Conceptual design of QCR load sensor
Figure 1 shows the concept for the miniaturized QCR load sensor made by microfabrication and bonding. Smaller structures can be fabricated by microfabrication. We used only three parts, and therefore, the assembly process was simplified. The parts are made by microfabrication and are bonded together (Figure 1). The QCR is fixed between two retention parts with leaf spring structures. Because of the gapless design, the previously used screw mechanism used to induce preload was not necessary. Without it, the number of the parts required was decreased and the assembly simplified. In addition, because each part is flat, we were able to employ microfablication to make the fine parts.
Sensor output and the QCR frequency shift depend on the load applied to the QCR. External loads compress both the retention mechanism and the QCR element. Therefore, we defined the ratio of the compressive load applied to the QCR (F_{
q
}) divided by the vertical component of external force (load, F_{
v
}) as “load transfer efficiency (η)” by the following:
\mathit{\eta}=\frac{{\mathit{F}}_{\mathit{q}}}{{\mathit{F}}_{\mathit{v}}}
(1)
The frequency shift (Δf) is proportional to the compressive load applied to the QCR (F_{
q
}), and we referred to this proportionality constant as “load sensitivity (S_{
l
})”.
{\mathit{S}}_{\mathit{l}}=\frac{{\mathrm{\Delta}}_{\mathit{f}}}{{\mathit{F}}_{\mathit{q}}}
(2)
Considering the load transfer efficiency (η), the sensor sensitivity (S_{
s
}) is given by the following equation:
{\mathit{S}}_{\mathit{s}}=\frac{{\mathrm{\Delta}}_{\mathit{f}}}{{\mathit{F}}_{\mathit{v}}}=\mathit{\eta}\cdot {\mathit{S}}_{\mathit{l}}
(3)
Here, load sensitivity (S_{
l
}) is constant and depends on the QCR material properties (cross sectional area, temperature, cut direction, etc.). Therefore, to increase the sensor sensitivity, it is necessary to improve the load transfer efficiency. The load transfer efficiency is improved if the rigidity of the leaf spring in the vertical direction is low. However, it is difficult to miniaturize the leaf spring further using conventional machining processes. Therefore, we used microfabrication to miniaturize the leaf spring [[15],[16]].
QCR design
An ATcut quartz crystal has superior temperature stability at room temperature [[17],[18]]. When AC voltage is applied between two metal electrodes on both sides of the ATcut QCR, thicknessshear vibration is generated along the quartz crystal’s electrical axis (xaxis).
Therefore, we designed the shape of the ATcut QCR as shown in Figure 2. The bonding plane and oscillation component of the QCR are separated by a slit. The load is applied in the direction 34.8° from the xaxis of the ATcut QCR. Load sensitivity is not a function of temperature fluctuations in this direction [[19]]. Stable vibration of the QCR is necessary to obtain highly stable sensor outputs; the QCR oscillates both mechanically and electrically. Vibration is generated from the center of the electrode of the QCR, and bonding to the surface will disturb the vibration of the QCR. Therefore, the bonding plane is kept at a distance from the electrode. Thus, the oscillation component of the QCR was designed with a rectangular cross section.
Retention mechanism design
A schematic of the retention mechanism is illustrated in Figure 3. The retention part is made by processing a single silicon (Si) wafer. The height of the leaf spring must be small to improve the sensor sensitivity. Therefore, we employed microfabrication techniques to fabricate the fine retention parts.
One surface of each retention part is slightly etched not to interfere with the oscillation and wiring components. The retention parts have a hole for wiring connections. Figure 4 shows the analytical model of the sensor where the total structure is regarded as the combination of the springs. Cpart and Vpart indicate the ideal contact parts between the center structure of the QCR and the leaf spring and between the leaf spring and the flame of the sensor, respectively. The parameters k_{
q
}, k_{
l
}, k_{
s
}, R_{
q
}, and R_{
s
} show the spring constants of the center structure of the QCR, the leaf spring, and the frame structure of the sensor, and reaction force to the center structure of the QCR, and to the frame structure of the sensor, respectively. From the calculation of equilibrium of force at the Cpart and Vparts, the following equation was derived:
{\mathit{F}}_{\mathit{v}}=\left(\frac{{\mathit{k}}_{\mathit{s}}}{{\mathit{K}}_{\mathit{q}}}\phantom{\rule{0.5em}{0ex}}\frac{{\mathit{k}}_{\mathit{l}}}{{\mathit{k}}_{\mathit{s}}+{\mathit{k}}_{\mathit{l}}}+1\right)\cdot {\mathit{R}}_{\mathit{q}}
(4)
Here, R_{
q
} is the reaction force of F_{
q
} in Eq. (2). Thus, the load transfer efficiency (η) is derived from Eqs. (2)–(4) as follows.
\mathit{\eta}=\frac{{\mathit{k}}_{\mathit{q}}\left({\mathit{k}}_{\mathit{s}}+{\mathit{k}}_{\mathit{l}}\right)}{{\mathit{k}}_{\mathit{s}}{\mathit{k}}_{\mathit{l}}+{\mathit{k}}_{\mathit{q}}{\mathit{k}}_{\mathit{s}}+{\mathit{k}}_{\mathit{l}}{\mathit{k}}_{\mathit{q}}}=\frac{1+{\mathit{k}}_{\mathit{l}}/{\mathit{k}}_{\mathit{s}}}{{\mathit{k}}_{\mathit{l}}/{\mathit{k}}_{\mathit{q}}+1+{\mathit{k}}_{\mathit{l}}/{\mathit{k}}_{\mathit{s}}}
(5)
Here, k_{
q
} and k_{
s
} are given by
{\mathit{k}}_{\mathit{q}}=\frac{\mathit{wt}\cdot {\mathit{E}}_{\mathit{q}}}{{\mathit{H}}_{\mathit{q}}}
(6)
{\mathit{k}}_{\mathit{s}}=\frac{\mathit{Wb}\cdot {\mathit{E}}_{\mathit{s}}}{{\mathit{H}}_{\mathit{s}}}
(7)
where E_{
q
} is the Young’s modulus of the quartz crystal and E_{
s
} is the Young’s modulus of Si. We assumed that both ends of the leaf spring are supported by the beam with a rectangular cross section (width is b, height is h, and length is l). Therefore, k_{
l
} is given by the following equation:
{\mathit{k}}_{\mathit{l}}=\frac{16{\mathit{E}}_{\mathit{s}}\mathit{b}{\mathit{h}}^{3}}{\mathit{L}}
(8)
k_{
l
} must be less than k_{
q
}, to increase the load transfer efficiency (η), which is from Eq. (5). From Eq. (8), it is evident that high load transfer efficiencies can be realized by decreasing h. However, b must be sufficiently large to firmly support the QCR. Therefore, the ideal leaf spring has a large aspect ratio.
Here, we determined the dimensions of the QCR and the retention parts via calculation using Eqs. (5)–(8) such that the load transfer efficiency (η) is 0.950: w = 2.0 mm, H_{
q
} = 3.5 mm, t = 0.1 mm, W = 4.0 mm, H_{
s
} = 5.0 mm, b = 1 mm, h = 0.69 mm, and L = 1.6 mm.
In practice, the base of the leaf spring was rounded to prevent stress concentration. We calculated load transfer efficiency using finite element analysis with SolidWorks Simulation (SolidWorks Corp.). The analysis was performed with the leaf spring having a radius of 0.1 mm. Von Mises stress of the sensor was analyzed via the assumption that the perpendicular compressive load applied to the sensor top was 10 N. Analytical results are shown in Figure 5. The results indicate that the load applied to the QCR was 9.42 N (it was calculated as 47.1 MPa by multiplying the average stress on AA’ , which has a section area of 0.2 mm^{2}). Thus, the load transfer efficiency was found analytically to be 0.942, which is 0.8% smaller than the value calculated using Eqs. (5)–(8). The maximum allowable load applied to the sensor is 31.8 N based on an allowable stress for ATcut quartz crystals of 150 MPa.
Fabrication
The sensor was fabricated with the following procedure (Figure 6).
Fabrication of the QCR

(a)
Electrode patterns were formed to both faces of the ATcut quartz crystal plate (thickness of 100 μm) using a photolithography technique liftoff process [[20]]. Chromium (Cr) and gold (Au) were deposited using sputtering equipment (E200S, Canon ANELVA).

(b)
Sheet resist (50X077, NichigoMorton Co.) was laminated to the quartz crystal.

(c)
Sheet resist was patterned by photolithography.

(d)
QCRs was formed into the pattern of sheet resist using sandblasting (ElfoBlaster, Elfotec CO.).
Fabrication of the Si structure

(e)
Photoresist (OFPR800 15CP,Tokyo Ohka Kogyo CO.,LTD) was patterned on the Si wafer (thickness of 500 μm).

(f)
Silicon wafer was hollowed to a depth of approximately 50 μm using deep reactiveion etching (DRIE) (MultiplexASEL, Sumitomo Precision Products Co.).

(g)
Photoresist (SU8 3025, MicroChem Corp.) was patterned on the Si wafer.

(h)
Silicon wafer was formed into the pattern of SU8 by DRIE, and SU8 was removed.
Assembly

(i)
Si structure was bonded from both sides of the QCR. Epoxy adhesive was used to bond the sensor parts, and wiring was attached using conductive silver paste.
A quartz crystal plate can be easily formed into any arbitrary shape using sandblasting. In addition, a Si wafer can be formed into minute structures having a high aspect ratio and high accuracy using DRIE.