Structure functions
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2004 of MEMS& MOEMS TRANSIENT THERMAL CHARACTERISATION OF HOT PLATES Gy. Bognár1, P. Fürjes2, V. Székely1, M. Rencz3 1BUTE, Budapest, Hungary 2KFKI-MFA Research Institute for Technical Physics and Materials Science, Hungary 3MicReD Ltd., Budapest, Hungary The physical structure to be characterised thermally: an integrated gas sensor • • • • Thermally isolated heater and sensing resistor filament (Pt) 100m x 100m x 1m Encapsulated by reduced stress silicon rich Mechanical support silicon-nitride (LPCVD) • Selective dissolution of electrochemically formed porous silicon (60-80m) • Mechanical support under the hotplate 100 m Thermal operation needs thermal characterisation Reasons of thermal characterisation • To check the maximal operation speed of the sensor device (strongly influenced by the thermal isolation of the membrane structure) • To check how to reach maximal temperature elevation with minimal heating power (e.g.: for explosion-proof detection of combustible gases) 100-600C achieved with 10-25mW • To detect the differences in the thermal behaviour of hotplates with and without mechanical support Outline • Presentation of the following studies: – Simulation: • Structure without mechanical support: steady-state, transient – Measurement – thermal transient • Structure with mechanical support • Structure without mechanical support • Comparison by means of – Time-constant spectra – Structure functions – Simple compact model created • Conclusions The simulation • Simulated by the SUNRED program (without mechanical support) • FD model, solved by SUccessive Network REDuction The model: The simulation results were verified by thermal transient measurements using the T3Ster equipment and related analysis software The simulation Transient result The 1µs .. 1s time range was covered on a logarithmic time-scale Time evaluation of temperature is not to scale The simulation Transient result The 1µs .. 1s time range was covered on a logarithmic time-scale The simulation Steady-state result (figure is not to scale) Max. temperature elevation is 227oC @ 8.5mW The simulation Steady-state result Uniform temperature distribution on the hotplate Verification by measurements • The resistor of the hotplate was used both as a heater and a temperature sensor – Sensitivity of the sensor was identified by a calibration process • The thermal response was recorded by T3Ster using the 4 wire method: Force: Idrive Sense: Isense Umeas ~ T DUT Verification by measurements Structure without mechanical support Measured 8.5mW Simulated 8.5mW Steady state values agree well Verification by measurements Structure without mechanical support Measured Simulated 1.10 ms 2.24 ms The dominant time constants are in a good agreement Verification by measurements Measured 8.5mW Temperature [C] Simulated 8.5mW Measured 6.5mW (with support) time [s] Verification by measurements Measured w Measured wo Simulated wo The dominant time constant is only slightly influenced by the mechanical support Structure functions • Foster type network model of the structure is constructed from the time constant spectra • Equivalent Cauer type network model corresponds to the real physical structure Structure functions • The discrete RC model network in the Cauer canonic form now corresponds to the physical structure, but • it is very hard to interpret its “meaning” • Its graphical representation helps: • This is called cumulative structure function n C Ci i 1 n R Ri i 1 Structure functions The cumulative structure function is the map of the heat-conduction path: n C Ci ambient i 1 n R Ri i 1 heater Structure functions hotplate 40 nWs/K 27000 K/W Agrees well with the volume calculated from exact geometry Structure functions • The thermal capacitance ~ 40 nWs/K • The thermal resistance ~ 27000 K/W • The structure has only one dominant time constant • The simplified thermal model constructed hotplate 40 nWs/K 27000 K/W Summary of transient characterisation Power level Thermal resistance Thermal capacitance Time constant measured w support 8.5mW 27000 K/W 40 nWs/K 1.10ms measured wo support 6.5mW 26000 K/W 40 nWs/K 1.12ms simulated wo support 8.5mW 30000 K/W 40 nWs/K 2.24ms Identified from the structure functions Summary of transient characterisation • The structures can be represented by one dominant time constant ( ~ 1.1ms) • The time constants of the two structures are nearly the same • The pillar support has small thermal capacitance and high resistance, so it hardly influences the thermal behavior of the hotplate Summary • The response time of the heater was investigated by time constant analysis, and the single dominant time constant of the structure was found in the range of milliseconds • We identified and generated a reduced order (compact) thermal model of the structure • The thermal properties (Rth, Cth, ) of the structures with and without support were nearly identical • Consequently the dynamic behaviour was not deteriorated significantly by the mechanical support Acknowledgment This work was partially supported by the • OTKA T033094 project of the Hungarian National Research Fund • INFOTERM NKFP 2/018/2001 project of the Hungarian Government and the • SAFEGAS and the REASON FW5 Projects of the EU Measurements: temperature calibration • Surface temperature was 700 600 measured by 500 resistance 400 calibration 300 200 technique calculated 100 measured • Rth26.5K/mW 0 0 10 20 30 (with mechanical Power loss [mW] support) • heat conduction in the suspending beams, • conduction and convection in the surrounding gas, • radiation from the hot surfaces Temperature [oC] 800 Frequency domain behavior derived from measured transient curves • The complex loci – Nyquist diagram – was calculated from the measured thermal impedance curves • Slight transfer effect can be observed that is due to the heat transfer between different sections of the heating meander Frequency domain behavior derived from measured transient curves Measured with support Measured without support
