On-Chip Temperature Compensation for Thermal Impedance Sensors ^†

Abstract

Electrical impedance spectroscopy is a widespread characterization method for solids or fluids in industrial applications. We here report on its thermal equivalent, the “thermal impedance spectroscopy”, improved by using a temperature compensation method for temperature dependent thermal measurements using an on-chip reference resistor.

1. Introduction

The electrical impedance spectroscopy uses a frequency dependent system response to a AC voltage signal and is determined by the electrical conductivity, capacity and inductivity of an analyte material. We measure in addition the frequency dependent thermal system response of a thermal excitation that depends basically on the thermal conductivity and heat capacity, using an adaption of the well-known 3-omega method [2].

2. Experimental

Here, an alternating current I₀ of frequency ω is applied to a resistive heater with resistance R_Bol, causing temperature oscillations T and thus a modulation of the temperature dependent heater resistance with the double frequency 2ω. This results in a 3ω part V_3ω of the measured heater voltage spectrum that can easily be separated and from that the amplitude of the temperature oscillation ΔT can be determined from:

V_3ω = 0.5 ΔT αR R_Bol I₀

where α_R is the temperature coefficient of the heater material [2]. The amplitudes ΔT get higher with lower thermal conductivity of the analyte since the thermal heating power R_BolI² needs a higher temperature difference ΔT for dissipation into the analyte.

Typically, the 3ω voltage is a factor of thousand smaller than the heater voltage with frequency ω. In order to get a better signal to noise ratio SNR, there are methods to subtract the one omega heater voltage. Figure 1 shows a possible evaluation circuit. The same AC current I₀ that drives the heater R_Bol flows through a reference resistor R_Ref connected in series. The bolometer voltage is amplified with gain G₁. In addition, the voltage of the reference resistor is amplified with gain G₂ and the two voltages are subtracted at amplifier 3.

Here it is important, that a temperature modulation only affects the heater but not the reference resistance. This can be done by using a reference resistor with negligible temperature dependence, for example constantan. Then, the gain factors can be adjusted to compensate widely the 1ω heater-voltage, leaving the 3ω voltage at a higher SNR or even enables a direct analogous measurement of the 3ω voltage. Often the reference resistor is integrated in the evaluation circuit board but this might be disadvantageous. For example, a change in the heater baseline temperature changes the resistance baseline due to the temperature dependency of the heater material and therefor the gain factors. That causes a signal drift unless the reference resistance is not adjusted at every temperature. To overcome this temperature drift, a reference resistor with the same temperature and temperature coefficient as the heater material is needed. We therefore used a reference resistor structure of the same material as the heater and placed it on the sensor chip. The temperature modulation in the reference R_Ref was avoided by using a much lower resistance value (for example with factor 20) so that the temperature modulation of the reference resistor is negligible.

The results presented were obtained within a current development of a small electronic tongue system consisting of partially insulated gold electrodes on a polymer substrate (Figure 2). Besides interdigital capacitors (IDC) for the measurement of electric impedances, there are a linear heater structure R_Bol and a reference resistor R_Ref on the chip that both are driven by the same AC heater current I₀. Here the heater structure R_Bol consists of a structured metal strip of gold (3700 µm long, 20 µm wide and 0.2 µm thick). The reference resistor R_Ref consists of 8 shorter metal strips (1470 µm long, 20 µm wide, 0.2 µm thick) connected in parallel, it is lower by a factor of about 20. If the gain ratio of G₁/G₂ = R_Ref/R_Bol, most of the 1ω part of the bolometer voltage is subtracted, the 3ω-part is passing amplifier 3 with a high signal to noise ratio. If the temperature of the analyte changes, both resistor structures change in resistance so the gain ratio inherently keeps constant and a temperature induced change of R_Bol is compensated automatically.

3. Results

If the resistivity of the reference is low enough, its heating power and thus the temperature modulation is insignificant and no 3ω -signal occurs. As an example, in Figure 3, the signal changes in water of a compensated configuration as described above (green) and an uncompensated measurement using a constant external reference resistor fixed at 20 °C (red) is shown over temperature.

The expected signal change due to the temperature dependent change of the water properties is shown as blue crosses. Here the sensor signal was simulated with a COMSOL model of the sensor with the temperature dependent properties of water. The uncompensated method shows strong deviations at higher temperatures. The measurement of the thermal impedance is a reasonable extension to electrical impedance measurements. Currently, such thermal-electric impedance spectroscopy measurements are tested for process and quality control in fluids [1].