Micro/nano-mechanical sensors and actuators based on SOI-MEMS technology

The sensing chip was designed to be able to simultaneously detect three components of force and three components of moment in three orthogonal directions (figure 1). Two-terminal and four-terminal p-type silicon piezoresistors were created by thermal diffusion of boron ions to suitable places on the surface of a crossbeam-shaped structure of (111) n-type silicon. The total number of piezoresistors is 18, much fewer than the previous piezoresistive-based 6-DOF force moment sensors known to the authors [23]. When a force or moment is applied to the sensor, the beams will be deformed; consequently, stresses will be induced at the piezoresistors, leading to a change of their resistance, thus changing the output of the corresponding bridge circuits. The sensor was fabricated based on IC compatible processes, e.g. photolithography, impurity diffusion, thin film deposition and etching, and silicon bulk micromachining technology, e.g. the deep-RIE etching process. The schematic of the fabrication process is shown in figure 2. The fabricated chip has dimensions of 3×3×0.5 ^{mm 3} as shown in figure 1(b). The sensor has been applied in robotics as fingertip tactile sensors (figure 1(c)) [24], and in hydraulics to measure the fluid force acting on small particles in water flow [25].

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Inertial sensors refer to accelerometers and angular rate sensors (or gyroscopes). Several kinds of micro-accelerometers, such as piezoresistive accelerometers [26, 28], thermo-resistive accelerometers [27], have been developed. A recently developed accelerometer is shown in figure 3 [28]. This accelerometer can independently detect three components of linear acceleration along three orthogonal directions. The detecting principle is based on piezoresistive effects in single-crystal silicon. The sensing chip is made of single-crystal Si, with a seismic mass being suspended at the middle of the four surrounding beams, which are themselves fixed to the 'rigid' frame at the ends. Si piezoresistors are formed by diffusing boron ions to suitable places on the surface of the n-type silicon sensing beams. When an external acceleration is applied to the sensor, the seismic mass is displaced due to the inertial force. This movement of the seismic mass deforms the beams. As a result, the resistance of the Si piezoresistors is changed due to the piezoresistive effect. The change of resistance is converted to an output voltage by Wheatstone bridges. The fabrication process is illustrated schematically in figure 4, and an SOI wafer was used. The dimensions of the accelerometer chip are 1 ^mm×1 ^mm×0.45 ^mm (L×W×T) . The sensitivities to the X-, Y- and Z-axis are 30, 30 and 23 μ^{V  g −1} , respectively, and cross-axis sensitivity is less than 5.5%. Thanks to the small size and high performance, the sensor can be applied to portable electronic devices, such as mobile phones or cameras to stabilize or automatically find the image orientation, or to remote game controllers, health monitoring sensors, etc.

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Figure 5 shows our recently developed 2-DOF convective angular rate sensor (gyroscope) [29, 30]. The sensor can detect two components of angular velocity based on the thermo-resistive effect of the low-doped silicon. The working principle is illustrated in figure 5(a). The gas flow generated by the piezoelectric diaphragm pump flows to the nozzle orifice and creates a jet flow in the chamber. The gas flows toward the sensing element, and goes through the symmetric center of the four thermistors. As an angular rate is applied, the gas flow is deflected (figure 5(a)) due to the Coriolis effect. This deflection causes differential cooling between opposing thermistors and, as a result, the resistances of the two thermistors change in opposite directions. A Wheatstone bridge is used to convert these resistance changes to output voltage. Therefore, angular rates ω_x around the X-axis and ω _y around the Y-axis can be measured independently. The sensing chip is fabricated from the SOI wafer by applying a fabrication process similar to that shown in figure 2. The gyroscope was packaged at Tamagawa Seiki Corp. (figure 5(b)). The sensitivities of the gyroscope for the X- and Y-axis are 0.082 and 0.078 ^{mV  deg −1  sec −1} , respectively. The cross-sensitivities between the two input axes are less than 0.26%; the nonlinearity was smaller than 0.5% F.S in the range of ±200 ^{deg  sec −1} .

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Several applications of this high-performance gyroscope mentioned here include automotive, ship stabilization systems and aerospace.

Silicon comb-drive electrostatic actuators are among the most frequently utilized in MEMS since they were first reported about 20 years ago [31]. The advantages of these actuators include the simple and mass fabrication process, accuracy, easy control and large displacement. In this paper, we propose novel ratcheting structures which allow converting reciprocating displacement of electrostatic comb-drive actuators to continuous, unidirectional, straight and turning movement of micrometer-scale objects. The working principle of the micro-transportation system is shown schematically in figure 6. Force induced from the electrostatic comb-drive actuator pushes the ratchet racks inward, causing the driving wings to move inward. As a result, the container (moved object) is moved forward. When the force is removed, the container will not move backward due to the ratchet mechanism of the anti-reverse wings. Figure 7 shows the silicon micro-transportation system [32, 33] made from SOI wafer by using D-RIE silicon etching and SiO₂ etching processes. The velocity of the object can be controlled by driving voltage and frequency. The maximum velocity was about 200 μ^{m  s −1} at 100 V and 20 Hz driving voltage. This miniaturized transmission system can be used to transport small objects, such as biomedical samples, micro/nano-particles and carbon nanotubes (CNTs) from one place to another.

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Another transmission system based on an electrostatic actuator and ratchet mechanism, called a gearing transmission system, was developed recently as shown in figure 8 [34]. The reciprocal movement of rotational comb actuators is converted to the unidirectional rotation of the gears through a driving mechanism as shown in the right SEM image of figure 8. The system was fabricated from SOI wafer using D-RIE and HF vapor etching processes. The angular velocity was changeable depending on the frequency of the driving voltage. The maximum angular velocity was about 40 ^{deg  s −1} at 80 V and 50 Hz driving voltage. The gearing system can be used in micro-motors, micro-watches or in other high- precision instruments.

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We have performed first-principles calculations based on density functional theory [35] with the generalized-gradient approximation (GGA) method [36]. We adopted the three-dimensional supercell approximation technique with norm-conserving pseudopotentials prepared according to the Hamann method [37]. The cutoff energy for wave functions of electrons with plane-wave expansion was set at 30 Rydberg (408 eV).

Si nanowire models were composed of a fragment of optimized bulk Si with a one-dimensional periodic boundary, and all dangling bonds at the wire wall were terminated with H atoms. Figure 9 shows ^Si ₈₉ ^H ₄₄〈001〉 (wire diameter 2R=2.21 ^nm ) and ^Si ₈₀ ^H ₂₈〈110〉 ( 2R=2.58 ^nm ) Si nanowire models, where the longitudinal directions with one-dimensional periodic boundary are respectively set to [001] and [110].

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A periodic boundary condition along the transverse directions, or perpendicular directions to the wire axis in the three-dimensional supercell, was given by inserting sufficient space between H-terminated Si nanowires with two large cell parameters perpendicular to the wire axis. On the condition that sufficient space in the Si nanowire model disturbs the interaction between the Si nanowires, the electronic band structure of the Si nanowire model can be reduced to one dimension, which is dependent on only one reciprocal coordinate, k_z . The effect of uniaxial tensile strain on structure was represented by partial optimization of bulk Si with a fixed lattice constant along the tensile direction.

The conductive properties of Si nanowire models have been discussed in terms of the band structures. The electrical conductivity G or the electrical resistivity ρ can be represented in terms of carrier density and effective mass. We have introduced the band carrier densities and their corresponding effective masses for each energy subband, and the conductivity has been added up over all valence-band (VB) subbands and conduction-band (CB) ones as follows:

where n_j is the jth CB carrier-electron density, p_j is the jth VB hole density, m _{^e, j} ^* and m _{^h, j} ^* are the band effective masses, τ _{^e, j} and τ _{^h, j} are the relaxation times and e² is the square of the absolute value of the elementary electric charge. Subscripts e and h, respectively, denote electron and hole carriers. In actual n- or p-doped Si nanowires, the total number of carriers per unit cell, δ , must be less than 1 by a few orders. Under the condition that a small amount of the carrier occupation does not cause significant changes in the band structure, δ can be given by an appropriate shift of the Fermi energy E ^_F as follows,

in the n-type carrier occupation, or

in the p-type carrier occupation with temperature T, where E_{j^, kz} is the intrinsic-semiconductor-state band energy of the jth band at the k_z point, w_kz is the k-point weight for k_z , V is the volume of Si nanowire in the unit cell and k ^_B is the Boltzmann constant. In practice, we first have to set δ to an appropriate constant such as 10⁻ⁿ ( n=2 , 3 and 4), and then E ^_F in n-type and p-type carrier occupations can be solved according to equations (2) and (3), respectively [38–41].

The effective mass is generally given by a 3×3 tensor, but it can be defined simply as a scalar for one-dimensional SiNW models [38, 39]:

at the maximum or minimum of band energy E_j . ℏ is Planck's constant divided by 2π . On the right-hand side, a positive sign is adopted for carrier electrons and a negative sign for holes. For the relaxation time, we have adopted the approximation that all of the band relaxation times are equal and constant regardless of stress [37–40].

The ^Si ₈₉ ^H ₄₄〈001〉 model has four VB subbands in the vicinity of the VB top as shown in figure 10. The highest VB subband of those without stress has a small hole effective mass, called the light-hole band, and by contrast, two of the second highest VB subbands in degeneracy have a larger hole effective mass, called the heavy-hole bands. The uniaxial tensile stress in the [001] longitudinal direction causes a sharp drop in the band energy of the light-hole band, leading to the alternation of the order of band energy levels between the light-hole band and the heavy-hole bands, and then most of the holes will be redistributed to the heavy-hole bands where hole effective mass is markedly raised due to the longitudinal tensile stress. This sudden change in the hole occupation with the increase in effective mass will bring a significant decrease in the hole conductivity. As a result, 1% longitudinal strain for the p-doped ^Si ₈₉ ^H ₄₄〈001〉 model, i.e., the H-terminated 〈001〉 SiNW model reduced the conductivity by as much as 66% in our calculation.

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The longitudinal piezoresistance coefficient π_l and transverse one π_t are given by

where σ_{l^, t} are the longitudinal and transverse tensile stresses, which have been represented by a linear-response approximation according to the classical Hooke's law,

with Young's modulus Y_{l^, t} and tensile strain ε_{l^, t} ^,ρ₀ is the resistivity along the wire axis without stress, and Δρ_{l^, t} are variations in ρ₀ due to σ_{l^, t} . Young's modulus of nanoscale low-dimensional Si materials [42] is somewhat smaller than that of bulk Si. According to the first-principles total energy calculation of tensile-strained models, we assumed Y_{l^, t} to be 25% of the experimental values of Young's modulus of bulk Si.

Figure 11 summarizes calculation results of the piezoresistance coefficients with respect to δ. Obviously, the values of ( π_l〈001〉) ^_p , longitudinal piezoresistance coefficients for the p-doped ^Si ₈₉ ^H ₄₄〈001〉 model, are by far the largest in figure 11. We have obtained 588×10^{−11  Pa −1} for ( π_l〈001〉) ^_p with δ=10⁻⁴ , i.e. two orders larger than that of the bulk silicon, and it is expected that p-doped 〈001〉 SiNW will have giant longitudinal piezoresistivity.

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A giant piezoresistive effect has been theoretically found in single crystalline SiNWs using the first-principles calculation method. It is necessary to verify these results experimentally. Accordingly, SiNWs with a length of 2 μ^m , thickness of 35 nm and width ranges from 35 nm to 480 nm have been fabricated from SIMOX (separation by implanted oxygen) SOI wafer using electron beam (EB) direct writing and RIE etching [43, 44]. Figures 12 (a) and (b) shows SEM images of the 35 nm width SiNWs array.

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The width dependence of the longitudinal piezoresistive coefficient π_l〈110〉 along the 〈110〉 crystallographic orientation at doping concentration of 1.2×10^{18  atoms  cm −3} of SiNWs has been measured (figure 12(c)). The results show a strong increase of the longitudinal piezoresistive coefficient when the width of the SiNW becomes smaller than 150 nm. The increase of π _^l〈110〉 is up to 62.5% when the SiNW's width decreases to 35 nm. This enhancement of π _^l〈110〉 can be qualitatively interpreted by introducing the one-dimensional (1D) hole transfer and the hole conduction mass shift mechanisms based on the 1D hole transport system, which might be expected to be induced in a nanowire p-type piezoresistor. This enhancement of the longitudinal piezoresistive coefficient is very significant for sensitivity improvement of piezoresistive-based ultra-small mechanical sensors, one of which will be presented in section 3.3.

The first demonstration of applying SiNWs as nanoscale piezoresistors to mechanical sensing was carried out. An ultra-small 3-DOF accelerometer utilizing Si nanowires as nanoscale piezoresistors was designed and fabricated. The model of the sensing chip is shown in figures 13(a) and (b). The seismic mass is suspended on four surrounding sensing beams, which are connected to the frame at the ends. Si nanowires are placed near the fixed ends on the surface of the sensing beams. When acceleration is applied to the sensor, the seismic mass will be moved due to the inertial force. This movement deforms the beams; as a result, the resistance of the nanowires changes. The change of resistance is converted to a voltage change by a Wheatstone bridge. The overall size of the accelerometer chip is 500×500×400 μ^{m 3} , ( L×W×T ). This accelerometer has been made from multi-layer SIMOX SOI wafer and fabricated by nano/micromachining technology, including EB lithography and RIE silicon etching [45]. The SiNW piezoresistor has dimensions of 128 ^nm×50 ^nm ( W×T ). The resistance of these piezoresistors was measured to be 20 ^kΩ , and the calculated sensitivity for each axis is about 50 μ^{V  G −1} , and the resolution is 30 mG. (G is the gravitational acceleration, i.e. =9.8 ^{m  s −2} ). Accordingly, by using SiNWs as piezoresistors, we can reduce the sensor's size while increasing the sensitivity. Smaller chip size means more chips per wafer, higher productivity, and therefore lower cost per chip. Ultra-small accelerometers are important for portable devices, such as camcorders, mobile phones, navigation systems, entertainment devices, and so on.

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