Online proceedings - EDA Publishing Association

11-13
May 2011, Aix-en-Provence, France
This means that the piston mode should take place before
reaching 300 Hz frequency at which the membrane runs
Central circle
high displacements. While increasing the frequency, though
the membrane vibration remains piston mode, the
displacement amplitude reduces enormously. As for the
emissive surface, it is indispensable to have a rigid and
undeformable suspended membrane. However, its lightness
is also an important factor as it plays a role in the
microspeaker efficiency η. This point is highlighted by Eq.
(3), which shows that the lighter it is, the higher the
efficiency can be.
=
4
.. rπρ 1 ⎛ f ⎞
Force
. .
4
⎜
⎟
Rc
⎝ coil
+ MM
membrane ⎠
η (3)
In this equation, ρ is the air density (1.2 kg/m 3 at 20°C), r
the membrane radius, c the sound speed (343 m/s at 20°C),
R the coil resistance, M coil and M membrane the weight of the
coil and that of the membrane. The force factor f Force which
is determined as a result of the driving force per current unit
meets 0.35 N/A. This value was attained through
electromagnetic optimization of the coil and the magnet [6].
III.
MEMBRANE DESIGN
The dynamic performances were first analyzed on a thin
silicon disc structure using FEM simulations. Silicon was
chosen deliberately because it fulfills both rigid and light
criteria. Its Young modulus to density ratio of 71
GPa.gr/cm 3 is actually three times higher than that of other
common materials used in MEMS technology such as
titanium or aluminum.
The modal results showed that for a 20 µm thick disc,
more than 40 different vibration modes exist in the
microspeaker bandwidth. High sound reproduction quality
asks for as little vibration modes as possible. Thickening the
membrane can be considered as a solution for shifting most
of the modes to frequencies higher than 20 kHz. For
instance, FEM modal simulations of a 320 µm thick disc
showed only two undesirable vibration modes, with the
drum mode at 20 kHz. Unfortunately, such solution strongly
increases the membrane weight, which reduces significantly
the loudspeaker's efficiency. Indeed, the 320 µm thick
membrane weights 132 mg, that is to say 16 times more
than the 20 µm one. According to Eq. (3), the efficiency
would be divided by a factor of 93 if considering an
optimized coil of 6 mg.
Several microstructures of the membrane were considered
to prevent efficiency deterioration while keeping most of
the vibration modes out of the frequency bandwidth. The
idea was to dig up some areas in the membrane and to find a
good trade-off between the membrane weight and its
rigidity. Comparing different possible designs such as
hexagonal shape or crossed beams, led us to conceive the
ribbed structure shown in Fig. 2, which includes one 3 mm
diameter central ring and one peripheral ring, each 200 µm
wide, joined together by a series of radial ribs. In order to
have results compatible with microfabrication process, the
2
Fig. 2. Structure of analyzed ribbed membrane for the microspeaker
depth of the structured part was set to 300 µm. The
thickness of the plain membrane was set to 20 µm. In fact,
the micromachining process is based on a silicon-oninsulator
(SOI) substrate for which the top side silicon layer
and the substrate are respectively 20 µm and 300 µm thick.
The effect of the number and the width of the radial ribs
on the vibration modes were analyzed using FEM
simulations. The results concerning the drum mode
frequency are shown on Fig. 3 computed with a number of
ribs between 10 and 40 and with four different widths of the
ribs: 50 µm, 100 µm, 150 µm, and 200 µm. These
simulation results show that the drum mode frequency is
optimally shifted towards high frequencies for a ribs
number between 14 and 15. The drum mode is the vibration
mode which deteriorates mainly the sound quality. In
particular, this vibration mode should not appear in the low
and medium frequencies, but one can consider that its effect
is not perceptible above 12 kHz.
The membrane weight varies also with the number and
the thickness of the radial ribs, as shown on Fig. 4. The
maximum drum mode frequency and the corresponding
membrane weight for each series of ribs thicknesses are
summarized in Table I for each series of ribs width. The 50
µm width seems theoretically promising to adopt, but
microfabrication defects due to high aspect ratio may be a
problem. Consequently, 100 or 150 µm width for the ribs
leads to a good trade-off between the sound quality (related
to the drum mode), the efficiency (related to the membrane
weight) and the microfabrication yield (related to the aspect
ratio of the ribs).
Drum mode frequency (Hz)
14000
13500
13000
12500
12000
11500
11000
Rib
Peripheral circle
50 µm
100 µm
150 µm
200 µm
10 15 20 25 30 35 40
Ribs number
Fig. 3. Drum mode frequency of structured membrane as a function of
ribs number, for four different ribs thicknesses, 50, 100, 150, and 200 µm
260