HEAT TRANSFER IN SILICON MICROHOTPLATE STRUCTURES ????????? ?????? ????????????? ? ?????????? ?????-?????????????? ??????????

1
HEAT TRANSFER IN SILICON MICROHOTPLATE
STRUCTURES????????? ?????? ????????????? ?
?????????? ?????-?????????????? ??????????
S. B. Beale R. Djebbar M. Post S.V. Zhubrin
B. Delesalle Heat/mass transfer MIF-2000
??????????????? - ???-2000

Institute for Chemical Process and Environmental
Technology???????? ??????????? ???????? ?
?????????? ?????????? ?????
2
Introduction????????

• Microhotplate (MHP) structures are subject of a
  four year NRC/industry/university collaborative
  research project??? ?????-??????????????
  ????????? ???????? ???????? ?????????????,
  NRC/INDUSTRY/UNIVERSITY, ??????????
  ??????-????????????????? ??????
• Fabricated using a CMOS process???????????????
  ? ?????????????? ???????? CMOS
• Typical size 200x200x5 mm???????? ??????
  200x200x5 ??????
• Operating temperature is around
  500ºC???????????? ??????????? - ????? 500º C

3
Schematic of MHP structure??????? ???????
????????? MHC
Supporting beams ?????
4
CMOS Process CMOS ???????
Platinum ???????
Si3N4
SiO2
SiO2
SiO2
SiO2
Polysilicon ???????????
SiO2
Elevation
5
Array of MHP structures????????? ???
Plan
6
Single MHP structure????????? ???
Plan
7
Background?????????? ??????

• Two designs considered Mark 1 and Mark
  2??????????? ??? ??????????? MHC 1 ? MHC 2
• Temperature on target surface to be within 10
  ºC.??????????? ??????? ??????????? ?? ???? 10
  ºC
• Temperature in surrounding silicon should not be
  too hot as it will damage signal processing
  circuitry??????????? ??????? ?? ?????? ????????
  ??????????? ???????

8
Background ?????????? ??????

• Experimental work on local temperature
  distribution difficult, due to micro-geometry,
  variable optical properties?????-???????
  ????????? ????????????
• Therefore embarked on a program of numerical heat
  transfer analysis???????, ?????????? ?????????
  ?????? ?????????????
• Software used PHOENICS multi-block body fitted
  coordinates and Cartesian grids both
  considered?po?pa??a PHOENICS, ?????????????
  BFC ? ?????????? ?????

9
Two layers of mark 1 design??? ???? ??? 1
Target area??????? ???????
Polysilicon heater??????????? ???????????

• Heater
  geometry Platinum contacts
  ????????? ??????????? ?????????? ????????

Plan
10
Two layers of mark 2 design??? ???? ??? 2
Target area??????? ???????
Polysilicon heater??????????? ???????????

• Heater
  geometry Platinum contacts
  ????????? ??????????? ?????????? ????????

Plan
11
Heat conduction?????????????

• Convection and radiation are negligible. Problem
  is a conduction heat transfer problem with
  variable properties????????? ? ????????? ????.
  ?????? ???????????????? ? ??????????? ??????????.
• NB The source term
  was assumed to be a constant volumetric
  term,???????? ?????????????? ?????????? ?
  ??????? ??????,

12
Thermal conductivity ????????????????

• l variations from layer to layer ????????? l
  ?? ?????
• Harmonic averaging used. ??????????????ec?oe
  oc?e?????e
• l variations within layer ????????? l ? ???e
• Large scale structures handled as above with
  multiple values of l.Kpy???e ?????????, ?a? ???e
  , c ??????????? l.

13
Thermal conductivity ????????????????

• Fine scale structures handled using an effective
  valueM????e, ?epe? ???e??????e ?e??????, ?a?
  ?
• approach often used in heat transfer in porous
  media?op?c??x cpe?ax

14
Meshing and boundary conditions????? ? ?????????
???????
Multi-block body-fitted grid????????????? BFC
T20ºC
Air ??????
Cells concentrated within MHP??????,
?????????????????? ? ???????? MHP
Etched cavity ????????????? ???????
Silicon substrate ???????
T20ºC
T20ºC
15
MeshingCartesian grid????? ?????????????
??????????
Air ??????
Cells concentrated within MHP??????,
?????????????????? ? ???????? MHP
16
Use of marker to identify different materials
????????????? ???????, ????? ????????????????
????????? ?????????
Air ??????
Platinum ?????????? ????????
Beams ?????
Polysilicon Heater??????????? ???????????
Silicon ???????
Harmonic averaging used ??????????????ec?oe
oc?e?????e
17
Experimental work????????????????? ??????
Power Supply ???????? ???a???
MHP die MHC ?op?a
Microscope objective O??????? ???poc?o?a

• Black body emission at l875 nm of Mark 1
  prototype measured. Calibration achieved with a
  larger constant-e sample, probed with a
  thermocouple. Imaging resolution 50 mm???epe?o
  ????????? a?co????o ?ep?o?o ?e?a ?p? l875 nm ???
  ?po???a MHC 1 Ka???po??a ?ep?o?apa?? ?oc????y?a
  ??? o?pa??a c ?o?????- e Pa?pe?e??e 50 mm

Infra-red detector ???pa?pac??? ?e?e??op
DIP package ?a?e?
18
Comparison with experimental data????????? ?
?????????????????? ???????

• Numerical data????????e pac?e??U1.71-1.76x
  103W/m2ºCExperimental data????????????????e
  ?????eU1.81-1.89x103W/m2ºC6 difference
  Quite reasonable considering imaging resolution
  only 50 mm for a 250x250 mm sample ???????? 6
  ?????? ?????????? , ???????????? ??????? ??????
  50 mm ??? 250x250 mm ???????

19
Temperature distributionMark 1??????????? ??? 1
20
Temperature distributionMark 2??????????? ??? 2
21
Target area Mark 1??????? ??????? ??? 1
22
Target area Mark 2??????? ??????? ??? 2
23
Grid dependence??????????? ?????
24
Comments???????????

• Mark 1 temperature distribution varies from 223ºC
  to a maximum 463ºC at the centre of target. The
  mean value predicted by the program is 388ºC for
  Q34mW??????????? ??? ??? 1 ????? ? ??e?e?ax o?
  223ºC ?o ?a?c??y?a 463ºC ? ?e??pe. Cpe????
  ?ac???a??a? ??????????? - 388ºC ??? Q34mW.
• Mark 2 temperature is a minimum of 315 ºC, a
  maximum of 430ºC with a mean value of 403ºC.
  However most of the deviation is confined to 4
  hot spots away from the central target area
  (between the platinum contacts). It is much
  better design overall.??????????? ??? ??? 2
  ??ee? ?????y? 315 ºC, ?a?c??y? 430ºC ? cpe??ee
  403ºC.

25
Comments???????????

• O??a?o, ?a?c??a???oe o???o?e??e o?pa???e?o 4-??
  '?op????? ?o??a??' ?a?e?o o? ?e??pa???o? ?????o?
  ???????. ??o ?y??ee c?????? ??????? ?????????
  MHC.
• There does not appear to be much risk of damage
  to the surrounding circuitry, the substrate is
  always at near ambient temperatures, due to the
  high conductivity of silicon and the insulating
  properties of air. P?c? ?o?pe??e??? o?py??????
  ???? ?e?e???, ??????????? cy?c?pa?a ?ce??a o?o?o
  ???????????. o?py?a??e? cpe?? ??-?a ??co?o?
  ???????????????? ??????? ? ??o??py???x c?o?c??
  ?o??yxa.

26
Electrical conduction????????????? ????????????

• Tested premise that the source term per unit
  volume is constant, by computing S using
  ????????, S, ?????????????? ?????????? ?
  ??????? ?????? ? ?ac?????ae???
• The voltage distribution, f, in the heater is
  solved using Laplaces equationHa?p??e??e, f, ?
  ??????????e ?ac?????ae??? ?? ypa??e??? ?a??aca
  

27
Electrical conduction????????????? ????????????
MHP 1 MHC 1
28
Electrical conduction????????????? ????????????
Non-linear voltage due to area changes
MHP 2 MHC 1
Voltage, f, Ha?p??e??e
Source term, S, ???????? ??????????????
29
Discussion??????????

• For the Mark 1 design the potential gradient is
  linear over most of the heater and the source
  term is consistent with the presumed constant
  value??? ??? 1 ??a??e?? ?o?e???a?a ???ee? ?a
  ?o????? ?ac?? ??????????? , ??o co??acye?c? c.
  ??e??o?o?e??e? o ???????c??e ????????a.
• In the bends however, grad f is closely/widely
  spaced at convex/concave boundaries and there are
  large local variations in S, from 90 less to
  170 greater than the presumed values.B c???ax,
  o??a?o, grad f ?e???ee? ????? ?????? ? ????????,
  S, ?? 90 ?e???? ? ?? 170 ?o????, ?e?
  ??e??o?a?ae??e ??a?e???.

30
Discussion??????????

• For the Mark 2 design the potential also varies
  due to changes in the cross-sectional area ???
  ??? 2 ?o?e???a? ?a??e ???e??e?c? ??-?a ???e?e???
  ce?e???

31
Conclusions??????????

• A 3-D thermal analysis and design tool was
  developed to calculate temperature distributions
  in MHP structuresPa???? 3-?ep??? a?a??? ?
  ??c?py?e?? ??? ?ac?e?a ??????????? ? ??????????
  ?????-?????????????? ??????????
• Experimental data agree to within 6 of the
  present calculations????????????????e ?????e
  co??acy??c? c ?ac?e?o? ? ??e?e?ax 6.
• Analysis showed that the heater source term is
  constant only in straight zones of constant
  widthA?a??? ?o?a?a?, ??o ???????? ? ??????????e
  ???????e? ?o???o ? ?p???x ?o?ax ????????o?.
  ???????

32
Conclusions??????????

• Future work will incorporate the non-linear
  source term into the heat transfer?y?y?a? pa?o?a
  pacc?o?p?? ?????e??e ?e???e??o?o ????????o?o?o
  ??e?a ? ?ac?e?. ?????????????
• Thermally-induced stress analysis calculations
  will also be performed?y?y? ???o??e?? ?a??e ?
  ?ac?e?? ?ep???ec??x ?a?p??e???

33
Acknowledgement?????????????

• Project resulted from an exchange program of 5th
  year students from LInstitut Catholique dArts
  et Métiers (France). It is a contribution
  towards an NRC/NSERC/Industry joint research
  project with Concordia University and Armstrong
  Monitoring Corporation
• We should like to thank the following individuals
  for their assistance in the work David Cheeke,
  Leslie Landsberger, Oleg Grudin, Radu Marinescu
  (Concordia), Don Singleton, Simon Fafard,
  Dongfang Yang, Ron Jerome (NRC)