Gy. Bognár 1, P. Fürjes 2, V. Székely 1, M. Rencz 3 TRANSIENT THERMAL CHARACTERISATION OF HOT PLATES &of MEMS MOEMS MicReD Ltd., Budapest, Hungary 1 BUTE, Budapest, Hungary 2 KFKI-MFA Research Institute for Technical Physics and Materials Science, Hungary

The physical structure to be characterised thermally: an integrated gas sensor Thermally isolated heater and sensing resistor filament (Pt) 100  m x 100  m x 1  m Encapsulated by reduced stress silicon rich silicon-nitride (LPCVD) Selective dissolution of electrochemically formed porous silicon (60-80  m) Mechanical support under the hotplate 100  m Mechanical support 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)  C 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 simulation results were verified by thermal transient measurements using the T3Ster equipment and related analysis software The model:

The simulation Transient result Time evaluation of temperature is not to scale The 1µs.. 1s time range was covered on a logarithmic time-scale

The simulation Transient result The 1µs.. 1s time range was covered on a logarithmic time-scale

Max. temperature elevation is 227 o 8.5mW The simulation Steady-state result (figure is not to scale)

Steady-state result The simulation 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: I drive I sense DUT U meas ~ T Force:Sense:

Verification by measurements Simulated 8.5mW Measured 8.5mW Structure without mechanical support Steady state values agree well

Verification by measurements Simulated Measured Structure without mechanical support The dominant time constants are in a good agreement 2.24 ms 1.10 ms

time [s] Temperature [  C] Simulated 8.5mW Measured 8.5mW Measured 6.5mW (with support) Verification by measurements

Simulated wo Measured w Measured wo The dominant time constant is only slightly influenced by the mechanical support

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 This is called cumulative structure function it is very hard to interpret its “meaning” Its graphical representation helps: Structure functions

The cumulative structure function is the map of the heat-conduction path: ambient heater Structure functions

Agrees well with the volume calculated from exact geometry hotplate K/W 40 nWs/K

Structure functions The thermal capacitance ~ 40 nWs/K The thermal resistance ~ K/W The structure has only one dominant time constant The simplified thermal model constructed hotplate K/W 40 nWs/K

Summary of transient characterisation Power level Thermal resistance Thermal capacitance Time constant measured w support8.5mW27000 K/W40 nWs/K1.10ms measured wo support6.5mW26000 K/W40 nWs/K1.12ms simulated wo support8.5mW30000 K/W40 nWs/K2.24ms Identified from the structure functions

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 of transient characterisation

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 (R th, C th,  ) 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 T 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 measured by resistance calibration technique R th  26.5K/mW (with mechanical support) heat conduction in the suspending beams, conduction and convection in the surrounding gas, radiation from the hot surfaces

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 without support Measured with support Frequency domain behavior derived from measured transient curves