Design of sub-1g microelectromechanical systems accelerometers^a)

Microelectromechanical systems (MEMS) capacitive accelerometers have been widely used in consumer electronics for sensing accelerations of mostly above 1 g (g = 9.8 m/s²) or upwards of several g's. Recent technology, on the other hand, demands accurate sub-1g sensing to realize applications such as human-activities monitoring or the integrated inertial measurement unit (IMU).¹ To detect such low acceleration in a compact sensor module, various types of MEMS capacitive accelerometer based on silicon bulk micromachining have been reported^2–4 to utilize a large proof mass to suppress the thermal-mechanical noise, i.e., the Brownian noise (B_N).⁵ For further miniaturization and high functionality of MEMS accelerometers, complementary metal-oxide semiconductor (CMOS)–MEMS technology has also been applied to accelerometer developments^6–11 by taking advantage of the foundry services for mass production, smaller chip size, high functionalities with CMOS circuitry, and minimal parasitic capacitances. Limited choices of materials and thickness for CMOS-MEMS accelerometer have been the major issue to reduce B_N, which would become critical for low-acceleration sensing with high precision when the parasitic capacitance is minimized.¹² Thus, in our previous report,^13,14 we demonstrated a miniaturized MEMS capacitive accelerometer by using a post-CMOS process with high-density metal, which enabled further size reduction of the proof mass and the device footprint without compromising the sensitivity. In this Letter, we show a design approach of sub-1g detectable MEMS capacitive accelerometers for the miniaturization of CMOS-MEMS inertial sensors. The minimum detectable acceleration can be determined by B_N that is inversely proportional to the mass of the proof mass; thanks to the high-density gold proof mass, our device footprint dominated by the proof mass area is nearly one order of magnitude smaller than the one made of silicon, which is commonly used for CMOS-MEMS accelerometers.

The design requirements for a MEMS capacitive accelerometer for sub-1g sensing have been set as follows; (I) a low B_N design, typically below 10 $μg/Hz$ at a device level, (II) the mechanical resonant frequency of the accelerometer higher than the frequency of common environmental vibrations, which was mostly below 100 Hz,^15,16 and (III) the MEMS structures integrated onto a CMOS circuitry without causing damage on the MOS transistors.

To accommodate sub-1g sensing, the reported accelerometer structures¹³ have been modified as shown in Fig. 1; mechanical stoppers have been allocated on the top and the side surfaces of the proof mass to protect the movable parts from severe damages at excess acceleration. The spring constant has been designed to be 0.3 N/m in z-axis direction; the feature size of the mechanical spring was designed to avoid physical contact between the proof mass and the fixed electrode at the input acceleration of mg range. An SiO₂ film was used on the fixed electrode to avoid stiction. To expedite mechanical design flexibilities, a post-CMOS process using multilayered-metal electroplating has been employed; thick metal layer would help to increase the size of proof mass, while thinner layer benefits to achieve low spring constant in the vertical direction and hence lead to shrink the footprint for the springs. Thermal-mechanical noise of the proof mass in an accelerometer can be gauged by B_N that arises from the random thermal motion of molecules in the surrounding gas, as described in the following equation:⁵ 

where k_B, T, b, and m are the Boltzmann constant (1.38 × 10⁻²³ J/K), the absolute temperature, the viscous damping coefficient, and the mass of the movable parts of an accelerometer, respectively. Equation (1) indicates that B_N can be subject largely to the size and density of proof mass. Fig. 2 shows the analytical modeling of B_N on the proof mass made of different materials; the proof mass made of gold, a high density material, has the smallest B_N compared to those of other materials; thus, using high density material could be a promising solution for a small-sized and low-noise proof mass.

From the above viewpoints, we proposed a sub-1g detectable CMOS-MEMS capacitive accelerometer with a proof mass made of gold; the density of gold (19.3 × 10³ kg/m³ at 298 K) is about ten times higher than that of silicon (2.33 × 10³ kg/m³ at 298 K),¹⁷ which is commonly used for MEMS accelerometers; therefore, the device footprint could be nearly one-tenth of a silicon device. All the MEMS device specification was designed to fulfill the aforementioned requirements from (I) to (III).

The proposed MEMS accelerometer has been developed through an electroplating process reported elsewhere;^18,19 owing to the low process temperature below 400 °C, the electroplating process could be suitable for post-CMOS process for CMOS-MEMS accelerometer developments. Fig. 3 shows the scanning electron microscope (SEM) micrographs of the developed accelerometer. Serpentine mechanical springs with the thickness of 3 μm have been used at each corner of the square proof mass with numbers of release holes for the sacrificial layer removal. Mechanical stoppers have also been placed at the corner of the proof mass and built in the uppermost layer to prevent self-destruction when exposed by a large acceleration. As shown in the SEM images, multilayers gold have been successfully integrated; the multilayer structures have enabled us to decrease the thickness of the mechanical springs to lower the vertical spring constant for the sub-1g sensing, while increasing the proof mass for a heavy mass to suppress the B_N as low as possible.

The gold-electroplated proof mass was designed to be 1020 μm × 1020 μm in area and 12 μm in thickness, which was thought to be sensitive to a sub-1g acceleration at the resolution of 1 mg or better owing to the small design value of B_N = 0.12 $μg/Hz$⁠. The resolution was speculated by considering the root-mean-square (rms) of the acceleration noise (a_n,rms). Assuming the single-pole roll-off characteristics, the equivalent noise bandwidth (Δf) is given by²⁰ 

where f_−3 dB is the cutoff frequency, at which the output of the circuit falls −3 dB off the nominal passband level. The a_n,rms is defined as²¹ 

For the Gaussian noise with a given rms value, the minimum detectable acceleration a_min can be statistically predicted by using a_min = 6.6 × a_n,rms.²² The B_N value to meet the requirement of a_min < 1 mg is B_N < 12 $μg/Hz$ for a typical f_−3dB of 100 Hz. We therefore set the target B_N to be lower than 10 $μg/Hz$ and designed a relatively heavy mass to make a yet smaller B_N = 0.12 $μg/Hz$ to allow for safety margin.

Acceleration responses as a function of capacitance between the proof mass and the fixed electrode (C-G characteristics) were experimentally obtained on the MEMS accelerometer as shown in Fig. 4. The MEMS chip was wire-bonded on a ceramic package and set on a vibration exciter to apply vertical accelerations of 19.9 Hz with the DC bias voltage of 1.5 V. Fig. 4(a) illustrates the measurement setup for the C-G characteristics; the semiconductor device analyzer (B1500A, Agilent Tech., Inc.) was used to supply the DC bias and measure the capacitance change on the device with a ±0.1-V sinusoidal voltage at the frequency of 300 kHz. Fig. 4(b) shows the accelerometer's capability of sensing a sub-1g input acceleration with a 0.1-g step.

Fig. 5 shows measurement results of the frequency response as a function of capacitance between the proof mass and fixed electrode (C-F characteristics). As seen in Fig. 5, the mechanical resonant frequency was measured to be 777 Hz by using an LCR meter (IM3533-01, HIOKI E.E. Corp.) at a 1.5-V DC bias with a ±0.1-V sinusoidal voltage. The resonant vibration of the proof mass was experimentally confirmed to be higher than the frequency of common environmental vibrations (<100 Hz). The quality factor (Q) of the device can be obtained to be 6.40 from the C-F characteristics by calculating the ratio between the real (Z_R) and imaginary (Z_I) parts of the electrical impedance at the resonant frequency; the Z_R and Z_I are 1.97 × 10⁷ and −1.26 × 10⁸, respectively.

To estimate the actual value of B_N on the developed MEMS accelerometer, we use the following analytical models. The Q of a proof mass is expressed as²¹ 

where $ωres$ is the resonant angular frequency. Using Eqs. (1) and (4), B_N can be given by

Equation (5) is used to evaluate B_N from the experimentally obtained data, as it is difficult to tell the actual value of b owing to the squeezed-film damping effect.²¹ The area and height of the proof mass were measured, and the m was experimentally obtained to be 2.17 × 10⁻⁷ kg. Therefore, the actual B_N was estimated to be 0.78 $μg/Hz$ at 300 K, which was well below the target value of 10 $μg/Hz$⁠.

In conclusion, a sub-1g detectable MEMS capacitive accelerometer was presented in order to miniaturize CMOS-MEMS inertial sensors. The microfabrication used was suitable for a post-CMOS process, and the developed high-density proof mass has been nearly one order of magnitude smaller than a commonly used silicon device at the same B_N performance. The C-G measurement demonstrated sub-1g sensing on the device without sensing circuit compensation. The measured C-F characteristics confirmed the mechanical resonant frequency being higher than environmental vibration frequency, and the Q of the proof mass, which then evaluate the actual B_N as low as 0.78 $μg/Hz$ despite the possible B_N degradation by the squeezed-film damping effect.

The authors would like to thank Dr. T. Maruno, Dr. Y. Akatsu, M. Yano, and K. Kudo with NTT-AT for the technical discussions. This work has been supported by JSPS Funding Program for Next Generation World-Leading Researchers (Grant ID: GR024) and KAKENHI Grant No. 23360149.