Online proceedings - EDA Publishing Association

suspended membrane can be pulled towards the ground
electrode, collapses onto 12 elevated contact pads and closes an
ohmic contact so that the RF signal path is closed.
The topography of the switches has been analyzed by applying
a white light interferometer (Veeco NT1100 DMEMS) and the
dynamics has been characterized by recording the transient
deflection of the moving membrane by a single spot laser
Doppler vibrometer (Polytec OFV-5000). An on-purpose
developed vacuum chamber with pressure control enables the
characterization of the microstructures under varying pressure
conditions in order to evaluate the applied models for viscous
damping. The experimental set up is shown in fig. 3.
11-13
May 2011, Aix-en-Provence, France
using the single point laser Doppler vibrometer depicted in
fig. 3, parameters like the pull-in/pull-out voltages (and from
that the actual gap height) or the resonance frequency of the
mechanical structure could be extracted. The parameters of the
investigated switch, which are the basis of our models, are
summarized in detail in table 1 below.
Table 1. Technical data of the investigated RF-MEMS switches. For the
electrode and the substrate, the gap width is given between the membrane and
the dielectric layers.
Membrane
Suspensions
Thickness 5.2 µm Thickness 2.0 µm
Length 260 µm Length 165 µm
Width 140 µm Width 10 µm
A
Side length of
holes
Spacing between
holes
20 µm
20 µm Other
Resonance frequency
14.7 kHz
C
B
C
Gap widths
Membrane to
contact pad
Membrane to
electrode
Membrane to
substrate
Thickness of 700 nm
dielectric on
electrode
1.7 µm Pull-in voltage 29-30 V
2.7 µm Release voltage 22-26 V
3.4 µm Effective residual
air gap (g min )
~20-50 nm
Figure 3. Photograph of the laser vibrometer (A) and the on-purpose
developed pressure chamber (B). Two pressure sensors (C) are used to
control the pressure inside the chamber .
Displacement [μm]
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
-1.4
-1.6
-1.8
-30 -20 -10 0 10 20 30
Voltage [V]
Figure 4. Quais-static pull-in/pull-out characteristic of the RF MEMS
switch. A trinangular waveform with zero mean voltage and 70 V amplitude
(peak to peak) at a frequency of 1 Hz has been applied. The pull-in voltage
lies between 29 V and 30 V, the release voltage between 23 V and 26 V.
As a first guess, the parameters of the switch have been taken
from the technical data given by the process description and
the design. In order to include also the manufacturing
tolerances in our model and, thus, to enhance its accuracy,
optical measurements appling a white ligth interferometer (see
fig. 1 and 2) have been carried out in order to extract the exact
dimensions of the device (electrode, contact pads, membrane
thickness, e.g.). From the quasi-statically measured pull-in and
pull-out characteristics (see fig. 4) and dynamic measurements
III. MODELING AND THEORETICAL BACKGROUND
The macromodel of the switch is derived on the basis of the
hierarchical modeling approach as reported in [2], which is
strictly based on flux-conserving reduced-order and/or compact
modeling techniques, so that the resulting system-level models
are rigorously formulated in terms of conjugated variables
(”across”- and ”through”-variables) and the generalized
Kirchhoffian network theory can be used as a theoretical
framework for the formulation of the entire system model.
Starting point of the modeling procedure is the decomposition
of the device into tractable subsystems. In this particular case,
these are the mechanical subsystem represented by the
perforated membrane and the four flat suspension springs, the
electrostatic subsystem, accounting for the electric field
between the perforated membrane and the actuation electrode
(see Fig. 2), and the fluidic subsystem comprising the ambient
air that exerts damping forces on the moving parts of the
structure. Additionally, adequate compact models have to be
derived that describe the closing phase of the switch properly.
The basis for the mechanical submodel of the suspended
membrane is the modal superposition technique described in
[3]. The eigenmode shapes and frequencies of the suspended
membrane are calculated in a FEM simulation tool. The most
significant modes – in the case of the considered switch the
fundamental and the next higher completely symmetric
eigenmode – are identified and used to formulate a
macromodel in terms of modal amplitudes consisting of only
one second-order differential equation per included eigenmode.
9