction force by using the probe sticking due to the static friction at the beginning of the

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

In the above method, the step structure that specially prepared is used. If the probe sticks to the substrate at the beginning of the probe scan by the static frictional force, the step structure is not necessary. In many cases, at the beginning of the scan, the probe remains still on the sample substrate due to static friction although the probe base or piezo scanner moves. After the elastic force overcomes the static friction, the probe start to slide on the substrate and the friction mode changes from the static to the kinetic friction. The conversion coefficient can be obtained from the relationship between the differential signal and piezo displacement before the probe sliding as shown in Fig. 10. Although this method is easily implemented, the error is possible to occur when the sample does not stick the probe enough. Therefore, the sample

In the previous report [13], the conversion coefficient of signal to the deflection, where the MMP was installed to the commercial AFM setup (NanoScope, Bruker), was of the order of several mV/nm. Here, this was determined by the step structure method. From this result, the minimum detection limit of the lateral deflection was obtained as the order of 0.1 nm because the typical noise level was around 1 mV. These results indicate that sub nN force can be detected when the lateral spring constant of the double cantilever is of the order of 1 N/m,

Figure 11 shows an example of the FFM measurement. The sample was a nm‐thick‐lubricant film on a substrate. In this example, the lubricant was pepfluoropolyehter (PFPE) and the substrate was a magnetic disk. Both of the lubricant and disk are used in the lubrication of the HDDs. In addition, the lubricant film was patterned by the ultra‐violet (UV) light treatment [14]. The UV light illumination bonds the lubricant molecule onto the disk surface by photo‐ chemical reaction. If some parts of the lubricated disk is irradiated and whole disk is rinsed

probe scan.

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for the calibration has to be carefully selected.

**3.5. Example of MMP‐based FFM measurement**

As described above, the significant problems of the dual‐axis probe can be solved by the MMP‐ based FFM and the MMP can provide the friction properties on the nanometer scale. This is expected to open up the new field of FFM as a quantitative evaluation method. For further advancements, the various sliding speeds are expected. In the current dual‐axis probes, the sliding speed is limited to the scan speed, typically around 1 μm/s, which is determined by

the scanner piezo. In many applications, especially mechanical applications such as MEMS/ NEMS or HDDs, the friction properties at a higher sliding speed is required.

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Measurement of Frictional Properties on the Micro/Nanometer Scale 205

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