INTRODUCTION
A micro-electromechanical system (MEMS) is a process technology used to create
tiny integrated devices or systems that combine mechanical and electrical components.
They are fabricated using integrated circuit (IC) batch processing techniques
and can range in size from micrometers to millimeters. These devices (or systems)
have the ability to sense, control and actuate on the micro scale and generate
effects on the macro scale. MEMS technology exhibits many advantages indigenous
to IC technology such as cost, size and weight reduction (Fokhrul
et al., 2008). MEMS has been identified as one of the most promising
technologies for the 21st century and has the potential to revolutionize both
industrial and consumer products by combining silicon-based microelectronics
with micromachining technology (Bernhard and Howe, 1996).
Accelerometers are probably the most common application of MEMS technology,
as they only require sensing the movement of a mass subject to acceleration
(Dan Haronian, 2000). Accelerometers which can be classified
according to their transduction mechanisms have been used in microaccelerometers
i.e., piezoresistive, tunneling, resonant, thermal, optical, electromagnetic,
piezoelectric and capacitive. Accelerometers that implement capacitive sensing
output measure acceleration based on a change in capacitance due to a moving
plate or sensing element. These devices are used across a very wide range of
applications i.e., automobile air bags (Zimmermann et
al., 1995), navigation (Josselin et al.,
1999) and instrumentation (Tan and Park, 2002). This
method of sensing is able to sense with high accuracy and stability.
In the past several years, extensive research has been done on the design,
fabrication, modeling and structural analysis to increase the sensitivity of
the device. For example, the sensitivity of the capacitive accelerometer can
be improved by increasing the proof mass and the number of sensing fingers arrays
and decreasing the spring stiffness. Majority of the effort goes towards improving
the performance characteristics and reducing manufacturing cost (Bernhard
and Howe, 1996; Gang et al., 1999; Junseok
et al., 2005; Vivek et al., 2006;
Seiji et al., 2007; Chih-Ming et al.,
2008; Krishnamoorthy et al., 2008;
John et al., 2008).
Voltage reference is an important building block for MEMS accelerometer read-out
circuit architecture (Fig. 1) because a stable bias voltage
or power supply source is needed.
|
| Fig. 1: |
Read-out circuit architecture for MEMS accelerometer |
A reference circuit is an independent voltage
or current source that has a high degree of precision and stability. A conventional
bandgap reference adds the forward-bias voltage across p-n diode and that voltage
is weighted by adjusting the ratio of two resistors. The output of the reference
voltage will be unstable in case of improper weighing. Thus, the bandgap reference
should utilize the negative-temperature-coefficient unsilicided N-island resistor
and unsilicided P-island resistor as a weighed component. This resistor ratio
can effectively eliminate the temperature drift of the reference voltage (Rasoul
and Atarodi, 2003).
The aim of this study is to analyze the capacitive MEMS accelerometer
using system-level simulation techniques, FEM and simple analytical modeling.
This simulation study will explain the behavior of the designed MEMS accelerometer
using DC operating point analysis, mechanical resonance frequency analysis,
vary analysis, DC transfer analysis and transient analysis. Simulation
results are discussed and performance of the design is presented. The
design methodology and circuit implementation of bandgap reference for
MEMS accelerometer also will be described because this voltage reference
is an important building block in read-out circuit for the designed MEMS
accelerometer.
MATERIALS AND METHODS
Proposed structure: The sensor transfers the position change into
capacitive variation to detect acceleration. It is composed of a proof
mass suspended by four straight beams and comb fingers (Fig.
2).
|
| Fig. 2: |
Schematic diagram of comb drive MEMS accelerometer designed
structure |
The central part of this mass is perforated to improve the technological
release step and the air damping. The total device structure size is 1021
by 1295 μm. The accelerometer has a proof mass of 140 μm by
1295 μm with multiple 10 μm by 10 μm releasing holes. The
100 movable sensing fingers and fixed fingers are the same size of 350
μm long and 6 μm wide. Each straight beam is 246 μm long
and 2 μm wide. The completely released structure is uniformly 60
μm thick. The silicon used as mechanical structures has a property
elastic modulus of 1.70x105 MPa, Poison’s ratio of 2.70x10-1 and density of 2.34x10-15 kg μm-3.
Modeling and simulation: Capacitive comb drive accelerometer has
been designed, modeled and simulated using Architect and Analyzer modules
in commercial software, CoventorWare®2006. Architect is a system-level
design environment that benefits from the combination of MEMS behavioral
models and the IC circuit components. Analyzer is a solver solution for
physics simulation starts with a 3-D model created from a 2-D layout and
process file, or a model imported from a third-party solid modeling tool.
The initial process starts with schematic creation using Architect module
(Fig. 3).
The silicon on insulator high aspect ratio micromachining (SOI-HARM)
process is used to fabricate the device. This process is a metal-last
process based on the deep dry etching (or DRIE) of silicon. A process
editor is used to create 3-D model building by defining various parameters
such as substrate, deposition of selected material, etching-type, depth
and masks. The completed schematic is transformed into a 2-D layout and
3-D solid model. This solid model is then meshed for further finite element
analysis (Fig. 4).
|
| Fig. 3: |
Schematic drawing of capacitive comb drives MEMS accelerometer
in Architect Module |
|
| Fig. 4: |
Meshed model of capacitive comb drive MEMS accelerometer |
The behavior of the device will be simulated using DC operating point
analysis, mechanical resonance frequency analysis, vary analysis, DC transfer
analysis and transient analysis.
DC operating point analysis: DC operating point analysis is run
to find values of the system during steady state at time zero. The DC
bias values of the electrical component and the initial displacements
of the mechanical components are determined from this analysis. The analysis
is repeated for several times by using various voltages. The electrostatic
force can be calculated by:
The restoring elastic force can be calculated by:
At equilibrium, the total force acting on the movable structure in x-axis
is zero:
By using Eq. 3, the accelerometer displacement in x direction
for a certain voltage can be calculated. The effective electrostatic spring
constant is as follows (Ka Nang et al., 2003):
The electrostatic force is in the opposite direction of the mechanical
spring force, so the actual effective spring constant is as follows:
Instability occurs when the actual effective spring constant is less
than zero. The voltage causes the instability to occur is as follows:
Mechanical resonance frequency analysis: This analysis is run
to obtain resonant frequency of the MEMS accelerometer. The analysis starts
with DC operating point analysis running with all voltage sources set
to zero and followed by frequency analysis with mechanical excitation.
This analysis linearizes the models around the values that can be found
from DC analysis and sweeps a frequency range to determine the frequency
response. This analysis is repeated for several times by applying various
DC voltages to the straight comb bottom to see the influence of DC voltage
on the resonant frequency of the accelerometer. Without DC voltage applied,
the resonant frequency fr of the accelerometer is given by
the following equation:
where, by ms is as follows:
Vary analysis: In this analysis, the width and length of the beams
are varied and the impact on the x resonance frequency is investigated.
Theoretically, the resonance frequency should increase as the width increases
and the length decreases. The resonant frequency fr of the
accelerometer can be calculated by using Eq. 7 and 8.
DC transfer analysis: A DC transfer analysis is conducted by sweeping
an independent source over a sweep range. During this analysis, all voltage
sources are set to zero and acceleration is applied relative to x-axis of the
reference frame to see its influence on the MEMS accelerometer. The displacement
sensitivity Sd of the accelerometer, which is defined as the displacement
of movable fingers per unit gravity acceleration, g along the sensitive direction,
can be obtained by the following equation (Xingguo et
al., 2005):
Dimension analysis: The performance of the accelerometer depends on
the dimensions of the structure. Thus, in this analysis, the number of moveable
fingers for each comb has been changed to characterize its performance. The
displacement of accelerometer with different voltage applied can be used as
an indicator of performance. Equation 2 is used to find the
displacement, while Eq. 4 and 5 were used
to calculate the voltage instability occurs.
Transient analysis: In this analysis, acceleration is applied
on the structure and its response in time is observed. A basic sensing
electronic circuit, consists of resistor, capacitor, diode ground and
Op Amp, is added to the comb drive accelerometer to produce a usable output
signal.
|
| Fig. 5: |
Schematic diagram of bandgap reference circuit |
Single-ended half-bridge capacitive sense interface is commonly
used to translate the displacement into output voltage. The sensitivity
of accelerometer, which is defined as the ratio of output voltage over
the input acceleration, can be obtained through the transient analysis.
The analysis starts with the voltage pulse value set to 1 V. The acceleration
control source that used in the DC transfer analysis is replaced by a
pulse. Some damping is added to the rigid plate, as it is useful to smooth
the x displacement response. This amount is near the critical damping.
The probe tool is used to view displacement in x direction, acceleration
and output voltage Vdemod of the peak detector.
Proposed design for voltage reference: The circuit topology (Fig.
5) of the designed bandgap reference shows a current that is proportional
to the absolute temperature is generated and added into the base emitter of
Q3. The high gain of folded cascode amplifier (Fig.
6) forces the voltages VA= VB. The voltage difference
ΔVEB between the emitter-base junctions of Q1 and
Q2 is obtained using an emitter area ratio of n = 8 and equal value
for currents, I. The circuit of Fig. 7 is referred to obtain
ΔVEB. (Razavi, 2000).
|
| Fig. 6: |
Schematic diagram of folded cascode amplifier circuit |
Derivation of reference voltage: Knowing that voltage at node
A, VA and voltage at node B, VB (Fig.
5) are equal, applying Kirchhoff’s Voltage Law (KVL)
on node, B derives the following Eq. 13:
| -VB + IR1
+ VEB2 = 0 |
(13) |
The voltage appearing at node B is:
Then the voltage across R1 can be expressed as:
| IR1 = VA
- VEB2 = VEB1 - VEB2 = ΔVEB |
(15) |
The output voltage reference can be written as follows:
By substituting Eq. 15 into 16 results
the reference voltage:
|
| Fig. 7: |
Generation of proportional to absolute temperature (PTAT)
voltage |
|
|
|
| Fig. 8: |
(a) VEB3 versus temperature (T), (b) R1/R2
VT ln (n) versus temperature (T) and (c) Vref
versus temperature (T) |
In practice, k is the ratio of R2/R1 and VEB
is negatively PTAT while VT has a positive temperature coefficient.
The temperature coefficient can be zero by getting a proper value of k. Equation
17 can be shown in Fig. 8. The negative slope, -m of VEB3
(Fig. 8a) over the temperature range is obtained by simulation.
It is followed by getting the exact values of R1 and R2
to ascertain the slope, m (Fig. 8b). The PTAT voltage increases
linearly with temperature, thereby efficiently cancelling the effect of the
negative linear temperature of the base emitter voltage (Rincon
and Alfonso, 2001). By summing the emitter-base voltage and PTAT voltage
results slope equal to zero for Vref over the temperature range (Fig.
8c).
RESULTS AND DISCUSSION
DC operating point analysis: The displacement of the accelerometer
increases with the increase in voltage (Fig. 9). When
a DC voltage is applied to the fixed fingers, electrostatic force is generated
on the proof mass. It will change the actual effective spring constant
of the accelerometer from its mechanical value. The lateral electrostatic
force may lead to instability if it increases more rapidly than the restoring
lateral elastic force. The instability will cause the movable fingers
to move laterally and collapsed to the fixed fingers. The pattern agrees
with hand derived calculation and FEM. The voltage instability occurred
between 2.4 and 2.45 V.
Mechanical resonance frequency analysis: The resonant frequency
decreases with the increase in applied voltage (Fig. 10)
due to the actual effective spring constant decreases when the voltage
increases. The results notice that the deviation of the calculated resonant
frequency from Architect simulation is small, which is less than 0.2%.
However, the resonant frequency difference between calculation value and
FEM analysis result is greater, which is in between 0.16 to 6.1%. The
resonant frequency drops when the voltage rises.
Vary analysis: In this analysis, dimension of the beams is varied
and the impact on the x resonance frequency is investigated. The beam
width, Wb is varied from 2 to 8 μm while the beam length,
Lb is varied from 246 to 396 μm. The result shows that
the resonance frequency increases with the decrease in beam length and
increase in beam width (Fig. 11, 12).
The pattern agrees with all results from calculation, Architect analysis
and FEM analysis. The deviation of the calculated resonant frequency from
Architect analysis result is small, which is less than 0.7%.
|
| Fig. 9: |
DC operating point analysis of MEMS accelerometer up
to 2.5 V |
|
| Fig. 10: |
Mechanical resonance frequency analysis up to 2 V |
|
| Fig. 11: |
Vary analysis on the beam length |
However,
the difference between calculation value and FEM analysis result is greater,
which is between 0.8 and 3.4%.
DC transfer analysis: The acceleration is applied in x direction
in the range of 0 to 686.7 m sec-2. The result shows the displacement
of the accelerometer is directly proportional to the acceleration applied
(Fig. 13).
|
| Fig. 12: |
Vary analysis on the beam width |
|
| Fig. 13: |
Displacement of the accelerometer versus applied acceleration |
|
| Fig. 14: |
Displacement of the accelerometer with respect to voltage
applied |
The analytical result of the displacement
sensitivity is 23.775 nm g-1, while in simulation is 23.713
nm g-1.
Dimension analysis: In this analysis, the number of movable fingers
has been reduced to 60. The result shows that the displacement decreases
with the increase voltage. The critical voltage where the instability
occurs is between 3.1 and 3.15 V (Fig. 14). This is
greater than the critical voltage of 100 movable fingers.
|
| Fig. 15: |
Resonant frequency for 100 of movable finger |
|
| Fig. 16: |
Resonant frequency for 60 of movable finger |
The resonant
frequency increases from 3238.2 to 3673.0 Hz (Fig. 15, 16) due to the decrease of sensing mass.
Transient analysis: The result shows that the displacement increases
with the increase in acceleration (Table 1, 2).
The largest acceleration that the accelerometer can detect before instabilities
occur is about 48 g. The displacement and demodulated signal for this
situation are 1.3487 μm and 54.535 V, respectively. The deviation
of modulated signal from calculation values and Architect simulation values
is at about 2.7%.
Voltage reference simulation: Various simulations were performed
in a standard 0.13 μm CMOS process to analyze the effects of the
process variation on the generated voltage reference in five different
process corners including TT (Typical), SS (Slow-Slow), FF (Fast-Fast),
FS (Fast-Slow) and SF (Slow-Fast).
| Table 1: |
Transient analysis of MEMS accelerometer using calculation |
 |
| Table 2: |
Transient analysis of MEMS accelerometer using architect
simulation |
 |
| Table 3: |
Variation in voltage reference for all process corners |
 |
|
| Fig. 17: |
Temperature variation of the output voltage of the BGR
at typical condition |
The reference voltage over temperature
at typical condition and in all process corners is shown in Fig.
17 and 18, respectively. The summary of variation
is shown in Table 3. The output reference exhibits ±
0.614 mV variation from the mean value when the supply changes from 2.25
to 2.75 V (Fig. 19). The design achieves a maximum
PSRR of -49.03 dB for frequency less than 18.5 kHz (Fig.
20). It is obvious that the proposed design achieves a small chip
area, low peak-to-peak output variation for typical condition and high
PSRR (Table 4).
|
| Fig. 18: |
Simulation result of the voltage reference vs. temperature
in all process corner |
|
| Fig. 19: |
Supply voltage variation of the output voltage of the
BGR |
|
| Fig. 20: |
Simulation result of PSRR of the proposed design at
room temperature with 2.5 V supply |
| Table 4: |
Summary of the performance of the proposed BGR |
 |
CONCLUSION
Design, simulation and analysis of capacitive comb drive MEMS accelerometer
using commercial software Coventorware® 2006 were presented in this
current study. The structure uses proof mass suspended by four straight
beams and interdigitated combs are used for driving the structure, as
well as sensing capacitors to provide differential capacitance measurement.
An analysis on the DC operating point, mechanical resonance frequency,
vary, DC transfer and transient has been presented and discussed. A simplified
analytical model to explain the analysis is also presented. The results
obtained by simulation were in close agreement with the analytical results.
A very low voltage variation in BGR has also been presented. The proposed
design produces an output voltage reference of 1.175837 over a temperature
range from -50 to 150°C. The reference voltage has a variation of
± 0.36 mV with temperature and exhibits ± 0.614 mV variation
from the mean value when the supply changes from 2.25 to 2.75 V. The design
achieved a maximum PSRR of -49 dB for frequency less than 18.5 kHz.
ACKNOWLEDGMENTS
The authors would like to express sincere appreciation of the assistance
of Mr. Mohd Kusairay Musa and Mr. Faisal Mohamad for his co-operation
and assistance in providing support of the software. To Mr. Fazlan, Mr.
Sanusi, Mr. Zamri and Puan Rohana, thanks for their kind help. Financial
support from the Universiti Sains Malaysia Short Term Grant, 304/PELECT/6035301
is gratefully acknowledged.
NOMENCLATURE
| η |
: |
No. of movable fingers |
| ε0 |
: |
The permittivity of free space |
| εr |
: |
The relative permittivity of the dielectric |
| h |
: |
Thickness of the accelerometer |
| V |
: |
Voltage applied to the Straight Comb Bottom |
| y0 |
: |
Initial capacitor length |
| y |
: |
Displacement in Y direction |
| x+ |
: |
Initial lateral gap |
| x¯ |
: |
Initial lateral gap |
| x |
: |
Displacement in X direction |
| kmech |
: |
Mechanical spring constant |
| E |
: |
Young’s modulus of silicon |
| h |
: |
Thickness of the accelerometer |
| wb |
: |
Beam width |
| Lb |
: |
Beam length |
| Wm |
: |
Width of the rigid plate |
| Lm |
: |
Length of the rigid plate |
| Wf |
: |
Finger width |
| Lf |
: |
Finger length |
| ηx |
: |
No. of perforation holes in x direction |
| ηy |
: |
No. of perforation holes in y direction |
| H |
: |
Distance between the perforation holes in x and y directions |
| ρ |
: |
Density of silicon |
| mS |
: |
Sensing mass |
| g |
: |
Acceleration due to gravity |
| k |
: |
Boltzmann’s constant |
| q |
: |
Electron charge |
| T |
: |
Absolute temperature |
| n |
: |
Emitter area |
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