Transient thermal response of micro-thermal conductivity detector (µTCD) for the identification of gas mixtures: An ultra-fast and low power method

Micro-thermal conductivity detector (µTCD) gas sensors work by detecting changes in the thermal conductivity of the surrounding medium and are used as detectors in many applications such as gas chromatography systems. Conventional TCDs use steady-state resistance (i.e., temperature) measurements of a micro-heater. In this work, we developed a new measurement method and hardware configuration based on the processing of the transient response of a low thermal mass TCD to an electric current step. The method was implemented for a 100-µm-long and 1-µm-thick micro-fabricated bridge that consisted of doped polysilicon conductive film passivated with a 200-nm silicon nitride layer. Transient resistance variations of the µTCD in response to a square current pulse were studied in multiple mixtures of dilute gases in nitrogen. Simulations and experimental results are presented and compared for the time resolved and steady-state regime of the sensor response. Thermal analysis and simulation show that the sensor response is exponential in the transient state, that the time constant of this exponential variation was a linear function of the thermal conductivity of the gas ambient, and that the sensor was able to quantify the mixture composition. The level of detection in nitrogen was estimated to be from 25 ppm for helium to 178 ppm for carbon dioxide. With this novel approach, the sensor requires approximately 3.6 nJ for a single measurement and needs only 300 µs of sampling time. This is less than the energy and time required for steady-state DC measurements. Researchers in the USA have developed a fast, energy-efficient measurement technique for use in micrometer-sized thermal gas sensors. Small and fast sensors are crucial for gas chromatography and other applications. Thermal gas sensors operate by measuring the characteristic thermal conductivity of gasses and gas mixtures. Peter Hesketh and Alireza Mahdavifar from the Georgia Institute of Technology and co-workers heated a 100-micrometers-long silicon bridge on a chip using pulsed electrical currents then measured the electrical resistance of the element as it changed with temperature. The time-dependent changes of the electrical resistance were characteristic of the thermal conductivity of the surrounding gas, providing a gas-specific detection mechanism that takes less than 300 μs and uses only 3.6 nJ per measurement. These robust sensors are particularly attractive because their use of electrical pulses means that they consume far less energy than DC-based techniques.


INTRODUCTION
During the past four decades, gas sensors, detectors, and analyzers have been widely used to measure the composition of gas mixtures or to detect the presence of particular species in a gas medium 1 . Many conventional gas detectors are based on electrochemical or chemo-resistive effects. Despite providing good selectivity in some cases, the performance of these technologies is limited by the nature of the chemical adsorption/diffusion process of the chemical at the surface or through the sensing film. Therefore, many types of conventional sensors suffer from a slow response time and memory effect and require frequent recalibration. Instability and poor shelf-life are additional challenges for gas sensing 1 . Important characteristics of different gas sensor technologies are: selectivity, sensitivity, size and power consumption, response time, and hysteresis effects.
An electrothermal gas sensor works based on the interaction between heat generation in an electrically conductive suspended element and heat transfer from the element via the surrounding gas medium. When electrical power dissipation occurs in a suspended hot element, the thermal conductivity of the gas surrounding the device determines the rate of heat loss. As a result, the steady-state temperature of the hot element is a function of the gas ambient properties. If the heater is constructed from an electric conductor with a sufficiently high temperature coefficient of resistance (TCR) this allows the average temperature of the heater to be determined by measuring the change in resistance when heating occurs in different gas ambient mixtures. Conventional thermal gas detectors have been employed in the form of relatively small pellistors 2 . Pellistors are solid-state devices used to detect gases that are either combustible or exhibit significantly different thermal conductivity relative to air.
Along with the development of MEMS technology, microhotplates were developed to operate at lower power and are based on a similar principal as pellistors. Zanini et al. 3 fabricated a calorimetric microhotplate sensor using silicon micromachining techniques. The device output was found to be proportional to the concentration of combustible gas, in this case hydrogen and propylene. The smaller size of these micro-plates allowed them to reach operating temperatures as high as 500°C in approximately 20 ms at a power level of 100 mW. An electric circuit consisting of a Wheatstone bridge with two external resistors and a reference sensor was used to measure the steady-state resistance of the microhotplate.
Suehle et al. 4,5 developed the first monolithic tin oxide gas sensor hotplate by commercial CMOS foundry fabrication. A response time of 200 s was observed for hydrogen detection and the device could achieve a temperature of 350°C at 45 mW. Later Elmi et al. 6 developed smaller metal oxide microhotplates (50-120 µm in diameter) for detection of volatile organic compounds (VOCs). The sensors required 8.9 mW for detection. Decarli et al. 7 integrated a technique for the controlled deposition of nanostructured metal oxide films with MEMS-based microfabrication technologies to fabricate microhotplate gas sensors with tungsten and iron oxides. These metal oxide technologies exhibited a slow response time of several minutes.
Micro-thermal conductivity detector (µTCD) gas sensors, unlike calorimetric or metal oxide gas sensors, are based on changes in the thermo-physical properties of the surrounding gas and do not rely on gas adsorption and reaction with a catalyst or thin films. Therefore, measurements can be taken more rapidly and the sensor can be operated in a continuous manner and repeatedly used without memory effects. Puente et al. 8 demonstrated a thermal conductivity micro-sensor for measurement and analysis of natural gas composition. Miniature thermal conductivity gas sensors have been developed as detectors for gas chromatography (GC) systems in which very fast response is required for the detector. Cruz et al. 9 fabricated a µTCD for this purpose. The design included a platinum heater resting on a silicon nitride membrane. The total size of the membrane structure was larger than 0.5 mm and the sensors consumed approximately 1 W power at typical GC flow rates. To improve sensitivity, four TCDs in a Wheatstone bridge arrangement were exposed to the reference flow, and column effluent and samples of output voltage were taken under a DC input voltage.
Because electro-thermal sensors rely on heat transfer as the sensing mechanism, some researchers have explored the nature of the thermal phenomena through modeling and simulations. The efforts include thermal modeling of microheater gas flow sensors 10,11 and electrothermal simulation of µTCD for geometry optimization 9 . However, previous works relied on significant simplifications in handling the complexity of physics and geometry.
Despite advancements in the fabrication of µTCDs and efforts to make them smaller, the methods of measurement are relatively undeveloped and reported investigation of TCDs has been based on steady-state readings from a conventional Wheatstone bridge with DC excitation. The frequency method of 3ω (3 omega) and time domain thermo-reflectance (TDTR) have been used in other applications for measuring thermal conductivity in solids, and transient hot wires (THW) have been studied in some fluid samples 12,13 . Relatively large geometries used in these studies involve long settling times, losses, complex 3D isotherms, natural convection effects, and radiation. Moreover, a frequency analysis method requires a lock-in amplifier and therefore relatively longer acquisition time. In the present work, a detection method based on transient thermal response was developed for detection of gas mixtures on a microfabricated ultra-low-power microbridge TCD fabricated from polysilicon. A test bed and associated experiments were designed to evaluate the power consumption and speed of this technique compared with conventional steady-state measurements. To provide more insights into transient phenomena and predict µTCD behavior, an accurate multiphysics model was developed that is capable of simulating transient response of the sensor in a gas medium with minimal simplification. The developed technology is especially suitable for emerging ultra-portable and wireless gas analyzers in the internet-of-things era in which power consumption and footprint are critical criteria.
TRANSIENT THERMAL ANALYSIS OF MICRO-ELECTROTHERMAL GAS SENSOR Figure 1 presents schematics of heat transfer components from the microbridge TCD. It has been shown that in the absence of forced convection and at temperatures of a few hundred degrees above ambient, the effects of radiation and natural convection from a µTCD are negligible 14 ; as a result, conduction via gas medium is the dominant heat loss mechanism. Because of the high aspect ratio of the microbridge (on the order of 100:1), conduction along the bridge to the substrate, q 3 , is smaller than conduction through the surrounding gas, q 1 and q 2 . Additionally, conduction from below the microbridge, q 2 , is expected to be larger than conduction from the top, q 1 , because of the small gap between the microbridge and the relatively cool substrate. The overall major heat transfer from the bridge, q 1 + q 2 , is a function of the thermal properties of the gas mixture. The small-mass microbridge is suspended in low-thermal-conductivity gases that make it capable of reaching high temperatures at very low power levels of few microwatts.
Even though the complex three-dimensional geometry of the microbridge makes it difficult to obtain an exact analytical solution of thermal phenomena, a lumped system analysis 15 can describe the relationship between sensor response, gas properties, and the applied power.
The lumped system method includes the assumption that temperature variations within an object can be neglected in thermal analyses whenever heat conduction within an object is much faster than heat transfer across the boundary of the object. This is a reasonable assumption for this case as the thermal conductivity of the silicon microbridge is three orders of magnitude larger than that of the surrounding gas medium. Therefore, spatial temperature variations within the object can be neglected in thermal analyses, although the average temperature of the microbridge used for lumped analysis can still vary over time.
At steady state, consideration of the energy balance implies that the rate of heat transfer from a lumped solid object is equal to the rate of heat generation within the object. For a high aspect ratio microbridge this can be written as: whereQ is the rate of heat generation in the microbridge, k f is the thermal conductivity of surrounding fluid, A is the surface area of the bridge, and dT f dy j wall is the temperature gradient of the gas medium at the external surface of the bridge. Inserting the temperature of the microbridge, the ambient temperature T ∞ and a characteristic length of conduction, L, we can write: The left-hand side of Equation (1) represents the dissipated electrical power I 2 R, where I is the electric current and R is the resistance. For doped silicon, the temperature dependence of resistance can be described with a linear model as: Transient thermal response of µTCD for gas sensing A Mahdavifar et al where R 0 is the resistance of the conductor at reference temperature T ref and α is the resistivity temperature coefficient. For easier analysis, let us choose T ref = T ∞ and then substitute Qi n Equation (1) by electrical power dissipation; then: As Equation (3) describes, the temperature (and therefore the resistance) of the microbridge sensor at steady-state operation is related to the thermal conductivity of the gas medium at a certain input power. The left-hand side of the equation describes the electrical phenomena and first-order dependency on the temperature; the right-hand side represents conduction heat loss and is proportional to the average temperature of the microbridge. From this equation, the temperature change in the microbridge can be obtained as: At steady state, therefore, the inverse of the average temperature change of the microbridge is proportional to the effective thermal conductivity of the surrounding gas. In a transient state (i.e., shortly after an electrical current step is applied to the sensor), the microbridge temperature rises from T ∞ to the hot steady-state operating temperature. By adding the transient term, Equation (3) is extended to: where ρ is the density of the microbridge that serves as the dominant thermal mass in the system. The time-resolved temperature solution is obtained from Equation (5) as: where τ is the time constant of heating and is defined as: This analysis indicates that the time constant of heating is inversely proportional to the gas mixture thermal conductivity and the input power. The term ρVC p represents the total thermal capacitance of the system and consists of two parts: that thermal mass of the solid material ρ s V s C s and the thermal mass of gas medium ρ g V g C g . However, it is estimated that the thermal mass of the solid bridge is much larger than that of its surrounding gas.
The parameter k f is the effective thermal conductivity of the gas medium that is responsible for most of the heat lost from the bridge. A portion of the heat is conducted along the bridge to the solid substrate; as a result, the thermal conductivity of solid, k s , plays a role. In analogy to electric circuits, Figure 2 presents a thermal circuit model for the microbridge sensor as a lumped system and provides insight on how the properties of solids and gases can affect sensor response. The resistors represent the thermal resistance of the gas and solid material and the capacitors represent the thermal capacitance of the system.

MATERIALS AND METHODS
Ultra-low power, superior sensitivity, and rapid response of the present sensor system were achieved through our newly developed µTCD. It consists of a 100-µm long microbridge fabricated from a 1Â2 µm doped polysilicon layer and suspended using a silicon dioxide sacrificial layer. As shown in Figure 3a, the bridge is passivated with a relatively thin 200-nm silicon nitride layer to provide electrical isolation and protect the bridge against any reactions at hot temperatures. Doped polysilicon resistance changes at a relatively large rate with temperature and the average temperature of the bridge can be correlated to its resistance. The fabrication process for this microbridge (i.e., the smallest polysilicon TCD) was described in our previous work 14 (see also Supplementary Figure S1). Figure 3b presents a scanning electron microscope image of a fabricated microbridge. Half of the microbridge at its center is fabricated to be narrower to locate more of the resistance and the generated heat at the center and away from the solid anchors.
Electrical characterization of the sensor was performed to determine base resistance R 0 and temperature coefficient of resistance α, for modeling and experiments. The sensor was placed in a temperature-controlled oven and subjected to a series of uniform steady temperatures up to 70°C. For the microbridge in this study, a TCR of α = 0.00131/°C and a base resistance of R 0 = 3084 Ω at 23°C were measured. Figure 2 Thermal circuit for the microbridge sensor as a lumped system; subscript "s" indicates solid material properties and "g" corresponds to surrounding gas properties. For the experimental studies, a flow system was designed that was capable of accurately subjecting the sensor to the target concentrations of gas mixtures. Ambient air is composed of 79% nitrogen and its thermo-physical properties are very similar to nitrogen. Therefore, nitrogen was selected as the carrier gas for our experiments in controlled lab conditions. Each specific target concentration of an analyte was achieved by mixing the flow from a bottle of premixed 5% analyte in nitrogen with the flow from a pure nitrogen bottle as shown in Figure 4a. By adjusting the flows through two precise mass flow controllers (Alicat Scientific), analyte concentration can be controlled between 0% to 5%. The sensor was installed in a small glass container connected to the gas flow tubing and was placed inside an insulated oven to provide temperature stability and eliminate room temperature fluctuations. Before each measurement the sensor container was flushed with the desired gas mixture for 5 minutes. The total volumetric flow rate of 500 standard cubic centimeters per minute (sccm) was maintained during data collection to ensure that the mixture of gas did not change over time. Mixtures of helium, methane, carbon dioxide, and argon in nitrogen were tested.
For data acquisition, 16-bit analog-to-digital and digital-toanalog converters (National Instrument PCIe-6351, National Instruments, Austin, TX, USA) at a high sampling rate of 1 MS s −1 were employed. Serving as an interface between PC and the circuit interface, they were capable of generating waveforms for pulsed excitation of the sensor while simultaneously reading the analog output from the measurement system. A circuit interface was designed to apply pulses of constant current across the sensor and translate sensor resistance into an output voltage measurable by the data acquisition card. Conventionally, a Wheatstone bridge is employed for such MEMS sensors; however, it cannot maintain a constant current nor voltage over the sensor and therefore expresses nonlinear output at an extended range of measurements. Figure 4b shows a schematic of the circuit interface consisting of a reference resistor (R r = 4 kΩ), two other auxiliary resistors (R 1 = 300 Ω), and an op-amp (Linear LT1028, Linear Technology, Milpitas, CA, USA). By changing the output voltage, V o , the op-amp pulls a constant current through the sensor equal to the current passing through the reference resistor for a given input voltage of V i . Therefore, the sensor resistance R s can be obtained from Equation (8) as: When no electric current is applied, the microbridge rests at an ambient temperature and its resistance is at a minimum; this is referred to as a cold state and its corresponding resistance is referred to as a base resistance or cold resistance, R 0 . The circuit can measure the base resistance by applying approximately 100 µA current and recording the corresponding V o . During hot operation, V o switches to a predefined high value and the microbridge temperature and its resistance increases; this state and the corresponding resistance are referred to as the hot state and hot resistance in this study. Initial evaluations indicated that a continuous direct current at the hot state causes drifts in both the hot and cold resistance values of the sensor over time in a reversible manner. The drift indicates that the dissipated heat from DC excitation at the operating levels heats the sensor chip. To avoid this drift and more importantly obtain transient response of the sensor, square pulses were used instead of DC current (see Supplementary Figure S2 for sample of pulse train and output signals). Because the thermal mass of the microbridge is very low, it can reach steady-state hot temperature in less than 2 ms and provide one measurement sample. Experiments showed that a 50 Hz pulse with a duty cycle of 10% can prevent drift while providing 50 measurements per second, fast enough even for applications such as GC.
Although the average microbridge temperature can be calculated from its changing resistance, the temperature distributed over the bridge is not uniform. To obtain further insights into the heat transfer phenomena, reveal the temperature distribution and predictability of sensor time resolved response, a model of the microbridge was simulated in COMSOL 4.4 (COMSOL, Stockholm, Sweden). A detailed geometry of the composite bridge, obtained from scanning electron microscopy images, was used as a basis for the simulation. The model was meshed with 500,000 tetrahedral grid points that are fine (i.e., approximately 0.04 µm) at the bridge and smoothly get larger close to the outer boundaries where gradients vanish. Previously we have simulated flow and mass transfer phenomena using the open source tool OpenFOAM 16 ; however, for the complex multiphysics and composite geometry of this problem, the more sophisticated software COMSOL was employed. Both solid materials and surrounding gas are included in the computational domain; therefore, no assumption and simplification was employed for thermal interaction between gas and solid surfaces. The computational domain is large and extended at least 200 µm from the bridge in each direction. In this method, the only thermal condition required on the domain outer boundaries is constant room temperature. As a wide range of temperatures are involved, properties of solids and gas are temperature-dependent and are taken into the account for further accuracy. Electrical and heat transfer physics are coupled in the model; the input current is provided as a boundary condition and the model handles heat generation, heat transfer, and resistance calculations simultaneously. Our previous simulation method 14 was developed further in this work to carry out a transient simulation with room temperature as the initial condition. Figure 5 presents the calculated steady-state temperature field under nitrogen at a power of I 2 R 0 = 1.5 mW. The maximum local temperature occurs at the center of the microbridge and can reach 494 K, whereas the anchors remain at approximately substrate room temperature. The simulation results also verify that maximum local temperatures at the applied power is safe for sensor operation. Figure 6 presents a close look at the resistance change of the microbridge in nitrogen in response to a square current pulse of 0.7 mA and 2 ms width. The first few hundred microseconds of the response corresponds to the transient heating; this part is ignored in the steady-state measurements. Instead, the steady-state regime (in this case, the second millisecond of hot operation) is used for conventional operation.

RESULTS
In this work we studied both transient and steady-state regimes for comparison. According to our lumped system analysis, described in the previous section, it is expected that the microbridge resistance (i.e., its average temperature) behaves exponentially during a heating as Equation (9): where R 0 is the base resistance, R 2 is the hot resistance, t is time, and τ is the time constant of the transient signal (i.e., the time required to achieve 63.2% of the total resistance change). The time constant τ was obtained from experimental and simulation results by fitting an exponential curve using the least-squares method. Figure 7 presents steady-state and transient microbridge response in pure nitrogen at three different power levels I 2 R 0 , where I is the high current value corresponding to the square excitation pulse train. As expected from our heat transfer analysis, 1/τ varies linearly with power, whereas 1/ΔR has an inverse relation with power. Both resistance change and τ are increased at higher powers and therefore the sensor can provide a better sensitivity at higher powers. However, for currents over 0.7 mA the sensor shows instabilities because of very high local temperatures; in practice, therefore, there is a limit to the input power. The trend of data coincides with the thermal analysis and suggests that at the lower end, as power approaches zero, ΔR approaches zero as well when τ is approaching a constant value.
Further experiments were conducted with gas mixtures at the higher power level of 1.5 mW. Figure 8 shows how the sensor responded to a change in concentration. A square current pulse of 50 Hz with a duty cycle of 10% (2 ms width) excited the microbridge. The transient time constant was extracted from the first 300 µs of the output pulse; simultaneously, the steady-state resistance change was calculated from the last 1 ms. The results    excitation pulse train. Considering that a 50 Hz pulse train with 10% duty cycle was applied for excitation in this method and bringing the sensor resistance change into account, the sensor actual power consumption was approximately 180 nW (3.6 nJ per single measurement), which is the lowest reported power management on a TCD so far. Efficient measurements do not arise from device design and microfabrication alone but also require the development of improved measurement methods and noise management. The lower power required in this method of operating this µTCD measurement system allows its integration into ultra-portable or wearable sensing devices. In addition, evolving miniature gas analyzer technologies such as micro-GC systems 17,18 demand the integration of highly efficient and fast micro-detectors, which could be another potential application for this technology.