Online proceedings - EDA Publishing Association

microphone diaphragm. The chosen CMOS technology
imposes the vertical structure dimensions i.e. the air gap and
the diaphragm thicknesses. Fig. 2 shows different views of the
microphone structure and the corresponding dimensions are
listed in Table I.
Fig. 2. Microphone cross-sectional view (a), top view of the diaphragm (b).
TABLE I
DIMENSIONS OF THE MICROPHONE ELEMENTS
Elements
Dimension (µm)
Diaphragm side length (L mem) 500
Diaphragm thickness (t mem) 1
Arm length (L arm) 71
Arm width (W arm) 141
Big hole side length (L hole1) 5
Big hole pitch (Pitch1) 10
Small hole side length (L hole2) 1
Small hole pitch (Pitch2) 5
Air gap thickness (h a) 2.64
We have considered a diaphragm supported by four beams
anchored by the oxide layer in order to obtain an optimum
stiffness and thus acceptable sensitivity. The air gap thickness
that was taken into account in this design corresponds to the
distance between the metal layers M4 and M2 of the CMOS
process. Two sets of holes are designed in the microphone
diaphragm. Small holes with the sides of 1 µm are densely
distributed on the diaphragm surface with the aim to allow fast
sacrificial layer etching. Larger holes with the sides of 5 µm
disposed on the diaphragm have the important role of
controlling the diaphragm damping and their dimensions were
optimized in order to obtain flat frequency response close the
resonance.
The microphone must work in the audible frequency range
from 20 Hz to 20 kHz. The required capacitance variation of
the microphone was obtained through the analysis of the
expected noise of the electronic circuit. For a minimum signalto-noise
ratio of 40 dB, the microphone capacitance variation
must be at least 60 fF.
In this section, we will describe the microphone equivalent
circuit with lumped parameters. We present the effect of holes
on the mechanical parameters and on the electrostatic field
distribution, as well as their influence on the mechanical
damping.
A. Equivalent circuit
Lumped parameters equivalent circuit (Fig. 3) is used to
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May 2011, Aix-en-Provence, France
study the frequency response of the microphone. An analogy
between the acoustic, mechanical, fluidic and electrical
domains is used to build the equivalent circuit.
To characterize the mechanical and fluidic part behavior of
the MEMS microphone, an equivalent spring-mass-damper
system under harmonic excitation is considered. The total
stiffness of the system is given by the rigidity of the
diaphragm and the spring effect of the air gap, k mem and k airgap
respectively. The resistance R airgap represents the damping
caused by the viscous losses in the air gap and M mem is the
effective diaphragm mass.
In the acoustic domain, a sound pressure (P g ) is applied to
the diaphragm through the radiation impedance composed of
the radiation resistance R rad , representing the frictional force,
and by the radiation mass M rad , representing the mass of the air
close to the diaphragm that is vibrating in phase with the plate.
In the electrical domain, the capacitance of the microphone
is represented by C 0 and the parasitic capacitance, due to the
electric field in the oxide (anchor of the microphone) is C p .
The link between the acoustic and mechanical domain is
modeled by the mechano-acoustic transformer with the ratio
A mem , representing the diaphragm area. The second transformer
represents the coupling between electrical and mechanical
domain with the ratio Γ.
Fig. 3. Microphone equivalent circuit.
The following paragraphs discuss the different parameters
of the equivalent circuit taking into account the effect of etch
holes.
B. Mechanical behavior with holes
The analytic description of the microphone mechanical
behavior is quite complex and difficult to solve because of the
diaphragm geometry (arms, holes). For this reason, an
approach using finite element simulations and reduced
elements approximation is used. Indeed, we can determine the
mechanical parameters of the equivalent circuit that represents
the diaphragm, namely its spring coefficient k mem and effective
mass M mem , with FEA performed in CoventorWare and
consider the diaphragm as a spring-mass system governed by
the well-known relations:
mem==
maxwkP (1) AF
kmem
=f
(2)
0
M
mem
Simulations can calculate the resonant frequency (f 0 ) and the
maximum displacement (w max ) of the structure when we
applied a uniform force F corresponding to a pressure P on the
diaphragm. From w max and knowing the diaphragm area (A),
we can calculate the spring coefficient of the diaphragm with
(1). From the resonant frequency and the calculated spring
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ISBN:978-2-35500-013-3