Development of a Biomimetic Eardrum for
Acoustic Sensing
Pieter Westerik, Erwin Berenschot and Gijs Krijnen
MESA+ Institute for Nanotechnology, University of Twente, The Netherlands
E-mail: gijs.krijnen@utwente.nl
Abstract—The desert locust (schistocerca gregaria) has ears integrating sound reception, impedance transformation and frequency discrimination in a single passive membrane. The anatomy and frequency dependent response of these ears to acoustic input have been extensively studied before. This is the inspiration for the development of a new acoustic sensor with integrated mechanical filtering. We have worked on a new micro-fabrication process based on conformal deposition of Parylene on silicon which was used to make membranes with similar variations in tension, thickness and mass density as the tympanal membrane of the locust. Mapped vibration measurements show similarities in the behaviour of the artificial membrane with the biological original, showing the potential of the approach for future energy efficient passive mechanical filtering approaches.
I. INTRODUCTION
In nature many elegant solutions to engineering problems can be found, and indeed this has often inspired engineers for their work. And with our growing understanding of organisms and biological systems in general, we can keep learning for the engineering problems of today.
In this contribution we explore how the ear of the desert locust (schistocerca gregaria) can inspire human-made acous-tical sensors. This ear is special because within a few cubic millimetres it achieves sound reception, impedance transfor-mation and frequency discrimination, probably all without spending any energy [1].
To explore the possibility of making a sensor with similar performance for low-energy applications like remote appli-cations or robotics, first a better understanding of the bio-logical device is obtained through literature on anatomical and biophysical studies. This understanding is deepened by considering the theory of vibrating membranes and plates, and by some modelling efforts. Then we report on a newly developed microfabrication process capable of reproducing many properties of the locust ear, and on the behaviour of devices produced with this method under acoustic stimulation.
II. BACKGROUND
A. Physical description
The ears of the desert locust are located on its first abdomi-nal segment (see figure 1). Visible from the outside is a mem-brane, which has a nonuniform thickness (values between 0.6 and 20 µm [2], or even down to 0.1 µm [3]). Two regions can be identified: a thick part with a typical thickness of 6-10 µm and a thin part, typically 1-3 µm thick. Based on the type of tissue [2] a typical Young’s modulus of 3 GPa in the transverse
Fig. 1. Location of locust ears. Inset: optical and electron micrograph of tympanal membrane (from Windmill et al. [6])
direction and a density of 1.2 ⇥ 103kg m 3 [4] is estimated.
Based on compliance measurements by Michelsen [5] and Stephen and Bennet-Clark [2] and vibration measurements by Michelsen [5] and Windmill et al. [6], [7] one can estimate the tension in the membrane. Assuming that the restoring force in the membrane is purely due to tension Michelsen [5] estimated it at 0.28 N m 1.
On the edge of the thicker region, M¨uller’s organ attaches to the back side of the membrane on different positions. It contains four distinct groups of receptors [8]. The membrane is backed by an air filled cavity [9].
B. Biomimetical motivation
Windmill et al. [6], [7] and Malkin et al. [3] performed laser Doppler vibrometer (LDV) measurements on locust tympanal membranes, and found waves originating at the thinner part of the membrane travelling to the thicker part and M¨uller’s organ, see for example figure 2. This would change the signal from high amplitude and low force to low amplitude and high force.
The exact travelling wave pattern was frequency dependent. Michelsen [8] found that each of the receptor groups had a maximum sensitivity to acoustic actuation of the membrane at a different frequency. This suggests that the combined mechanical behaviour of the membrane and M¨uller’s organ makes for a mechanical frequency filtering system, enabling frequency sensitivity to the locust without the high energy cost of extensive neural processing.
Fig. 2. Travelling wave in locust tympanal membrane; top: measurements on locust ears from Malkin et al. [3] (6.1 kHz); middle: simulations (6.1 kHz); bottom: measurements on our artificial membranes (7.6 kHz).
C. Theoretical considerations
According to Wenzel et al. [10], assuming a plate in the x-y plane with no change in properties or displacement in the y direction, one can describe its dynamic bending as a function of only x and t (time) with
@2w @t2 = 1 d⇢ ✓ T@ 2w @x2 Ed3 12(1 ⌫2) @4w @x4 ◆ , (1)
with w the displacement in the z-direction, d the thickness of the plate, ⇢ the density of the material, T the tensile force (in x direction) per unit length of plate (in y direction) (so in plane stress integrated over the thickness of the plate), E the Young’s modulus of the material and ⌫ the Poisson’s ratio of the material. The right-hand side represents two restoring forces: one due to stretching and one due to bending. By inserting a general sinusoidal travelling wave and solving the equation one can find the wave speed
cp= v u u u t Ed3!2 6(1 ⌫2) T +qT2+Ed4!2⇢ 3(1 ⌫2) (2) (with ! = 2⇡f the angular frequency), in which we can find again the contributions from the tension, T2 and the
stiffness, 1
3Ed4!2⇢/(1 ⌫2). If either is much larger than
the other the equation can be much simplified to the wave speeds for ‘membrane’ behaviour and ‘plate’ behaviour. This is illustrated in figure 3. The distribution of local wave speeds in a membrane determines how a wave will propagate exactly through that membrane.
D. Modelling
A finite element model of the membrane was built in COM-SOL MultiphysicsR. The thickness was taken as described
by Stephen and Bennet-Clark [2] and the Young’s modulus and density were taken to be uniform over the membrane. For the density 1.2 ⇥ 103kg m 3 was taken as described
above. Stiffness and tension were adjusted until the resonance frequencies corresponded more or less with values reported in
10 1 100 101 102 103 101 102 103 f d(m/s) cp (m/s) universal formula plate formula membrane formula
Fig. 3. Theoretical relation between phase velocity and the product of frequency and membrane thickness for constant tension per thickness, for membrane-like and plate-like structures, and the transition between the two for a real membrane.
literature, and until the steady state compliance was similar to the values reported by Michelsen [5] and Stephen and Bennet-Clark [2]. From the resulting model the eigenmodes and their eigenfrequencies were extracted.
These eigenmodes were used as the degrees of freedom in a mathematical model in which a damping force and a driving force were added to find the vibration of the membrane as a function of frequency. Although the frequency response of the membrane differed significantly from the behaviour reported in literature, the travelling wave behaviour could be replicated, as shown in the middle row of figure 2.
III. EXPERIMENTAL
A. Fabrication
As a membrane material Parylene-C was chosen, because its as-deposited tension is much lower than most other thin film materials that are used in microfabrication. It has the additional advantage that its deposition process leads to a perfectly conformal film.
Silicon was used as a sacrificial mould and also as a support, because of the many techniques that are available to shape it. The fabrication process is summarized in figure 4. First mould features are created on the top of a silicon wafer using a deep reactive ion etching (DRIE) process. Then the mould is thinned down from the bottom at the location where the membrane will be. Subsequently the Parylene is deposited on the top, and finally the membrane is released completely by etching the remainder of the mould. The silicon around the membrane remains as a support.
Three types of mould features can be distinguished (com-pare figure 4, 5 and 6). Around the membrane, in the silicon that remains as a support, there is a trench which is thinner
1)
2)
3) anti-delamination
trenches stress releasewrinkles thickened region
Fig. 4. Fabrication: 1) DRIE etching of Si, 2) Conformal Parylene deposition and 3) isotropic etching to release the membrane.
thin region thickened region stress control trenches support by remaining Si
Fig. 5. Structured parylene membrane. Inset: SEM of fabricated (and partly removed) membrane.
than twice the parylene film thickness. Therefore it will be completely filled with Parylene, giving the membrane an anchor on the support. The second type of features are wider trenches at the edge of the membrane. Because they are wider they are not completely filled, and after the removal of the silicon they leave wrinkles in the membrane that reduce the stress in the membrane below the as-deposited value, to get closer to the tension reported for the desert locust.
The third type of feature is a network of trenches that are again at least as narrow as the anchor trenches, so that they are again completely filled. After removal of the silicon they leave a network of supporting ribs of Parylene in the membrane, which dramatically increases its stiffness. By varying the width and distance of these ribs the stiffness, and thereby the local wave speed, can be varied over the membrane. Figure 5 shows the resulting Parylene structures.
Based on this process several membrane designs were made. Figure 6 shows a simplified design with a thicker and a thinner region. Also designs were made that resembled the biological example more closely in terms of shape and estimated local
thickened region stress release wrinkles thin region anti-delamination trench
Fig. 6. The mask for forming the silicon mould for a simplified design with a thicker and a thinner region in the membrane.
wave speed. B. Measurements
Vibrations of the membrane were measured using a scan-ning laser Doppler vibrometer [11] integrated in a Polytec MSA-400. The measurement setup is shown schematically in figure 7. The microfabricated membrane was placed under the laser beam of the vibrometer, and was actuated acous-tically with a loudspeaker. The loudspeaker signal and the vibrometer output were synchronised to get a phase relation between the vibrations at different locations on the membrane. Prior to measurement, instead of the membrane a reference microphone was used to determine the frequency dependent amplitude of the sound at the location of the membrane in this particular acoustic environment.
The laser beam was scanned over the surface of the mem-brane to obtain the spatial distribution of the vibrations of the membrane. This resulted in a complex amplitude for every measurement point and for every measured frequency. A better understanding of all this data was obtained by performing proper orthogonal decomposition [12] to obtain the dominant vibrational modes. Subsequently the amplitude of each of these modes as a function of actuation frequency was determined, see figure 8.
signal generator signal
data acquisition trigger
velocity
wafer with membrane vibration decoupling Fig. 7. Schematic of the measurement setup.
Fig. 8. Frequency dependent amplitude of the first four membrane eigen-modes found with POD from measurements on artificial membranes, and the fitted 2ndorder system responses.
IV. RESULTS AND DISCUSSION
The fabrication process was successful. However the inner stress release wrinkles collapsed at some points. This caused severe deformation of parts of the membrane, which is proba-bly the main reason for differences that were observed between the behaviour of the biological and artificial membranes.
Figure 8 shows the frequency dependent amplitude for the first four eigenmodes found from the measurements. They were fitted with the theoretical response of a mass-spring-damper system to find the resonance frequencies and quality factors of each of these modes. This shows that by probing at the right locations one could indeed obtain some frequency discrimination from these membranes. Strong deviations from the model curves are probably due to small but important differences in acoustic environment between the reference set-up and the actual measurement set-set-up.
For some frequencies also the travelling wave behaviour was observed, as shown in the bottom row of figure 2, con-firming that these membranes can also perform the impedance transformation function.
V. CONCLUSION
Based on literature, theory and modelling an estimate of the (local) properties of the tympanal membrane of the desert lo-cust was made. A microfabrication process was developed that allows the fabrication of membranes with similar properties.
The collapse of the ‘stress release wrinkles’ had a strong influence on the vibration behaviour of the membranes, caus-ing clear differences in behaviour between the biological and artificial membranes. Nevertheless membranes were made that are, like the tympanal ear of the desert locust, capable of sound reception, passive impedance transformation and frequency discrimination.
ACKNOWLEDGMENT
The authors would like to thank the staff of the MESA+
clean room for their support in the fabrication process, and Remco Sanders and Harmen Drogendijk for their practical support and sharing their insights for the measurements.
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