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In this paper, an optimal and robust design method to implement a two-chip out-of-plane microaccelerometer system is presented. The two-chip microsystem consists of a MEMS chip for sensing the external acceleration and a CMOS chip for signal processing. An optimized design method to determine the device thickness, the sacrificial gap, and the vertical gap length of the M EMS sensing element is applied to minimize the fundamental noise level and also to achieve the robustness to the fabrication variations. In order to cancel out the offset and gain variations due to parasitic capacitances and process variations, a digitally trimmable architecture consisting of an 11 bit capacitor array is adopted in the analog front-end of the CMOS capacitive readout circuit. The out-of-plane microaccelerometer has the scale factor of 372 mV/g∼389 mV/g, the output nonlinearity of 0.43% FSO∼0.60% FSO, the input range of ±2 g and a bias instability of 122 μg∼229 μg. The signal-to-noise ratio and the noise equivalent resolution are measured to be 74.00 dB∼75.23 dB and 180 μg/rtHz∼190 μg/rtHz, respectively. The in-plane cross-axis sensitivities are measured to be 1.1%∼1.9% and 0.3%∼0.7% of the out-of-plane sensitivity, respectively. The results show that the optimal and robust design method for the MEMS sensing element and the highly trimmable capacity of the CMOS capacitive readout circuit are suitable to enhance the die-to-die uniformity of the packaged microsystem, without compromising the performance characteristics.

Over the last decade, extensive efforts have been devoted to the continuously maturing Microelectromechanical System (MEMS) technologies. Above all, MEMS microaccelerometers have been successfully commercialized in a wide range of application areas including automotive safety control, ubiquitous robots, inertial navigation and consumer electronics [

Recently, a microsystem using a two-chip solution consisting of a MEMS element and a CMOS readout circuit has been implemented so as to improve the noise performance [

The capacitive sensing scheme provides advantages in low temperature dependency, good DC response, and good noise performance [

In this paper, an implementation of an out-of-plane microaccelerometer system employing an optimal and robust design method that achieves robustness towards the fabrication variations and enhances the die-to-die uniformity without compromising the performance characteristics is presented. The optimal design method is based on the minimization of the total noise equivalent acceleration (TNEA) of the two-chip implemented microsystem. Besides lateral dimensions such as width and length of the torsional spring and gap between the comb electrodes, vertical dimensions such as structural thickness and sacrificial gap of the sensing element and vertical gap length between the moving and stationary vertical comb electrode are taken into consideration for the several reasons, which are discussed later in this paper. The sensor operation is based on a coplanar sense electrode movement wherein the change in capacitance is caused by variation of the overlap area [

The brief features mentioned above will be described in the following sections. Beginning with a concept of a two-chip implemented microsystem, the optimal design analysis to determine the device thickness and the vertical gap length will be followed. The design will be substantiated by both electrostatic and mechanical analysis as well as finite element method (FEM) simulation. Then, the advantages of the separate two-chip implemented microsystem will be discussed. After the fabrication principles and fabrication results, the experimental results are evaluated. Finally, conclusions will be drawn.

In this microaccelerometer system, a two-chip solution comprising of separated CMOS sensing electronics and MEMS element is adopted. This two-chip solution allows specialized and optimized processing for CMOS and MEMS [

In

The conceptual schematic diagram of a capacitive out-of-plane torsional microaccelerometer is illustrated in

In this paper, the lateral dimensions are fixed and only the vertical dimensions, which is determined by the fabrication process is taken into consideration. As the gap between the comb electrodes is increased, the mechanical damping gets smaller and the Brownian noise equivalent acceleration (BNEA) is improved. However, the mechanical sensitivity, which is determined by the capacitance change between the interdigitated comb electrodes, is decreased and the circuit noise equivalent acceleration (CNEA) is increased. Therefore the minimum gap size of 4 μm is chosen to maximize the mechanical sensitivity. The torsional spring stiffness is determined by considering the input dynamic range of ±2 g. As the torsional spring stiffness is decreased, the noise performance is enhanced due to the decrement of the 1st order natural frequency and also mechanical sensitivity can be improved. However, the process yield during the fabrication process and the impact resistance of the sensing element get poor due to the decreased torsional stiffness [

The design parameters of the MEMS sensing element are listed in _{B}^{−23} m^{2}kg/s^{2}/K), _{n}

The squeeze film damping coefficient of the two parallel plates [_{eff}_{0}_{s}_{n}^{−5} Ns/m^{2}), the device layer thickness of silicon-on-insulator (SOI) wafer (65 μm), the structural layer thickness of the sensing element, the density of the silicon (2,330 kg/m^{3}), the natural frequency of the MEMS sensing element [598 Hz (

For the case where t << a, the quality factor is given as:

Since the device layer of the SOI wafer has a thickness limit of 65 μm, the sacrificial gap between two plates decreases as the device thickness increases, as illustrated in

Another limiting factor is the circuit noise equivalent acceleration (CNEA) that depends on the simulated minimum detectable capacitance of the readout circuit (Δ_{min}_{0}^{−12} F/m), the gap between the comb fingers, the overlap length between the comb fingers, the effective distance from the center to the comb fingers, and the torsion angle at 1 g (9.8 m/s^{2}) input, respectively. As structural thickness is increased, the torsion angle at 1 g input (

^{1/2}, the CNEA for Δ_{min}^{1/2} is 15.45 μg/(Hz)^{1/2}, and the TNEA is 45.06 μg/(Hz)^{1/2}.

The proposed out-of-plane microaccelerometer has a vertical gap formed between stationary comb electrodes and movable comb electrodes in the upper and lower parts. In previous studied out-of-plane accelerometers [

In order to derive the capacitance, a simplified three dimensional simulation model with two parallel-plates is used. A 10 V (_{0}_{1}_{ANSYS}

The simulation is performed for the zero input acceleration and the 1 g input acceleration to derive the mechanical sensitivity. In this out-of-plane microaccelerometer, due to the dimensional limitation of the design constraints, the vertical gap length is set to have a value below 15 μm. Therefore variation of the vertical gap length is carried out from 0 μm to 15 μm. The analyzed result of the mechanical sensitivity using FEM simulation is plotted in

In order to compare the result, the mechanical sensitivity derived from a conventional parallel-plate formula and a constant fringing capacitance formula is also plotted. The mechanical sensitivity increases due to the increase of the vertical gap length from 0 μm to 10 μm. However, at length between 11 μm and 15 μm, the mechanical sensitivity is in the range from 20.6 fF/g to 21.5 fF/g. Due to the analyzed result and the consideration of fabrication process error about 10%, the vertical gap length is determined to be within the range from 12 μm to 14 μm.

Although many advanced micromachining processes are developed, fabrication imperfection is inevitable with current MEMS fabrication techniques [_{O}

The proposed schematic of the capacitive analog front-end is shown in _{OUT}_{REF}_{F}_{1}, _{AC}_{P1}_{P2}_{U}_{D}_{F}_{P1}_{P2}_{U}_{D}_{0}

In this capacitive interface circuit design, a continuous-time chopper stabilized sensing scheme is adopted. Since the capacitive circuit is implemented with a large feedback resistor (_{F}

Thus, by trimming the _{F}

The MEMS sensing element is fabricated using the ESBM process. The ESBM process allow the fabrication of both upper and lower vertical comb gaps using only two photomasks and four DRIE steps, to achieve differential sensing. The differential sensing scheme results in a highly sensitive sensing element. Also, using the ESBM process, it is possible to fabricate a structure with an inherent high-aspect-ratio with a large sacrificial gap and a structure free from the footing phenomenon. A large sacrificial gap is required to minimize the disadvantages of a large parasitic capacitance, which results in higher gain and reduction in input-referred circuit noise. In addition, the large sacrificial gap has an advantage in protecting the suspended proof mass of the MEMS sensing element from drops and impacts. The WLHP process is employed by the glass-to-silicon anodic bonding to protect the MEMS sensing element and to achieve the reliability of the microsystem.

Process flow of the ESBM process is shown in

The WLHP process is employed by glass-to-silicon anodic bonding process. The Pyrex 7740 glass wafer with the thickness of 350 μm is used, and fabricated using HF glass wet etching. In order to neglect the damping inside the protection cavity, the thickness of fabricated protection cavity is fabricated to be 180 μm∼190 μm. After bonding, metal interconnections are fabricated by metal sputtering. A schematic diagram of the packaged MEMS sensing element and cross-sectional view are shown in

In

The fabrication result of CMOS capacitive readout circuit is shown in

The block diagram and photograph of the experimental setup are shown in

Before measuring the performance characteristics of the out-of-plane microaccelerometer system, the offset and gain calibration is carried out. From _{O}_{REF}_{P1}_{P2}_{U}_{D}_{F}_{OFFSET}_{I}_{GAIN}_{P1}_{P2}_{O}_{U}_{D}_{F}_{OFFSET}_{GAIN}_{U}_{D}_{P1}_{P2}_{F}_{GAIN}_{OFFSET}_{U}_{D}_{F}_{GAIN}_{OFFSET}

The performance characteristic results are shown in

The root-Allan variance (_{total}_{VRW}_{BiasInst}

In this paper, an optimal and robust design method to implement a two-chip out-of-plane microsystem consisting of a MEMS chip for sensing the external acceleration and a CMOS chip for signal processing is presented. An optimized design method to determine the device thickness, the sacrificial gap, and the vertical gap length of the MEMS sensing element is applied to minimize the fundamental noise level and also to achieve the robustness to the fabrication variations. The MEMS sensing element is fabricated by the ESBM process to have a vertical differential sensing, and the WLHP process is performed so as to achieve the high reliability of the microsystem. In order to cancel out the offset and gain variations due to parasitic capacitance and to minimize the die-to-die variation due to fabrication mismatches, a digitally trimmable architecture consisting of the 11 bit capacitor array is adopted in CMOS capacitive readout circuit.

The summarized performance specifications are listed in

This work was supported partly by the R&D program of the Korea Ministry of Knowledge and Economy (MKE) and the Korea Evaluation Institute of Industrial Technology (KEIT). [2008-F-037-01, Development of HRI Solutions and Core Chipsets for u-Robot].

Top level block diagram of the two-chip implemented microsystem.

A Simplified schematic of the torsional microaccelerometer.

Modal analysis result of 1st order natural frequency.

Noise Equivalent Acceleration

Simulation result of mechanical sensitivity

Schematic of analog front-end capacitive sensing circuit.

Test pattern fabricated using the ESBM process.

Microscope image of CMOS fabricated capacitive readout circuit.

Summarized design parameters of the MEMS sensing element.

| ||
---|---|---|

Chip size | 3.4 mm × 2.0 mm | |

Device layer thickness of (111) SOI wafer | _{0} |
65 μm |

| ||

| ||

Width | _{spring} |
4 μm |

Length | _{spring} |
150 μm |

Thickness | 25 μm (±2 μm) | |

Number of springs | _{spring} |
2 |

Torsion angle at 1 g input (at |
2.59 × 10^{−4} rad | |

| ||

| ||

Width | 5 μm | |

Length | _{comb} |
210 μm |

Thickness | 25 μm (±2 μm) | |

Comb overlap length | 200 μm | |

Vertical gap length | 13 μm (±1 μm) | |

Gap between comb finger | 4 μm | |

Effective distance from center to comb finger | 8.13 × 10^{−4} m | |

Number of combs | 254 | |

| ||

| ||

Area size | - | 9.72 × 10^{−6} m^{2} |

Area of asymmetric part | - | 2.74 × 10^{−7} m^{2} |

Center of mass | _{cm} |
5.58 × 10^{−4} m |

Thickness | 25 μm (±2 μm) | |

Device length | 2.53 mm | |

Device width | 1.388 mm | |

1st mode natural frequency (at |
_{n} |
598 Hz |

Summarized performance characteristics.

| |||
---|---|---|---|

373 mV/g | 372 mV/g | 389 mV/g | |

0.60%FSO | 0.59%FSO | 0.43%FSO | |

74.00 dB | 74.74 dB | 75.23 dB | |

180 μg/rtHz | 183 μg/rtHz | 190 μg/rtHz | |

229 μg | 148 μg | 122 μg | |

1.3% | 1.9% | 1.1% | |

0.7% | 0.4% | 0.3% |