System-level modeling with temperature compensation for a CMOS-MEMS monolithic calorimetric flow sensing SoC

Abstract

We present a system-level model with an on-chip temperature compensation technique for a CMOS-MEMS monolithic calorimetric flow sensing SoC. The model encompasses mechanical, thermal, and electrical domains to facilitate the co-design of a MEMS sensor and CMOS interface circuits on the EDA platform. The compensation strategy is implemented on-chip with a variable temperature difference heating circuit. Results show that the linear programming for the low-temperature drift in the SoC output is characterized by a compensation resistor R_c with a resistance value of 748.21 Ω and a temperature coefficient of resistance of 3.037 × 10^-3 °C^-1 at 25 °C. Experimental validation demonstrates that within an ambient temperature range of 0-50 °C and a flow range of 0-10 m/s, the temperature drift of the sensor is reduced to ±1.6%, as compared to ±8.9% observed in a counterpart with the constant temperature difference circuit. Therefore, this on-chip temperature-compensated CMOS-MEMS flow sensing SoC is promising for low-cost sensing applications such as respiratory monitoring and smart energy-efficient buildings.

Fig. 1. Design and system-level modeling of the CMOS-MEMS thermal flow sensing SoC.

a Schematic of a monolithically integrated thermal flow sensing SoC based on the 0.18 μm 1P6M CMOS-MEMS technology. b System-level model of the flow sensing SoC, where the resistance and TCR of the resistor R_c will be delicately optimized to achieve on-chip temperature compensation

Fig. 2. Sensor interface circuit and its performance.

a Block diagram of the implemented folded-cascode operational amplifier (OPA) with a PMOS buffer for large driving current. b The OPA provides an output current drive capability of 1.93 mA for the VTD control circuit with a 1.5 kΩ load, allowing it to deliver a maximum power of 3.1 mW to the microheater, which exceeds the microheater’s maximum required power of 1 mW. c Block diagram of the implemented low-noise current feedback instrument amplifier (CFIA). d The simulated linear output swing of the proposed CFIA is ±1.44 V, and the pink area indicates that the amplified signal is saturated and distorted

Fig. 3. Structural design and performance analysis of the MEMS flow sensor.

a 3-D structural view of a MEMS calorimetric flow sensor, which consists of a central microheater and two pairs of thermistors arranged symmetrically. b A-A′ cross-section of the MEMS sensor with critical structural parameters: 2l_c = 1500 μm, 2l_ca = 200 μm, 2w_h = 31 μm, D_hs = 13 μm, H_ca = 50 μm, and t_f = 2.52 μm. c Distorted temperature profile around the microheater at an input gas flow velocity of 10 m/s. d Comparison of the sensor’s output between 1-D thermal model and CFD model at the ambient temperature T_a of 25 °C, and the fitting factor is ε = 2.56. e Comparison of the microheater power between theoretical and CFD models, where the calculated values are: A = 1.458 × 10⁻⁵ and B = 1.469 × 10⁻⁶. Note, the overheated temperature of the microheater ΔT_h is set at 50 °C in these models

Fig. 4. Simulated overheated temperature ΔT_h and system output V_out of the flow sensing SoC in the CTD mode under different ambient temperatures.

a ΔT_h remains almost constant for the sensor in the CTD mode; b V_out in the CTD mode (±7.9% at 9 m/s). Note that the system-level model is verified using the CFD results with the CFIA readout circuit at 0 °C, 25 °C, and 50 °C

Fig. 5. The determined ΔT_h of the microheater by Eq. (1) and compared to system-level model results.

a T_a = 0 °C, b T_a = 25 °C, c T_a = 50 °C. Note that the maximum error between the mathematical formula and the system-level model is less than 0.175 °C

Fig. 6. Optimization and simulation of temperature-compensated interface circuit.

a Linear programming (LP) range of the resistor R_c based on the on-chip temperature compensation of the system output, where red indicates overcompensation, and blue indicates undercompensation. Note that the compensation resistor is set at a resistance of R_c0 = 748.21 Ω with a TCR of α_c = 3.037 × 10⁻³ °C⁻¹ at 25 °C. b, c Simulated overheated temperature ΔT_h and system output V_out of the flow sensing SoC in the VTD mode under different ambient temperatures: b ΔT_h of the microheater in the VTD mode (ΔT_h with PTC); c V_out in the VTD mode (±0.6% at 10 m/s)

Fig. 7. Fabrication and experimental setup of the flow sensing SoC.

a Fabrication process of the proposed calorimetric flow sensing SoC. b Experimental setup for the calorimetric flow sensing SoC with nitrogen gas flow. c Experimental configuration in the temperature chamber, system-packaged PCB with a 3D printed flow channel, and microscopic image of the fabricated monolithic calorimetric flow sensing SoC

Fig. 8. Comparison of the overheated temperature ΔT_h and system output V_out of the flow sensing SoC in CTD and VTD modes under different ambient temperatures.

a ΔT_h remains almost constant for the sensor in the CTD mode; b V_out in the CTD mode (±8.9% at 9 m/s); c ΔT_h of the microheater in the VTD mode (ΔT_h with PTC); d V_out in the VTD mode (±1.6% at 10 m/s)