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Chapter 6
Contact Studies for Reliable Ohmic Switch
As discussed in introduction of RF MEMS ohmic switches, the major problem in ohmic
switches is the contact degradation. For reliable ohmic switch, it is mandatory to select
the appropriate contact material for switch. Two important contact parameters i.e.
effective contact area and contact resistance have been discussed in this chapter.
Simulation of contact mechanism are carried out using multiphysics Finite Element
Method (FEM) software ANSYS and COMSOL and obtained results are used to select
the optimum contact material and material is modified by making a composite of gold and
nickel (Ni). The Ni composition changes gold properties in term of hardness. The
composite layer of Au/Ni is deposited and its property is studied using XRD, AFM and
Nano indentation. Au/Ni composite is suitable for contact material to be used in reliable
ohmic switch.
6.1 Contact mechanics
The mechanical contact can be defined as the mechanical interaction between two bodies
which may lead to deformation at contact point. When the surfaces of two solids in
contact do not show a sufficient degree of compliance, the load transmitted is distributed
over a contact area of small dimensions leading to deformations due to the pressures. The
surfaces in contact have following characteristics:
They do not interpenetrate.
They can transmit compressive forces normal and tangential friction.
Often they do not transmit normal forces in tension and are therefore free to
separate and move away.
The contact appears as a severe non-linearity, because there is a significant change in the
rigidity of both normal and tangential areas of contact surfaces when contact status
changes (figure 6.1). The abrupt changes of stiffness are often a source of great difficulty
of convergence. Contact problems arise when the two flat surfaces without contact
friction are in contact under static conditions (figure 6.2 a). The problem is linear, since
the contact area remains unchanged during loading and is reversible since the system is
conservative. If two bodies in contact have curved surfaces, the area of contact is a
144
function of applied load and the problem becomes nonlinear (figure 6.2 b). However it is
still reversible in nature since no conservative forces are reached within the model. The
problem becomes more complex when friction appears. The problem is non-linear and
irreversible. Other nonlinearities, such as material nonlinearities (plasticity, hyper-
elasticity, creep) and geometrical (large deformations, large displacements, geometric
stiffness) are added to the model.
Figure 6.1: Change of rigidity in a contact problem.
Figure 6.2: Two classes of contact (a) the line contact and (b) advanced contact.
6.2 Evaluation of effective contact area for RF MEMS micro switches
Modelling the electrical contact resistance has been carried out by several researchers [1-
4] to compare their experimental results of RF MEMS micro switch contact resistance
with analytical values. Modelling contact resistance is divided into three stages in the case
of ohmic switch to electrostatic actuation:
Evaluation of the contact force as a function of applied voltage (analysis finite
differences)
Force
Displaceme
nt
Contact
Open Contact
formed
(a) (b)
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Evaluation of the size and distribution of spots of contact interface, Contact
according to the contact force
Evaluation of the contact resistance according to the size and distribution
contact spots.
In this section a method for evaluating the effective contact area is presented. The second
step on the contact mechanics is to take into account the mode of deformation of the
contact material (elastic, plastic or elastoplastic). When pressure is applied on the rough
surface of the micro switch, the asperities contact is deformed in three modes: elastic
(reversible deformation), plastic (irreversible deformation) and elastoplastic (interpolation
between the two modes previous deformation). Figure 6.3 illustrates the three modes of
deformation of contact material. For low stresses, the deformation is elastic and
reversible.
Figure 6.3: Stress-strain law of a material and highlighting the three modes of
deformation.
The slope of the curve corresponds to the Young's modulus E. When exceeding a
threshold of σy plasticity under stress, the material behaviour changes by adding a
component plastic deformation becomes irreversible. The slope of the curve corresponds
to the tangent modulus Et. If the stress increases further, the gradient vanishes and this is
purely plastic regime before complete rupture of the material.
3σy
σy
Plastic ideal Elastic Elastoplastic
Deformation
Const
rain
t
146
6.2.1 Elastic Deformation
When contact is established between the two contact surfaces micro-switch, the applied
force is low and the surface asperities deform purely spring described by Hooke's law [3].
Considering a single asperity contact spherical, the contact area and force can be
calculated in function of the deformation vertical α consistent with the theory of Holm
using the following equation: Under elastic deformation, the contact area and contact
force in single asperity model is expressed by equation 6.1 and equation 6.2
(6.1)
where A is contact area, R is asperity peak radius of curvature, and α is asperity vertical
deformation.
√ (6.2)
Where Fc is the normal contact force and E* is the Hertzian modulus which can be
derived from equation 6.3.
(
+
)
(6.3)
where, E1 is the elastic modulus for contact one, v1 is Poisson’s ratio for contact one, E2 is
the elastic modulus for contact two, and v2 is Poisson’s ratio for contact two. Assume it is
a circular area (A = πr ²), the effective contact radius is derived based on equation 6.1 and
equation 6.2.
√
(6.4)
In the case of several asperities in contact, the contact force is distributed on Fc the set of
n asperities and the radius of the contact area becomes:
√
(6.5)
This effective radius is one of the important parameters that determine the switch contact
resistance in the case of pure elastic deformation. When the load increases to
approximately 3 times the yield (σy), the elastic deformation is no longer purely reversible
and plastic deformation the material begins.
6.2.2 Plastic Deformation
The plastic material deformation is modelled using the model of Abbott and Firestone
considering a sufficiently large contact pressure and no creep material [5]. The pressure
147
remains constant and equal to the hardness of the material softest H. The contact area of a
single asperity contact force and are defined by equation 6.6 and equation 6.7:
(6.6)
(6.7)
Where, H is the hardness of the material Meyer softest and A is the contact area [6, 7].
Thus the circular contact area is connected to the contact force by the equation:
√
(6.8)
In MEMS community, this simple expression of effective contact resistance has been
frequently used to calculate the device contact resistance. However, a discontinuity exists
in the area of transition between the ideal and the elastic ideal plastic regime. The
elastoplastic model of Chang, Etzion and Bogy (CEB model) corrects this discontinuity
by considering the conservation of volume surface asperities deformed.
6.2.3 Elastoplastic Deformation (The CEB Model)
Chang, Etison & Bogy (CEB) model accounts for the transition region between elastic
deformation and plastic deformation. Elastoplastic deformation [8] of the material state
for which the contact area plastically deforms but is enveloped by a material elastically
deformed [9].
Contact area is calculated based on conservation of volume of the deformed asperity and
the resulted expression is shown by equation 6.9, where R denotes the end radius of the
curvature of the asperity, αc is the critical vertical deformation for which the critical
elastoplastic begins or where plastic yielding is assumed to occur. This parameter is
defined by equation 6.10, where KH is the hardness coefficient which is assumed to be
equal to 0.6 at the onset of plastic deformation [7].
−
(6.9)
(6.10)
The contact force on this asperity and the effective contact radius can be calculated
respectively using equation 6.11 and 6.12:
(6.11)
√ ( −
) (6.12)
148
+ (6.13)
Where ν is poision ratio of softer material
A discontinuity in the contact load is present in the CEB model for transition between the
elastic regime and the regime of elastic-plastic deformation of the material. Chang
observed that the ideal plastic behaviour takes place 3σy and not KY σy (KY is the
coefficient elastic limit) and has updated the CEB model with linear interpolation. The
new force equation for elastoplastic deformation is given according to Chang by:
[ + (
− )
] (6.14)
+ (6.15)
(6.16)
When KY and the equation of Y are substituted into the equation of force Fc become:
[ + (
− (
))] (6.17)
Thus, equations (6.11) and (6.17) represent the CEB model updated by Chang. For
circular contact areas (6.17) is used to connect the contact radius and the force contact:
√
[ (
)]
(6.18)
Thus the radius of the contact determined from the model of deformation is a function of
the contact force generated by the micro switch.
Mechanical contact models are used to calculate the radius of the contact spots depending
on the deformation regime reached. Rigorous modelling requires knowing properties of
the contact material and the radius of curvature of the asperities. Figure 6.4 shows SEM
micrographs of fabricated contact pad and metal bumps range from 3-4μm. The shape of
contact bumps is also a matter of study; in this work only square bump of 8x8 µm2 is
designed. After the fabrication the circular bumps ranges from 3-4µm are observed. Once
the spot size and distribution of contact within the contact area determined apparent,
contact models used to calculate the electric contact resistance.
149
Figure 6.4: SEM photography of a contact pad range is 3-4μm.
6.3 Contact Resistance Modelling
With no contamination film presented in the contact area, contact resistance is generally
equivalent to the constriction resistance of the connection between two conductors. It is
called “restriction” because electrical current can only flow through metal-metal contact
spots during switch closure. For micro-contacts in MEMS switches, real metal-metal
contact sizes may affect the way electrons are transported through these constricted
contact spots. And different electron transport mechanisms may result in different forms
of constriction resistance. There are three types of electron transport mechanisms that
could occur in MEMS switches: diffusive transport, ballistic transport and quasi-ballistic
transport [10]. The ballistic transport occurs when the electron mean free path le is larger
than the effective contact radius r (le > r); the quasi-ballistic transport occurs when the
electron mean free path is comparable to the effective contact radius (le ~ r); diffusion
occurs when the electron mean free path is much smaller than the effective contact radius
(le << r). The distinctively different physical transport processes for diffusive and
ballistic transport are shown in figure 6.5.
Figure 6.5: Schematic illustration of (a) diffusive and (b) ballistic electron transport
through a constricted conductor [11].
underpass
metal
bumps or
Contact pad
(a) Diffusive (b) Ballistic
150
6.3.1 Diffusive Electron Transport
For diffusive transport, well-established Maxwell spreading resistance equation is used to
calculate the contact resistance [12].
(6.19)
Where, ρ is electrical resistivity. For elastic deformation, substitute equation 6.4 into
equation 6.19, contact resistance RcDE (DE denotes diffusive transport and elastic
deformation) is expressed in terms of asperity properties and contact force.
√
(6.20)
Where, E* again is the Hertzian Modulus which is dependent on the elastic modulus of
the upper and bottom contacts, and is derived from equation 6.3. For plastic deformation,
substitute equation 6.8 into equation 6.19, contact resistance RcDP (DE denotes diffusive
transport and plastic deformation) also expressed in terms of asperity properties and
contact force.
√
(6.21)
For metal contact MEMS switches with a contact force above 100 μN, it is generally
believed that plastic deformation occurs during making contact. Therefore this simple
equation has been widely used to predict switch contact resistance.
6.3.2 Ballistic and Quasi-ballistic Electron Transport
For ballistic transport, Sharvin resistance is the major contributor to the contact resistance
[13]. the form of Sharvin resistance is given in equation 6.22.
(6.22)
where, K is the Knudsen number that can be expressed by equation 6.23.
(6.23)
An interpolation between the ballistic and diffusive electron transport regions is made
using the Gamma function Γ (K) [14]. A well behaved form of Gamma function is given
in equation 6.24 [15].
∫ i
(6.24)
151
A plot of “Gamma function vs. Knudsen number” is shown in figure 6.6.
Figure 6.6: Plot of ‘Gamma function vs. Knudsen Number [15].
A complete form of contact resistance is derived by Wexler [14] and is shown in equation
6.25.
+ (6.25)
Contact resistance modelling approach is contingent on two assessments. One is to check
whether the effective contact radius is much larger than the electron mean free path so
that electron transport mechanism is determined. The estimated effective contact radius is
more than 100 nm and the mean free path of electrons in gold is only ~ 36 nm. Therefore,
diffusive transport model is used for the resistance calculation. The second is to check
whether the plastic yielding point is reached so that deformation model is properly
assessed. Plastic deformation is assumed based on the contact force and critical yielding
estimation.
6.4 Contact simulation software approach
The experimental method faces several obstacles, the level of manufacturing technology
and the level of experimental measurements. Indeed the optimization of the
manufacturing process to test a single candidate materials contact or one form of contact
pad is very time consuming. Experimentally, it is difficult to reproduce the actual
operating conditions of micro switches, particularly in terms of the application of the
contact force. Finally, this method is very expensive when interpreting the results may be
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very difficult when various physical phenomena may come into play at the same time
(heating, creep, surface contamination). A numerical method or analytical, by cons, do
not constrain the choice of material, topology, architecture and the surface condition.
Moreover, it is possible to study each parameter independently.
6.4.1 Simulation software choice
With the explosive growth of computer technology, the use of analysis software finite
element to model the roughness is of great interest to study the contact between surfaces.
To confirm the choice of a numerical analysis in modelling methodology the micro
switch contact, it is crucial to test the simulation tools, available in the laboratory to check
that at least one of them respond to needs. Simulation software for finite element analysis
of contact mechanical is selected. The combination of mechanical simulations with other
behaviours physical is also interesting to consider the effects of conduction heat or
electrical current through the contact area. And multiphysics software is tested. Contact
problems are highly nonlinear and require resources important computer workstation. In
this part, simulation software is used in CSIR-CEERI to achieve the numerical
simulations of contact are examined. Two commercial available finite element used
software are:
The industry standard tool for finite element analysis ANSYS (version 12),
historically known in the mechanical and thermal simulation multiphysics
tool.
The tool COMSOL Multiphysics (COMSOL 3.5), formerly FEMLAB.
COMSOL was founded in 2005 and has modules for simulation Multiphysics
(structural, electromagnetic, chemical, MEMS, thermal.)
The objective of this part of thesis is find best candidate to simulate problems of
mechanical contact, with a reduced computing time and accuracy of results. The tool is
required to simulate mechanical contact problems, coupled with other physical (heat
conduction, conduction electric). The frictionless contact problems are studied, which are
dominant as the normal contact force. After describing the principle of modelling contact
with the two tools, a comparison of two software are made. The principles of
electromechanical analysis with both software are presented. Finally, the originality and
disadvantages of each program is presented to select the best candidate in the analysis of
153
contacts RF MEMS micro switches. The successful software is then tested to treat contact
problems typically encountered in the study of metal-metal contact micro-switches.
6.4.2 Principle of finite element modelling of contact
The two bodies in contact elements are divided into three category two-dimensional
planar, axisymmetric and three-dimensional. Between the external nodes that are likely to
come into contact during loading, is defined a set of contact elements. The properties of
materials, boundary conditions and nodal loads are shown. Programs have graphical
interfaces to assist in mesh generation, although with ANSYS it is recommended to
generate a "script" to build the model. Preprocessing interface is typically used to create
an input file. Then the results are analysed by a post-processing. The performances of
these interfaces facilitate user understanding of the physical phenomena involved. To
solve a nonlinear problem of mechanical contact with commercial tools ANSYS and
COMSOL, it is necessary to construct a coherent model of contact and adjust the
parameters of contact correctly.
6.4.3 Definition of contact
Thus, once the geometry is made, it is crucial to clearly define the contact pair, the two
boundary surfaces which may come into contact (figure 6.7). Table 6.1 summarizes the
characteristics of each contact surface. The user specify a destination surface "Contact" or
"Slave" and a surface source (target) "Target" or "Master". The target surface must be
more rigid than the contact surface. Then, the contact surface should preferably be convex
and the target surface or plane concave. To facilitate the convergence of the contact
problem, the contact surface meshing is finer than the target surface.
Figure 6.7: A Pair of contact.
Target/Master
Contact/Slave
154
6.4.5 Contact set parameters
To solve a contact problem with nonlinear tools ANSYS and COMSOL, the augmented
Lagrangian method is selected. This method also called penalty with penetration control.
ANSYS also offers the possibility to use other algorithms for solving contact problems
such as contact the penalty or Lagrange multipliers. The parameters of contact are
defined. A key parameter is the constant contact stiffness, denoted FKN in ANSYS.
Table 6.1: Defining contact pairs in environments ANSYS and COMSOL
ANSYS COMSOL Rigidity of
material
Profile of
surface
Mesh Dimensions of
surface contact
CONTACT
PAIR
CONTACT
surface
SLAVE
surface
material
surface as soft
surface
convex
mesh
thinner
Surface more
small
TARGET
surface
MASTER
surface
material
surface as hard
surface flat
or concave
mesh
more
coarse
Surface more
wide
The contact stiffness is defined as being equal to the spring constant multiplied by the
stiffness of the elements contact underlying:
(6.26)
In the COMSOL, this constant contact stiffness is reflected in the penalty factor pn,
defined as a scale factor of the stiffness divided by a boundary element typical length
(mesh size). In COMSOL, the user must also set the initial contact pressure Tn. It is a key
parameter for convergence in contact problems in ordered strength. In ANSYS, a second
factor may be adjusted: it is the maximum penetration FTOLN (user-defined constant
multiplied by the thickness of the underlying elements). The compatibility of the contact
is satisfied if penetration is within the permitted tolerance. ANSYS and COMSOL
software default choose the constants FKN and pn, thus providing the user with few
features; it did just create one scale factor. However, this scale factor is optimized to
obtain reliable results with a reasonable computation time. Indeed, the contact stiffness is
a parameter very important and affects the accuracy of the results and the convergence
behaviour. A higher stiffness gives better accuracy, but with a convergence more
155
difficult. Tolerance of penetration also affects the convergence and accuracy, in a lesser
extent than the rigidity of contact.
6.4.6 Influence of contact stiffness on the convergence of results
To highlight the influence of the stiffness constant contact on the mechanical results, an
axisymmetric contact problem involving a roughness height of 6 nm and 50 nm radius is
considered. The choice of dimensions is carried out following the observations on
topographic surfaces evaporated gold. Elastoplastic materials properties are chosen.
ANSYS mesh model is shown in figure 6.8. The target surfaces impose a displacement of
0.5 to 5.5 nm. To evaluate the influence of the contact stiffness and succeed in
determining the minimum factor to be considered in this example, FKN are varying from
0.1 to 1000. For each imposed displacement, the maximum equivalent stress of von Mises
and the length of contact are measured. Figure 6.8 and Table 6.2 shows the evolution of
these two parameters according to the value of a fixture for FKN of 0.5 nm. The
importance of choosing the spring constant is observed in results. In this case, a 10-FKN
provides satisfactory accuracy. Choosing a FKN higher would increase the calculations
without significantly improve in accuracy. The influence of the stiffness constant is also
important.
Solution by increments of charge: Typically, contact problems involving distributed
loads on small areas of contact. This results in significant stress gradients in the vicinity
of the contact. The mesh in this region must be fairly refined. Thus, even the simple Hertz
contact is analysed with a mesh fine enough for accurate results.
Figure 6.8: Modelling of axisymmetric asperity in ANSYS.
156
Nonlinearities associated with the contact, such as contact stiffness or plasticity causes
the solution is usually related to loading path. The load (or displacement) is applied
incrementally; a solution is sought at each increment (figure 6.9). The smaller increments
are used if convergence is difficult or larger if easy. To achieve convergence at each step
equilibrium iterations is defined. These successive iterative calculations lead quickly to
prohibitive calculation times when a fine mesh is also necessary. This is particularly the
case of three dimensional analyses, when taking into account the surface roughness. The
residue (imbalance) appears in purple dark, the convergence criterion in force in light
blue (figure 6.10). When the residue falls below the criterion, the sub step has converged,
and the following charge increment is applied.
Table 6.2: Length of contact as a function of the contact spring constant
FKN Contact length (nm) Von Mises (GPa)
0.1 7.489 0.679
0.31 7.485 0.671
1 7.480 0.65
3.16 6.333 0.695
10 5.756 0.72
31.62 5.756 0.73
100 5.755 0.735
316 5.755 0.738
1000 5.754 0.7395
157
0.1 1 10 100 10000.64
0.66
0.68
0.70
0.72
0.74
Vo
n M
ises (
GP
a)
FKN
Figure 6.9: Maximum equivalent stress of Von Mises (GPa) Spring constant FKN.
Figure 6.10: Example of convergence in ANSYS.
6.4.7 Multiphysics Simulation
The use of finite element software for simulating multiphysics problems mechanical
contact coupled with other physical properties are beneficial to assess directly the
electrical contact resistance between two conducting bodies, or to analyse the thermal
effects due to current flow. The simulation of mechanical contact coupled with the
conduction of electric current conduction are easy to create with both commercial
software ANSYS and COMSOL. The method consists of indirect coupling (mechanical
and thermal).
6.4.7.1 COMSOL multiphysics analysis
In COMSOL, Multiphysics analysis is very simple to implement and intuitive. The
methodologies used to evaluate the electrical contact resistance between two conductive
contact materials are implementing as an example.
158
Problem description: The possibility for COMSOL 3.5 of electromagnetic coupling the
module with the analysis of mechanical contact to solve a contact problem that addresses
the conduction electric current is described for a model of classical Hertz contact. This
model consists of a solid cylinder of gold indented by a hemisphere in Ruthenium (figure
6.11). Both materials are assumed elastic, homogeneous and isotropic. In addition,
friction is neglected and the problem consists of small deformations. Because of the
symmetry of the problem, an axisymmetric model is build.
Methodology
The method consists of a sequence analysis coupled physically. A simulation mechanical
contact is first made between the two bodies in contact under the effect of a
force (figure 6.12) or displacement. Post-processing generates the distribution of the
contact pressure at the interface. In a second step, an analysis in conduction DC power is
achieved by applying a potential difference V1-V2. The electric current is passed
through the contact area. Finally, the electrical resistance is extracted by estimating the
current density on each side of the contact interface and calculating the intensity
of electric current.
Figure 6.11: (a) Hertz contact model static, 3D representation in COMSOL
with defining contact pairs and boundary conditions (b) axisymmetric mesh model.
Electrical conduction using COMSOL
The predefined environment for conduction static DC case has been selected. The partial
differential equation used (PDE) is
Force Applied
Ru
sphere
Contact Pair
Slave/contact
Master/target
Gold Solid
Fixed
surface
(a) (b)
159
− − (6.27)
where V is the electrical potential, conductivity σ and the current source Qj. E is the
density Je external current, such that the total current density is given
+ + (6.28)
where E = - V is the electric field.
Figure 6.12: Modelling of contact and axisymmetric mesh in COMSOL.
Here Je = 0. Boundary conditions used for insulating borders are - nJ = 0, that is to say
that the normal component of the current density is zero. The borders potential is set to V
= V0. A current density of a border is set instead of electric potential - n J = Jn. Generally,
the surface corresponding to the circular base of the hemisphere is set to have a fixed
potential or a fixed current density. The lower surface of the solid cylinder is fixed to a
zero potential. For the internal boundaries separating two domains 1 and 2, the continuity
equation is expressed as follows:
− (6.29)
160
The stability of solutions using the finite element method is verified by solving the
problem for different mesh densities. The current density is calculated by COMSOL and
the current through the structure is determined by performing a linear integration of the
current density on a section of model. The current density depends on r and z coordinates.
∫ (6.30)
The electrical power of a field n is also determined by performing integration surface (on
a subdomain) of the current density.
= 2π∬
rdS (6.31)
with σn conductivity of the n field. The electrical resistance of the field is then calculated
knowing that Pelec = Ri2. Figure 6.13 show the stress and current density distribution of
contact problem solved using COMSOL.
Figure 6.13: Illustration of the distribution of Von Mises and streamlines.
6.4.7.2 ANSYS multiphysics analysis
Similarly in ANSYS, after realizing the simulation of mechanical contact, the structure is
used to study the electric effect. The contact elements surfaces are then combined with
thermoelectric elements. The algorithm for solving the problem of electromechanical
simulation is presented in figure 6.14. Following are the process steps to contact
simulation in ANSYS:
Definition of the geometry and physical data
161
Mechanical simulation
Backup of the deformed structure
Change elements by mechanical elements thermoelectric
Electrical analysis
Post-treatment: analysis of results Contact pressure
Simulation of mechanical contact requires introducing the parameter Ecc corresponding
to the electrical conductance of contact and defined as follows:
− (6.32)
J represents the electric current density and Vt and Vc are the voltages at points contact on
the target surface "target" and the source surface "contact" respectively. Distribution of
the Von Mises stress-axisymmetric contact model simulated under ANSYS is shown in
figure 6.15. Despite the success of multiphysics analysis by finite elements, a method of
extracting the electrical contact resistance has not yet been implemented and research is
going on.
Figure 6.14: Algorithm of problem solving systems (indirect coupling method) in ANSYS.
Contact Pair
Contact Pressure
Fixed potential V1
Zero potential V2=0
"Target"
"Contact"
162
Figure 6.15: Distribution of the Von Mises stress-axisymmetric contact model simulated
under ANSYS.
6.4.8 Merits and demerits of two simulation software
COMSOL consist of graphical interface that allows the user to build and define models
easily and intuitively. In addition, COMSOL is software dedicated to multiphysics
simulation and is used to simulate simple problems of mechanical contact coupled with
other physical (conduction electric currents, heat conduction). However, for solving the
high degree of freedom model, out of memory error occurred. This is a problem in the
simulation of 3D contact problem where one is forced mesh refinement at the contact
interface for accurate results.
In addition, this software requires several nonlinearities to successfully converge the
solution or when geometry of the model becomes too complex. The algorithms automatic
implanted in COMSOL but required lot of time and efforts to converged the problem.
In ANSYS simulated problems, the calculations speed and that characteristic are
generalized to any design i.e. 3D nonlinearities of geometric contact materials. In
addition, contact problems mechanics are easily coupled with other physical (conduction
currents electric, heat conduction). This software requires less effort on the part of the
user to adjust the model parameters of contact. Indeed, the algorithms automatic applied
in ANSYS are generally very competent. Generally, when this contact problem
convergence is difficult, lowering the factor contact stiffness, increasing the tolerance of
penetration and by increasing the number of sub-steps (load increments) are helpful.
Finally, two commercial finite element software, ANSYS and COMSOL, are tested to
simulate mechanical contact problems. A reduced computational time and accuracy of the
results are the two key criteria in choosing the simulation platform. The results of contact
163
problems studied showed that COMSOL 3.5 is limited in terms of computation time and
suffered from a limitation memory to simulate problems of contact with a number of
degrees of freedom important. ANSYS shows good accuracy of the results with a time
reduced calculation and is able to solve contact problems requiring an effort minimum
intervention from the user. ANSYS is an excellent candidate for contact study.
6.5 Contact metal selection
In order to build a solid material knowledge base for micro switch designers, correlations
among material properties, contacting performance (such as contact resistance and
lifetime), and failure modes (such as stiction and wear or material transfer) need to be
built based on systematic experimental data for different materials. The research in this
area has been slowed by the long time requirement for fabricating a micro switch with a
particular new contact material [16]. Typically, these micro switches are fabricated in Si
foundries, and only a limited range of materials may enter the fabrication facility. Second,
the fabrication process must be optimized for each material, and it may take many months
to fabricate a set of switches to test a candidate contact material. Materials’ compatibility
and process integration issues must be addressed in advance for every material to be
tested [17]. Selection of contact metal depends on material hardness, resistivity, melting
point and process difficulty. Cleaner contacts have stiction problems. Pitting and
Hardening damage are dominating failure mechanism of contact switches. It may cause
melting of soft metal like gold [18-20]. Contact metal must satisfy three major criteria:
1. Low contact resistance,
2. Long contact lifetime,
3. A clean contact surface,
Pure Au has low contact resistance, inert to oxidation. Au contacts have damage and
stiction problems. Harder metal have less stiction problems and higher contact resistance
because real contact area reduced. Au and AuNi very stable contact resistance with
contact force <30µN, Whereas Rh require 50µN for stable contact. AuNi contact
resistance 1.5ohm with 5µN contact stiction force, Rh contact resistance 3ohm with
undetectable contact force. Rh film experienced a slight oxidation over the time periods,
resultant change in contact resistance. Rh oxide is still conducting only experience large
contact force >1000µN, Similar is the case with Ru, Ir. Not suitable for switches with
actuation voltage (<20V) low contact force (<100µN) due to unstable and high contact
resistance. W and Mo have larger hardness values show less stiction issue, due to high
164
melting temperature can be handle more power, sensitive to oxidation hence high contact
force (>150µN) needed to achieve contact resistance [17]. Keeping in view the process
compatibility and complexity, the Au-Ni alloy or compositions are the best candidate and
easy integration with available device fabrication processes.
Table 6.3: Contact metal selection parameters [17]
Metal Symbol Resistivity
10-6
Ω-cm
Estimated
Hardness
(Mpa)
Melting
Point
(°C)
Chemical
Reactivity
Process
Complexity
Gold Au ~2.2 ~250 ~1060 Lowest Simple Etch
Gold Nickel AuNi5 ~12 ~1600 ~1040 Very Low Simple Etch
Rhodium Rh ~4.3 ~2500 ~1960 Low Difficult Etch
Ruthenium Ru ~7.1 ~2700 ~2330 Low Difficult Etch
Iridium Ir ~4.7 ~2700 ~2460 Low Difficult Etch
Tungsten W ~5.48 >3000 ~3420 Medium Simple Etch
Molybdenum Mo ~5 ~2000 ~2620 Medium low Simple Etch
6.6 Au and AuNi alloys as contact materials for RF MEMS switch
Gold is widely used as a MEMS metal contact material to achieve low contact resistance
due to gold’s low resistivity, low force and resistance to surface oxide. Stiction and wear
are prone to occur between two soft adhesive contact (Au-to-Au contact) surfaces while
switching. Wear is described as contact deformation or material redistribution, ultimately
causing contact surface roughening and affecting local contact force and contact
resistance. MEMS switches with Au-to-Au contacts (figure 6.4) are prone to the above
failure mechanisms due to gold’s relatively low hardness (0.2–1GPa).
The purpose of this work is to develop a method for selecting metal or alloy as contact
materials for micro-switches that are optimized for increased wear, low contact
resistance, low susceptibility to oxidation and process compatible. On the materials’ side,
a few alternative metals and alloys have been investigated as contact materials for metal-
contact MEMS switches. McGruer et al. [21] showed that ruthenium (Ru), platinum (Pt),
and rhodium (Rh) are susceptible to contamination and the contact resistance increased
after a characteristic number of cycles, while gold alloys with a high gold percentage
showed no contact resistance degradation under the same test conditions. Coutu et al. [3,
165
19] showed that alloying gold with a small amount of palladium (Pd) or platinum (Pt)
extended the microswitch lifetimes, with a small increase in contact resistance.
Aside from the alloys mentioned in the above paragraphs, Au–Ni composite has showing
a potentially promising alternative to gold. It has been reported that Au–Ni alloy contacts
yield much lower adhesion than pure gold contacts [16]. However, in the initial study,
only samples with Au/Ni are investigated, using Si samples as test components instead of
a MEMS test structure. Therefore, a study of a wider range of Au-Ni compositions is
considered.
This section reports on contact materials gold and gold–nickel alloys for RF MEMS
switch. The deposition of Au and Ni are carried out using two different processes i.e.
electroplating and E-beam evaporation. The process conditions for electroplating are DC
constant current and pulse mode. The multilayer depositions using electroplating and E-
beam evaporation are studied on small pieces of silicon. Thin layers are deposited in
various combination of layer like Au/Ni, Ni/Au, and Au/Ni/Au on silicon. After
multilayer deposition the layers are anneal at 1800C to create composite material. The
rapid thermal annealing (RTA) is used for better alloy composition. The different
deposition approaches are used to improve surface quality. The Au–Ni phase diagram is
shown in figure 6.16 [22]. Both the metals are Face Cantered Cubic (FCC) structures and
exist as a two-phase mixture at a relatively low temperature under equilibrium conditions.
However, a metastable single phase alloy is also produced under the low processing
temperatures utilized for the film deposition. Thus, a comparison of the metastable solid
solutions and the two-phase mixtures of the same overall composition is undertaken so
that both microstructure and composition effects are examined.
Gold sample as deposited
Seed layer of gold (Ti/Au) is deposit using E-beam process, AFM image is shown in
figure 6.17. This seed layer is used to deposit electroplating of 2µm, the AFM image is
depicted in 6.18. These AFM micrographs are used to find grain size and roughness of the
deposited gold.
An X-ray diffraction spectrum of a plated gold film sample as deposited and anneal on
the silicon substrate is shown in figure 6.19. In the spectrum, Au (1 1 1) and Au (2 0 0)
peaks are clearly identified. The structure of the gold sample from electroplating of 2µm
consists primarily of Au (1 1 1), Au (2 0 0) and some Au (2 2 0).
166
Figure 6.16: Equilibrium binary alloy phase diagram for gold–nickel alloys. [22]
Figure 6.17: AFM images of pure seed layer Au sample.
Figure 6.18: AFM images of 2µm electroplated Au sample.
167
Gold plating process is optimised using pulse power supply at varying duty cycle (5-
20%). Figure 6.20 shows the AFM micrographs of pulse plated gold at 20, 14 and 10%
duty cycle and corresponding XRD peaks. The results of XRD and AFM are used to find
grain size (30-45nm) and RMS roughness (5-8nm). Recipes for pulse plating are fixed for
gold plating and next task is to optimised plating parameters for Au/Ni layer. Figure 6.21
shows the AFM images and XRD spectrum of Au/Ni pulse plated at 20, 16 and 10% duty
cycle [23]. RMS roughness in this case varied from 5-12nm. After the plating parameters
optimisation, next step is to find Ni atomic percentage in Au. The accurate atomic
percentage of Ni can be measured using XPS. Due to unavailability of the XPS system,
the EDX is used to find Ni atomic percentage in Au.
30 40 50 60 70
0
100
200
300
400
500
600
700
800
900
1000
Au(220)
64.7Au(200)
44.5
Inte
nsi
ty (
cou
nts
)
Two Theta (degree)
Au as depositAu(111)
38.4
25 30 35 40 45 50 55 60 65 70
0
50
100
150
200
250
300
350
Inte
nsit
y (
co
un
ts)
Two Theta (degree)
Au after anneal
Si (200)
Si (111)
Au (111)
38.36
Au (220)
64.77
Au (200)
44.45
Figure 6.19: XRD spectrum of plated gold film as deposited and after annealing.
168
Figure 6.20: AFM and XRD spectrum of gold plated at duty cycle 20, 14 and 10%.
Figure 6.21: AFM and XRD spectrum of Au Ni plated at duty cycle 20,16 and 10%.
169
Figure 6.22 shows the EDX spectrum of Au/Ni composite layer and atomic% of
respective elements. Au-Ni layers are deposited using electroplating and alloy is formed
after rapid thermal annealing (RTA) at 2000C for 10sec. The Au with 5, 14 and 20 atomic
% of Ni is prepared. XRD, AFM and EDX data are used to find the grain size, roughness
and atomic %. Figure 6.23 shows the XRD spectrum of Au-Ni alloy with 14 and 20
atomic % of Ni. Table 6.4 shows the measured grain size from XRD and AFM. The data
is measured at solid solution phase after deposit and two phases after annealing for Ni
atomic % 14 and 20.The average grain size of plated Au is 50±20nm and for Au-Ni alloy
are ranges from 100-150nm after two phase formation.
Figure 6.22: EDX spectra of Au/Ni composite layer and elements percentage.
25 30 35 40 45 50 55 60
0
100
200
300
400
500
600
700
Inte
nsit
y (
co
un
ts)
Two Theta (degree)
14% Ni
Au(200)
44.4
Ni(111)
44.6
Au(111)
38.4
Si(111)
30 40 50 60
0
200
400
600
800
1000
Inte
nsit
y (
co
un
ts)
Two Theta (degree)
20% Ni
Ni (111)
44.54
Au (111)
38.4
Figure 6.23: XRD spectrum of Au-Ni alloy with 14 and 20 at. % Ni after annealing.
170
Table 6.4: Surface characterisation of plated Au and Au-Ni alloy samples
Au(111) Grain
size from XRD
analysis (nm)
Au(111)
Grain size
from AFM
analysis (nm)
Ni(111) Grain
size from XRD
analysis (nm)
Ni(111) Grain
size from
AFM analysis
(nm)
Hardness
(GPa)
Plated Au sample 50±20 50±20 1.17
Solid-solution Au-
Ni alloy 14 at% Ni
20±5 20±10
Two-phase Au-Ni
alloy 14 at% Ni
150±10 160±20 20±5 20±10 2.28
Solid-solution Au-
Ni alloy 20 at% Ni
10±5 15±10
Two-phase Au-Ni
alloy 20 at% Ni
130±10 130±20 12±2 15±5 2.68
6.7 Conclusions
Contact mechanics to solve the contact problems are highlighted with reference to
effective contact area and contact resistance. Simulation of contact mechanism was
studied using FEM software ANSYS and COMSOL. ANSYS was found suitable
candidate to solve micro contact problems. Au-Ni alloy or composite layers are deposited
using E-beam and electroplating. Pulse plating of Au-Ni layer was carried out at three
different duty cycles (20, 16 and 10%). The rapid thermal annealing (RTA) at 2000C for
10 seconds was used to create composite layers. Three samples of Ni compositions (5, 14,
and 20 atomic %) in Au were prepared and analysed. The average grain size of plated Au
is 50±20 nm and Au-Ni alloy grain size ranges from 100-150 nm after two phase
formation. The Ni was introduced to improve the hardness of the gold layer, the gold
hardness increases from 1 GPa to 2.5 GPa.
In summary, the method and process used to deposit the series of pure gold and Au-Ni
alloy samples is introduced. Surface characterization and topological analyses using
XRD, AFM, Nano indentation and EDX of each sample have been carried out. Surface
characterisation of plated Au and Au-Ni alloy samples are summarized in table 6.4.
Au/Ni composite has been found to be suitable material for contact in reliable ohmic
switches.
171
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