3.1.

Fabrication and Experimental Setup

Figure 2 shows a fabricated optical accelerometer with actual dimensions. In order to investigate sensitivity dependence on waveguide position, 17 straight ridge-type polystyrene waveguides spaced 0.25 mm apart were formed on both sides of a diaphragm. Figure 2(d) indicates a cross-sectional view of the waveguide. Width of the waveguide was 7.0 μm, and thickness of the polystyrene guided layer at the waveguide was 1.1 μm, thicker by 0.1 μm than the surroundings. Thickness of the buffer layer was determined to be 1.0 μm in order to sufficiently reduce the radiation loss of the guided waves into the silicon with high refractive index. On the top surface, the area of the diaphragm and proof mass were $10\times 10{\mathrm{mm}}^2$ and $5\times 5{\mathrm{mm}}^2$, respectively. Also, the thicknesses of the diaphragm and proof mass were 50 and 300 μm, respectively. The overall dimensions of the sensor were 20 mm long, 20 mm wide and 300 μm thick.

Fig. 2

(a) Cross-sectional view and (b) bottom view of a fabricated guided-wave optical accelerometer and (c) cross-section of a ridge-type polystyrene waveguide.

In fabrication, a silicon substrate was first thermally wet-oxidized at 1100°C to form a silicon dioxide layer. The silicon dioxide layer of the bottom surface was selectively removed by an etchant of buffered HF acid, using a patterned photoresist as an etching mask. During etching, the silicon dioxide of the top surface was protected by a thick layer of electron wax. Then, the exposed silicon was anisotropically etched in aqueous KOH solution at 50°C to form the diaphragm. Diaphragm thickness was controlled by etching time. After diaphragm formation, the silicon dioxide layer 1.0 μm thick was regrown by thermal oxidation to serve as a buffer layer. Shallow 7.0 μm-wide and 0.1 mm-deep grooves were engraved on the silicon dioxide layer, parallel to the diaphragm edge, using buffered HF acid. The polystyrene layer was spin-coated as the guided layer, and its thickness at the grooves was 1.1 μm.

Figure 3 shows the experimental setup to measure output power as a function of applied force, as simulated inertial force due to acceleration. A linearly polarized He-Ne laser at 633 nm in wavelength was used as the light source. The polarization of the laser beam was set at 45 deg to the sensor surface, so that the input polarizer was not utilized during measurement. A pinhole was placed in front of a photodetector to block stray light. In this study, rather than inertial force by acceleration, static force directly applied on the proof mass by a spring connected to a micrometer was used since valuable data to consider sensitivity dependences can be sufficiently obtain even from static response.

Fig. 3

Experimental setup to measure output power as a function of applied force, which simulates inertial force due to acceleration.

3.2.

Experimental Results

In order to examine sensitivity dependence versus waveguide position, sensitivity was measured for each waveguide formed on the diaphragm. Here, phase sensitivity is used as sensor sensitivity, which is defined as the induced phase difference between the two modes per unit force or unit gravity. Phase sensitivity can be evaluated from a half period of the output power as a function of the applied force, since a half period corresponds to a phase difference of $\pi$ rad. Figure 4 shows examples of normalized output power versus the applied force. Figure 4(a) and 4(b) is for waveguide positions nearest the edges of the diaphragm and proof mass, respectively. Dots represent measured values, and the sinusoidal curves indicate the computer projection of the experimental data. The measured output power sinusoidally changes in response to the applied force. A half period of the output power is called the half-wave force and corresponds to the dynamic range. The half-wave force is equivalent to the phase difference of $\pi$ rad. From Fig. 4(a) and 4(b), the half-wave forces were evaluated to be 7.1 and 16 mN, and the phase sensitivities in radian per milli-Newton were calculated 0.44 and $0.20\mathrm{rad}/\mathrm{mN}$ from the measured half-wave force, respectively. Moreover, phase sensitivity in milli-radian per gravity is estimated to be 76 and $34\mathrm{mrad}/\mathrm{g}$ when the mass of the proof mass is 17.5 mg ($5\mathrm{mm}\times 5\mathrm{mm}\times 300\mu \mathrm{m}$). Incidentally, the extinction ratios were quite low mainly due to undesired stray light passing through the pinhole. A low extinction ratio does not affect sensitivity dependence, but it should be improved for practical use.

Fig. 4

Phase sensitivity as a function of applied force for the waveguides (a) nearest the diaphragm edge and (b) nearest the edge of the proof mass.

Figure 5 shows the evaluated phase sensitivity versus waveguide position. In the graph, positions of $\pm 5\mathrm{mm}$ and $\pm 2.5\mathrm{mm}$ correspond to the diaphragm edges and the edges of the proof mass, respectively. From the figure, phase sensitivity is highest when the waveguide is placed along the diaphragm edge. Moreover, sensitivity is relatively high for the waveguide along the edge of proof mass and is very low between the edges of the diaphragm and the proof mass. Therefore, to maximize sensitivity, the diaphragm edge is the best waveguide position.

Fig. 5

Phase sensitivity as a function of waveguide position for an accelerometer with a 10 mm-square, 50 μm-thick diaphragm and a 5 mm-square, 300 μm-thick proof mass.

This sensitivity dependence is quite similar to the results of some guided-wave optical pressure sensors with a diaphragm^5,11 if the edge of proof mass is set relative to the center of diaphragm of the pressure sensor. However, the sign of the sensitivity cannot be distinguished simply from the experimental data. According to the theoretical analysis of the pressure sensor, the sign of the sensitivity at the diaphragm edge must be opposite to that at the center of diaphragm.¹¹ When inertial force is exerted to the accelerometer, if deflection around the diaphragm edge is convex, then deflection around the edge of the proof mass is concave, and vice versa. So, the sign of the sensitivity at the diaphragm edge would be opposite to that at the edge of the proof mass although the sensitivities at the edges of diaphragm and proof mass are both high with the same sign in Fig. 5. Hence, it may be possible to improve sensitivity by a push-pull configuration, which can be realized by a Mach-Zehnder interferometer, with paths along the edges of diaphragm and proof mass.

4.1.

Fabrication

Figure 6 shows fabricated optical accelerometers with actual dimensions. In order to examine sensitivity dependence on diaphragm thickness, two accelerometers for each diaphragm thickness of 50, 60, 70, 80, and 90 μm were fabricated. Thirty-five straight waveguides spaced 0.1 mm apart were formed on both sides of a diaphragm to confirm the sensitivity nearest the diaphragm edge. Although waveguide structure does not affect sensitivity dependences, strip-loaded-type BK7 waveguides were used in this experiment. Figure 6(d) shows a cross-sectional view of the waveguide. Thickness of the BK7 guided layer was 1.2 μm. Thickness and width of the loaded strip were 0.4 and 8.0 μm, so that the waveguide width was 8.0 μm. Thickness of the buffer layer was determined to be 1.4 μm in order to sufficiently reduce the radiation loss of the guided modes into the high-index silicon. On the top surface, the area of the diaphragm and 300 μm-thick proof mass were $10\times 10{\mathrm{mm}}^2$ and $5\times 5{\mathrm{mm}}^2$, respectively. The overall dimensions of the sensor were 20 mm long, 20 mm wide, and 300 μm thick.

Fig. 6

(a) Cross-sectional view and (b) bottom view of fabricated guided-wave optical accelerometers and (c) cross-section of a strip-loaded-type BK7 waveguide.

In fabrication, a diaphragm was first formed on a silicon substrate as described in Sec. 3.1. After diaphragm formation, the silicon dioxide was removed from the substrate in order to form strip-loaded-type waveguides on the diaphragm, following redeposition of a 1.4 μm-thick silicon dioxide film by sputtering as a buffer layer. Then, a 1.2 μm-thick BK7 glass film was deposited as the guided layer by sputtering. Moreover, 8 μm-wide and 0.4 μm-thick silicon dioxide strips were formed on the guided layer parallel to the diaphragm edge by sputtering and lift-off method. Experimental setup and measurement were same as described in Sec. 3.1.

4.2.

Experimental Results

Figure 7 shows normalized output power for the waveguide location nearest the diaphragm edge as a function of the applied force for fabricated accelerometers of diaphragm thicknesses, 50, 70, and 90 μm. In the figures, dots represent measured values, and sinusoidal curves indicate the computer projection of the experimental data. From Fig. 7(a)–7(c), the half-wave forces are evaluated to be 5.8, 11, and 18 mN, corresponding to phase sensitivities in radian per milli-Newton of 0.54, 0.28, and $0.17\mathrm{rad}/\mathrm{mN}$, respectively. Moreover, phase sensitivity in milli-radian per gravity is estimated to be 93, 49, and $30\mathrm{mrad}/\mathrm{g}$ when the mass of the proof mass is 17.5 mg. Figure 8 shows phase sensitivity versus diaphragm thickness. Dots represent the evaluated phase sensitivities, and the line indicates the regression line for the experimental data. The slope of the regression line is $-2.0$ in a log-log graph. Therefore, the phase sensitivity is experimentally determined to be inversely proportional to the square of the diaphragm thickness. Sensitivity can be adjusted in the 10’s mrad/g range for accelerometers with a $10\times 10{\mathrm{mm}}^2$ diaphragm and a $5\mathrm{mm}\times 5\mathrm{mm}\times 300\mu \mathrm{m}$ proof mass by designing the diaphragm thickness although the frequency range also varies. When detailed sensitivity dependences on dimensions of diaphragm and proof mass are determined theoretically and experimentally in the on-going study, they are expected to expand the designable sensitivity range.

Fig. 7

Normalized output powers versus applied force for (a) 50 μm-, (b) 70 μm- and (c) 90 μm-thick diaphragms.

Fig. 8

Evaluated phase sensitivity as a function of diaphragm thickness for accelerometers with a 10 mm-square, 50 μm-thick diaphragm and a 5 mm-square, 300 μm-thick proof mass.

Incidentally, flexural rigidity of the diaphragm is defined as $D=Y{h}^3/12(1-{\rho }^2)$, where $Y$, $\rho$, and $h$ denote the modulus of elasticity, Poisson’s ratio, and diaphragm thickness, respectively.¹³ Hence, flexibility of the diaphragm is inversely proportional to the cube of the diaphragm thickness. In addition, strain at the diaphragm surface, where a waveguide is formed, is known to be proportional to the diaphragm thickness, while the curvature of the diaphragm is kept constant. From both effects, sensitivity is expected to be inversely proportional to the square of the diaphragm thickness. Such sensitivity dependence has been identified in previous theoretical and experimental studies of the pressure sensor.^8,12 The results shown in this section agree well with the findings of the pressure sensor^8,12 and are quite reasonable, although the accelerometer has a thick proof mass.