Thermo-Electro-Mechanical Simulation of Semiconductor Metal Oxide Gas Sensors

Abstract

There is a growing demand in the semiconductor industry to integrate many functionalities on a single portable device. The integration of sensor fabrication with the mature CMOS technology has made this level of integration a reality. However, sensors still require calibration and optimization before full integration. For this, modeling and simulation is essential, since attempting new, innovative designs in a laboratory requires a long time and expensive tests. In this manuscript we address aspects for the modeling and simulation of semiconductor metal oxide gas sensors, devices which have the highest potential for integration because of their CMOS-friendly fabrication capability and low operating power. We analyze recent advancements using FEM models to simulate the thermo-electro-mechanical behavior of the sensors. These simulations are essentials to calibrate the design choices and ensure low operating power and improve reliability. The primary consumer of power is a microheater which is essential to heat the sensing film to appropriately high temperatures in order to initiate the sensing mechanism. Electro-thermal models to simulate its operation are presented here, using FEM and the Cauer network model. We show that the simpler Cauer model, which uses an electrical circuit to model the thermo-electrical behavior, can efficiently reproduce experimental observations.

Keywords: CMOS fabrication; Joule effect; MEMS membrane; electro-thermo-mechanical modeling; finite element method; gas sensors; hotplate; microheater; modeling and simulation; semiconductor metal oxide.

Figure 1

Summary of techniques used for SMO film deposition, where CVD is chemical vapor deposition and ALE is atomic layer epitaxy.

Figure 2

Schematic of an SMO sensor with interface blocks. The sensor includes a heating element and sensing film, a voltage follower, and an analog-to-digital converter (ADC). To process the sensor data, it is connected to a microcontroller, which contains a read-only-memory (ROM), random access memory(RAM), and input/output (I/O) interfaces.

Figure 3

Sensing response of an SnO2 film after exposure to carbon monoxide from several publications. (a) Köck et al. [74,75] show the influence of temperature and gold doping on the operation of a 50 nm thin film. (b) Mädler et al. [77] show the role that platinum (Pt) doping plays on CO detection. (c) Tangirala et al. [78] study the influence of dopants and doping methods on the sensitivity of SnO${}_2$ films towards the detection of CO.

Figure 4

Suspended membrane of an SMO sensor device with a side view shown in (a,b) and a top view is given in (c). In (a,b) wet chemical etching using KOH and dry etching using SF${}_6$ plasma, respectively, are shown, with their differences clearly evident. In (c) the top view of the final suspended structure is shown.

Figure 5

Simplified geometry of a device used in the electro-thermo-mechanical FEM model. In (a) the membrane materials are highlighted, which can include silicon nitride and silicon dioxide. In (b) the microheater is highlighted. The sensing layer and electrodes are not shown.

Figure 6

Schematic of the layers composing the membrane of the hotplate.

Figure 7

Resistance of the conductive layer of the sensor at different applied biases.

Figure 8

Temperature obtained using an FEM model compared with one calculated using the measured resistance.

Figure 9

FEM simulation and measured power dissipated by the sensor for different applied biases.

Figure 10

Simulation results of the out-of-plane displacement of the top surface of the membrane along its radius. The hotplate is biased and the deformation is caused by the intrinsic and the thermal stress caused by the temperature increase due to the Joule effect.

Figure 11

Microheater geometries characterized and modeled over the last decades. The shapes depicted are: (a) Meander, (b) S-meander, (c) Curved, (d) S-curved, (e) Double spiral, (f) Square double spiral, (g) Drive wheel, (h) Elliptical, (i) Circular, (j) Plane plate, (k) Fin shape, (l) Honeycomb, (m) Loop shape, (n) Irregular.

Figure 12

Heat loss mechanisms through the SMO gas sensor, where T${}_h$ and T${}_a$ correspond to the temperature of the microheater and the ambient temperature. The figure shows the locations of the principal heat losses of conduction, convection, and radiation which is represented by red ellipses.

Figure 13

Sensor geometry from [17] used to test the Cauer network model. In (a) the geometry used when considering heat loss by conduction is shown, while in (b) the treatment of the heat loss mechanism by convection is depicted on the bottom and the membrane size and extracted thermal resistances are shown on top.

Figure 14

Cauer model reproduction of a microheater design presented in [17], which is further used to analyze the transient behavior of the heater.

Figure 15

Transient response of the reference temperature (potential V${}_{\mathrm{Ref}}$) when a perfect square signal with an amplitude of 13.55 mW is applied at the power (current I1) source from Figure 14.

Figure 16

Experimental and simulated results for the temperature versus applied power relationship for a microheater design described in [17]. It is evident that the analytical Cauer model can reproduce the temperature-power relationship of an SMO sensor.

Figure 17

The influence of temperature on the electron mobility ($\mathsf{\mu }$), the electron concentration (n), and the SnO${}_2$ conductivity.

Figure 18

Gas sensing and resulting band bending for a granular film. (a) O${}^{\alpha -}$ adsorbs on the surface, creating a depletion region and band bending, (b) CO reacts with oxygen, thinning the depletion region and reducing band bending, and (c) CO adsorbs directly on the surface, creating an accumulation region and band bending.

Figure 19

Sensing response of two different designs towards exposure to formaldehyde (CH${}_2$O) and ethanol (C${}_2$H${}_5$OH) concentrations up to 5 ppm on an SnO${}_2$ film with Pt nanoparticles. The symbols are measured results and lines are best fits lines using the Langmuir adsorption model.