The obtained parameter values.
This chapter describes technical features and solutions to realize a highly sensitive CMOS-MEMS accelerometer with gold proof mass. The multi-physics simulation platform for designing the CMOS-MEMS device has been developed to understand simultaneously both mechanical and electrical behaviors of MEMS stacked on LSI. MEMS accelerometer fabrication process is established by the multi-layer metal technology, which consists of the gold electroplating and the photo-sensitive polyimide film. The proposed MEMS accelerometers are fabricated and evaluated to verify the effectiveness of the proposed techniques regarding sub-1G MEMS and arrayed MEMS devices. The experimental results show that the Brownian noise of the sub-1G MEMS accelerometer can achieve 780 nG/(Hz)1/2 and the arrayed MEMS accelerometer has a wide detection, ranging from 1.0 to 20 G. Moreover, using the developed simulation platform, we demonstrate the proposed capacitive CMOS-MEMS accelerometer implemented by the multi-layer metal technology. In conclusion, it is confirmed that the multi-physics simulation platform and the multi-layer metal technology for the CMOS-MEMS device have a potential to realize a nano-gravity sensing technology.
- MEMS accelerometer
- multi-physics simulation
- gold proof mass
- multi-layer metal technology
Microelectromechanical systems (MEMS) capacitive accelerometers have been widely used in application fields such as mobile devices, air bag ignition for vehicles, and vital sign monitoring systems [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Also, in the progress of the attractive Internet of the Thing (IoT) technology, MEMS accelerometers have played an important role in key devices. Recently, for several applications such as activities monitoring or the integrated inertial measurement unit (IMU), the accurate sensing devices below 1 G (G = 9.8 m/s2) have been researched and developed regarding various types of MEMS capacitive accelerometer, while conventional MEMS accelerometers have an ability of sensing about 1 G or over several G’s. The performance of the MEMS capacitive accelerometer can be determined by Brownian noise (BN) that is inversely proportional to the mass of the proof mass. Figure 1 shows the transition of BN of the reported MEMS accelerometers. In order to establish a micro-gravity sensing technology based on silicon bulk or surface micromachining technologies, various types of MEMS capacitive accelerometer and complementary metal-oxide semiconductor (CMOS)–MEMS accelerometer have been reported [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. We have developed the MEMS accelerometer and also added the data of our miniaturized sub-1G MEMS capacitive accelerometer  to this figure. The proof mass area of our device is nearly one-tenth of a silicon proof mass area size. As a result, in terms of the technological trend, it is suggested that this research and development would be continuing toward a nano-gravity sensing.
On the other hand, the above applications require the devices, which have a wide detectable range of acceleration, small size, and low power consumption. In fact, there are many difficulties in making the devices because the large size of the proof mass makes the device size larger, and also the accelerometer chip is usually combined with the LSI chips on the assembly board. In order to overcome these technical barriers, we have proposed a CMOS-MEMS accelerometer that implements a MEMS on CMOS-LSI [24, 25]. Figure 2 shows prospects and challenges of the CMOS-MEMS technology from the view point of CMOS-LSI. It indicates that this technology has a solution of the difficulties in developing high functional devices. Especially, digital micro mirror device (DMD) is well-known as a successful example of MEMS business. The technology has the features of high functionality, high accuracy, and mass production. Thus, we have developed the multi-layer metal technology that consists of gold electroplating and sacrificial layer formation using thick polyimide film. Its features include the suitability to realize the various MEMS structures and the post-CMOS processes, which does not degrade CMOS device because the process temperature is below 310°C. Using the multi-layer metal technology, MEMS devices on CMOS LSI have been fabricated [26, 27].
Moreover, to facilitate the design of the CMOS-MEMS devices, we have researched and proposed a multi-physics simulation technique to develop such CMOS-MEMS devices using an electrical circuit simulator with a Verilog-A compatible hardware description language (HDL) for equivalent circuit description [28, 29]. Thus, we have developed a capacitive CMOS-MEMS sensor designed by our multi-physics simulation. The developed sensor shows that the capacitive MEMS device is implemented on the sensor LSI .
In this chapter, first, the multi-physics simulation platform for the CMOS-MEMS technology is presented. Next, we describe the newly developed sensor structure and the multi-layer metal technology, which can be compatible with post-CMOS process. Third, the sub-1G MEMS accelerometer is described. Fourth, the arrayed MEMS accelerometer for wide range detection is demonstrated. Fifth, we then show the proposed sensor circuit using our multi-physics simulation environment. Finally, we demonstrate the evaluation results of the fabricated CMOS-MEMS accelerometer by the multi-layer metal technology.
2. The multi-physics simulation
2.1 Analytical model for MEMS accelerometer
Figure 3 shows a diagram of an analytical model for the MEMS accelerometer. The electrostatic capacitive MEMS accelerometer basically consists of the upper electrode of a proof mass and the bottom plate of the fixed electrode. The upper plate is supported by the spring connected to the mechanical anchor. When the proof mass detects an input acceleration in the vertical direction, the electrical capacitance between the upper and the bottom plates is modulated. The fixed electrode is applied by the input voltage V to measure the capacitance change. The analytical model includes the capacitances of C1, C2, and Cair as shown in Figure 3. The capacitance of Ctotal can be obtained as the following equations:
where ε0 is the permittivity of vacuum, ε1 is the relative permittivity of the SiO2, ε2 is the relative permittivity of the air, S1 is the areas of the SiO2 coverage, S2 is the total areas of the movable electrode, ti is the thickness of the SiO2, gini is the initial air gap, and x is the displacement of the proof mass.
The input force due to the acceleration Facc, the mechanical viscoelastic force Fm, the electrostatic attractive force Fe, and the relationship of their contributions is expressed in the following equations:
where m is the proof mass, Gin is the input acceleration value measured in gravitational acceleration, k is the spring constant, and c is the damping coefficient including the viscosity of the air.
2.2 Equivalent circuit model for MEMS accelerometer
Module (I) represents the acceleration to provide an eternal force system.
Module (II) is the parallel-plate electrostatic actuator to calculate the electrostatic attractive force and inductive charge as a function of the applied voltages.
Module (III) is the viscoelastic suspension module.
Module (IV) is the core of the equivalent circuit, where the equation of motion (EOM) is carried out under conditions of force applied to the mass m.
Module (V) represents the mechanical anchor.
These modules are described in a Verilog-A compatible HDL. We also have established modules (I) and (II) by extending our previous work reported elsewhere ; likewise, modules (III), (IV), and (V) are interpreted using Eqs. (6) and (8). Meandering suspensions are used in this chapter to lower the elastic rigidity in the direction normal to the chip surface.
For verification, we performed simulation. Thus, we applied the simulation to a single MEMS accelerometer to detect a 20 G using the above equivalent circuit. Figure 5 shows the simulation results of a capacitance change of the MEMS accelerometer under the condition of 20 G at the period of 10 ms. The result suggests that the accelerometer can detect the capacitance change without stiction. From these results, it can be concluded that the equivalent circuit would quantitatively represent the device in this chapter.
3. MEMS accelerometer
3.1 Accelerometer structure
Figure 6 shows the concept of the proposed MEMS accelerometer structure, which is composed of the movable proof mass, the fixed bottom electrode, stopper, and suspension. The accelerometer structure has the following three features; (i) in order to facilitate flexibilities of design, we have utilized the multi-layer metal technology [12, 32, 33, 34]. The multi-layer metal technology can adjust the weight of the proof mass and the spring constant of mechanical suspensions, (ii) the stopper structure is built to prevent mechanical destruction from lateral and vertical over-swings of the proof mass, and (iii) the SiO2 film is formed to prevent sticking and electrical short between the proof mass and the fixed electrode.
3.2 Proof mass material
The proof mass size should be substantially reduced while keeping adequate weight on it, we can then downscale the sensor area without compromising the sensitivity. The minimum detection sensitivity of the accelerometer is limited by Brownian noise (BN) as described in the following equation :
where T, b, kB, and m are the absolute temperature, the viscous damping coefficient, the Boltzmann constant (1.38 × 10−23 J/K), the absolute temperature, and the proof mass of an accelerometer, respectively. We have searched the suitable materials for the proof mass to further minimize BN. Figure 7 shows the comparison of the Brownian noise on the proof masses made of different types of materials. Our target value of the BN can be below 100 μG/(Hz)1/2 to provide a sufficiently low Brownian noise [24, 25] for a practical use. Thus, gold could be a candidate material for small proof mass size. In addition, gold material should also be suitable for the fabrication process of the CMOS-MEMS accelerometer that gold electroplating has successfully stacked MEMS on an LSI circuit [26, 35, 36].
3.3 Fabrication process
Figure 8 shows the fabrication process flow for the designed MEMS accelerometer. Firstly, Ti/Au adhesion and seed layers were deposited by the vacuum evaporation on a thermal SiO2 (Figure 8a). After forming the electrodes and interconnections using the patterning process, photo-sensitive polyimide film was then spin-coated and annealed at 310°C as a first sacrificial layer. The gold electroplating formed the bottom gold layer (Figure 8b); this metallization was applied in every metal layer process as described in the following. After depositing next sacrificial layer of photo-sensitive polyimide film supporting gold of the thickness of 3 μm (Figure 8c), contact holes for interconnections were made, and then a 0.5 μm thick SiO2 was deposited by sputtering (Figure 8d). Finally, the proof mass and stopper structures 15 μm in thickness were formed on the uppermost gold (Figure 8e) followed by removing all sacrificial films by oxygen plasma etching (Figure 8f). Thus, this fabrication process is compatible with CMOS-LSI due to the control of the process temperature below 400°C.
3.4 Experimental results of MEMS accelerometer
Figure 9 shows the SEM micrograph of the MEMS accelerometer, which has been successfully developed through the proposed fabrication process. We show the evaluation results of the measured characteristics of the developed MEMS accelerometer. Figure 10 shows the capacitance vs. voltage characteristics were measured and plotted by applying a direct-current voltage between the movable proof mass and the fixed electrodes without applying acceleration. The initial capacitance C0 at a voltage of 0 V, the electrostatic pull-in at a voltage of 6.4 V, and the release operation without stiction failure were observed from the hysteresis curve in Figure 10. The actual initial gap and spring constant have been estimated to be 4.3 μm and 0.26 N/m, respectively, in good agreement with the designed values. Figure 11 shows the capacitance vs. frequency characteristics under the condition of a bias voltage of 2 V with 100 mV-amplitude oscillation. The measured mechanical resonant frequency showed approximately 1037 Hz. The result suggested that it was higher than the designed value of 687 Hz due to the difference between the actual and the designed spring constants.
Figure 12 shows the capacitance vs. the applied acceleration characteristics. We measured the capacitance value at a bias voltage of 2 V with a frequency of 50 Hz. The measured results and the calculated data were square dots and the solid line, respectively. The calculated data used the actual proof mass of 6.12 × 10−9 kg. The designed proof mass was 1.07 × 10−8 kg. The result indicated that the experimental data was coincident with the calculated data.
Table 1 shows the comparison of the design and the obtained parameter values. The measured spring constant of 0.26 N/m is higher than the designed value of 0.2 N/m. The Brownian noise was measured to be 90.6 μG/(Hz)1/2 for a proof mass with a size of 140 × 140 μm2. Thus, this result attained the target value of less than 100 μG/(Hz)1/2. Therefore, these evaluation results have verified the feasibility of our proposed structure and the multi-layer metal technology utilizing gold as a material for MEMS accelerometers.
4. Sub-1G MEMS accelerometer
4.1 Design of sub-1G MEMS accelerometer
This section shows 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 the Brownian noise BN. Utilizing the high-density gold proof mass, the proof mass area of our device is nearly one-tenth of a silicon proof mass area size. The MEMS capacitive accelerometer for sub-1G sensing have been designed as follows: (i) a low BN design below 10 μG/(Hz)1/2, (ii) the mechanical resonant frequency of the accelerometer higher than the frequency of common environmental vibrations, which was mostly below 100 Hz [37, 38], and (iii) the multi-layer metal technology has been employed. Moreover, the feature size of the mechanical spring was designed to avoid physical contact between the proof mass and the fixed electrode. An SiO2 film was used on the fixed electrode to avoid stiction as shown Figure 6.
We proposed a sub-1G detectable MEMS capacitive accelerometer with a proof mass made of gold. The proposed MEMS accelerometer has been developed by the multi-layer metal technology reported elsewhere [26, 27]. Figure 13 shows the scanning electron microscope (SEM) micrographs of the fabricated accelerometer. The micrographs indicate the mechanical springs, the square proof mass with numbers of release holes, and mechanical stoppers. Thus, multi-layer gold has been successfully formed; the multi-layer metal structures have realized the decreased 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. The proof mass was designed to be 1020 μm × 1020 μm in area and 12 μm in thickness. From the designed result, we obtained the small value of BN = 120 nG/(Hz)1/2. The value was considered to be sensitive to a sub-1G acceleration at the resolution of 1 mG. The resolution was presumed by considering the root-mean-square (rms) of the acceleration noise (an,rms). Assuming the single-pole roll-off characteristics, the equivalent noise bandwidth (Δf) is given by :
where f−3dB is the cutoff frequency, at which the output of the circuit falls −3 dB off the nominal passband level. The an,rms is defined as 
For the Gaussian noise with a given rms value, the minimum detectable acceleration amin can be statistically predicted by using amin = 6.6 × an,rms . The BN value should satisfy the requirement of amin < 1 mG is BN < 12 μG/(Hz)1/2 for a typical f−3dB of 100 Hz. Thus, we determined the target BN to be lower than 10 μG/(Hz)1/2 and designed a heavy proof mass with BN = 120 nG/(Hz)1/2 to allow for safety margin. Figure 14 shows the capacitance vs. input acceleration (gravity) characteristics. The MEMS chip was set on a vibration exciter to apply vertical accelerations of 19.9 Hz with the DC bias voltage of 1.5 V. The result suggests the accelerometer’s capability of sensing a sub-1G input acceleration with a 0.1-G step. Figure 15 shows the capacitance vs. frequency characteristics. The measurement result indicates that the mechanical resonant frequency was measured to be 777 Hz and the resonant vibration of the proof mass was higher than the frequency of common environmental vibrations (<100 Hz). The quality factor (Q) of the device was 6.40 from the C-F characteristics by calculating the ratio between the real (ZR) and imaginary (ZI) parts of the electrical impedance at the resonant frequency; the ZR and ZI are 1.97 × 107 and − 1.26 × 108, respectively.
To estimate the actual value of BN on the developed MEMS accelerometer, we use the following analytical models. The Q of a proof mass is expressed as 
We can obtain the BN value by the Eq. (13) and the experimentally obtained data, when it is difficult to explain the actual value of b due to the squeezed-film damping effect . Measuring the area and height of the proof mass, and the m was obtained to be 2.17 × 10−7 kg. Thus, the actual BN can be estimated to be 780 nG/(Hz)1/2 at 300 K, which was below the target value of 10 μG/(Hz)1/2.
Therefore, it is confirmed that the Brownian noise of the sub-1G MEMS accelerometer can achieve 780 nG/(Hz)1/2 in spite of the small proof mass.
5. Arrayed MEMS accelerometer
5.1 Proposed MEMS accelerometer
Figure 16 shows that an arrayed CMOS MEMS accelerometer stacked on a single LSI chip . In order to solve the issues on the conventional MEMS accelerometers, the proposed accelerometer has the following requirements: (i) the accelerometer should be in an arrayed type to detect a wide range of acceleration, (ii) the structure material for the accelerometer should be chosen to reduce the sensor size and the mechanical noise floor, and (iii) the accelerometer should be stacked on the single CMOS LSI. Proof masses of three different designs (areas 80 × 80, 140 × 140, and 200 × 200 μm2) are combined with three types of different spring constants (0.2, 0.3, and 0.4 N/m) to detect the wide range of acceleration from 1 to 20 G. The total layout area is less than 4 × 4 mm2, which is small enough for monolithically integration with CMOS circuits. Figure 17 shows the calculated electrostatic capacitance as a function of the input acceleration by using the multi-physics simulation; a bias voltage of 1 V was applied to the sensing electrode for electrostatic capacitive readout. The acceleration was swept from 0 to ±20 G in 10 s for each branch. The simulation results showed that the capacitance was changed by the input acceleration within the limited mechanical displacement range between the bottom electrode and the mechanical stopper. In the positive acceleration, the capacitance gradually increases by squeezing the air gap between the proof mass and the fixed electrode. Owing to the bias voltage of 1 V, the proof mass was brought into pull-in contact. In the opposite acceleration, the air gap is enlarged to decrease the capacitance. Figure 17 also suggests that a wide range of acceleration between 1 and 20 G is covered by the arrayed accelerometers; for instance, any one of accelerometer #2, 3, 5, 6, 8, or 9 can detect an acceleration of 3 G or greater. For a range lower than 2 G, accelerometer #3 can be used.
5.2 Results and discussion of arrayed MEMS accelerometer
Figure 18 shows a scanning electron microscopy (SEM) image of the developed MEMS accelerometers in 3 × 3 formation. Figure 19 shows the measured acceleration characteristics (dots) as a function of the capacitance change compared to the simulation results. The measurement was carried out under the condition of the acceleration frequency of 50 Hz and the bias voltage of 100 mV. The simulation results include the effect of the parasitic capacitance Cpa of the measurement system. The measured data of devices #1, 2, 4, 5, 7, and 8 exhibited good agreement with the simulation results. On the other hand, the data of devices #3, 6, and 9 showed the capacitance change smaller than the simulation. This is because these latter three devices used a proof mass of 200 × 200 μm2 size so that the mismatch might be caused by a size effect such as warpage.
Therefore, it is confirmed that the proposed arrayed MEMS accelerometer could detect a wide range of acceleration from 1 to 20 G.
6. CMOS-MEMS accelerometer
6.1 Capacitive CMOS sensor
In order to verify the validity of our CMOS-MEMS technology, we have developed a capacitive CMOS-MEMS accelerometer designed by our multi-physics simulation. The developed accelerometer is composed of the capacitive sensor LSI circuit and the MEMS accelerometer. We propose the sensor circuit to detect the capacitance change of the MEMS device by comparing with the reference capacitor built-in LSI. The MEMS accelerometer and the proposed sensor circuit are simultaneously designed by the multi-physics simulation with a newly developed equivalent circuit of the capacitive MEMS sensor for CMOS-MEMS technology.
6.2 Sensor circuit
Figure 20 shows the comparison of our capacitive MEMS sensor circuit and the conventional MEMS sensor circuit. In conventional MEMS sensor circuits [42, 43, 44], capacitance change of the movable electrodes is differentially detected in response to the changes of another electrode pair within the identical MEMS chip such as the comb-drive devices. On the other hand, in our capacitive MEMS sensor circuit, it is needed to adopt other detection architecture different from the conventional sensor circuit as described above. It is because the electrode is only placed at the bottom side of the proof mass and also differential capacitance values are not produced.
In order to solve the above requirements, we propose the sensor circuit to detect a capacitance signal from a MEMS sensing element and compare it with a reference capacitor integrated within the sensor LSI. Figure 20 shows the concept of our proposed sensor circuit. This circuit does not need other electrodes or structures for the differential capacitance. Thus, it is applicable to our capacitive CMOS-MEMS accelerometer. The circuit also has other features: (i) a reference capacitor in a MEMS chip is not needed, and hence the total device footprint is reduced, (ii) it is applicable and scalable to various types of capacitive MEMS devices including accelerometer in an arrayed format [24, 25], and (iii) calibration is simply proceeded as we can know the reference capacitor values at the stage of circuit design.
6.3 Capacitive CMOS-MEMS accelerometer design
To realize a capacitive CMOS-MEMS accelerometer, we utilized the multi-physics simulation platform based on our previous work . Figure 21 shows the proposed sensor circuit with an equivalent circuit of the capacitive MEMS accelerometer. The equivalent circuit consists of five modules. These modules are described by a Verilog-a compatible HDL, and designed to handle the multi-physics simulations in a single LSI design environment such as Cadence Virtuoso .
The behaviors of both LSI and MEMS should be simultaneously simulated to design the capacitive CMOS-MEMS accelerometer stacked on the sensor circuit. Capacitance values Ctm and Ctr of the capacitor are set to be 8 pF with the parasitic capacitance of 7 pF in the LSI and the measurement system. In these parameters, we performed a transient analysis for the acceleration of sinusoidal wave of 2 Gin at 49 Hz superposed onto a DC level acceleration of 1 G. Figure 22 shows the simulation results of the output voltage from the proposed sensor circuit under given input acceleration. This result suggests that the output voltage has changed from 869.3 to 892.1 mV depending upon the input acceleration waveforms.
As a result, it is confirmed that the proposed sensor circuit could detect the capacitance change of the MEMS device.
6.4 Experimental results of capacitive CMOS-MEMS accelerometer
Figure 23 shows a scanning electron microscopy (SEM) image and a close-up optical microscope view of the developed capacitive CMOS-MEMS accelerometer. It is clear that the MEMS structure interconnected to the LSI has been successfully fabricated by the micro fabrication process. Figure 24 shows the output voltage as a function of the input acceleration obtained by both measurement and simulation. The simulation result was coincident with the experimental results for the input acceleration of 3 G or lower. For the input acceleration of 3 G or larger, notable deviations were observed in the experimental result possibly due to excess mechanical motion of the proof mass. The result suggested that fabricated capacitive CMOS-MEMS sensor can detect the capacitance change of a single-axis MEMS accelerometer.
Therefore, it is confirmed that the validity of the simultaneous design of both MEMS and sensor circuit using multi-physics simulation environment with an equivalent circuit of the MEMS accelerometer was verified.
This chapter presented technical features and solutions to realize a high sensitive CMOS-MEMS accelerometer with gold proof mass. The multi-physics simulation platform for the design of the CMOS-MEMS device was developed to understand simultaneously both the mechanical and electrical behaviors of MEMS stacked on LSI. An equivalent circuit for the accelerometer module was built by an electrical circuit simulator.
MEMS accelerometer fabrication process was formed by the multi-layer metal technology, which consists of the gold electroplating and the sacrificial layer formation using the photo-sensitive polyimide film. We proposed a sensor structure for MEMS accelerometers. The measured characteristics of the developed accelerometer were in good agreement with the designed values, and the actual Brownian noise was estimated to be below the target of 100 μG/(Hz)1/2. Moreover, the experimental results showed that the Brownian noise of the sub-1G MEMS accelerometer could achieve 780 nG/(Hz)1/2. We also proposed an arrayed accelerometer device with a wide range of detection between 1 and 20 G. An arrayed accelerometer was successfully developed in a single chip of 4 × 4 mm2 in area by electroplated gold. The experimental results suggested that a wide detection range of acceleration has been achieved.
The proposed sensor LSI was fabricated by a 0.35-μm CMOS process and the MEMS accelerometer was implemented onto the LSI. The measured characteristics of the capacitive CMOS-MEMS accelerometer showed a good agreement with the simulation results. Thus, the validity of our multi-physics simulation was verified.
In conclusion, it is confirmed that the multi-physics simulation platform and the multi-layer metal technology for the CMOS-MEMS device will open the way to the future of nano-gravity sensing technology.
The authors would like to thank S. Iida, M. Yano, T. Safu, and K. Kudo with NTT-AT for technical discussions.
This work was supported by JST CREST Grant Number JPMJCR1433 and by the Grant-in-Aid for Scientific Research (B) (No. 23360149) of the Japan Society for the Promotion of Science (JSPS).
Conflicts of interest
I confirm there are no conflicts of interest.