A micromachined capacitive pressure sensor which allows the sensing element to flatten onto an insulation layer deposited on the bottom electrode is known as touch mode capacitive pressure sensor (TMCPS). The TMCPS was firstly introduced in 1990 by Ding et al. [15], while an array of capacitive sensing elements in parallel was presented in the work of Dudaicevs et al. [16] in 1994. We have developed a TMCPS which is made of an array of elements supported by a SiO₂ honeycomb structure. The fabrication process, where the top plate is given by the device layer of a silicon on insulator wafer, was previously described by Pedersen et al. [17]. In Figure 1 an artistic view of the sensor is shown; the old design, Figure 1(a), which has a flat substrate surface is compared to the new solution, Figure 1(b), where part of the membrane has been removed in order to make the newly introduced nanopillars structure visible.

This type of sensor has the advantage of eliminating interconnection between elements, thus minimizing the active area and the parasitic capacitance. Furthermore, its flat sensing surface is well suited for coating with a corrosion resistant layer, thus making this sensor a good candidate for harsh environment applications where also a low power consumption is needed.

Moreover, an analytical solution for the deflection of the membrane in all the operation regimes has been found and used to fit the experimental data [18]. In normal mode, i.e., when the maximum deflection of the membrane is less than its distance from the substrate, the governing equation for the deflection, w, as a function of the radial distance, r, and the pressure, p, of a clamped circular isotropic plate is well known [19] (1) w ( r , p ) = pa 0 4 64 D ( 1 − ( r a 0 ) 2 ) 2where a₀ is the radius of the plate and D is the flexural rigidity of the plate given by (2) D = Et 3 12 ( 1 − ν 2 )It will be shown that, in normal mode operations, the sensor proposed can be modeled under the assumption of linear elasticity and therefore described by Equation (1). A good approximation for the shape of the plate when working in touch mode (see Figure 2) is instead given by (3) w ( r , p ) = { g 0 < r < a b ( p ) g ( 1 − ( r − a b ( p ) a v ( p ) ) 2 ) 2 a b ( p ) < r < a 0where g is the distance between the top electrode and the substrate at zero pressure, a_b is the radius of the part of the membrane touching the substrate and a_v is calculated with (4) a v = a 0 − a bThe radius of the plate touching the bottom of the cavity, a_b, is a function of pressure as is also the part of the diaphragm not touching the bottom plate, a_v. In the simplified model proposed, the radius a_v is simply given by the center deflection being fixed at (5) a v ( p ) ≡ ( 64 Dg p ) 1 / 4

In Figure 3 it is possible to see the results given by the approximate model proposed; the blue dots represent the data points measured on the TMCPS described in [17] while the solid line is the fitting curve. From this curve parameters such as the parasitic capacitance, the flexural rigidity and the thickness of the insulation layer used to prevent short circuit when working in touch mode has been extracted. An excellent match between them and the measured ones was reported in [18] where also a solution for the integral (6) C = ∫ 0 2 π ∫ 0 a 0 ɛ 0 ɛ ox rdrd θ t ox + ɛ ox ( g − w ( r , p ) )has been found for both operating modes.

At this point, based on the amount of research done in the field and the fact that the working principle of the TMCPS has been fully investigated and tested, we can state that this is definitely the most developed of the devices proposed. None the less, process reliability, conditioning circuit complexity and hysteresis are some of the obstacles for the commercialization of this sensor at a level comparable to its piezoresistive counterpart. We present, with the new design, a solution to the hysteresis problem of TMCPS.

The process sequence for the fabrication of the new device is shown in Figure 4. Firstly a silicon and a SOI (Silicon On Insulator) wafer with 2 μm are subjected to a one-hour phosphorous pre deposition in the first processing step, Figure 4 (a). A 600 nm thick oxide is grown on the silicon wafer and the cavity is etched to form the hexagonal structure mentioned earlier, Figure 4 (b). The nanopillars are then developed on the bottom of the cavities with the process described later in this section, Figure 4 (c). A second oxidation is performed to grow a 30 nm SiO₂ layer around the pillars. This SiO₂ layer serves as a short circuit protection when the sensor works in touch mode operation. In the next step a 10 μm wide groove is etched all the way through the device layer of the SOI wafer to the buried oxide such that it will serve as an electrical insulation between the active part of the sensor, i.e., the membrane area and the rest of the highly doped device layer. If these regions are not separated from each other, the area outside the membrane will add a considerable parasitic capacitance to the system. Then, the SOI wafer is turned upside down and fusion bonded with DSP wafer. Figure 4 (d) shows the result of etching the insulation groove, bonding and removing the handle wafer. Finally, the separated part of the device layer, the upper and lower electrode are contacted by means of Al evaporation, Figure 4(e).

It must be noticed that, in order to reduce the amount of hysteresis, whether due to stiction forces or to poor quality of the insulating layer, a reduction in the contact area between the top electrode and the insulation layer is needed. Two different types of corrugation can serve this purpose, a definite one obtained with a lithographic step or a random corrugated surface obtained without the use of a mask. Even though the first option requires an extra mask step (illustrated in Figure 4(c)), it must be preferred if the process involve fusion bonding of two wafers in order to keep a sufficiently smooth bonding surface. Furthermore, in the first case, the lithography limits when defining structures in a cavity (i.e., with a proximity distance between the mask and the photoresist) must be considered. Experimental results has proven to be extremely difficult to approach the theoretical critical dimension, CD, given by [20] (7) CD ≡ 2 3 λ ( d − t r 2 ) ,where λ is the wavelength of the source used, d is the proximity distance between the mask and the photoresist and t_r is the photoresist thickness. In our case, with a photoresist thickness of 1.5 μm, a wavelength of 365 nm and a proximity distance equal to the gap distance between the two electrodes (600 nm) the theoretical limit was calculated to be 1.3 μm. However, to achieve good results pillars of 6 μm radius and around 50 nm height were fabricated with an isotropic SF6/O2 plasma etch (STS ICP Advanced Silicon Etcher). Figure 5 shows a contact profilometer (Dektak8) measurement of the nanopillars structure fabricated on the bottom of a 600 nm cavity etched in SiO₂

A SEM image of a TMCPS fabricated with the pillar structure and diced afterwards is shown in Figure 6.

In Figure 7 capacitance as a function of the pressure at different temperature is reported, from these curves 14 pF/bar sensitivity in touch mode (where there is a nearly linear relation) was calculated. Furthermore, a relative temperature coefficient, α, of 0.008 %/°C, 0.023 %/°C and 0.044 %/°C have been calculated near 40 °C, 60 °C and 80 °C using (8) α ≡ C T − C T 0 C T 0 ( T − T 0 ) ⋅ 100where C_T is the output signal at the temperature T and C_T0 is the output signal at room temperature, T₀. Pressure cycles (where the pressure has been risen up to 10 Bar and lowered back to 500 mbar) have been carried on in order to evaluate the hysteresis, κ, of the sensor as (9) κ ≡ C down ( p ) − C up ( p ) C up ( p ) ⋅ 100where C_down(p) is the value of the capacitance when the pressure is lowered and C_up(p) is the value of the capacitance when the pressure is raised. In Figure 8 a hysteresis comparison between a sensor fabricated without the nanopillars structure and one were the nanopillars were added in the process flow is presented. In the letter case, the hysteresis was reduced to less than 1% in the entire pressure range. Moreover the hysteresis peak at touch point has been eliminated. These new results bring the TMCPS closer to the actual needs required for its commercialization.

It is in many situations in oil exploration critical to obtain real-time measurements of the pressure at different locations several kilometers under ground, far from the actual readout point. Also pressure and temperature at these depths can be very high. Electrical sensors are not well suited for this scenario as as they in general do not lend themselves towards remote distributed sensing due to transmission loss and parasitic capacitances and furthermore they carry the risk of a potential short circuit causing ignition, which could be fatal in this environment. Here we present an all-optical Bragg grating sensor for high pressure and remote distributed sensing. The basic principle behind Bragg grating sensors is mechanically induced modulations of the period of a Bragg grating, causing a change in the wavelength of the reflected wave from the Bragg grating. The Bragg wavelength, λ_B, is expressed through the equation (10) λ B = 2 n eff Λwhere n_eff is the effective refractive index and Λ is the period of the Bragg grating. The relative change in wavelength of such a sensor is given by (11) Δ λ B λ B = ( α + ζ ) Δ T + ( 1 − p e ) ε lwhere α is the thermal expansion coefficient of the part of the waveguide containing the grating, ε_l is the longitudinal strain, ζ is the thermooptic coefficient, p_e is the photoelastic coefficient for longitudinal strain and ΔT is the temperature change. Hence, the wavelength change is proportional to both temperature and the refractive index change due to strain. We will assume constant temperature, that the minimum detectable wavelength shift is 1 pm and that the Bragg wavelength is 1550 nm, hence the strain should be larger than approximately 10⁻⁶. Considering a circular plate with a waveguide with integrated Bragg grating on top and under uniform load, p, see Figure 9, the strain components in polar coordinates, r, θ, are [31] (12) ε r = − σ r − ν σ θ E = − 3 8 ( 3 r 2 − a 2 + ν 2 a 2 − 3 r 2 ν 2 ) p h 2 E (13) ε θ = − σ θ − ν σ r E = − 3 8 ( r 2 − a 2 + ν 2 a 2 − r 2 ν 2 ) p h 2 Ewhere ν is the Poisson ratio, σ is the stress, E is Young’s module, a is the plate radius and h is the plate thickness. The two strains have been plotted in Figure 10.

Since the radial strain is not constant the Bragg grating would experience a non-uniform strain if it was place radially on the plate, causing lower reflection and broader reflection peak. However, while the tangentially strain is generally lower than the radial strain it would give a uniform strain in the Bragg grating was it to be placed along this direction. Since the tangential strain is monotonically decreasing with r, the grating should be placed as close to the center of the plate as possible, while the waveguide bending loss is kept at a minimum. The grating will still experience the radial strain, but only at a perpendicular angle. Due to the finite width of the waveguide there will be a difference in tangential strain across the waveguide. For typical waveguide widths, this will however be negligible. The minimum radius of curvature for which the waveguide can still carry a mode is [32] (14) R min = λ 8 1 n core 2 n cladding 2 − 1 − cos − 1 ( n cladding n core )

This puts a theoretical maximum limit on the sensitivity of this device. Assuming that the core is made of SiON (n_core = 1.47) and that the cladding is made of SiO₂ (n_cladding = 1.45) the minimum radius is R_min = 128 μm. The power transmitted through this waveguide as function of its radius of curvature [32] is shown in Figure 11.

For a loss of less than 0.5 dB, the radius should be larger than 405 μm. From equations 12 and 13 the two unknowns, a and h, fulfilling the requirements of pressure range, bending loss and max pressure, i.e., |ε(r = a, p = p_max, r = R_min)|≤ σ_safe/E and ε_θ(r, p_min, r = R_min) ≥ ε_min, can be found as (15) a = p safe p min p safe p min + 2 ε min E p max R min (16) h = 3 p min p max ( 1 − ν 2 ) 8 ε min E p max + 4 σ safe p min R minwhere σ_safe is the maximum allowable stress, p_max and p_min are the maximum and minimum pressure the sensor should be able to detect, respectively and ε_min is the minimum detectable strain change. In oil exploration situations pressures up to 350 bar can occur. If we assume a pressure range from 0 to 350 bar (p_max = 350 bar) with a resolution of p_min = 1 bar, a maximum allowable stress of σ_safe = 500 MPa, minimum strain of ε_min = 10⁻⁶, a silicon membrane with E = 170 GPa and ν = 0.28, one obtains h = 102 μm and a = 464 μm. A SEM image of a sensor realized using the previous design rules is seen in Figure 12. The Bragg grating is located in the half circular part of the waveguide while the fiber connectors are located at the two ends of the waveguide. The waveguide and Bragg grating are made using a combination of deep reactive ion etching (DRIE) and electron beam lithography.

By using different period in each optical sensor in combination with low loss optical fibers, several sensors can be multiplexed on one single fiber transmission line. Also the small form factor (approx 2 × 2 mm²) and compatibility with high pressure and harsh environments make this sensor ideal for a number of applications, specifically underground oil exploration. While the temperature dependence has been neglected so far, any temperature related measurement errors can easily be compensated by integrating a pressure insensitive Bragg grating (i.e., placed outside the membrane) and measuring the differential wavelength shift. For zero strain, the two reflection peaks will shift equally in wavelength when subjected to temperature changes. For non-zero strain, the two peaks will separate proportional to the strain, hence temperature and strain can be measured uncoupled.

An application for passive wireless pressure sensor is to measure the pressure inside the urinary bladder, to monitor it for patients with urinary incontinence [42]. Urinary incontinence is a common problem but it is often concealed and associated with great discomfort [42]. Sensing the pressure in the urinary bladder can, via a feedback stimulation system, control the bladder, hence give control over the involuntarily excretion of urine as is characteristic for urinary incontinence [43]. Conventional sensing systems have been based on wired pressure sensors with the wires penetrating the bladder wall, causing undesirable side effects [44]. In these systems a wireless pressure sensor is designed to make reliable measurements without damaging the tissue inside the bladder.

In the medical industry new products are under heavy restrictions when it comes to lifetime and choice of material. This limits the sensor in many different ways, e.g., the device has to be biological compatible, the form factor has to be small and the design has to take diffusion and mechanical fatigue into account. From these limitations a design has been made to accommodate the different restrictions.

The sensing principle is capacitive, where the varying capacitance is included in a LC circuit. The capacitor plates are a circular membrane coated with metal on one side, and an electroplated copper spiral on a glass substrate on the other side. Furthermore, the spiral also functions as the inductor for the LC circuit. Combining the coil as one of the capacitor plates enables the device to become smaller and more compact compared to similar designs. The first conceptual design was a simple structure, made by a KOH etched membrane, copper electroplated coil, e-beam evaporated capacitor plate and anodic bonding, see Figure 13(a). To improve the design, simulation of a bossed membrane is used to optimize sensitivity, Q-factor and resonance frequency. The new design can be seen in Figure 13(b). According to classical electrodynamics this circuit has angular resonance frequency, ω_res, and a Q-factor, Q, that can be calculated knowing the inductance, L, the capacitance, C, and the resistance, R, of the circuit (17) ω res = 1 LC (18) Q = 1 R L C

To measure this angular resonance frequency through an external measuring circuit, the circuit is coupled to the sensor through a mutual inductance using a tuned transformer coupling, see Figure 14. Here the resonance of the sensor is reflected in the external measuring circuit through the coupling constant, k, and the external coil, L₁. The impedance of the system seen from the external terminals is given by (19) Z ( j ω ) = R 1 + j ( ω ω 01 ) 2 + 1 ω C 1 + j ω L 1 k 2 ( ω ω 02 ) 2 j ω Q 2 ω 02 − ( ω ω 02 ) 2 + 1 ,where Q₂ is the Q-factor of the sensor, j is the imaginary constant, ω is the angular frequency, ω₀₁ and ω₀₂ are the resonance angular frequencies of the external system and the sensor, respectively.

Scaling the sensor implies scaling the radius of the sensor, as the inductance of a spiral is proportional with the radius cubed, whereas the capacitor is proportional to the radius squared. This implies that the Q-factor of the sensor increases with its dimensions. This also gives rise to an increase in the impedance of the system, see Equation 19. Unfortunately, due to the biological application of the device the size is restricted to avoid excessive discomfort and side effects. A trade off between these has to be made. The old design is 6 × 6 mm wide and has a thickness below 1 mm, the same outer dimensions as the new design. This is small enough to avoid disturbing the bladder, and large enough to produce a measurable signal. The inductor and capacitor are also important; since the capacitance change governs the sensitivity and the inductor governs the signal strength there is a trade-off between these as well. Finite element method (FEM) simulation is made using the commercial software COMSOL in order to optimize the sensor. Figure 15 shows a structural mechanical simulation made with the parameters for the new design shown in Table 1 at 1 bar and used to extract the deflection of the sensor. Then the parallel plate capacitor approximation is used to calculate the capacitance. The quasi-static magnetic module in COMSOL, see Figure 16, is then used to simulate the inductance by solving the magnetic vector potential using Maxwell equations. The inductor is enclosed in a sphere with radius twice as large as the inductor radius, in order to encapsulate all of the electromagnetic fields. These two FEM simulations are programmed to investigate the resonance frequency, sensitivity and Q-factor as a function of the design parameters shown in Table 1. The simulation are made for an absolute pressure range of 0 to 330 mmHg, which for safety reasons is 10 times higher than the pressure range of interest.

From the simulations it can be seen that the sensitivity is monotonically increasing as the bossed structure gets thicker and membrane gets thinner and plate distance decreases, whereas the Q-factor is monotonically decreasing. More interesting are the variations of the radius of the bossed structure on the new design, see Figure 17(a). Here the optimal radius, in terms of sensitivity, can be read from the numerical simulations shown on the graph and is approximately 1.2 mm, whereas the Q-factor, see Figure 17(b), is increasing up to a radius of approximately 2.4 mm. It can be seen that a higher sensitivity, if compared to the old design, can be reached implementing a radius of approximately 1 to 1.5 mm, still keeping a satisfactory Q-factor. According to the simulation made with the new design parameters shown in Table 1 a sensitivity of 650 kHz/mmHg, Q-factor of 240 and a resonance frequency of 86 MHz can be reached compared to the old design which had a sensitivity of 30 kHz/mmHg, Q-factor of 150 and a resonance frequency of 63 MHz.

From the work done it has been shown that a more sensitive sensor can be produced by adding a bossed structure and still keeping the original features of an hermetically sealed small sensor. The design modifications introduced lead to a more complicated fabrication process but, with the improvements on the performances of the sensor, this is of secondary importance. Finally, the simulation tool presented allows a fast evaluation of the impact on the performances of these sensors given by a modification of their fabrication parameters.