Online proceedings - EDA Publishing Association

l c
11-13 May 2011, Aix-en-Provence, France
t c t p
w c
t m
l
w m
(a)
(b)
h 0
Air film
Fig. 1. Schematic representation of the modeled PMPG, which consists of a
double-layer cantilever structure (composed of supporting Si layer t c and
piezoelectric layer t p atop) with proof mass at the free end. Air film of
thickness h 0 is present between an imaginary fixed ground surface
and the bottom boundary of the proof mass (drawn not to scale).
TABLE I
DESIGN PARAMETERS OF THE PMPG
Description and symbol Value Unit
Length of uniform cantilever l c 2500 μm
Length of proof mass l m 1500 μm
Width of cantilever w c 300 μm
Width of proof mass w m 3000 μm
Thickness of cantilever supporting layer t c 20 μm
Thickness of piezoelectric layer t p 20 μm
Thickness of proof mass t m 1000 μm
Young’s modulus of supporting layer and proof mass (Si) E Si 200 GPa
Density of supporting layer and proof mass (Si) ρ Si 2330 kg/m 3
Poisson’s ratio of supporting layer and proof mass (Si) ν Si 0.33 -
and accumulation subsystems; (b) improvement of charge
density via material and structural enhancements including
expansion of operating frequency range of the devices by
means of tuning of their resonant frequency or widening
their bandwidth [1-4].
Research results reported in this paper deal with the
design and material issues of the PMPGs. The second
section presents finite element modeling and simulation
results of the device with emphasis on dynamic analysis of
viscous air damping (squeezed air-film) effects that may be
encountered during operation of the micropower generator.
The third section considers aspects of fabrication of PVDF
thin films and provides results of their experimental
characterization by using SEM, AFM, XRD and FT-IR
analysis methods.
II.
FINITE ELEMENT MODELING AND SIMULATION
A. Model Description
The design of analyzed PMPG is based on bi-layer
cantilever structure with proof mass at the free end (Fig. 1
and Table I). The supporting cantilever layer and the proof
mass are made from silicon, while PZT-5A is used for
piezoelectric layer, which is positioned on the top of the
supporting layer and is poled along the thickness direction
resulting in transverse (“d 31 ”) operation mode. Such
configuration is chosen since it enables the condition of low
resonance frequency to be fulfilled. This is required in
typical applications of vibrational PMPGs, i.e. powering
of wireless sensors installed in industrial or civil structures.
(c)
(d)
Fig. 2. The first four vibration modes of the analyzed PMPG: (a) the 1 st out-ofplane
flexural mode (184 Hz), (b) the 1 st torsional mode (458 Hz), (c) the 2 nd
torsional mode (1628 Hz), (d) the 2 nd out-of-plane flexural mode (1689 Hz).
(a)
(c)
(d)
Fig. 3. 3D contour plots illustrating distribution of air pressure forces in the
gap for the corresponding structural mode shapes in Fig. 2.
These environments commonly generate vibrations that are
characterized by small acceleration (< 1g) and low
frequencies (up to approximately 200 Hz).
Finite element model of the PMPG was realized within
COMSOL Multiphysics by employing the “Piezoelectric
Application” mode. Piezoelectric layer has got electrodes on
its bottom and top faces. Due to low thickness mechanical
behavior of the electrodes may be neglected. Their electrical
behavior is evaluated by imposing proper electrostatic
boundary conditions: the bottom face is grounded, while the
top one is set to “Floating potential” condition. For the rest
of faces of the piezoelectric layer the condition of “Zero
charge/Symmetry” is applied.
When designing PMPGs with bulky proof mass at the end
of the cantilever structure one should consider a possibility
of manifestation of a specific case of viscous air damping
phenomenon referred to as squeeze-film damping, which
occurs when a structure of large lateral dimensions, that
is in relatively close proximity to a fixed surface, vertically
(b)
165