Gy. Bognár1, P. Fürjes2, V. Székely1, M. Rencz3

TRANSIENT THERMAL CHARACTERISATION OF HOT

PLATES

&of MEMS MOEMS

200

4

3MicReD Ltd., Budapest, Hungary

1BUTE, Budapest, Hungary

2KFKI-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)• 100m x 100m x 1m• Encapsulated by reduced

stress silicon rich silicon-nitride (LPCVD)

• Selective dissolution ofelectrochemically formedporous silicon (60-80m)

• Mechanical support under the hotplate

100m

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)

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 simulation results were verified by thermal transient measurements using the T3Ster equipment and related analysis software

The model:

The simulationTransient result

Time evaluation of temperature is not to scale

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

The simulationTransient result

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

Max. temperature elevation is 227oC @ 8.5mW

The simulationSteady-state result (figure is not to scale)

Steady-state resultThe 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:

Idrive Isense

DUT

Umeas ~ T

Force: Sense:

Verification by measurements

Simulated8.5mW

Measured8.5mW

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 ms1.10 ms

time [s]

Tem

pera

ture

[C

]

Simulated8.5mW

Measured8.5mW

Measured6.5mW

(with support)

Verification by measurements

Verification by measurements

Simulated woMeasured 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

n

iiRR

1

n

iiCC

1

• 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:

n

iiRR

1

n

iiCC

1

ambi

ent

heater

Structure functions

Structure functions

Agrees well with the volume calculated from exact geometry

hotplate

27000 K/W40 nWs/K

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

27000 K/W40 nWs/K

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

• 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 (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

0

100

200

300

400

500

600

700

800

0 10 20 30

Power loss [mW]

Tem

per

atur

e [o

C]

calculated

measured

• Surface temperature was measured by resistance calibration technique

• Rth26.5K/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

Measuredwithout support

Measuredwith support

Frequency domain behavior derived from measured transient curves