Transcript Structure functions

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)
100m x 100m x 1m
Encapsulated by reduced
stress silicon rich
Mechanical support
silicon-nitride (LPCVD)
• Selective dissolution of
electrochemically formed
porous silicon (60-80m)
• 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)
100-600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 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
• Rth26.5K/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