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1 Microelectronics Research and Development Ltd. Budapest XI, Gulyás utca 27, H-1112 Hungary E-mail: [email protected]. 2 Technical University of Budapest, Department of Electron Devices Budapest XI, Goldmann Gy. tér 3, H-1521 Hungary E-mail: @eet.bme.hu. - PowerPoint PPT Presentation
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A method for thermal model generation of MEMS packages
Márta Rencz1 Vladimír Székely2 Zsolt Kohári2 Bernard Courtois3
2Technical University of Budapest, Department of Electron Devices Budapest XI, Goldmann Gy. tér 3, H-1521 Hungary E-mail: <szekely|kohari>@eet.bme.hu
1Microelectronics Research and Development Ltd. Budapest XI, Gulyás utca 27, H-1112 Hungary E-mail: [email protected]
3TIMA Laboratory, 46 Avenue Felix Viallet 38031 Grenoble cedex, France E-mail: [email protected]
Paper presented by András Poppe1,2
Outline Introduction Basic theory of generating reduced order models
the time-constant spectrum concept generation of reduced order models from transient
results direct calculation of time-constant spectra
Benchmark problem: SP10 MEMS package Results by ANSYS + THERMODEL Results by SUNRED + THERMODEL Results by SUNRED direct calculations Measurement + THERMODEL
Use of the different approaches Conclusions, future plans
Introduction
MEMS applications are frequently thermally operated, so knowing the thermal characteristics of their packages is very important.
Now we present a method for the generation of reduced order dynamic thermal models, either from simulated or from measured transient results.
The applicability of the method is presented on a benchmark package used for (pressure) sensor applications.
The time-constant spectrum concept
))/exp(1()( ii
i tRta
1 2 3
R
iii RC /
C1
R2
C2
R3
C3
R1
Lumped RC systems: discrete lines
dtRta ))exp(/exp(1()()(
R
Si chip
Ideal heat sink
Dissipator
Distributed RC systems: continuos spectrum
a(t) is the unit-step response. The Ri set is replaced by the R() continuous spectrum of the distributed RC system, defined on the z = ln t, = ln logarithmic time scale.
Time constant spectrum is a useful representation of the dynamic behavior of linear RC systems, such as thermal systems.
Compact model generation from transient results
dtRta ))exp(/exp(1()()(
As shown before, the unit-step response can be expressed as:
which is a convolution-type formula. Differentiating both sides yields:
)()()( zwzRzadz
d
where is the convolution operator and
)exp(exp)( zzzw
Compact model generation from transient results (contd.)
Restoration of the R(z) time-constant spectrum involves the following steps:
1) The a(t) unit-step has to be transformed to logarithmic time scale
2) a(z) has to be differentiated (numerically)
3) da(z)/dz has to be deconvolved by w(z)
This is the basis of the NID method (network identification by deconvolution).
Compact model generation from transient results (contd.)
Once the time-constant spectrum is known, compact model generation is straightforward:
1) Discretize the spectrum
2) For the discrete spectrum generate the corresponding Foster-model
3) Convert the Foster-model into a Cauer-ladder network
Impelementation: THERMODEL
http://www.micred.com/thermodel.htm
Direct calculation of time-constant spectra
))exp((Im1
)( zzR sZ
)exp()sin(cos zj s
)()()( zezRzR rC
))2exp()exp(cos21
)exp(sin)(
zz
zzer
0
5
10
15
20
25
30
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
er(z
)
z
2 degree4 degree
It can be proven that the the time constant spectrum can be calculated from the complex Z(s) thermal impedance by the expression below:
To avoid singularities on the - axis in practice we deviate from the axis by a small angle , as shown in the figure:
The calculated Rc(z) spectrum is the convolution of the real one with a known er(z) function:
The er(z) function is a narrow pulse (see the figure) which can be diminished by setting to any small value.
Calculation on a line deviated by a small angle from the - axis.
Width of the er(z) function at different values.
Direct calculation of time-constant spectra in different thermal field solvers
The frequency domain solution algorithm of both the THERMAN and SUNRED thermal field solvers has been extended according to the presented approach to allow direct calculation of thermal time-constant spectra.
Setting parameters of the time constant analysis in the THERMAN program.
Calculated time constant spectra that describe driving point and transfer behavior of a membrane.
http://www.micred.com/therman.html
http://www.micred.com/sunred.htm
Example – feature extraction for the veri-fication of detailed models of a package
Time-constant spectra are easy to compare. Good match
suggests that even the 2D model is accurate enough in
this case.
Time-constant spectrum calculated with the 2D model:
2D SUNRED model and its steady state simulation results:
Measured unit-step transient response:
Time-constant spectrum extracted by THERMODEL from above measured transient response:
3D SUNRED model and its steady state simulation results:
Time-constant spectrum calculated with the 3D model:
Our options for generating reduced order models
Thermal transient measurement + THERMODEL Transient simulation with a field solver +
THERMODELWe tried in the present study: ANSYS + THERMODEL SUNRED + THERMODEL
Direct calculation with a field solverWe tried in the present study: SUNRED
Our benchmark problem: SP10 sensor package
The first simulation model
Part(s) Material Thermalconductivity
[W/mK]
Specific heatC [Ws/kgK]
Mass density103 [kg/m3]
Chip Silicon 100 678 2.33Die attachadhesive
QMI 505 2 525 1.6
Capsule NittoMP-7410TA
0.882 270 2
Leadframe OLIN C 194 262.5 383 8.9
Due to plane symmetry only half of the structure was simulated. The package was treated as if mounted on a PCB (ideal heat-sink).Convection was neglected.P=1W applied on the chip.
ANSYS simulation, reduced order modeling by THERMODEL
Steady-state results by ANSYS
0
5
10
15
20
25
30
1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000
Tem
pe
ratu
re [
K]
Time [s]
Transient step-response by ANSYS
-10
0
10
20
30
40
50
60
1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000
R(z
)
[K/W
/de
ca
de
]
Time [s]
THERMODEL result: the R(z) time-constant spectrum
Corresponding time-constant spectrum calculated by THERMODEL
Element values of the identified 3 stage model network:N R [K/W] C [Ws/K]1 2.89 4.74e-022 7.54 3.12e-02 3 1.62e+01 2.03e-01
SUNRED simulation, reduced order modeling by THERMODEL
Transient step-response by SUNRED Corresponding time-constant spectrum calculated by THERMODEL
0
5
10
15
20
25
30
0.0001 0.001 0.01 0.1 1 10 100
Tem
pe
ratu
re [K
]
Time [s]
-5
0
5
10
15
20
25
30
0.0001 0.001 0.01 0.1 1 10 100
R(z
)
[K/W
/de
ca
de
]
Time [s]
THERMODEL result: the R(z) time-constant spectrumTue Dec 14 12:19:38 1999
.SUBCKT cauer 1 0
C0 1 6 1.299838e-02
R0 1 2 1.406075e-01
C1 2 6 2.946844e-02
R1 2 3 1.809813e+00
C2 3 6 1.734340e-02
R2 3 4 6.302130e+00
C3 4 6 1.910058e-01
R3 4 5 1.730904e+01
C4 5 0 7.794206e+00
R4 5 0 2.187223e+00
.ENDS cauer
SPICE netlist of the model generated by THERMODEL
SUNRED simulation, time-constant spectrum calculated by direct method
-5
0
5
10
15
20
25
30
35
40
45
0.001 0.01 0.1 1 10 100
R(z
) [K
/W/d
aca
de
]
Time [s]
Verification by measurement
-10
0
10
20
30
40
50
60
70
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000
Te
mp
era
ture
[K
]
Time [s]
THERMODEL: input and model-response for 1W step
INPUTMODEL
-10
0
10
20
30
40
50
60
70
80
1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000
R(z
) [
K/W
/de
cad
e]
Time [s]
THERMODEL result: the R(z) time-constant spectrum
Measured transient step response and the response of the model generated by THERMODEL from the measured data
Time constant spectrum extracted by THERMODEL from the measured unit-step response
Modified simulation model
The package was treated as if mounted on a PCB and the back surface of the PCB was attached to an ideal heat-sink. Convection was neglected. P=1W applied on the chip. PCB=0.55 W/mK
During simulation the conditions of the measurement setup have to be considered to help model verification.
SUNRED transient simulation + THERMODEL
Loci of main spectrum lines coincide, and the peak temperature is also close to the measured one.
0
10
20
30
40
50
60
70
80
1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000
Te
mp
era
ture
[K
]
Time [s]
THERMODEL: input and model-response for 1W step
INPUTMODEL
-20
0
20
40
60
80
100
120
0.0001 0.001 0.01 0.1 1 10 100
R(z
) [
K/W
/de
cad
e]
Time [s]
THERMODEL result: the R(z) time-constant spectrum
Transient step response simulated by SUNRED and the response of the model generated by THERMODEL from the measured data
Time constant spectrum extracted by THERMODEL from the simulated unit-step response. Even a single RC stage is enough for modeling.
Execution timesTool # of nodes Time-scale Points/decade Run time*
[min/decade]ANSYS transient 17823 logarithmic 10 33.3SUNRED transient 8192 quasi-log 20 20.3SUNRED direct t.c. 8192 logarithmic 20 313
Comments
1) Note, that the ANSYS runs were done on a DEC AXP 500 MHz computer, while SUNRED was running on a PC with a 200 MHz Pentium processor.
2) In direct time-constant calculation SUNRED can not take advantage some of its algorithmic features which enable a rather quick transient simulation.
3) Run-time of THERMODEL is a few seconds even on PC, it can be neglected with respect to the execution times of the field solvers.
Summary We propose a method for reduced order thermal
modeling of packages: transient simulation by a field solver followed
by model identification with THERMODEL
transient measurement results evaluation by THERMODEL
Only one example was shown here, but we carried out a lot of similar simulations. We realized, that MEMS packages are well described with very simple reduced order models.
SummaryTHERMAL
SIMULATION (FEM, FDM, BEM)
THERMODEL
THERMAL TRANSIENT
MEASUREMENT
Multi-domain simulation and design systems
Library of reduced order models (e.g. in SPICE format)
Summary
Sensitivity of different sensors are very much dependent on temperature. Thus, simple but accurate behavioral thermal models of MEMS packages are essential.
In sensor design considering thermal characteristics of packages on system level is important. Our reduced order models can be applied to support this.
