Received: 19 March 2019 Revised: 17 August 2019 Accepted: 11 October 2019

DOI: 10.1002/sia.6719

R E S E A R CH AR T I C L E

Comparison of the adhesion forces in single and double‐layercoatings on the MEMS surfaces by JKR and DMT models

Mahdi Joulaei1 | Mojtaba Kolahdoozan1 | Mehdi Salehi1 | Mehdi Zadsar2 |

Meisam Vahabi1

1Department of Mechanical Engineering,

Najafabad Branch, Islamic Azad University,

Najafabad, Iran

2Department of Physics, Najafabad Branch,

Islamic Azad University, Najafabad, Iran

Correspondence

Mojtaba Kolahdoozan, Department of

Mechanical Engineering, Najafabad Branch,

Islamic Azad University, Najafabad, Iran.

Email: kolahdoozan@pmc.iaun.ac.ir

Surf Interface Anal. 2019;1–8.

In many medical and industrial applications, some strategies are needed to control the

adhesion forces between the materials, because surface forces can activate or hinder

the function of the device. All actual surfaces present some levels of roughness and

the contact between two surfaces is transferred by the asperities on the surfaces.

The force of the adhesion, which depends on the operating situations, can be influ-

enced by the contact region. The aim of the present study is to predict the adhesion

force in MEMS surfaces using the JKR and DMT models. The surfaces of the coating

material in this research consisted of the single‐layer coating of Gold and Silver, and

the double‐layer coating of TiO2/Gold and TiO2/Silver on the silicon (100) substrates.

The depositing was done by the thermal evaporation method. The results showed

that the double‐layer coating developed by the new deposition method helped the

reduction of the adhesion forces between the probe tip and the specimen surface.

The predicted adhesion forces between the probe and the specimens with DMT

and JKR models were compared with the experimental results. For all specimens,

the simulated data by applying the JKR theory were in a good agreement with the

adhesion force experimental values.

KEYWORDS

adhesion forces, double‐layer coatings, MEMS surfaces, JKR and DMT models

1 | INTRODUCTION

The contact between the two flat surfaces is limited; in fact, many

of the asperities are randomly scattered on the surface. As a result,

the actual contact area is much smaller than the apparent area of

contact. The proximity of asperities creates adhesive contacts with

interatomic attractions. Adhesion has long been the focus of

study.1-3 This phenomenon is used in magnetic storage devices,

Micro/Nano‐Electro‐Mechanical Systems (MEMS/NEMS), and

other miniaturized devices, especially in Microgrippers. Adhesion

force can affect the power, efficiency, and steady‐state ope-

ration systems and devices.4,5 Adhesion phenomenon also influences

the frictional and wear efficiency of the materials in medical

devices.6-8

wileyonlinelibrary.com/jou

For reducing the adhesion force, much search has been conducted

on the coating process. In most studies, Si<100> is used as one of the

most applicable materials in MEMS for the selected surface.9-11

The most important property of microgrippers is their high electric-

ity transmission. So, surface deposition should have low surface adhe-

sion and high conductivity. The thin film gold and silver on the silicon

substrate, because of having conductivity and low surface adhesion,

are used in MEMS appliances, especially in microgrippers.12,13

Titanium dioxide grows in a crystalline manner and has a high

dielectric constant. TiO2 thin films have some properties that lead to

improved surface roughness for less adhesion force,12 they also are

suitable for multilayer thin film device applications,14 Considering the

advantageous properties of TiO2 thin films, in this study, they were

incorporated between silicon and other layers (gold and silver).

© 2019 John Wiley & Sons, Ltd.rnal/sia 1

2 JOULAEI ET AL.

Thermal evaporation is one of the simplest physical vapor deposi-

tion (PVD) techniques in a vacuum environment. Microgrippers are

prepared particularly using MEMS/NEMS.15-20 In this study, this

method was used to coat the surfaces of the specimens.

Surface adhesion forces are obtained by experimental and model-

ing methods. The modeling methods included Hertz, JKR, DMT, and

etc. Traditionally, the Hertz theory has been used to model the elastic

adhesion, while adhesion in the deformable bodies has been modeled

by taking into account the energy of surface (JKR theory21) or the

cohesive forces in the contact with the environments (DMT theory22).

For high surface energy and “soft” elastic materials with large tip

radii, the JKR model is applicable, while for low surface energy and

“hard” stiff solids with small tip radii, the DMT model is used. Accord-

ing to Tabor23, DMT and JKR models represent two extreme cases in

the interactions of adhesive forces, proposing a unitless number

(Tabor parameter) to determine which model could be used in describ-

ing a given condition. Later, Maugis24 proposed a more accurate com-

posite, which was the continuous transition regime between DMT and

JKR limits. Theory of Maugis could be applied to any system (any

materials) with both low and high adhesion forces. These adhesion

models have been improved for the smooth molecular surfaces. How-

ever, such surfaces with ideal smoothness do not exist in practice due

to the manufacturing processes. A large number of theoretical and

experimental works have been conducted on single asperity contact

adhesion.25,26 Some other studies have investigated the effect of sur-

face roughness on adhesion.27-30 However, not enough studies have

been conducted on multi‐asperity contact models.31-38 To model

adhesion forces, it is required to take surface topography images.

The Atomic Force Microscopy (AFM) is equipped with a cantilever

that at its free end has a tip that driven near the surface of the inves-

tigated specimen. Also, the cantilever is deflected owing to the inter-

action that happens between the tip and the specimen. The

rotational and/or bending deflections of the cantilever are determined

by the aid of a laser and a detector.39 The surface topographic charac-

terizations provided by an AFM include the surface topography and

important statistical surface parameters.40,41

In this study, a comparison was made regarding the prediction of

adhesion by the DMT and JKR models. The five specimens examined

included the surface of silicon non‐deposited and the single‐layer

and double‐layer deposition of Silver, Gold, TiO2/Silver, and TiO2/

Gold. Double‐layer coatings could cause a change in the roughness

FIGURE 1 a) Schematic picture of the single‐layer coating and b) Schem

of the substrate that could affect the properties of the latter layer.31

This method could be regarded as a novel approach for more reduc-

tion of the adhesion force. All films were created by the thermal evap-

oration method. The values obtained from the existing mathematical

models (DMT and JKR) were validated according to the experimental

values of the adhesion force.

2 | MATERIALS AND METHODS

2.1 | Surface

The specimens containing five single crystal (mono‐crystal) silicon

(100) wafers of polished were given in the size of 8×8×0.5 mm3, one

specimen surface without deposition and four specimen surfaces with

deposition. Two of the surfaces were deposited with a Silver and Gold

single‐layer film with a thickness of about 100 nm. Two other surfaces

were deposited with the double‐layer films of TiO2/Silver and TiO2/

Gold. The thickness of the TiO2, Silver, and Gold film was 150, 100,

and 100 nm, respectively. This thickness of deposition usually was

used in MEMS especially in microgrippers.12,42 Fig. 1 presents the

schematic picture of the single‐layer and double‐layer coatings. Depo-

sitions on the specimen's surface were done via the thermal evapora-

tion in pressure of 6×10‐6 mbar and temperature of 40°C and with the

thickness monitoring of quartz crystals.

Then, the specimens’ surfaces were photographed with AFM in the

contact mode. Each specimen has a specific geometric parameter.

Table 1 illustrates the surface geometric properties of the specimens,

types, and thickness of deposition for the five specimens. The table

presents the root‐mean‐square (RMS), and the minimum, maximum

and the average values of surface asperities heights, the surface

parameter of roughness average, Ra and roughness of the specimens.

2.2 | AFM measurements

The thin films were investigated at the nanoscale using an Easy Scan 2

Flex AFM. The characterizations were conducted in the contact mode

and in the atmospheric condition, at the temperature of 22°C, the rela-

tive air humidity during tests was 15% for all samples. and the scanning

frequency of 0.74 Hz. Accordingly, a 228 μm long micro‐fabricated sil-

icon cantilever with an integrated tip (Fig. 2) was used and the

atic picture of the double‐layer coating

TABLE 1 Materials and thickness of all investigated specimens

SpecimenFirstlayer thickness

Secondlayer thickness RMS Ra

Minimum of

asperitiesheights (μm)

Maximum of

asperitiesheights (μm)

Average value

of asperitiesheights (μm)

Schematicpicture

1 ‐ ‐ ‐ ‐ 1.2 0.8 2.93 2.97 2.97 ‐

2 Silver 100nm ‐ ‐ 3.7 1.7 2.93 3 2.96 a

3 Gold 100nm ‐ ‐ 4.3 1.8 2.94 3 2.96 a

4 TiO2 150nm Silver 100nm 11.3 5.5 3.1 3.1 3.1 b

5 TiO2 150nm Gold 100nm 12.8 6.5 3.2 3.4 3.3 b

FIGURE 2 Cantilever

JOULAEI ET AL. 3

coefficient of impact of the cantilever spring was 0.29 N/m. The tip

radius was 10 nm, the speed was 4 μm/s, and the voltage was 1 V.

The type of the probe used was silicon and its shape was conic.

2.3 | Surface Morphology

Surface coordinates of the assayed materials were obtained using

atomic force microscopy (AFM; Easy Scan 2 Flex AFM). The scan

was applied to a region size of 10 μm×10 μm. The scanned surfaces

of these specimens are shown in Fig. 3. As can be seen from Fig. 3a,

the surface was not coated with Silicon <100>. Fig. 3b and Fig. 3c

show the surfaces deposited with the single‐layer films of Silver

and Gold, respectively. Fig. 3d and Fig. 3e represent the surfaces

with the double‐layer films of TiO2/Silver and TiO2/Gold,

respectively.

2.4 | Theoretical formula

Adhesion measurements are influenced by the type of contact

between the surfaces. Heinrich Hertz has been the pioneer in the field

of contact mechanics. His formula, which is based on a certain normal

load for the radius of a circular contact area between a sphere and a

flat plane pressed together, has been used by now in macroscopic

scale applications. For many years, the research in this field has led

to other models. Using the Hertz theory at low loads can cause the

discrepancies between the experimentally obtained values and the

predicted ones.

Johnson, Kendall, and Roberts (JKR),21 offered a new theory that

computed adhesion between two elastic bodies. In this theory, they

were motivated by experimentally measured contact regions that

were larger than those augured by the Hertz theory in the low loads,

based on the observation of the limited contact area at the zero

applied load.

The Hertz equation, which is used to explain the radius of the

circular contact in the region between a surface and a sphere of

radius R, was modified to take into account the efficacy of the

surface energy γ:

a ¼ RK

Pþ 3γπRþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi6 γ πRPþ 3γπRð Þ2

ph i� �1=3 (1)

Where K is a constant depending on the Poisson's ratio and

Young's modulus corresponding to each surface, and P is the

applied load.

The surface energy γ is also called the work of adhesion,43-45 or

Dupré energy of adhesion.43 It is indeed the energy per unit area

and represents the work done in completely separating a unit

area of the interface.46 The pull‐off force, which is indeed the mini-

mum value of the load needed to separate the surfaces in contact, is

given by:21

FJKRad ¼ 32γπR (2)

The generalization of this model, which contains surface effect, has

been recently proposed.47 Shortly after, Derjaguin, Muller, and

Toporov (DMT),46 proposed a separate equation to address the adhe-

sion in the contact of elastic bodies. They supposed that the deformed

contact profile remained the same as that in Hertz's theory, though

with a higher load all over due to adhesion. This is equipollent to the

attractive interactions activity on all separations between the sphere

and the surface, like a dead weight; thus:

a ¼ RK

Pþ 2γπRð Þ� �

1=3 (3)

FIGURE 3 3D images of the surface of Silicon (a), Silver (b), Gold (c), TiO2/Silver (d), and TiO2/Gold (e)

4 JOULAEI ET AL.

In addition, according to this model, the pull‐off force is given by:

FDMTad ¼ 2γπR (4)

In the state of the contact between two spheres of radii R1 and R2,

Eqs. 2 and 4 for the adhesion force, as ordained by the two defined

models, can be represented by Eq. 5:39

Fad ¼ CγπR1R2

R1 þ R2(5)

Where C is a constant equal to 1.5 in the JKR model and to 2 in the

DMT model.

FIGURE 4 16 squares considered in the 2D topography image

3 | RESULTS AND DISCUSSIONS

3.1 | Modeling Results

In this section, the values of the adhesion force in the multiple points

of each specimen, as obtained by the mathematical models, are pre-

sented. For each specimen, a grid of 16 squares was considered (Fig. 4)

for sampling and the adhesion force was designated for the center of

each square.41

The contact between specimens and the AFM tip was investi-

gated as a contact between the two spheres using Eq. 5. The value

of 10 nm was used in all computations for the AFM tip radius; i.e.,

R1 =10 nm.

To measure each of the points in the specimens, it was needed to

obtain an asperity radius in the specimen surface. For example, as can

be seen in Fig. 5, the radius of the asperity,41 was R2 = 4.3 nm.

The common molecular dynamics method, which is a precise

method based on statistical mechanics, was used to examine the sur-

face energy more precisely. This method is one of the most basic

methods to analyze the behaviour of matter on the atomic scale and

FIGURE 5 Estimating the density of the network on the specimen surface to obtain the radius

JOULAEI ET AL. 5

is a bottom‐up analysis method. In this method, the nanostructure sur-

face energy is obtained from the flat surface energy. In the past stud-

ies, nanostructure surface energy was calculated from two methods,

“particle radius size” and “nanoplates thickness”. 48,49

a)Nanoplate thickness method:

According to previous studies, the nanostructure surface energy is

calculated according to the thickness of the nanoplates and the flat

surface energy. In silver and gold nanostructures with thicknesses

between 3 and 121 atomic layers (each atomic layer of silver and gold

is approximately 0.264, ie, in coatings thicknesses between 0.8 and

32.4 nm), surface energy increases with increasing nanoplate thickness

and becomes close to the flat surface energy, and at thicknesses

above 121 atomic layers, it equals the flat surface energy.8 In this

study, the surface energy of single layers and double layers gold and

silver samples (100 and 150 nm) is equal to the flat surface energy.

b)Particle Radius Size Method:

According to past studies, the nanostructure surface energy is cal-

culated according to the particle radius of the layer surfaces and the

flat surface energy. By increasing radius of the surface particle from

1 to 7 nm, the nanostructure surface energy becomes closer to the flat

surface energy and at larger sizes, the nanostructure surface energy is

equal to the flat surface energy.49 Metallographic and microscopic

images were analyzed using the MIP Software. The mean radius of

particle for the silver coating was approximately 35 nm, for the gold

coating was approximately 35 nm, for the TiO2/silver coating was

approximately 37 nm, and for the TiO2/gold coating was approxi-

mately 35 nm. The surface energy of the uncoated Si sample with

the crystalline structure and single layers and double layers gold and

silver samples with nanoscale of approximately 35 nm is equal to the

flat surface energy.

As a result, the surface energy in all single layers and double layers

samples was considered equal to the flat surface energy.

From the investigated specimens, the single crystal (or mono‐

crystal) silicon <100> with the surface energy γ of 1.51 J/m2 was

obtained.50 The theoretical values for the adhesion force gained in

each point varied from 9.8 nN to 36.53 nN for the JKR model and

from 13 nN to 48.7 nN for the DMT model (Fig 6a). As can be seen,

16 point numbers represent the vertical axis and the adhesion force

is the horizontal axis. For the Silver thin film on the Silicon substrate

with the flat surface energy of 1.25 J/m2,51 the theoretical values of

the adhesion force were between 7.3 nN and 32.4 nN for the JKR

model and between 9.7 nN and 43.2 nN for the DMT model

(Fig 6b).

For the Gold thin film on the Silicon substrate with the flat sur-

face energy of 1 J/m2,51 the theoretical values of the adhesion force

were between 6.7 nN and 31 nN for the JKR model. As shown in

Fig 6c, these values were between 8.9 nN and 41.3 nN for the

DMT model.

For the two‐layer coating of theTiO2/Silver thin film on the Silicon

substrate with the flat surface energy of 1.25 J/m2,51 the theoretical

values of the adhesion force were between 5.2 nN and 28.6 nN for

the JKR model and between 7 nN and 38.1 nN for the DMT model

(Fig 6d).

For the two‐layer coating of the TiO2/Gold thin film on the Silicon

substrate with the flat surface energy of 1 J/m2,51 the theoretical

values of the adhesion force were varied from 3.8 nN to 25.2 nN for

the JKR model and from 5 nN to 33.6 nN for the DMT model (Fig 6e).

3.2 | Comparison of experimental and theoreticalresults

The main parameters that influence the adhesion force are surface

energy,21-47 surface roughness,52-54 and specifications of the AFM

probe tip (i.e., radius, shape, and material).39,41,54 In this study, the

radius, shape, and material of the AFM probe were constant and the

other two parameters were changed.

According to Eq. 5 and previous studies,21,39,43-47 surface energy

has a direct relationship with the adhesion force. The increase in the

main parameters of surface roughness (Table 1) causes declined radius

of the asperity and, according to Eq. 5 and previous studies, decreases

the adhesion force.52-54

FIGURE 6 The theoretical values obtained using JKR and DMT models for Silicon (a), Silver (b), Gold (c), TiO2/Silver (d), and TiO2/Gold (e)

6 JOULAEI ET AL.

The mean obtained values are presented in the diagrams in Fig. 6,

compared with the experimental values,55 in Table 2 and Fig. 7.

In the theoretical models and the experimental results in Table 2

and Fig. 7, the following results were achieved:

1‐ In a comparison of all specimens of coated with the non‐coated

specimen; reduction of surface energy and increment of surface

roughness caused the reduction of the adhesion force in all spec-

imens of coated.

TABLE 2 Comparison of mean values of the adhesion force of theJKR and DMT models and the experimental values

Specimens

experimentaladhesion

force (nN),55

Mean values of theoreticaladhesion force (nN)

DMT JKR

1: non‐coating 23.6 27.56 20.67

2: Ag 21.56 25.37 19.02

3: Au 20.5 24.22 18.17

4: TiO2/Ag 17.48 22 16.5

5: TiO2/Au 14.86 18.78 14.08

FIGURE 7 Comparison of mean values of the adhesion force of the

JKR and DMT models and the experimental values

2‐ In a comparison of the double‐layer coating of TiO2/Gold with the

single‐layer coating of Gold; both coatings had equal surface

energy, but the surface roughness of the TiO2/Gold was higher

JOULAEI ET AL. 7

and caused further reduction of the adhesion force. This result is

also true for the comparison of TiO2/Silver and Silver coating.

3‐ In a comparison of Gold coatings (single and double‐layer coating)

with silver coatings, more reduction of surface energy and more

increment of surface roughness caused a greater reduction of

the adhesion force in Gold coatings.

4‐ Comparison of the adhesion models (JKR, DMT) with the

experimental results revealed that decreasing and increasing the

adhesion force in the specimens in both models yielded similar

results to experimental values. Experimental values were

between the two theoretical limits. But, the results obtained

from the JKR model were closer to the experimental values

due to relatively high surface energy and “soft” elastic materials

with large tip radii.22

4 | CONCLUSIONS

In this paper, a comparison was made between JKR and DMT‐based

adhesion models in different layers (double‐layer and single‐layer) of

surface deposition on the contact adhesion force between the AFM

tip and surfaces. The results showed that double‐layer and single‐layer

coatings reduced the surface adhesion force. Moreover, it was found

that double‐layer coatings as a new approach could be effective on

the more reduction of the adhesion force. The JKR‐based model as

compared to the DMT‐based model provided a more accurate predic-

tion. Thermal evaporation depositing method was useful for this pur-

pose. These findings could be employed for depositing in MEMS,

especially for microgrippers to reduce the adhesion forces between

tools and parts.

ACKNOWLEDGMENT

The authors would like to thank Dr. Ghasemi for the deposition. They

also appreciate Mrs. Maghfourian for the AFM tests.

ORCID

Mojtaba Kolahdoozan https://orcid.org/0000-0002-3177-4602

REFERENCES

1. Bradley RS. The cohesion force between solid surfaces and the surface

energy of solids. Philos Mag. 1932;13(86):853‐862.

2. Derjaguin BV. Untersuchungen über die Reibung und Adhäsion. Kolloid

Z. 1934;69:155‐164.

3. Johnson KL. A note on the adhesion of elastic solids. Br J Appl Phys.

1958;9(5):199‐200.

4. Maboudian R, Howe RT. Critical review: adhesion in surface

micromachined structures. J Vac Sci Technol B. 1997;15:1‐20.

5. Bhushan B, Nosonovsky M. Comprehensive model for scale effects in

friction due to adhesion and two‐ and three‐body deformation

(plowing). Acta Mater. 2004;52:2461‐2472.

6. Prokopovich P, Theodossiades S, Rahnejat H, Hodson D. Nano‐ and

component level scale friction of rubber seals in dispensing devices.

Wear. 2010;268:845‐852.

7. Prokopovich P, Perni S. Frictional behaviour prediction of

mammalian tissue against biomaterials. Acta Biomater. 2010;6(10):

4052‐4059.

8. Prokopovich P, Perni S. A multi‐asperity contact adhesion model for

universal asperity height and radius of curvature distributions. Lang-

muir. 2010;26(22):17028‐17036.

9. Balabanava N, Wierzbicki R, Zielecka M, Rymuza Z. Effect of roughness

on adhesion of polymeric coatings used for microgrippers.

Microelectron Eng. 2007;84:1227‐1230.

10. Sausse LM, Delchambre A, Régnier S, Lambert P. Electrostatic forces in

micromanipulations:review of analytical models and simulations includ-

ing roughness. Appl Surf Sci. 2007;253:6203‐6210.

11. Colak A, Wormeester H, Zandvliet HJW, Poelsema B. Surface adhesion

and its dependence on surface roughness and humidity measured with

a flat tip. Appl Surf Sci. 2012;258:6938‐6942.

12. Kolahdoozan M, Hamedi M, Nikkhah‐Bahrami M. A novel model for

the effect of geometric properties of micro/nanoscale asperities on

surface adhesion. International Journal of Adhesion and Adhesives.

2014;48:280‐287.

13. Casa M, Sarno M, Liguori R, et al. Conductive Adhesive Based on

Mussel‐Inspired Graphene Decoration with Silver Nanoparticles. J

Nanosci Nanotechnol. 2018;18(2):1176‐1185.

14. Narasimha RK. Influence of deposition parameters on optical proper-

ties of TiO2 films. optical Engineering. 2002;41(9):2357‐2364.

15. Jazirehpour M, Bahahrvandi HR, Alizadeh A, Ehsani N. Facile synthesis

of boron carbide elongated nanostructures via a simple in situ thermal

evaporation process. Ceram Int. 2011;37:1055‐1061.

16. Ohzono T, Monobe H. Microwrinkles: shape‐tunability and applica-

tions. J Colloid Interface Sci. 2012;368(1):1‐8.

17. Lee KC, Lee SS. Deep X‐ray mask with integrated actuator for 3D

microfabrication. Sens Actuat A. 2003;108:121‐127.

18. Lee KC, Lee SS. Deep X‐ray mask with integrated electro‐thermal

microxystage for 3D fabrication. Sens Actuat A. 2004;111:37‐43.

19. Fang W, Lo CY. On the thermal expansion coefficients of thin films.

Sens Actuat A. 2000;84:310‐314.

20. Wilson SA, Jourdain RPJ, Zhang Q, et al. New materials for micro‐scalesensors and actuators. An engineering review. Mater Sci Eng R.

2007;56:1‐129.

21. Johnson KL, Kendall K, Roberts AD. Surface energy and the contact of

elastic solids. Proc R Soc A. 1971;324(1558):301‐313.

22. Derjaguin KL, Muller VM, Toporov YP. Effect of contact

deformation on the adhesion of particles. J Colloid Interface Sci.

1975;53(2):314‐326.

23. Tabor D. Surface forces and surface interactions. J Colloid Interface Sci.

1977;58:2‐13.

24. Maugis D. Adhesion of spheres: the JKR–DMT transition using a

Dugdale model. J Colloid Interface Sci. 1992;150:243‐269.

25. Bhushan B. Contact mechanics of rough surfaces in tribology: single

asperity contact. ASME J Appl Mech Rev. 1996;49:275‐298.

26. Szlufarska I, Chandross M, Carpick RW. Recent advances in single‐asperity Nano tribology. J Phys D‐Appl Phys. 2008;41(12):1‐39.

27. Rabinovich YI, Ya I, Adler JJ, Ata A, Singh RK, Moudgil BM.

Adhesion between Nanoscale Rough Surfaces I. Role of Asperity

Geometry. J Colloid Interface Sci. 2000;232:10‐16.

28. Rabinovich YI, Ya I, Adler JJ, Ata A, Singh RK, Moudgil BM. Adhesion

between nanoscale rough surfaces II. Measurement and comparison

with theory. J Colloid Interface Sci. 2000;232:17‐24.

29. Johnson KL. Non‐Hertzian contact of elastic spheres. The mechanics of

the contact between deformable bodies. In: de Pater AD, Kalker JJ, eds.

8 JOULAEI ET AL.

Proceedings of the IUTAM Symposium. Delft: Delft University Press;

1975:26‐40.

30. Maugis D. Contact, Adhesion and Rupture of Elastic Solids. Berlin Hei-

delberg: Publisher of Springer‐Verlag; 1999:414.

31. Cooper K, Ohler N, Gupta A, Beaudoin S. Analysis of contact interac-

tions between a rough deformable colloid and a smooth substrate. J

Colloid Interface Sci. 2000;222:63‐74.

32. Eichenlaub S, Gelb A, Beaudoin S. Roughness models for particle adhe-

sion. J Colloid Interface Sci. 2004;280(2):289‐298.

33. Archard JF. Elastic deformation and the laws of friction. Proc R Soc A.

1957;243:190‐205.

34. Greenwood JA, Williamson JBP. Contact of nominally flat surfaces.

Proc R Soc Lond A. 1966;295:300‐319.

35. Fuller KNG, Tabor D. The effect of surface roughness on the adhesion

of elastic solids. Proc Roy Soc Lond A. 1975;345:327‐342.

36. McCool JI. Comparison of models for the contact of rough surfaces.

Wear. 1986;107:37‐60.

37. Greenwood JA, Tripp JH. The contact of two nominally flat rough

surfaces. Proc Inst Mech Eng. 1971;185:625‐633.

38. Zhuravlev VA. on question of theoretical justification of the

Amontons–Coulomb law for friction of unlubricated surfaces. Zh Tekh

Fiz. 1940;10(17):1447‐1452.

39. Birleanu C, Pustan M, Dudescu C, Belcin O, Rymuza Z.

Nanotribological investigations on adhesion effect applied to MEMS

materials. Acta Tech Napoc Ser: Applied Mathematics and Mechanics.

2012;55(3):671‐676.

40. Wu L, Noels L, Rochus V, Pustan M, Golinval JC. A micro‐macro

approach to predict stiction due to surface contact in

microelectromechanical systems. J MEMS. 2011;20:976‐990.

41. Rusu F, Pustan M, Bîrleanu C, Müllerb R, Voicu R, Baracu A. Analysis of

the surface effects on adhesion in MEMS structures. Appl Surf Sci.

2015;358:634‐640.

42. Katainen J, Paajanen M, Ahtola E, Pore V, Lahtinen J. Adhesion as an

interplay between particle size and surface roughness. J Colloid Inter-

face Sci. 2006;304(2):524‐529.

43. Johnson KL, Kendall K, Roberts AD. Surface energy and the contact of

elastic solids. Proc R Soc Lond A. 1971;324:301‐313.

44. Mastrangelo CH and Hsu CH. A simple experimental technique for the

measurement of the work of adhesion of microstructures.in: Proc. IEEE

Solid‐State Sensors and Actuators Workshop. 1992: 208–212.

45. Jan Król D, Wymysłowski A, Allaf KN. Adhesion work analysis through

molecular modeling and wetting angle measurement. Microelectron

Reliab. 2015;55(5):758‐764.

46. Grierson DS, Flater EE, Carpick RW. Accounting for the JKR–DMT

transition in adhesion and friction measurements with atomic force

microscopy. J Adhes Sci Technol. 2005;19:291‐311.

47. Gao X, Hao F, Huang Z, Fang D. Mechanics of adhesive contact at the

nanoscale: the effect of surface stress. Int J Solids Struct. 2014;51(3–4):566‐574.

48. Jamshidian M, Dehghani A, Talaei MS, Rabczuk T. Size dependent sur-

face energy of nanoplates: Molecular dynamics and nanoscale

continuum theory correlations. Physics Letters A. 2018;382(2–3):61‐65.

49. Vollath D, Fischer FD, Holec D. Surface energy of nanoparticles –influence of particle size and structure. Beilstein J Nanotechnol.

2018;9:2265‐2276.

50. Jaccodine RJ. Surface energy of germanium and silicon. J Electrochem

Soc. 1963;110:524‐527.

51. Zhang JM, Ma F, Xu KW. Calculation of the surface energy of FCC

metals with modified embedded‐atom method. Appl Surf Sci.

2004;229:34‐42.

52. LaMarche CQ, Leadley S, Liu P, Kellogg KM, Hrenya CM. Method of

quantifying surface roughness for accurate adhesive force predictions.

Chem Eng Sci. 2017;158:140‐153.

53. Ren W, Chen Y, Wang Z, Zhang C, Zhai G. Investigation of the level

adhesion force characteristics of gold‐coated materials in air. The Jour-

nal of Adhesion. 2017;93(12):1‐32.

54. Götzinger M, Peukert W. adhesion forces of spherical alumina particles

on ceramic substrates. The Journal of Adhesion. 2004;80(3):223‐242.

55. Joulaei M, Kolahdoozan M, Salehi M, Zadsar M And Vahabi M. Exper-

imental investigation of the adhesion force of single and double‐layercoatings on MEMS surfaces. Surf Interface Anal. 2019;51(4):419‐426.

How to cite this article: Joulaei M, Kolahdoozan M, Salehi M,

Zadsar M, Vahabi M. Comparison of the adhesion forces in sin-

gle and double‐layer coatings on the MEMS surfaces by JKR

and DMT models. Surf Interface Anal. 2019. https://doi.org/

10.1002/sia.6719