A bionic approach for the mechanical and electrical decoupling of an MEMS capacitive sensor in ultralow force measurement

Abstract

Capacitive sensors are efficient tools for biophysical force measurement, which is essential for the exploration of cellular behavior. However, attention has been rarely given on the influences of external mechanical and internal electrical interferences on capacitive sensors. In this work, a bionic swallow structure design norm was developed for mechanical decoupling, and the influences of structural parameters on mechanical behavior were fully analyzed and optimized. A bionic feather comb distribution strategy and a portable readout circuit were proposed for eliminating electrostatic interferences. Electrostatic instability was evaluated, and electrostatic decoupling performance was verified on the basis of a novel measurement method utilizing four complementary comb arrays and application-specific integrated circuit readouts. An electrostatic pulling experiment showed that the bionic swallow structure hardly moved by 0.770 nm, and the measurement error was less than 0.009% for the area-variant sensor and 1.118% for the gap-variant sensor, which can be easily compensated in readouts. The proposed sensor also exhibited high resistance against electrostatic rotation, and the resulting measurement error dropped below 0.751%. The rotation interferences were less than 0.330 nm and (1.829 × 10⁻⁷)°, which were 35 times smaller than those of the traditional differential one. Based on the proposed bionic decoupling method, the fabricated sensor exhibited overwhelming capacitive sensitivity values of 7.078 and 1.473 pF/µm for gap-variant and area-variant devices, respectively, which were the highest among the current devices. High immunity to mechanical disturbances was maintained simultaneously, i.e., less than 0.369% and 0.058% of the sensor outputs for the gap-variant and area-variant devices, respectively, indicating its great performance improvements over existing devices and feasibility in ultralow biomedical force measurement.

Graphical abstract

Keywords

micro-electro-mechanical system capacitive sensor / bionics / operation instability / mechanical and electrical decoupling / biomedical force measurement

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Nomenclature

Abbreviations
AFM	Atomic force microscope
ASIC	Application-specific integrated circuit
CCD	Charge coupled device
GUI	Graphical user interface
MEMS	Micro-electro-mechanical system
PCB	Print circuit board
PMMA	Polymethyl methacrylate
SOI	Silicon-on-insulator
Variables
c	Damping of the swallow structure
C	Overlapped area of the comb capacitor
CC1, CC2, CC3, CC4	Complementary comb arrays
Cd1, Cd2	Frequency decoupling capacitors of the bias-scaling circuit
Cin+, Cin−	Inputs of the ASIC chip
CN1, CN2, CN3	Negative sensing arrays
CP1, CP2, CP3	Positive sensing arrays
d	Gap of the combs
da0	Initial gap of the area-variant combs
dg1, dg2	Air gap of the gap-variant combs
Δd	Step size of the manipulation stage movements
D1, D2, D3	Distances between six supporting beams and the structure center
E	Young’s modulus of the movable structure
Eeg	Measurement error from the electrostatic force of gap-variant device
F0yi, F0zi (i = 1,2,…,6)	Reaction forces along the y and z axis at the fixed end of supporting beams, respectively
Fe	General pulling electrostatic force of comb arrays
Fea, Feg	Pulling electrostatic forces of the area- and gap-variant comb arrays, respectively
Fx, Fy, Fz	Loading forces along the x, y, and z axis at the beak tip, respectively
F_{\mathit{\text{z}}}^{\prime }	Equivalent force along the z axis at the structure center
Iy, Iz	Moment inertia around the y and z axis of the beam lateral section, respectively
ky	Stiffness of the swallow structure
Lb	Length of the supporting beam
Lbody, Lbeak	Lengths of the swallow body region and beak probe, respectively
Lc	Length of the comb plate
Lco	Overlapped length of the combs
Lhead, Ltail, Lwing	Lengths of the swallow head region, tail region, and wing region, respectively
Loff	Offset distance between the structure center and front frame of the head region
Line_1	Sampling line along the swallow body
Line_2	Sampling line along the inside frames of the swallow wing
Line_3	Sampling line along the outside frames of the swallow wing
m	Mass of the swallow structure
M0y, M0z	Reaction moments around the y and z axis at the fixed end of supporting beams, respectively
Me	Planar electrostatic moment of comb arrays
Mx	Moment around the x axis derived from Fz
Na, Ng	Numbers of the area- and gap-variant combs, respectively
PADCi (i = 1,2,…,4)	Comb pads of the complementary sensing arrays
PADNi (i = 1,2,3)	Comb pads of the negative sensing arrays
PADPi (i = 1,2,3)	Comb pads of the positive sensing arrays
PADEXC	Excitation pad
r	Stiffness ratio
R	Scaling factor of the bias-scaling circuit
R1, R2	Scaling resistors of the bias-scaling circuit
Sc	Capacitive sensitivity of the complementary comb arrays
Tb	Thickness of the supporting beam
Tc	Thickness of the combs
Va	Applied voltage bias between the combs
Vapi	Critical voltage applied to the gap-variant combs
Vcc	Power supply of the ASIC chip
Vdc	DC bias applied to the combs
VEXC	Scaled excitation voltages of the ASIC chip
VEXCA, VEXCB	Excitation voltages of the ASIC chip
wE	Elastic deformation along the z axis derived from Fz
w_{F_{\mathit{\text{z}}}}	Translation bending deformation along the z axis derived from Fz
w_{M_x}	Rotation bending deformation along the z axis derived from Mx
wx	Bending deformation along the x axis
wy	Bending deformation along the y axis
{\dot{w}}_y	First order derivative of wy
{\ddot{w}}_y	Second order derivative of wy
wz	Bending deformation along the z axis
Wb	Width of the supporting beams
Wbody, Wis, Wwing	Widths of the swallow body region, island region, and wing region, respectively
y0	Initial misalignment of the asymmetrical gap-variant combs
ε	Dielectric permittivity in air
δy	Bending angle along the y axis

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 52105589 and U1909221), in part by the China Postdoctoral Science Foundation (Grant No. 2021M692590), in part by the Fundamental Research Funds for the Central Universities, China (Grant No. xzy012021009), in part by the State Key Laboratory of Robotics and Systems (HIT), China (Grant No. SKLRS2021KF17), and in part by the Beijing Advanced Innovation Center for Intelligent Robots and Systems, China (Grant No. 2019IRS08).

Conflict of Interest

The authors declare that they have no conflict of interest.

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