A review of micromachined thermal accelerometers

The device performance can be mathematically analyzed by modeling the accelerometer using simple geometries. For the structure in figure 1(a), which has a centrally placed heating element and working fluid enclosed by cavity and outer cover, the heater can be modeled as a cylindrical heat source and the outer cover as a larger cylinder at ambient temperature [12]. The model can be even simplified to a spherical structure where the heater is a spherical source, and the outer cover is a larger sphere centering the heater and kept at ambient temperature [13, 14]. Such a simplified geometry is shown in figure 2(a). Here, r and θ are the radial distance and angle of the spherical coordinate system respectively. The inner sphere represents the heater with radius r_i and surface temperature T_i. On the other hand, the outer sphere represents the cavity wall surface having radius r_o and wall temperature T_o (where T_i  >  T_o). AA' represents the vertical axis along midsection. Ratio of the outer to inner sphere radius is R (=r_o/r_i). The concentric cylinder model is generally used for single-axis accelerometers, while concentric sphere for the dual axis ones. In three-axis accelerometers, the x and y-axes accelerations are applied in-plane while the z-axis acceleration is applied out-of-plane and these too can be modeled with concentric spheres.

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The governing equations predicting temperature profile of a thermal accelerometer device are based on the principle of conservation of mass, momentum and energy [15] which are as follows:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \frac{\partial \rho }{\partial t}+\nabla \cdot (\rho {\bf u})=0\nonumber \end{align} \tag{ 1 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \rho \left( \frac{\partial {\bf u}}{\partial t}+{\bf u}\cdot \nabla {\bf u} \right)=-\nabla p+\nabla \cdot {\bf I}+{\bf f}\nonumber \end{align} \tag{ 2 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \rho {{C}_{{\rm p}}}\left( \frac{\partial T}{\partial t}+u\cdot \nabla T \right)=k{{\nabla }^{2}}T.\nonumber \end{align} \tag{ 3 }$$

Here, u is the flow velocity vector field, $\nabla$ is spatial divergence operator, p is the pressure, I is the total stress tensor, f denotes the body forces acting on the fluid. The parameters C_p, ρ and k are the specific heat, density and thermal conductivity of the fluid in the cavity, respectively. In the realm of micro-fluidics, various parameters determine the convective and conductive thermal energy flow in a fluid. For simplification, these parameters are clubbed together to define some non-dimensional numbers as stated below. Use of these dimensionless numbers help to simplify the governing equations as well as the overall analysis.

• (i)  
  Fourier number is defined as the ratio of the rate of heat conducted through a body to the rate of heat stored.

  $$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm Fourier}\,{\rm number}:{{F}_{0}}=\frac{\tau \alpha }{r_{i}^{2}}\nonumber \end{align} \tag{ 4 }$$

  where, τ is the characteristic time, and α is the thermal diffusivity of the fluid defined as the ratio of heat conducted to heat stored which essentially represents how fast the heat diffuses through a material and is expressed as:

  $$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \alpha =\frac{k}{\rho {{C}_{{\rm p}}}}.\nonumber \end{align} \tag{ 5 }$$

  Higher value of the Fourier number indicates a faster heat propagation through the body.
• (ii)  
  Prandtl number represents the ratio of diffusion of momentum to diffusion of heat in a fluid.

  $$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm Prandtl}\,{\rm number}:{\rm Pr}=\frac{\mu {{C}_{{\rm p}}}}{k}\nonumber \end{align} \tag{ 6 }$$

  Here µ is the dynamic viscosity of the fluid. For air, the Pandtl number is around 0.7–0.8 and the value is higher for oils (e.g. SAE10, SAE40 etc). The sensitivity of thermal accelerometer, depends upon the Prandtl number of the fluid present in the cavity. With higher values of Pr, the sensitivity of the device increases. However, for a working fluid with lower Pr, the differential temperature reaches its steady-state value quickly due to a faster development of the temperature field. Consequently, with a lower value of Prandtl number, the characteristic time is low and the bandwidth of the device is higher. τ also depends on the value of R and the bandwidth reduces as R is increased.
• (iii)  
  Grashof number is the ratio of buoyancy force to viscous force.

  $$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm Grashof}\,{\rm number}:{\rm Gr}=\frac{{{\rho }^{2}}a\beta (T-{{T}_{0}})}{{{\mu }^{2}}}{{l}^{3}}\nonumber \end{align} \tag{ 7 }$$

  where, a is the applied acceleration, β is coefficient of fluid expansion, l is the characteristic length of the device and $(T-{{T}_{0}})$ is the temperature difference between the heater and the bulk substrate. As the sensitivity of convective accelerometer depends on the working fluid, characteristic length of the device and the temperature difference between the heater and the bulk substrate, the Grashof number qualitatively indicates the sensitivity of the device.
• (iv)  
  Rayleigh number is the product of Prandtl and Grashof numbers.

  $$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm Rayleigh}\,{\rm number}:{\rm Ra}={\rm Pr}\cdot {\rm Gr}{\rm }\nonumber \end{align} \tag{ 8 }$$

The sensitivity of thermal accelerometer is directly proportional to the Rayleigh number [16].

The governing equations (1)–(3) can be solved using the boundary conditions of the thermal accelerometer under consideration to obtain the temperature distribution and the velocity profile. The temperature distribution (T') can be obtained as follows [17, 18]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{T}^{\prime}}={{T}_{0}}+({\rm Gr}\cdot {\rm Pr}){{T}_{1}}+{{\left( {\rm Gr}\cdot {\rm Pr} \right)}^{2}}{{T}_{2}}+{{\left( {\rm Gr}\cdot {\rm Pr} \right)}^{3}}{{T}_{3}}+\ldots .\nonumber \end{align} \tag{ 9 }$$

Where, T₀, T₁, T₂, T₃,... are dimensionless functions of radius ratio (R) and the radial distance (r). This can be further approximated as:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{T}^{\prime}}={{T}_{0}}+({\rm Gr}\cdot {\rm Pr}){{T}_{1}}.\nonumber \end{align} \tag{ 10 }$$

Here, T₀ is the temperature profile due to thermal conduction from the inner to the outer sphere, and T₁ is the temperature profile due to fluid convection, as given by:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{T}_{0}}=-\frac{1}{R-1}+\frac{R}{R-1}.\frac{1}{r}\nonumber \end{align} \tag{ 11 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{T}_{1}}=\left( {{C}_{1}}{{R}^{2}}+{{A}_{3}}R+{{C}_{2}}+{{C}_{3}}\frac{1}{R}+{{A}_{4}}\frac{1}{{{R}^{2}}}+{{C}_{4}}\frac{1}{{{R}^{3}}}+{{C}_{4}}R~{\rm ln}~R \right){\rm cos}\theta \nonumber \end{align} \tag{ 12 }$$

where, C_i and A_i are coefficients which are functions of R. It is to be noted that the governing equations can also be solved using numerical computing tools like MATLAB [19] to obtain the temperature contours (e.g. in figure 2(b)) and temperature profile inside the cavity and, hence the device sensitivity.

As the structure of a practical accelerometer is quite complex, it cannot be easily analyzed by means of the analytical equations. To study its various performance parameters like temperature profile etc, numerical simulators are required to be used. Different software tools are commercially available to this end, like ANSYS [20], CoventorWare [21], and COMSOL Multiphysics [22]. Here, an example has been presented in COMSOL to illustrate the numerical simulation steps involved in finite element method (FEM) analysis of thermal accelerometers. The tool provides an environment where effects of different intercoupled physical phenomena can be simulated together to predict the overall effect. Through a number of physics user interfaces, information corresponding to the physical phenomena can be incorporated by means of variables and equations. For a convective accelerometer, to get the effect of acceleration on the heated fluid within the cavity, Joule heating physics and laminar flow physics can be used in the numerical simulator [22]. The devices may be specified in 2D (two dimensions) or in 3D (three dimensions). Compared to the 2D modeling where the simulator considers dimension in one axis (z-axis) is infinite, in 3D, all dimensions are finite. As expected, simulation in 3D provides more accurate results but at the cost of CPU time.

Figure 3 illustrates an example of a micromachined dual-axis convective accelerometer having a planar square-shaped heater placed at the center of a cuboid cavity. Using the same principle as a single-axis thermal accelerometer as discussed in section 2, a dual-axis accelerometer measures acceleration along two orthogonal axes using two pairs of temperature sensors placed equidistant from the central heater. The heater plate is supported by four arms clamped from the four corners of the cavity. The arms may be made of polysilicon or metal (as electrical conductor), and oxide and/or nitride layers (as insulating layer around the conductor). For the purpose of finding the temperature distribution due to the heating element within the cavity, the temperature sensing structures may be omitted. The working fluid (here air) also needs to be defined with its properties set as functions of temperature. In this example, the temperature of the outer walls (cavity and top cover) of the device has been set at 300 K. The device has been meshed in free tetrahedral mode [22, 23]. The critical regions like the square heater corner regions and tapered regions of the supporting arms have been meshed with higher resolution (smaller size of elements) to get better accuracy. The heat flows from the heater to the surrounding air as well as into the supporting arms creating the temperature contour as seen in figure 3(b). Further, acceleration has been applied towards the right side using volume force of laminar flow physics in the air volume. This produces the skewed temperature contour of figures 3(c) and (d). The temperature at any point of the structure, or along any straight line can be plotted using stationary study. With the help of these data, the sensitivity of the device can be determined by subtracting the temperature at two opposite equidistant points from the heater (prospective location for the temperature sensors).

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With the help of time dependent study in simulation, the transient response and hence, the  −3 dB bandwidth of the sensor can also be determined [24, 25]. One can play with the heater and cavity shape/size, constituent material and fluid properties, etc for improving the sensitivity of the device. Apart from sensitivity and bandwidth, other relevant performance parameters (specifications) are its measurement range, linearity, resolution, voltage noise density or noise equivalent acceleration (NEA), overload shock limit, power consumption, size etc [26, 27].

The concept of thermal convective accelerometer without solid proof mass was first patented in 1996 by Dao et al [28]. Subsequently, Leung's group from Simon Fraser University was the first to implement such accelerometers by custom fabrication on silicon substrate [11, 29]. Although the implemented devices were single-axis ones, but, dual-axis thermal accelerometers were also conceptualized. A cavity of dimension 1.5 mm  ×  4 mm was generated by front-side bulk micromachining of Si wafer. Lightly doped polysilicon was used to realize the heater and thermistor bridges (1.5 µm thick, 10 µm wide and 1500 µm long). Poly-Si heater is quite popular because of its higher sheet resistance compared to metals, and thus, suitable resistance can be achieved in a miniaturized portion. However, polysilicon shows long-term drift of electrical resistance owing to electro-migration [30, 31]. The convection accelerometer device was sealed in ceramic DIP-16 (dual inline package). The output sensitivity was high (~60 mV g⁻¹ at a heater power of 20 mW) due to a large cavity size. It was shown experimentally that the device sensitivity increases linearly with the heater power and the square of the air pressure within the cavity. The measured frequency response was from DC to 20 Hz. A relatively lower bandwidth is characteristic of thermal accelerometers (compared to capacitive accelerometers) owing to the slower response of thermal exchange.

Using silicon-on-insulator (SOI) technology, a thermal convection based inclinometer was reported in 2001, that can also be utilized as an accelerometer [32, 33]. SOI is a costlier variant of conventional Si wafer, with advantages like superior electrical insulation from the bulk substrate, and excellent etch stop and sacrificial layer functions due to the buried oxide layer underneath the active Si layer; hence, yielding better process control and device performance [33, 34]. The heater and thermistors of the reported device were made of lightly doped silicon, and the device was sealed in a TO-8 (Transistor Outline) metal can package with either air or SF₆ as the fluid in it. It was reported that the sensitivity increased with increase of package volume reaching maximum at a package volume of 12 000 mm³. With air as the working fluid, the sensitivity was 132µV/° and the response time was 110 ms at heater power of 45 mW. The sensitivity got enhanced to 6.6 mV/° with SF₆ due to its higher density, though the response became slow (240 ms). Another report on SOI-MEMS dual-axis accelerometer studied the effect of thermal stress (due to temperature changes) appearing in the Si thermistor structures causing its out-of-plane deformation and change in resistance due to piezoresistive effect, reducing the sensitivity [35]. The 2 mm  ×  2 mm  ×  0.4 mm device as seen in figure 4, consists of four thermistors (of two different designs) arranged in a ring-like shape around the central heater (that was heated up to 200 °C using 12.5 mW). The novel shape allowed the thermistor to deform freely with temperature, hence, reducing the thermally induced stress by 90% in comparison to a usual clamped–clamped bridge thermistor. An off-chip circuit was employed to condition the sensor output. When tested in a measurement range of  ±5 g, the sensitivity was ~13 mV g⁻¹ (figure 4(c)) with a resolution of 10 mg and the total noise (thermal and 1/f) was estimated as 0.33 µV.

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The dependence of sensitivity on the cavity gas-pressure was studied experimentally in [36]. Here, platinum was used to realize the heater and thermistors, and the cavity dimension was 2 mm  ×  2 mm  ×  0.4 mm. Pt while being expensive is preferred for its linear temperature coefficient (TCR) of resistance over a wide range, better reliability and accuracy of resistor, and higher thermal resistance with respect to other commonly used materials like Al or Si. However, Pt is not CMOS compatible as opposed to poly-Si, Al and Cu; so, cannot be used in accelerometers in a CMOS process line. The device here was packaged in TO-16 metal can with the gas pressure being varied through a hole. The heater temperature was raised to 238 K above ambient temperature by applying a heater power of 54 mW. At atmospheric pressure, the sensitivity was 2.5 mV g⁻¹. However, it increased proportionally to the square of gas pressure to a value of 138 mV g⁻¹ at 25 bar. Also, using three pairs of detectors placed at 100, 300 and 500 µm from the heater, it was demonstrated that with an increase of gas pressure, the optimum sensitivity position comes closer to the heater.

Thermal accelerometers generally tend to become nonlinear in the case of a large characteristic length (i.e. large cavity size), at elevated levels of the heater temperature, and with higher acceleration. The linearity of convective accelerometers was studied by numerical and experimental methods in [37] using a device structure as in figure 1. The simulation revealed that the device output was linear with acceleration for Gr in the range of 10⁻² to 10³. The sensitivity and linearity were both optimum when the temperature sensor was positioned at one-third distance between the heater and the cavity wall. The fabricated device had a cavity dimension of 3 mm  ×  2 mm  ×  0.25 mm and the sensitivity was measured as 600 µV g⁻¹ in a range of 0–10 g with an operating power of 87 mW [38]. The bandwidth of the device was 75 Hz. The NEA (due to thermal noise of the device) was 1 mg (√Hz)⁻¹ at 25 Hz. The resolution was found to increase (due to noise reduction) along with the sensitivity with increase in heating power. Although a large cavity volume ensures higher sensitivity due to increased heat exchange, but it leads the device towards nonlinearity region.

Garraud et al [39] were able to measure high values of acceleration with good linearity by reducing the sensitivity of the device to 0.0045 K g⁻¹. The sensitivity was reduced by means of reducing the cavity width to 600 µm and by lowering the heater temperature. The device detected acceleration in the linear region up to 10 000 g.

Sensitivity of a thermal accelerometer depends on the size and shape of the heater structure. Four types of heater structures were compared (in [16, 40]) and it was shown that a diamond-shaped heater (shown in figure 5) provided higher temperature gradient at the temperature sensing point in comparison to a square-shaped heater. The diamond-shaped heating element was further modified by using high resistive material at the corners due to which the temperature gradient at the sensor position got increased. Al/poly-Si thermopiles were utilized here as temperature sensors. Unlike other commonly reported structures, here, back-side etching was also used in addition to front-side etching to create a well-defined cavity, minimizing performance variation due to cavity etching defects and ensuring device reliability and reproducibility. The sensitivity and bandwidth were 3.5 mV g⁻¹ and 25 Hz respectively, at input power of 7.4 mW and SF₆ as the working fluid. However, the sensitivity reduced to 30 µV g⁻¹ with air. An illustration of the involved fabrications steps are also shown in the figure.

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To improve the bandwidth of thermal accelerometers, the cavity size should be made small and thermal diffusivity of the working fluid must be high. This was analyzed by Courteaud et al [24] who obtained a  −3 dB bandwidth of 120 Hz. The sensitivity of the device was 0.12 K g⁻¹ when the heater power and the characteristic dimension were 70 mW and 1120 µm respectively. It was also shown that the sensitivity decreased almost linearly with increase of the external ambient temperature. The effect of different working fluids like air, CO₂, N₂, water, Ar, He, and ethylene glycol in static and dynamic conditions were studied numerically in [41]. Different fluids yield different Gr and Pr, hence, producing different heat convection behavior and temperature distribution within the accelerometer. This in turn affects the frequency response, sensitivity, and linearity of the device. The highest temperature difference hence, highest sensitivity was obtained using Ar due to its low dynamic viscosity. Air, CO₂ and N₂ produced practically identical results because of similar thermo-physical properties. The accelerometer's sensitivity and frequency response were experimentally studied as a function of the nature and pressure of fluid in [42] where a 320 Hz bandwidth with He gas at 2.15 bar was achieved. Bandwidth was found to increase proportionally with thermal diffusivity of the enclosed fluid, and decrease as the pressure of the fluid increases. Gases with lower molecular weight (like He) improves the frequency response, but increases the sensitivity to the ambient temperature of the package and hence, needs more heater power [28]. The use of inert gases is further preferred because other gases might cause the heater and detector to oxidize or age quickly. Liquids used as working fluid would produce a relatively slower response while requiring large heater power. An isopropanol-filled structure in [43] achieved a sensitivity of about 700 times of that of an air-filled accelerometer, but, having an order of magnitude greater response time.

Triple-axis accelerometers that can detect acceleration along all the three directions have considerably higher design and fabrication challenges. So, it took a while for such a convective device to be implemented. By means of integration of polymeric materials into MEMS process to attain the required mechanical flexibility, the first tri-axial accelerometer was reported in 2008 [44, 45]. Using surface micromachining on Si substrates with polyimide as a structural layer, out-of-plane/buckled sensing structures were assembled. A Cr/Au bilayer and a Ni layer were used to form thermocouple junctions for the thermopiles placed on the sensor plates. The measured sensitivity were 66, 64, and 25 µV g⁻¹ on the X, Y, and Z-axes respectively, using SF₆ as working fluid at a total heater power of 2.5 mW. Later, a novel design consisting of three flexible polyimide membranes (two identical Z-axis membranes on either side of a central membrane) encapsulated within four polymeric microparts was reported, as seen in figure 6 [46, 47]. The central membrane included the heater and temperature sensors for X and Y-axes, while the upper and lower membranes had sensors for Z-axis. The X and Y sensitivity was about 8 mV g⁻¹ and the Z-axis sensitivity was 2.2 mV g⁻¹, with an overall power of 45 mW and the bandwidth was 4 Hz.

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In contrast to the accelerometers in the previous subsection, monolithic CMOS-MEMS thermal accelerometers can have the signal conditioning circuit on the same chip as the sensor as both are fabricated on the same substrate (die) using CMOS IC process in conjunction with some MEMS specific process steps (e.g. a post-CMOS etching to realize the cavity and the hanging heater and temperature sensor structures) [48, 49]. Hence, these are compact, cost effective, and insensitive to parasitic component effects. Moreover, the frequency response might also improve along with a lower power requirement. As thermal accelerometer has no solid proof-mass, the fabrication of the device is simpler in comparison to capacitive accelerometers which are also fabricated using CMOS-MEMS process by front-side or back-side etching. Higher amount of stresses are generated at the anchored positions of the supporting beams in a capacitive sensor. The suspended bridges are often required to be released by deep reactive ion etching (DRIE) which is expensive [50, 51]. On the other hand, thermal accelerometer suspended structures can be released using wet etching (with TMAH solution) and/or dry etching (reactive ion etching) in the post-CMOS processing step.

In the custom MEMS process based accelerometers discussed previously, various materials can be utilized for implementing the heating element and the temperature sensor; and the material layer thicknesses can also be set as desired. But, in a standard CMOS process, the layer materials and thicknesses are predefined by the IC fabrication foundry. Moreover, the cavity size of the device cannot be made large as the device cost increases with the die size. Hence, the major limitation of thermal accelerometers implemented in this process is its comparatively lower sensitivity due to limited cavity size and available materials.

The foremost report was a single-axis convective accelerometer implemented in a 2 µm CMOS process and packaged in ambient air by Milanovic et al in 1998 [52, 53]. Both thermopile and thermistor types of temperature detectors were tested which yielded sensitivities of 136 µV g⁻¹ and 146 µV g⁻¹ respectively, with relatively lower power requirement (81 mW) with thermopile. Good linearity in the range of 0–7 g was observed for both the devices, and frequency response of up to hundreds of Hz was obtained. Sensitivity of the devices was found to be a nearly linear function of heater power (temperature).

A single-axis thermal accelerometer fabricated in AMS 0.8 µm CMOS process is shown in figure 7 [25, 54]. The cavity (of dimension 740 µm  ×  740 µm) was generated by front-side bulk micromachining process, and poly-Si resistors were used to realize the heater (40 µm  ×  1040 µm) and thermistor (30 µm  ×  700 µm) bridges having a separation of 200 µm. The sensor output voltage was processed by a CMOS signal conditioning amplifier with controllable gain, which was present on the same chip as the sensor as seen in figure 7. The heater temperature was 438 °C using 35 mW of power and the device sensitivity was experimentally measured as 375 mV g⁻¹ (or equivalently, 1.53 °C g⁻¹) with a resolution of 30 mg. It had good linearity till 10 g and the  −3 dB bandwidth was 14.5 Hz. Optimum device dimensions were formulated by means of FEM study of the effect of the cavity and package width and height on the device sensitivity and time constant [55, 56]. The sensitivity was found to increase linearly with the package cover height for a wide range. Due to etching defects, the cavity depth can get reduced due to which the thermal bubble size gets reduced leading to deterioration of sensitivity [56]. The temperature distribution and maximum sensitivity positions were obtained via 2D and 3D simulations and were compared in [57]. With respect to 2D, in 3D simulation, the thermal bubble got constricted and sensitivity reduced to a value closer to that obtained experimentally. The optimum sensitivity position for the temperature sensors also changed from middle to one-third distance between heater and cavity wall.

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A dual-axis thermal accelerometer fabricated in TSMC 0.35 µm CMOS process was designed using a micro heater and two pairs of thermopiles being used as temperature sensors [58–60]. The cavity dimension was 830 µm  ×  830 µm. The thermocouple was made by n-type poly-Si and Al junctions. The heater and thermopiles were connected by net like structures of SiO₂/Si₃N₄ to enhance the mechanical stability. The cold junctions were placed on the Si substrate and the hot junctions were formed over the net near to the heater. The device was tested as an inclinometer from which the acceleration sensitivity was derived to be 22 µV g⁻¹ at input power of 9.05 mW. As the temperature is sensed at the junction of two different materials in a thermocouple, it requires less space at the hot junction where the temperature difference is measured. The noise voltage was under 0.25 µV and the NEA was 0.159 g.

Another reported dual-axis accelerometer fabricated in AMS 0.35 µm CMOS process used meander-shaped heater of size 100 µm  ×  100 µm and a cavity dimension of 600 µm  ×  600 µm [14, 61]. The sensitivity was found to be 0.024 K g⁻¹ which is somewhat low due to a low Seebeck coefficient of 6.54 µV K⁻¹ of the Al/poly-Si thermopiles used, and lower cavity size and heater temperature. Acceleration was measured till 150 g using heater temperature of 200 ºC. They also utilized infrared temperature mapping to experimentally determine the temperature profile within the device. An optimized square-ring shaped heater structure was reported in [62] to improve the sensitivity. It was also shown that the sensitivity improved when a given peak temperature is generated at the edges of the heater rather than at its center.

A monolithic triple-axis thermal accelerometer was implemented by Mailly et al using AMS 0.35 µm CMOS process, which did not require the complex assembly operations of the tri-axial sensors as discussed in the previous subsection [63, 64]. The principle is to sense the acceleration in the third axis by means of common-mode temperature measurement using X and Y detectors of a 2-axis convective accelerometer structure as illustrated in figure 8. Acceleration in the positive Z direction stretches the hot bubble leading to temperature drop at the detectors, while reverse occurs due to negative Z-axis acceleration. Experimentally obtained sensitivity values were 8.8 mV g⁻¹, 12.6 mV g⁻¹ and 0.45 mV g⁻¹ for X, Y and Z-axes respectively at heater power of 8.3 mW. In comparison to the in-plane sensitivity, the low Z-axis sensitivity was attributed to unoptimized thermal sensor position and 3D thermal effects that demand proper understanding. Accelerometers based on a similar sensing method have also been commercialized by MEMSIC [65, 66].

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A number of unique instances of reported thermal accelerometers that incorporate innovative materials and structures have been presented in this subsection. Such modifications are targeted towards enhancement of the different performance aspects.

4.3.1. Organic and plastic substrate.

4.3.2. CNT based components.

4.3.3. Porous silicon based device.

4.3.4. Novel device structures.

In a recent report, the cavity structure of accelerometer was modified to improve the sensitivity [75]. Silicon islands were placed in between the heater and temperature sensors as in figure 9. Since the thermal conductivity of Si is much more than that of the fluid, presence of Si islands modulates the fluid movement and hence, the temperature profile. The sensitivity obtained from the cavity with island structure was 0.657 K g⁻¹ which is double of that without islands (0.335 K g⁻¹).

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Due to the good temperature sensitivity (typically  −2.2 mV °C^–1) of a diode [76], it can be utilized as the temperature sensor in thermal accelerometer to improve its sensitivity. Additionally, the sensitivity can be further enhanced by connecting two or more diodes in series [77]. However, it is extremely challenging to integrate Si diode in the cavity because of the need to etch silicon to realize the suspended membrane within the cavity.

Capacitive sensing being the most common and popular accelerometer variety in the market, it seems pertinent that its performance aspects be compared with that of a thermal accelerometer. While a large number of manufacturers like Analog Devices, Bosch, NXP/Freescale, STM, TDK/InvenSense, etc market capacitive MEMS acceleration sensor chips, MEMSIC is currently the only major player providing commercially available thermal accelerometers since 2002. In table 2, a tri-axial thermal accelerometer from MEMSIC manufactured in standard submicron CMOS process with Al/poly-Si thermopiles [78] have been compared against an Analog Devices capacitive sensor that uses a poly-Si surface-micromachined proof-mass built on top of Si wafer [79]. The devices have been selected to have the same DOF, comparable measurement range, and both provides analog output voltages that are proportional to the applied acceleration. As evident, the thermal one has a remarkable shock survival rating while its frequency response is comparatively poor.

A latest offering MXC4005XC from MEMSIC uses a relatively new wafer-level packaging technology that integrates the step of packaging with the fabrication of the wafer which is later diced yielding packaged chips that are practically of the same size as the die. This is very efficient in terms of size and cost, with a reported shock survival of 200 000 g.