Download A MEMS based electrometer with a low

A MEMS based electrometer with a low-noise switched
reset amplifier for charge measurement
G. Jaramillo, D. A. Horsley
C. Buffa, G. Langfelder
University of California, Davis
Berkeley Sensor and Actuator Center
Davis, CA, USA
Department of Electronics and Information Technology
Politecnico di Milano
Milano, Italy
[email protected]
Abstract— Electrostatic charge measurements are at the base of
chemical, physical and biological experiments. In this work the
authors present an electrometer based on the vibrating
capacitance
of
a
microelectromechanical
(MEMS)
micromachined resonator. We present improvements on the
low-noise readout amplifier by reducing input-referred voltage
noise and parasitic capacitances. An amplifier has been designed
to have a noise corner frequency well below the device’s
operating frequency fn. The electrometer geometry allows for
charge output signal measurements at 2fn minimizing
feedthrough of driving signals. The sensor consists of a set of
comb-finger capacitors placed on each side of a moving mass for
push-pull driving. Operating at resonance, charge collected on
the moving electrode is modulated and the induced voltage is
read with a low-leakage very high-input impedance feedback
amplifier. Due to the specific readout technique, a switched-reset
is used to prevent charge saturation. Reduction of parasitic
capacitance and increase in resolution is achieved through the
careful selection and placement of discrete electronic
components alongside the silicon MEMS chip.
I.
INTRODUCTION
Electrometry is a technique for measuring small electrical
currents. Electrometer instruments are commonly used in mass
spectrometry, surface charge analysis, and the development
and delivery of pharmaceuticals [1]. Electrometer techniques
include
single-electron
transistors,
nano-mechanical
resonators at cryogenic temperatures [2], graphene resonators
[3], and devices based on the vibrating reed technique. The
time-varying capacitance electrometer or vibrating reed can be
implemented using MEMS surface micromachining of parallel
plate sensors and actuators.
MEMS based electrometry can play an important role in
the field of aerosol technology [4]. The device can be
employed for the counting of nanometer-sized aerosol
particulate. MEMS technology permits the reduction of the
cost, size, weight and power of current commercial
electrometers used in the aerosol scientific field. The MEMS
electrometer is based on parallel plates to sense charge and
comb drive capacitive actuators to generate a time varying
capacitance, thereby modulating a slowly-varying input
charge signal to a frequency > 1 kHz where the measurement
noise is greatly reduced.
The need for highly accurate, high precision, low cost
electrostatic sensors continues to expand into many fields.
This demand drives the development and improvement of
electrometer circuits. Electrometer circuits suffer from a
variety of error sources, including noise, parasitic, noise
mixing and leakage currents [5]. In this paper we tackle two
sources of error: parasitic capacitances and noise.
II.
DEVICE AND PRINCIPLE OF OPERATON
The miniaturized electrometer consists of a mechanical
sensing element based on MEMS technology. The
electrometer works as a variable capacitor coupled to the
excitation and readout electronics. When an external amount
of charge is deposited onto a conductive electrode electrically
connected to the MEMS capacitor, a voltage signal builds up
on the capacitor. There is a universal relation between the
measured voltage and the detected input charge, .
The device, shown in Fig. 1, is manufactured using 15µmthick epitaxial polysilicon by STMicroelectronics ThELMA
(Thick Epitaxial Layer for Micro-actuators and
Accelerometers) process. It consists of a main shuttle
anchored by four springs. At opposite ends of the shuttle,
comb-finger actuators placed in the push-pull driving
configuration force the shuttle into resonance. The middle of
the structure contains a set of parallel-plate capacitors, CCV,
that sense the input charge.
Figure 1. SEM picture with a close-up of drive comb-finger and readout
parallel-plate capacitors. MEMS electrometer device oscillates at fn and
generates a detection signal at 2fn which is proportional to the deposited
charge, QC, on parallel-plate electrodes.
In order to minimize the power consumption, the device is
voltage driven at its mechanical resonance frequency fn,
designed to be 2.3kHz, since electrostatic forces are amplified
by the quality factor Q. The lower driving voltage makes the
electrometer compatible with most CMOS integrated circuits
and discrete components. A high Q will allow a final system
implementation with a self-oscillating closed loop circuit.
This first demonstration prototype run in open-loop requires a
preliminary mechanical characterization of the device to
identify fn.
The operating principle of the vibrating reed electrometer
was previously proposed [6]. When an external unknown
amount of charge QC is deposited on the parallel-plate
electrodes, it is converted to an alternating voltage signal as a
consequence of the modulation of the resonating capacitor:
.
(1)
where Cpar contains all parasitic components loading the input
node.
In order to avoid a capacitive feedthrough at fn which
might shadow the weak charge signal, each moving parallelplate armature is faced by two fixed and electrically shorted
electrodes with the consequent generation of a charge signal
at the second harmonic, 2fn, where the feedthrough signal is
negligible.
The sensitivity, here intended as the variation of
modulated voltage per input charge variation, is defined as [6]:
√
⋅
⋅
,
(2)
where x is the displacement of the moving mass and g is the
capacitance air gap at rest. Once the geometry and rest
capacitance of the device are fixed, a highly sensitive system
can be obtained by minimizing all parasitic capacitances and
maximizing the displacement of the moving mass as long as
the resonator remains in a stable linear operating region.
A. Electromechanical characterization
Preliminary electro-mechanical characterization of the
devices used for charge measurements was carried out in order
to obtain an applied force vs. displacement curve, to estimate
the mechanical offset, resonance frequency and pull-in voltage
[4,7].
The actual gap, g = 3.6 µm, was carefully extracted from
these electro-mechanical measures and its difference with
respect to the air gap drawn on the mask (3.0 µm) is in line
with common overetch values for this manufacturing process.
The importance of this mechanical characterization is justified
by the strong dependence of device sensitivity on the gap.
Also the non-linear behavior of the device is estimated by
applying increasing voltages on the actuator and measuring
the corresponding displacement. Fig. 2 shows the
displacement amplitude at resonance with respect to the
amplitude of the driving signal. For displacements larger than
x = 430 nm, the device enters a non-linear working region.
III.
ELECTRONICS DESIGN
Customized driving and analog readout electronics have
been designed based on the mechanical parameters of the
device (i.e. resonance frequency, required actuation voltage)
using a discrete component solution on a printed circuit board
(PCB) and carefully choosing components in order to
minimize additional unwanted parasitic capacitances and
noise with respect to previous implementations [4].
A. Push-pull driving stage
Push-pull drive is widely used in micromachined actuators
as the actuation force can be linearly controlled by the
amplitude of applied voltage [8]. At the current state of setup
development, as the device is not included in an oscillating
loop, an external excitation stimulus must be provided with a
function generator. In order to split this signal into a phase and
an anti-phase component (required for push-pull driving), a
differential driving scheme has been designed using two
difference amplifiers with unity gain, as shown in Fig. 3. They
are based on operational amplifier (OPA445) that is capable to
stand high voltage with a low temperature drift coefficient
(typical offset drift about 25 µV/°C) and fast slew rate
(15 V/µs).
Each driving signal consists of a DC component, VOS,
which can be set using an onboard potentiometer and an ac
component (180° phase shifted in one channel) applied with
an external function generator. Considering an input voltage
,! ! ⋅ sin2& ⋅ '( ⋅ provided by an external
function generator, the two output signals fed to MEMS
driving electrodes are:
Figure 2. The normalized displacement of the suspended mass, x0 = x/g, at
resonance is plotted with respect to drive voltage amplitude. Non-linear
response for displacement larger than x = 430 nm.
)*+, ,- . ! ⋅ sin2& ⋅ '( ⋅ ,
(3)
)*+,/ ,- . ! ⋅ sin2& ⋅ '( ⋅ . & ,
(4)
With these signals the electrostatic force applied to the
comb-finger actuators in push-pull configuration becomes:
0)*( 12 34
56
⋅ ,- ⋅ ! ⋅ sin2& ⋅ '( ⋅ ,
(5)
where ε0 is the air permittivity, H the comb electrode height, N
the overall number of driving cells and gcf the gap of comb
finger capacitors. As H and N are known from design and gcf
can be precisely estimated with electromechanical
characterization, the total driving applied force is finely
controlled by offset and ac voltage amplitudes.
package, is done to minimize leakage current. This particular
kind of transistor has lower loss and higher isolation
capabilities compared to other traditional discrete component
transistors.
Figure 4. The first stage of analog readout electronics is based on a
feedback amplifier and the device output votlage is readout with the positive
high impedance input. G = 14.6.
Figure 3. Schematic of push-pull dirving circuit. The two stages are used to
generate driving signals with 180° phase shift. Signals offset can be on-board
selected using two trimming resistors.
The frequency response of driving amplifiers, with a
precise gain due to the choice of 0.1% tolerance resistances
(R3 = 10 kΩ), is flat up to a few tens of kHz, enough to
guarantee symmetric driving at the device resonance
frequency with a negligible phase shift.
B. Low-noise switched reset readout amplifier
Readout analog frontend specifications are set by the need
to measure low amounts of charge flowing on the vibrating
capacitor and converted into a small ac signal. First, a study of
the architecture used was done with the final choice of a highinput impedance amplifier based on a non-inverting closedloop scheme. The main advantage of this scheme lies on the
high input impedance guaranteed by the operational amplifier
input, see frontend schematic in Fig. 4. The operational
amplifier was carefully selected to minimize input
capacitances, leakage current and noise. AD8067 by Analog
Devices has an input voltage noise density 78( 9
10 < ⁄√=> with a noise corner frequency around 1 kHz, a
leakage current on the order of pA and an input common
mode capacitance CCM = 1.5 pF thanks to the tiny package
SOT23-5.
The MEMS device, schematically represented as a
variable capacitor in Fig. 4, is connected to the positive input
of the amplifier with a set gain, G = 14.6, chosen high enough
to achieve a phase margin close to 85° for a stable operation
and low enough to allow a 15 s charge measurement period
before reaching saturation. Indeed all leakage current
components are integrated on capacitances (device + parasitic)
generating drift of the input voltage. In order to reset this ramp
when the amplifier has reached saturation, a reset transistor is
connected in parallel to the device. The choice of NXP
BF1107, a depletion type field-effect transistor in a SOT23
The choice of the values of gain resistors, R1 = 49.9 Ω and
R2 = 680 Ω, is made in order the make their noise negligible
with respect to the input voltage noise of the amplifier which
is unavoidable. An experimental confirmation of the design is
given in Fig. 5: the measured noise is close to theoretical
operational amplifier noise after the 1/f noise corner frequency
of 100 Hz.
Figure 5. Input referred measured noise of readout amplifier. Flicker noise
component is well below the device operating frequency, nominally equal to
2.3 kHz.
The voltage output of the first stage is then further
amplified and filtered using Stanford Research System SR810,
selecting the second harmonic (2fn) component. The lock-in
amplifier output is acquired using NI PCI 6251 acquisition
board for further signal processing.
The MEMS device is glued on a small PCB close to the
first-stage amplifier’s positive input pin to minimize parasitic
capacitance. The same PCB also hosts a reset mechanism and
a tiny connector to interface an off-board electrode for charge
collection. This PCB is then socketed into a motherboard with
the rest of electronics and ±10 V power supply with filtering.
A metal box shields the whole system, shown in Fig. 7.
Sensitivity calibration is performed using a step voltage
applied to a known capacitor Ccal = 0.2 pF and measuring the
voltage output variation at 2fn, output signal shown in Fig. 6a.
A low leakage depletion FET resets input charge every
measurement. The electrometer in the new configuration
achieved a sensitivity of 53.25 µV/fC or 5.33 × 1010 V/C, see
Fig. 6b. The sensitivity corresponds to almost a 1000x
improvement from our previous reported sensitivity.
was swept over a range of frequencies surrounding the natural
frequency fn. The magnitude and phase of the charge
measurement output (Fig. 9) show the characteristic peak and
180 phase dependence of the MEMS resonator.
(a)
(b)
Figure 9. Frequency response showing magnitude and phase measured at
the second harmonic of the drive frequency. The amplitude peak and 180°
phase transition at 2fn = 4750 Hz are clearly observed.
IV.
Figure 6. Sensitivity calibration. (a) Amplifier output signal with applied
voltage steps. (b) 2fn voltage outout vs. input charge.
CONCLUSION AND FUTURE WORK
We implemented a switched reset electrometer based on
discrete circuitry and a MEMS-based vibrating capacitance
electrometer. Parasitic capacitances were reduced by carefully
designing board layout and circuit implementation. These
modifications achieved a ~1000x improvement in device
responsivity. Charge measurements can be conducted using
the new electrometer in a scanning mobility particle sizer
(SMPS) configuration [4]. These experiments will consist of
an aerosol particulate source and a particle selection system
which accurately charges and feeds a known particle diameter
to the electrode-MEMS electrometer device.
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Figure 7. Image of the board showing the main components for the MEMS
electrometer. The board is placed inside a grounded metal box.
[4]
[5]
[6]
Figure 8. Illustration of the charge reset and sampling/integration of the
charge using the MEMS electrometer system.
To demonstrate the sensitivity of the charge measurement to
the MEMS displacement amplitude, the excitation frequency
[7]
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