A development guide for high-performance MEMS sensors
Introduction: the story of inertial sensors
The story started nearly two centuries ago with French physicist Leon Foucault. He used his famous pendulum – a 28kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris – to demonstrate the rotational rate of the earth in 1851, and then went on to perfect the measurement using a gyro in 1852.
In order to grasp the underlying mechanics, one has to imagine that the plane of oscillation of the pendulum remains fixed relative to the far distant masses of the universe, while Earth rotates underneath it.
Figure 1: Foucault Pendulum, Pantheon, Paris.
Gyroscopes and accelerometers — also called inertial sensors — remained scientific curiosities for almost a century but had a huge impact during the Second World War, as they were used in a large set of applications such as ship navigation, guided missiles, battery fire control, aircraft artificial horizon and flight controls.
Figure 2: Mechanical gyros used for German V2 rockets during World War II.
Since the end of the Second World War, these sensors have progressed from complex electromechanical devices assembled with more than 100 parts to the modern solid-state devices. In 1999, the first high performance inertial MEMS measurement unit (IMU) was launched: this first MEMS IMU and its evolutions have paved the way to well-established industry standards with up and running production. We will review in this article, the main standards of these high performance inertial MEMS sensors.
MEMS Architecture
A lot of different MEMS architectures have been developed and studied since the 1980s. We will review hereafter the designs families that have emerged as the dominant ones for high performance inertial sensors.
For high performance accelerometers, the “in-plane force-rebalance” is the dominant design family. A symmetric silicon proof mass is suspended by pairs of opposing spring flexures on either side of the proof mass. An applied acceleration acts on the proof mass. This in-plane motion is counterbalanced by applying voltages that generate electrostatic forces to rebalance the proof mass (closed-loop operation). The applied voltage is directly proportional to the input acceleration [1].
Figure 3: MEMS Accelerometer design principle.
For high performance gyroscopes, the “tuning fork” design family is the dominant design implantation. This design family is based on a pair of proof-masses (this type of gyro is also called dual-mass) that are electrostatically driven to oscillate with equal amplitude but in opposite directions. When the device is rotated, the Coriolis force creates an orthogonal vibration that can be sensed by capacitive electrodes [2].
Figure 4: MEMS gyroscope design principle
Electronics Architecture
The dominant interface electronics includes ultra-low noise capacitive to voltage converters (C2V) followed by high-resolution voltage digitization (ADC). Excitation voltage required for capacitance sensing circuits is generated on the common electrode node. 1-bit force feedback DACs are used for system actuation [3].
The choice for the implemented closed-loop architecture based on a sigma-delta principle is particularly well adapted as it brings the following key advantages:
1) Sigma-delta is well suited for low-frequency signals. Noise shaping principle rejects quantization noise in high frequency bands.
2) Sigma-delta implementation is well adapted with time multiplexing concept. This allows the usage of the same electrodes for both sense readout and electrostatic force actuation.
3) Simplicity of hardware implementation. Oversampling concept allows significant design relaxation of the analog detection chain signal resolution. Additionally the voltage reference used for actuation force feedback is also of simple implementation as it is a 1-bit D/A converter, thus simplifying its design.
4) Linearization of the electrostatic forces thanks to the Sigma-delta principle (through force averaging) furthermore reduces non-linearity overall and more importantly its even-order terms, which result in rectification error.
5) Sigma-delta signal output is inherently a digital signal, thus suppressing the need for costly high resolution A/D converter.
Last but not least, ceramic packages are the dominant ones. They provide near-perfect hermeticity and thereby excellent long-term environmental protection for the silicon die, as shown in the following figure [4].
Figure 5: View of high performance inertial MEMS package with MEMS die on the left and interface circuit die on the right (lid removed).
Metrics
For the sake of simplicity, an inertial sensor’s precision is usually defined by a single parameter, namely its “bias stability” over the whole mission profile. This is the accuracy of the output of the sensor when there is no mechanical stimulus applied. Ideally, bias stability should be equal to 0 but, in practice, there are always some errors created by the environment (thermal variations, vibrations, linear accelerations and others) or due to the sensor itself (misalignment, noise, aging and others). The main components contributing to the bias stability are presented in the following table. Best values obtained with MEMS gyros (range of ±450°/s) and accelerometers (range of ±15g) are given according to latest publications and product releases.
Table 1: Bias instability, in-run and run-to-run bias stability.
As a general comment, “bias stability” is usually several hundred times greater than “bias instability”:
1) Bias instability is the best performance achievable in a lab set-up,
2) Bias stability (in-run or run-to-run) is the real performance achieved during the mission.
The value of bias stability strongly depends on each mission profile: for some missions, it may be dominated by temperature errors, for others missions by aging. So its value will depend on each specific “use case” and cannot be summarized with a single figure.
The Allan variance method and bias instability
We will now explain how the bias instability is measured. This measurement is typically performed in a lab set-up, without any vibration nor acceleration, and at room temperature. It is based on the Allan variance approach, also known as two-sample variance.
Allan variance is defined as half of the time average of the squares of the differences between successive readings of the frequency deviation sampled over the sampling period. The Allan variance depends on the time period used between samples: therefore it is a function of the sample period, commonly denoted as τ, likewise the distribution being measured, and is displayed as a graph rather than a single number.
Allan variance plots are used to quantify stochastic errors i.e. that change while the sensor is operating. These errors, coming from different physical phenomena, are reasonably separated in the frequency and time domain and therefore can be extracted from the plots in log-log format (see IEEE Std 962-1997, R2003, Standard Specification Format Guide and Test Procedure for Single-Axis). These errors include quantization or non-integrating white noise, random walk or integrating white noise, bias stability and are widely used in sensor modeling to provide predictions of navigation performance. To quantify these errors is also useful in order to find root cause of sensor performance issues.
Figure 6: Measured root Allan variance: bias instability of 0.8 °/h (Tronics product GYPRO2300, single-axis gyro).
Figure 7: Measured root Allan variance: bias instability of 6µg (Tronics product AXO1500, single-axis accelerometer).
Application grade and impact of consumer products
As shown in the following table, the application grade is defined by the relative accuracy, i.e. the ratio between the bias stability to the measurement range:
Table 2: High performance inertial sensors application-grade.
In the consumer market, the unit price of an IMU is typically less than $2, a key requirement to be compatible with the bill of materials of the smartphone industry. To satisfy this cost constraint, the design integration is achieved with very small proof masses that lead to poor bias stability. A typical consumer-grade inertial sensor has a relative accuracy in the range of a few percent, a value that did not really change over the last 10 years.
In comparison, a relative accuracy of a few ppm is required for tactical grade: this means a 10,000 times performance improvement. As performance is more or less proportional to the MEMS proof mass, i.e. the MEMS die area, it is clear that specific MEMS processes and products are needed in order to improve performance. As an example, automotive sensors do offer a better accuracy that consumer ones but their size and unit price are typically ten times larger.
Supply chain
Engineers now design systems and products that include MEMS inertial sensors as essential components. These applications range from smartphones to critical safety systems. A large majority of engineers will be more than happy to buy Commercial off-the-shelf consumer-grade and automotive-grade sensors that are largely available on electronics components distributors.
Nevertheless, there is a growing number of industrial applications, such as offshore and downhole drilling, mobile mapping, UAV or agriculture, that cannot cope with automotive or consumer-grade sensors. Up to now, these needs could not be fulfilled, as the high performance inertial sensors were mainly sold directly within IMUs by vertically integrated companies. And these large system makers are not really interested in addressing applications outside their field.
To satisfy these needs, design engineers are considering new solutions and new partners who can connect the high performance world to the industry. In 2010, TRONICS, an independent European supplier of high performance MEMS, and Si-Ware Systems, an analog and mixed-signal ASIC provider, partnered to answer to these unmet market needs. Such inertial sensors are helping design engineers innovate and differentiate their designs by enabling new products that may not have been possible earlier.
Conclusion
Looking back over the last two decades, inertial MEMS performance has continually improved. Starting from the first functional MEMS inertial sensors demonstrated in the 1980s, automotive-grade MEMS were developed one decade later and low-end tactical in the following decade. It is clear that inertial MEMS sensors still have the potential for an additional order-of-magnitude performance improvement over the next decade.
Methods for further optimization are known and can be achieved by improving the precision of the microfabrication, reducing the sensitivity to packaging, and improving the electronics. Therefore, the quest for inertial MEMS performance improvement to tactical grade and beyond will continue in the coming years.
Antoine Filipe, PhD is business unit manager and Christophe Kergueris, PhD, is product development manager at Tronics. Amr Hafez, PhD is business unit manager and Botros George is engineering manager at Si-Ware Systems.
References:
[1] C. Condemine et al. “A 0.8 mA 50 Hz 15 bits SNDR DS Closed-Loop 10 g accelerometer using an 8th-order digital compensator”, pp. 248-249, International Solid-State Circuits Conference (ISSCC), 2005.
[2] A. Filipe et al., “Toward tactical grade MEMS gyros”, pp. 2.1-2.10, Symposium Gyro Technology, 2013.
[3] A. El-Sayed et al., “A Self-Clocked ASIC Interface for MEMS Gyroscope with 1m°/s/√Hz Noise Floor”, pp. 1-4, Custom Integrated Circuits Conference (CICC), 2011.
[4] A. Filipe et al., “Impact of die-attach materials on MEMS Gyro performance”, pp125-126, International Symposium on Inertial Sensors and Systems (ISISS), 2014.
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