Download Institutionen för systemteknik Department of Electrical Engineering Camera Chip

Institutionen för systemteknik
Department of Electrical Engineering
Examensarbete
Simulation of Temperature Distribution in IR
Camera Chip
Examensarbete utfört i informationskodning
vid Tekniska högskolan vid Linköpings universitet
av
Stefan Salomonsson
LiTH-ISY-EX--11/4421--SE
Linköping 2011
Department of Electrical Engineering
Linköpings universitet
SE-581 83 Linköping, Sweden
Linköpings tekniska högskola
Linköpings universitet
581 83 Linköping
Simulation of Temperature Distribution in IR
Camera Chip
Examensarbete utfört i informationskodning
vid Tekniska högskolan i Linköping
av
Stefan Salomonsson
LiTH-ISY-EX--11/4421--SE
Handledare:
Darius Jakonis
Acreo AB
Examinator:
Robert Forchheimer
ISY, Linköpings universitet
Linköping, 14 February, 2011
Avdelning, Institution
Division, Department
Datum
Date
Information Coding
Department of Electrical Engineering
Linköpings universitet
SE-581 83 Linköping, Sweden
Språk
Language
Rapporttyp
Report category
ISBN
Svenska/Swedish
Licentiatavhandling
ISRN
Engelska/English
Examensarbete
C-uppsats
D-uppsats
Övrig rapport
2011-02-14
—
LiTH-ISY-EX--11/4421--SE
Serietitel och serienummer ISSN
Title of series, numbering
—
URL för elektronisk version
http://www.icg.isy.liu.se
http://www.ep.liu.se
Titel
Title
Simulering av temperaturdistribution i IR-kamerachip
Simulation of Temperature Distribution in IR Camera Chip
Författare Stefan Salomonsson
Author
Sammanfattning
Abstract
The thesis investigates the temperature distribution in the chip of an infrared
camera caused by its read out integrated circuit. The heat from the read out
circuits can cause distortions to the thermal image. Knowing the temperature
gradient caused by internal heating, it will later be possible to correct the image
by implementing algorithms subtracting temperature contribution from the read
out integrated circuit.
The simulated temperature distribution shows a temperature gradient along the
edges of the matrix of active bolometers. There are also three hot spots at both
the left and right edge of the matrix, caused by heat from the chip temperature
sensors and I/O pads. Heat from the chip temperature sensors also causes an
uneven temperature profile in the column of reference pixels, possibly causing
imperfections in the image at the levels of the sensors.
Simulations of bolometer row biasing are carried out to get information about
how biasing affects temperatures in neighbouring rows. The simulations show
some row-to-row interference, but the thermal model suffers from having biasing
heat inserted directly onto the top surface of the chip, as opposed to having heat
originate from the bolometers. To get better simulation results describing the row
biasing, a thermal model of the bolometers needs to be included.
The results indicate a very small temperature increase in the active pixel array,
with temperatures not exceeding ten millikelvin. Through comparisons with another similar simulation of the chip, there is reason to believe the simulated temperature increase is a bit low. The other simulation cannot be used to draw any
conclusions about the distribution of temperature.
Nyckelord
Keywords
Thermal modeling, Thermal imaging, Bolometer detector, Finite Element Method,
COMSOL Multiphysics.
Abstract
The thesis investigates the temperature distribution in the chip of an infrared
camera caused by its read out integrated circuit. The heat from the read out
circuits can cause distortions to the thermal image. Knowing the temperature
gradient caused by internal heating, it will later be possible to correct the image
by implementing algorithms subtracting temperature contribution from the read
out integrated circuit.
The simulated temperature distribution shows a temperature gradient along the
edges of the matrix of active bolometers. There are also three hot spots at both
the left and right edge of the matrix, caused by heat from the chip temperature
sensors and I/O pads. Heat from the chip temperature sensors also causes an
uneven temperature profile in the column of reference pixels, possibly causing
imperfections in the image at the levels of the sensors.
Simulations of bolometer row biasing are carried out to get information about
how biasing affects temperatures in neighbouring rows. The simulations show
some row-to-row interference, but the thermal model suffers from having biasing
heat inserted directly onto the top surface of the chip, as opposed to having heat
originate from the bolometers. To get better simulation results describing the row
biasing, a thermal model of the bolometers needs to be included.
The results indicate a very small temperature increase in the active pixel array,
with temperatures not exceeding ten millikelvin. Through comparisons with another similar simulation of the chip, there is reason to believe the simulated temperature increase is a bit low. The other simulation cannot be used to draw any
conclusions about the distribution of temperature.
v
Sammanfattning
Examensarbetet undersöker den temperaturdistribution som uppkommer i ett chip
till en IR-kamera till följd av värmeutvecklingen i dess egna utläsningskretsar. Genom att ha information om temperaturdistributionen är det möjligt att längre
fram i utvecklingsprocessen skapa algoritmer som subtraherar bort chippets interna värmetillskott från den termiska bilden.
Den simulerade temperaturdistributionen visar att de största temperaturgradienterna uppkommer längs den aktiva pixelmatrisens sidor. Det är även möjligt att se
tre varmare områden vid både den vänstra och högra sidan av matrisen skapade
av värme från chippets temperatursensorer och I/O-kretsar. Värme från temperatursensorerna påverkar även temperaturen i kolumnen med referenspixlar, vilket
kan ge upphov till avvikelser i den termiska bilden i höjd med dessa temperatursensorer.
Simuleringar av radvis basering av bolometrar utförs för att få information om
hur bolometerbiaseringen påverkar temperaturen i angränsade rader. Simuleringarna visar att det finns störningar mellan rader, men simuleringsmodellen lider
av avsaknaden av en termisk bolometermodell och tvingas applicera värme direkt
på chipytan istället för att låta värme utvecklas i bolometrarna. För bättre simuleringsresultat innefattande bolometerbiasering bör en termisk bolometermodell
inkluderas i simuleringen.
Resultaten visar på en mycket liten temperaturökning inom den värmekänsliga
aktiva pixelmatrisen, med temperaturökningar inom detta område som inte överstiger tio millikelvin. Genom jämförelser med en liknande simulering av samma
chip är det inte omöjligt att dra slutsatsen att temperaturökningen är något låg.
Det går inte att dra några slutsatser om temperaturens distribution genom denna
jämförelse av simuleringar.
vii
Contents
1 Introduction
1.1 Project background . . . . . .
1.2 Problem description . . . . .
1.3 Thermal imaging applications
1.4 Method . . . . . . . . . . . .
1.5 Limitations . . . . . . . . . .
.
.
.
.
.
1
1
1
2
2
3
IR camera
IR camera description . . . . . . . . . . . . . . . . . . . . . . . . .
Read out integrated circuit . . . . . . . . . . . . . . . . . . . . . .
Temperature read out . . . . . . . . . . . . . . . . . . . . . . . . .
5
6
7
9
3 Heat transfer
3.1 Heat transfer theory . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . .
11
11
14
4 Chip thermal conductivity
4.1 Silicon substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Interconnect layer . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Thermal properties of pixel cell . . . . . . . . . . . . . . . . . . . .
15
15
15
16
5 Thermal modeling using COMSOL Multiphysics
5.1 COMSOL Multiphysics introduction . . . . . . . .
5.2 Heat sources . . . . . . . . . . . . . . . . . . . . .
5.3 Heat application . . . . . . . . . . . . . . . . . . .
5.4 Meshing . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Two-dimensional mesh . . . . . . . . . . . .
5.4.2 Three-dimensional mesh . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
19
19
20
21
22
22
24
6 Simulations and results
6.1 Thermal conductivity of pixel cell . . .
6.1.1 Model setup . . . . . . . . . . .
6.1.2 Meshing . . . . . . . . . . . . .
6.1.3 Simulation results . . . . . . .
6.2 Temperature distribution in IR camera
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
25
25
26
28
28
29
2 The
2.1
2.2
2.3
.
.
.
.
.
.
.
.
.
.
ix
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . .
. . .
. . .
. . .
chip
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
x
Contents
6.3
6.4
6.5
6.2.1 Temperature dependency . .
6.2.2 Model setup . . . . . . . . . .
6.2.3 Meshing . . . . . . . . . . . .
6.2.4 Simulation results . . . . . .
Row biasing simulation . . . . . . . .
6.3.1 Model setup . . . . . . . . . .
6.3.2 Simulation results . . . . . .
Heat transfer on pixel level . . . . .
6.4.1 Model setup . . . . . . . . . .
6.4.2 Simulation results . . . . . .
Temperature distribution when using
6.5.1 Model setup . . . . . . . . . .
6.5.2 Simulation results . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
polysilicon resistors
. . . . . . . . . . . .
. . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
29
29
30
31
38
38
40
42
42
43
43
44
44
7 Discussion
45
8 Improvements and future work
47
Bibliography
49
Contents
xi
List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
Light spectrum. . . . . . . . . . . . . . . .
Atmospheric transmittance in the infrared
Illustration of bolometer placement on the
Typical layers in an integrated circuit . .
Placement of the chip’s circuit blocks . . .
Schematic of typical pixel bias circuit . .
. . . . . .
spectrum
chip . . .
. . . . . .
. . . . . .
. . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5
6
7
8
9
10
5.1
5.2
5.3
Insertion levels of heat sources in IC model . . . . . . . . . . . . .
Illustration of general two-dimensional meshes . . . . . . . . . . . .
Adapting quadrilateral boundary mesh for further meshing . . . .
21
23
24
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
6.20
Rendering of pixel cell . . . . . . . . . . . . . . . . . . . . . .
Via outline simplification . . . . . . . . . . . . . . . . . . . .
Removal of metal layer overlap . . . . . . . . . . . . . . . . .
Results of pixel cell thermal conductivity simulation . . . . .
Active pixel array mesh . . . . . . . . . . . . . . . . . . . . .
Temperature map of ROIC contribution (27◦ C) . . . . . . . .
Active pixels temperature map (27◦ C) . . . . . . . . . . . . .
Temperature in reference pixel column (27◦ C) . . . . . . . . .
Temperature difference compared to reference pixels (27◦ C) .
Active pixels temperature map (-40◦ C) . . . . . . . . . . . . .
Temperature in reference pixel column (-40◦ C) . . . . . . . .
Temperature difference compared to reference pixels (-40◦ C) .
Active pixels temperature map (95◦ C) . . . . . . . . . . . . .
Temperature in reference pixel column (95◦ C) . . . . . . . . .
Temperature difference compared to reference pixels (95◦ C) .
Temperature distribution near biased pixel (27◦ C) . . . . . .
Temperature distribution near biased pixel (-40◦ C) . . . . . .
Temperature distribution near biased pixel (95◦ C) . . . . . .
Thermal correlation between neighbouring pixels . . . . . . .
Temperature distribution when using polysilicon resistors . .
26
26
27
28
30
31
32
33
33
34
35
35
36
37
37
40
41
41
43
44
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Chapter 1
Introduction
As technologies to detect infrared (IR) light become more developed, the detectors
become smaller and cheaper, generating products that are finding their way into
everyday life. A recent example is the emerging practice of installing infrared
cameras in vehicles. By having an infrared camera mounted to the front of the
vehicle it is possible to increase sight range and make it easier to detect pedestrians
and wildlife in low light condition.
1.1
Project background
An infrared camera has been developed by several partners, including Acreo AB,
that aims to be cheaper and less complex than infrared cameras on the market
today. The camera is intended for the automobile market as a tool to improve
sight in low light conditions.
1.2
Problem description
In the ideal case, the extremely temperature sensitive IR detectors would only
absorb heat emitted from the viewed object. However, there are more components
than just the IR sensor on the camera chip; mainly the read out integrated circuit
(ROIC) which consists of all the circuits needed to extract, amplify and convert
temperature information coming from the detector. The ROIC will inevitably
dissipate heat when operating. Some of this heat will likely find its way to the
extremely temperature sensitive infrared pixels, which will absorb the heat and
produce an image containing distortions. Besides the ROIC, the chip also have
sensors monitoring chip temperature and internal pressure, components which also
produce heat.
1
2
Introduction
This thesis investigates the heat contribution from the integrated circuit (IC).
Knowing the temperature gradient caused by internal heat, it is possible to later
in the development process implement algorithms that subtract the ROIC’s temperature contribution when the image is processed.
1.3
Thermal imaging applications
Besides being used in dark environment, the physical properties of infrared light
makes it very suitable in other applications as well. Light in the infrared spectrum
has wavelengths more than ten times as long as the wavelengths of visible light.
The longer wavelength means infrared passes through certain media that visible
light does not, such as smoke or fog, increasing sight range in these conditions.
Thermal imaging is well suited for searching for people in difficult terrain. Common areas of use are in law enforcement, surveillance and search and rescue operations. In all these situations the primary objective is to detect people; either
trying to detect people in dark environments, or trying to find a person in, for
example, a forest or in water where a person is hard to spot.
Some products, like the camera investigated in this thesis, operate passively by
catching infrared light constantly emitted from all objects. Other use an infrared
light source to light up the vicinity, the area still seems dark to the human eye, but
is fully lit to an infrared camera. Using an extra light source is especially suited
for stationary surveillance cameras.
For home owners thermal imaging can be an important tool in finding weak spots
in a house’s insulation where indoor heat is allowed to escape. Once the problem
areas are identified they can be corrected and save the owner money on heating.
1.4
Method
The simulations are performed in COMSOL Multiphysics, with some additional
data processing and visualization being made in MATLAB. The process of getting
acquainted with finite element analysis and the software interface is carried out
by examining the tutorial models included in COMSOL Multiphysics.
The choice of COMSOL Multiphysics as a simulation tool is made with cost in
mind. As Acreo has already purchased licences to make simulations in other
areas, it would be cost-efficient to also use COMSOL Multiphysics for temperature
distribution simulations. A secondary purpose of this project is to see how well
COMSOL Multiphysics is suited for thermal modelling of an integrated circuit.
1.5 Limitations
1.5
3
Limitations
The purpose of this project is to investigate the internal heat contribution from
the ROIC. This does not include thermal modeling of the IR sensors mounted on
the chip surface.
It is necessary for the model to be simple, with the ability of easy modification of
parameters, while still keeping a good degree of accuracy. It is crucial the model
is easy to understand, interpret and modify even after the end of this project. It
should only be necessary to have basic knowledge about the simulation software
to make minor changes to the model.
Chapter 2
The IR camera
The basic idea of every kind of camera is to capture and interpret light. Most
cameras operate by detecting light in the visible spectrum. The infrared camera on
the other hand detects light in the infrared spectrum, light invisible to the human
eye. The infrared region of the electromagnetic spectrum is found at frequencies
just below the red end of the visible spectrum, hence the name infrared which
literally means “below red”. An overview of the electromagnetic spectrum is found
in figure 2.1.
Objects emit infrared light proportional to their internal temperature. As infrared
light is always emitted from warm objects, an infrared camera can create images
of otherwise completely dark environments lacking all visible light.
Figure 2.1: Overview showing a portion of the electromagnetic spectrum. Infrared
is found at frequencies just below the visible light.
There are two main technologies for thermal imaging. The first uses cooled IR
detectors constantly held at a low temperature to prevent its internal radiation
from interfering with the image. The detectors work by catching incoming photons
5
6
The IR camera
in a quantum detector where they activate carriers in a semiconductor material,
creating currents proportional to the amount of incoming light.
The camera analysed in this project belongs to the second group using uncooled
infrared detectors. Instead of catching photons they absorb IR radiation as heat,
which increases their internal temperature. The temperature can then be measured
and translated into a thermal image. [1]
2.1
IR camera description
Infrared radiation is scattered by gases in the atmosphere, preventing light from
reaching its destination. Depending on the size of the gas molecules some wavelengths are scattered more easily, greatly decreasing the usable range for applications operating at these wavelengths. The presence of the atmosphere gives the
infrared spectrum a very characteristic distribution with two larger bands clearly
distinguishable, see figure 2.2. Most far field infrared cameras sense wavelengths
between 7µm and 14µm in the long wave infrared (LWIR) band where atmospheric
transmittance is high. [1]
Figure 2.2: Atmospheric transmittance in the infrared spectrum. [1]
Light reaching the camera is first of all passed through a lens. The lens is designed
to filter out all light except infrared light in the LWIR band and is also responsible
for focusing the light onto the IR sensor.
Once inside the camera, the light hits a large array of heat sensitive detectors
called bolometers. The bolometers are made in a way that their electrical resistance changes dramatically with change in temperature. When a bolometer absorbs infrared light, its internal temperature raises, causing its electrical resistance
to decrease. By measuring the bolometer’s electrical resistance, it is possible to
determine its temperature. After having sampled all bolometers, a viewable thermal image can be composed. Figure 2.3 provides a simple overview of how the
bolometers are bonded to the chip and sealed in a vacuum package [2].
2.2 Read out integrated circuit
7
Figure 2.3: Illustration of where bolometers are placed on the chip. The size of
the bolometers is greatly exaggerated for illustrative purposes. The image also
includes some additional chip packaging. [2]
2.2
Read out integrated circuit
The read out integrated circuit is responsible for extracting temperature information from the bolometers; this includes sending current through the bolometer
to sense its resistance, as well as amplification, sampling and digitization of the
resulting signals. Its final task is to export data to external components where
further video analysis is carried out.
It is necessary to have basic knowledge about the components that make up an
integrated circuit. The integrated circuit consists of many layers, as illustrated
in figure 2.4. Starting from the bottom there is a relatively thick slab of silicon.
Some areas of the silicon’s top surface are doped to form transistors. From the
transistor gates there are conductor materials transporting the current up into
the interconnect layer where the routing is done to give the circuit its functionality. The metal conductors are separated by silicon dioxide, which is an electric
insulator. The top metal layer is covered with a thin oxide layer to protect the
circuit. The oxide can be removed to enable external connections to the chip. The
areas of the camera chip containing pixels have gaps in the oxide layer to allow
for bolometers to be bonded. All layers above the silicon substrate make up the
interconnect layer.
8
The IR camera
Figure 2.4: Typical layers in an integrated circuit. The picture is not drawn to
scale, this is especially worth noting when it comes to layer thicknesses since the
silicon substrate in reality is much thicker than the interconnect layer.
Since the chip measures thermal energy, the ROIC has been designed to minimize
its temperature gradient and impact on readout. The most power intense circuits
are placed further away from the bolometer array than less power intense circuits.
There is also a high degree of symmetry in the design, meant to ensure a more
predictable temperature distribution. A drawing of the chip layout is found in
figure 2.5.
The most crucial circuits in the signal path are placed just below the bolometer
array. The area of the chip where bolometers are attached is generally kept free
from power intense circuits, although some circuits controlling the current through
the bolometers have been placed in the IC underneath the bolometers.
At the lower portion of the chip there are circuits responsible for sampling and
digital conversion of the signals coming from the bolometers. Above these circuits
is the pixel array. The main portion of the pixel array is devoted to the matrix
of active bolometers. Within the pixel array there are also reference bolometers,
pressure sensors and temperature sensors. The input- and output-pads are placed
at the top and bottom edges of the chip.
2.3 Temperature read out
9
Figure 2.5: Placement of the chip’s blocks. The figure is not drawn to scale nor
is the placement of circuit blocks completely accurate. The figure is intended as a
general illustration of the most interesting blocks’ general placement and relative
size.
2.3
Temperature read out
Having uncooled detectors makes temperature readout challenging. The chip temperature will vary significantly depending on the ambient temperature. Therefore,
simply measuring the bolometer temperature will yield completely different results
depending on external environments.
The objective is to only measure contribution from external infrared radiation
emitted by the viewed objects. To estimate how much of the bolometer’s temperature is due to chip temperature, a dedicated set of reference bolometers is
used. The reference bolometers are identical to the active bolometers except that
they are shielded from incoming IR radiation. The shield ensures the reference
bolometers are being kept at the same temperature as the chip.
To start with, the active bolometers have the same temperature as the chip. When
infrared light hits the bolometers their temperature will rise further. By comparing
the temperature between the active and reference bolometer, contribution from the
infrared light can be determined by simple subtraction [3] [4] [5]. When sending
10
The IR camera
a signal through the bolometer to read its temperature, the bolometer is said to
be biased. There are two common ways of performing bolometer biasing. Either
the voltage is kept constant across the bolometer and the resulting current is
measured, or, a constant current is applied and the voltage drop over the bolometer
is measured. By also applying the exact same voltage or current to the reference
bolometers and sending the two resulting signals to a differential amplifier, the
temperature difference between the two is obtained. Which technology used is not
crucial to thermal modeling, what is important is that internal heating will cause
image distortions if the reference and active bolometers are suffering from different
amounts of internal heating. [6]
Figure 2.6: Simplified schematic of a typical pixel bias circuit.
The chip does not constantly measure temperature in each bolometer. It generates
images by biasing one row of bolometers at a time, sweeping across the surface very
rapidly. The biasing itself will also cause the bolometer to heat up. This heating
in itself does not interfere with the readout as long as the reference bolometer is
biased the same way as the active bolometers, but due to them being placed in
different parts of the chip the resulting temperature increase might differ.
Chapter 3
Heat transfer
The basic idea of heat transfer is not very complex, the difficulty lies in solving large
systems of differential equations with all of them having their own restrictions.
Instead of solving the very large system of equations analytically, it is possible to
solve the system with good accuracy with a numerical approach using the finite
element method (FEM).
3.1
Heat transfer theory
Heat transfer describes how heat flows in a system. When two thermally connected
objects are at different temperatures the temperature difference will cause heat to
migrate to the cooler portions, striving to obtain temperature equilibrium. Just
as voltage is the driving force in electrical circuits, temperature is what initiates
heat flow in thermal systems. The heat flowing through a system is called heat
flux, and will depend on the medium’s thermal conductivity.
For heat simulations, there are three material properties that must be included for
the solver to be able to calculate the result:
• Thermal conductivity
• Heat capacity
• Material
Thermal conductivity is the material’s ability to transport heat. Metals are generally good thermal conductors. Other materials with low thermal conductivity
are considered thermal insulators.
11
12
Heat transfer
Heat capacity is simply put the amount of energy an object can store for a change
in temperature, or to put it in another way, the amount of energy needed to
heat the object 1K. Heat capacity is measured in J/K. Using heat capacity as
a property causes problems since heat capacity is not a material property, it is
an object property depending heavily on object size. A common example is the
fact that a large bathtub full of tepid water holds more energy than a small glass
containing hot water. To get around this, all simulations are performed using
specific heat capacity, which is the heat capacity per unit mass (J/Kg K). The
specific heat capacity is a material property fixed for each material, thus making
it suitable to use in simulations.
Density is not connected to heat transfer specifically. As all objects in the simulation environment are created as geometric entities with a specific volume, density
needs to be included to obtain the objects’ mass through equation 3.1.
m=ρ·V
where
m =
ρ
=
V =
(3.1)
Object mass [kg]
Material density [kg/m3 ]
Object volume [m3 ]
For anyone familiar with electronics, thermal conduction should not be too hard
to understand; many of the relations applicable to electrical systems can also be
applied to thermal systems. Just as Ohm’s law is fundamental in electronics,
the corresponding thermal version of Ohm’s law is just as fundamental to heat
conduction. After changing the physical quantities from electrical to the thermal
counterpart according to table 3.1, Ohm’s law can be used to describe heat transfer
between to thermally connected nodes. The two versions of Ohm’s law are shown
in equation 3.2.
Table 3.1: Electrical physical quantities and their corresponding thermal equivalent.
Electrical
Thermal
Voltage - U
Current - I
Electrical conductivity - G
Capacitance - Cel
Temperature - T
Heat flux - φq
Thermal conductivity - k
Heat capacity - Cth
3.1 Heat transfer theory
13
I = G · ∆U
Electrical
φq = k · ∆T
T hermal
where
I =
G =
∆U =
φq =
k =
∆T =
(3.2a)
(3.2b)
Current [A]
Electric conductance [S]
Voltage difference [U ]
Heat flux [W ]
Thermal conductance [W/K]
Temperature difference [K]
Equations 3.2 apply to lumped components. To make them suitable for distributed
objects the conductivity must be related to conductor length as in equation 3.3.
This distributed form is still only applicable to objects where heat is conducted in
one dimension.
T hermal
where
φq
k
T
l
=
=
=
=
φq = k · l · ∆T
(3.3)
Heat flux [W/m]
Thermal conductivity [W/m K]
Temperature [K]
Length [m]
The full heat equation also includes the specific heat capacity and is defined in three
dimensions according to equation 3.4. The heat source is negative to ensure the
direction of the heat flux being toward the cooler temperatures [7]. By describing
the conductivity with a matrix instead of a scalar it is possible to have anisotropic
thermal conductivity, that is, having materials where heat travels more easily in
certain directions.
dT
+ ∇ · (k∇T )
dt
dT
d2 T
d2 T
d2 T
= −ρc
+ kx
+ ky
+ kz
2
2
dt
dx
dy
dz 2
−Q = −ρc
where
k =
ρ =
c =
Q =
Thermal conductivity matrix [W/m K]
Material density [kg/m3 ]
Specific heat capacity [J/kg K]
Inserted heat [W/m3 ]
(3.4)
14
Heat transfer
Often it is not interesting to simulate the transient behavior of a system, instead
it is often more interesting to see the state where all transients have died out
and the system have stabilized. This is called a steady state simulation. As the
temperature distribution converges to a final state, there is no longer any change
in temperature and dT/dt equals zero. Using this it is possible to remove the
term containing heat capacity from the heat equation, which is now reduced to
equation 3.5.
−Q = ∇ · (k∇T )
(3.5)
d2 T
d2 T
d2 T
+ ky
+ kz
= kx
2
2
dx
dy
dz 2
where
k =
ρ =
Q =
3.2
Thermal conductivity matrix [W/m K]
Material density [kg/m3 ]
Inserted heat [W/m3 ]
Finite Element Method
Many field of physics, including heat transfer, are governed by partial differential
equations. The system of differential equations is often impossible to solve in a
practical way, especially when geometries become complex. This is where the finite
element method comes in. The finite elements works by dividing the geometry into
a great number of small subregions, all having their own set of equations. The
simulations software is then able to use numerical methods to simultaneously solve
the equations in all subregions. [8]
Chapter 4
Chip thermal conductivity
For thermal simulation purposes, the chip is divided into two layers. The bottom
layer is a block of silicon. The top layer consists of an imaginary material having
thermal properties equivalent to the interconnect layer.
4.1
Silicon substrate
The silicon substrate is a simple block of pure silicon with known thermal properties, presented in table 4.1.
Table 4.1: Thermal properties of silicon.
Silicon
4.2
Thermal conductivity
W/m K
Density
kg/m3
Specific heat capacity
J/kg K
163
2330
703
Interconnect layer
In contrast to the silicon substrate, the interconnect layer is not as straightforward
to include in full-chip simulations. It is practically impossible to include all metal
conductors that make up the chip in the simulations, as the model would be
extremely complex. It is obvious the interconnect layer needs to be simplified.
When simulating on full-chip level, the interconnect layer is assumed to have the
same thermal properties throughout the whole chip. The interconnect layer is
15
16
Chip thermal conductivity
transformed into a new homogeneous material having thermal properties equivalent to the pixel cells directly underneath the active bolometers. Since the routing
is not symmetrical in all three dimensions and contains metal passages where heat
travels more easily, the thermal conductivity of the pixel is anisotropic with heat
travelling more easily in the y-direction because of the large power supply lines
running along the pixel columns.
The properties of the homogenized interconnect layer in table 4.2 are based from
simulation results described in section 6.1.
Table 4.2: Thermal properties of interconnect layer
Thermal conductivity
W/m K
x
y
z
Interconnect layer
4.3
3.9
8.4
5.6
Density
kg/m3
Specific heat capacity
J/kg K
2600
687
Thermal properties of pixel cell
The IC area directly below the bolometers is comprised of a large array of nearly
identical cells, each having a single bolometer attached to it. By investigating
the thermal properties of a single cell it is possible to create a new homogeneous
material that is a good approximation of the cell. This new material is then used
as the whole interconnect layer in full-chip simulations.
The very complex routing in the pixel cell makes it extremely hard to calculate
an equivalent thermal conductivity analytically; instead it is possible to determine
the average thermal conductivity in each direction by simulations. The resulting
conductivities are used to define the material properties of the interconnect layer
used in full-chip simulations.
The interconnect layer is composed of aluminum, copper and silicon dioxide. Their
thermal properties are summarized in table 4.3.
Table 4.3: Thermal properties of materials in interconnect layer [9].
Aluminum
Copper
Silicon dioxide
Thermal Conductivity
W/m K
Density
kg/m3
Specific Heat Capacity
J/kg K
238
400
1
2700
8700
740
903
385
2200
4.3 Thermal properties of pixel cell
17
For time-dependent simulations it is also necessary to include a material’s specific
heat capacity. In contrast with thermal conductivity, the equivalent heat capacity
can be calculated analytically with equation 4.1.
Cth
where
Cth
V
ρ
i
=
=
=
=
Vtot
=
ρtot
X
i
Vi
Cthi · ρi
Specific heat capacity [J/kg K]
Volume [m3 ]
Density [kg/m3 ]
Materials
!−1
(4.1)
Chapter 5
Thermal modeling using
COMSOL Multiphysics
This chapter describes the general way of setting up thermal models in COMSOL Multiphysics, with emphasis on heat sources and meshing. All references to
functions and limitations are based on experiences with COMSOL Multiphysics
version 4.0a.
5.1
COMSOL Multiphysics introduction
This project uses COMSOL Multiphysics 4.0a as the simulation tool. Creating
models does require some proficiency that can be gained by tutorial models included in the installation package. These models can then be expanded to include
special meshing and additional simulations steps. When trying out model settings
it can be warmly recommended to first set up a tiny model where settings can be
experimented with. Simulating tiny models takes nearly no time at all, whereas
the actual full-chip model can take hours. When the desired settings have been
found it is easy to apply them to the main model.
A bit simplified, models are set up by completing the following six steps:
Draw or import geometries
Model geometries can be created in the COMSOL Multiphysics drawing
environment or be imported from other design tools. If the geometry is
not extremely simple, the use of another drawing environment than the one
in COMSOL Multiphysics can be recommended since it lacks most of the
features found in dedicated design tools.
Define materials and their properties
19
20
Thermal modeling using COMSOL Multiphysics
All geometries need to have thermal properties assigned to them. There is
a library of materials included in COMSOL Multiphysics that covers a good
amount of materials. New materials can be defined and added to the library.
Define and apply physics settings
The physics setup is used to define all physical parameters. In heat transfer simulations the inputs used are: constant temperature, heat source and
constant heat flux. The model also needs initial values, which are especially
important in time-dependent simulations. The choice of initial values is not
as important in steady state simulations where the system is converging toward a final value; but setting totally unrealistic initial values can cause
problems to the solver.
Mesh geometries
The finite element method divides the geometry into smaller regions by applying a mesh to the geometry to be able to perform the calculations. Meshing is an important part of modeling and determines simulation resolution
and simulation time. For systems with lots of details the meshing itself can
consume as much time as the equation solver.
Set up studies
Setting up studies includes choosing between steady state simulations and
time-dependent simulations. The default solver parameters often work fine,
the exception is when performing parametric sweeps or when simulations
are based on previous results. Other settings include defining solver type,
defining variables to solve for, and in time-dependent simulations, defining
time steps for the solver.
Display results
When the simulations are completed, it is time to extract and present the
results of interest. In heat transfer simulations images with color maps describing temperature distribution are common to plot. It also possible to
create one- or two-dimensional graphs plotting results from parts of the geometry.
5.2
Heat sources
There are two ways of inserting heat into a model. A heat source inserts a constant
amount of heat flux causing the temperature at the heat source to vary depending
on the thermal properties of the model. Heat sources are applied as W/m3 , W/m2
or even W/m depending on how many dimensions the heat source has. All heat
originating from electrical circuits with a known power consumption are modeled
using heat sources.
Other times it is more appropriate to apply a constant temperature. This means
whatever heat flux necessary will be inserted, or removed, to maintain the constant
5.3 Heat application
21
temperature at the source. Applying a constant temperature can be likened to a
heat sink where large amounts of heat can exit the system without.
Gathering information about the chip’s heat sources is an important part of thermal modeling. For simplicity, all circuit blocks are assumed to produce heat evenly
across their geometry. In reality, heat will be produced in the individual transistors, but applying the heat evenly distributed is a well motivated simplification
because of the large number of very small transistors in an integrated circuit.
5.3
Heat application
Power is mainly dissipated in the chip’s transistors and passive components. All
power sources are modeled to originate from the boundary between the interconnect layer and the silicon substrate, the exception being power consumed by the
bolometers, see figue 5.1. Since the height of the components is much smaller
than the thickness of the two adjacent chip layers the heat sources are considered two-dimensional, dramatically decreasing the level of complexity in the FEM
simulation.
Figure 5.1: Side view of the layers in the IC model showing the levels where heat
from bolometers as well as heat from circuits blocks is inserted. Image not drawn
to scale.
When biasing of bolometer rows is added to the simulation, heat originating from
power dissipation in the bolometers is applied to the top of the interconnect layer
according to figure 5.1. This is not a very accurate representation since heat
generated in a bolometer would experience much more capacitative effects before
finding its way into the chip. When power is applied directly to the top surface,
these capacitative effects are lost.
The power density of the blocks is calculated as the block’s power consumption
divided by the block’s area, as specified in equation 5.1, to create a value for the
two-dimensional heat source.
22
Thermal modeling using COMSOL Multiphysics
block power [W ]
Block power density W/m2 =
block area [m2 ]
5.4
(5.1)
Meshing
The finite element method is based on the geometry being divided into smaller
subregions where the heat equation can be solved locally. The geometry is divided
by applying a mesh to the model geometry. Meshing is crucial in determining the
accuracy of the simulation and the resolution of the solution. Meshing is a compromise between simulation resolution and computation load. COMSOL Multiphysics
is able to automatically mesh geometries, but in most cases it is preferable to apply
the mesh step by step where each step can be controlled to generate mesh of the
right size and shape.
There are too many methods and considerations of meshing to give a comprehensive overview of all of them in this document. The following sections explain
meshing suitable for this project; even though they briefly explain general meshing
techniques not used in this project, they do not provide a complete overview.
5.4.1
Two-dimensional mesh
Two-dimensional mesh are used in either a two-dimensional model, or as a boundary mesh on three-dimensional blocks acting as the starting point for the mesh in
the rest of the volume.
Meshing creates a large number of data points called mesh vertices. All these
vertices have lines tying them together into either a quadrilateral1 or triangular
mesh. The triangular meshing is generally created by letting the software create
the mesh automatically, with the only input being a few growth and size parameters. Meshes like these generally look like figure 5.2a. If more control over the
process is needed to ensure a more evenly distributed triangular pattern, it is possible to convert an evenly distributed quadrilateral pattern into triangular elements
as seen in figure 5.2d
Meshes consisting of quadrilateral elements like figure 5.2b can also be created
automatically by the software. It is also possible to create a mapped distribution
where the position of all vertices is controlled. An example of mapped meshing is
found in figure 5.2c
1A
quadrilateral is a polygon having four sides. The rectangle is a special case of quadrilateral.
5.4 Meshing
23
(a) Triangular mesh
(b) Qquadrilateral mesh
(c) Mapped mesh
(d) Converted mapped mesh
Figure 5.2: Illustration of general two-dimensional meshes.
24
5.4.2
Thermal modeling using COMSOL Multiphysics
Three-dimensional mesh
Three-dimensional meshes are applied to volumes. There are two ways of applying
3D meshes; letting the software automatically generate tetrahedral2 elements, or
sweeping a 2D mesh into the geometry. The three-dimensional tetrahedral mesh is
basically a three-dimensional version of the triangular mesh. It is created automatically by the software and conforms to boundaries already meshed with triangular
elements.
Sweeping the mesh of a boundary into the volume creates levels with copies of the
original boundary mesh, see figure 5.3a. This is an easy way of keeping control
of element distribution. The swept mesh is limited to nice geometries where the
geometry’s cross section in the sweep direction is fairly constant.
It is not possible to apply a three-dimensional tetrahedral mesh to a volume where
one of its boundaries is already meshed with quadrilateral elements. The fact
that there is no three-dimensional version of the quadrilateral mesh means the
boundary mesh must be converted to triangular elements before the rest of the
volume can be meshed. Inserting diagonal lines is the easiest way of adapting the
boundary for further meshing. Quadrilateral meshes can still be swept into the
geometry and should be considered as an option. Figure 5.3 illustrates the two
ways of meshing the rest of a volume.
(a) Boundary with mapped mesh swept into
the geometry.
(b) Boundary mapped with a converted
mapped mesh. The rest of the volume is
meshed with tetrahedral elements.
Figure 5.3: Two ways to apply mesh to a volume having a boundary already
meshed with quadrilateral elements.
2 A tetrahedron is composed of four triangular faces connected at the corners to look something
like a pyramid with a three-sided base.
Chapter 6
Simulations and results
It is important to note that all temperature values displayed in all simulations are
showing temperature increase compared to ambient temperature. All equations
solved are linear and it does not matter at which ambient temperature the simulations are performed, the temperature of the chip will always increase by the same
amount.
6.1
Thermal conductivity of pixel cell
Three separate simulations are performed to determine the equivalent thermal
conductivity for all three dimensions of the pixel. A two-dimensional cross section
of each pixel layer is imported to COMSOL Multiphysics. The original layout file
does not contain any information about layer thickness; this has to be retrieved
from documentation of the manufacturing process. Each layer is then extruded to
the right thickness to create a three-dimensional pixel geometry like figure 6.1.
25
26
Simulations and results
Figure 6.1: The interconnect layer of a pixel cell
6.1.1
Model setup
COMSOL Multiphysics does have some limitations when it comes to the size of
the model. When models become to large, they require more memory to run.
If the workstation does not have enough memory to handle the workload, the
simulation is aborted. To reduce the simulation load, some of the via layers have
been simplified by replacing the clusters of small vias with one larger via following
the outline of the group as seen in figure 6.2. The impact on heat transmission
should be insignificant.
(a) Original vias
(b) Modified vias
Figure 6.2: The vias have been simplified into the outline of the original via cluster.
6.1 Thermal conductivity of pixel cell
27
The lower metal layers have also been manipulated. The metallization does not fit
to the adjacent layer perfectly, but has a small overlap creating a small ledge. The
ledges are intentional to comply with the design rules for the used manufacturing
process. In the simulation these ledges create problems as COMSOL Multiphysics
will apply additional mesh to this tiny surface making the mesh unnecessarily
complex. The outline of the conductors has therefore been adjusted slightly to
make them fit perfectly onto each other, as exemplified in figure 6.3. This is
a minor adjustment whose impact is much smaller than the via simplifications
already carried out.
(a) Original layout
(b) Modified layout
Figure 6.3: The layout of some parts of the metal layers are modified to improve
simulation performance.
By applying a heat source on one side of the cell, and a constant temperature on
the opposite side as thermal ground, the resulting temperature increase will depend
on the cell’s thermal conductivity. The temperature difference is used to calculate
the overall thermal conductivity in the examined dimension. The temperature
on the top surface will not be constant across the whole surface due to some
parts having metal conductors transporting heat away from the heat source more
efficiently. The temperature on the top surface needs to be averaged for the cell
to be considered a homogeneous material.
The same procedure is also performed in the x- and y-direction to estimate the
conductivity in each direction. By inserting the averaged temperature into equation 6.1, an equivalent conductivity for the examined dimension is obtained.
ki =
where
k
l
Q
∆T
i
=
=
=
=
=
Q
li · ∆Ti
Thermal conductivity [W/m K]
Distance between heat source and thermal ground [m]
Applied heat [W ]
Average temperature difference [K]
Analyzed dimension {x, y, z}
(6.1)
28
6.1.2
Simulations and results
Meshing
The meshing of the pixel is done with automatically generated tetrahedral mesh
elements. This is the simplest way of creating meshes and is well suited for this
kind of geometry where the size of all subdomains do not differ too much from all
the others.
6.1.3
Simulation results
The simulation results from the pixel cell simulation is displayed in figure 6.4.
As seen, the surface temperature is significantly lower at the metal pads where
the large amount of metal efficiently transports heat toward the heat sink at the
bottom. Heat entering the pixel through the silicon dioxide portions of the surface
are experiencing more thermal resistance and generates higher temperatures.
Figure 6.4: Simulations of thermal conductivity in z-direction of the pixel cell.
Heat is applied to the top surface and a constant temperature of 0K is applied to
the bottom side.
6.2 Temperature distribution in IR camera chip
6.2
6.2.1
29
Temperature distribution in IR camera chip
Temperature dependency
The steady state simulation is carried out three times, each one representing a
different ambient temperature. The circuit blocks on the chip are very temperature
dependent with currents being constantly adjusted according to chip temperature.
This leads to power consumption in the chip being very temperature dependent
and difficult to model.
In the simulated model the ambient temperature is kept constant, and the heat
sources are manually chosen to mimic power consumption at different ambient
temperatures. The chip is simulated at room temperature (27◦ C) and at the two
extremes of its specified operating range (-40◦ C and 95◦ C).
6.2.2
Model setup
The temperature distribution simulation does not contain any heat from biased
bolometers. There are two reasons for this. First of all, a row of bolometers would
never be biased during such a long time that all temperature transients would die
out. Second, the results of these steady state simulations serve as initial values for
the subsequent time-dependent simulation where the bolometers are biased only
during an assigned time slot.
The bottom side of the silicon substrate is attached to a heat sink. The heat sink
is modeled as a constant temperature on the substrate’s bottom side and is the
only place where energy is exiting the system. The sides of the chip are connected
to part of the packaging, but the area of the sides is much smaller than the bottom
surface, reducing their importance as a heat sink to such a degree that they have
been omitted.
The chip’s top side with the bolometers is contained in a vacuum package. Being in
vacuum there is no heat transfer through either conduction or convection, leaving
radiation as the only way for energy to escape. Bolometers are designed to absorb
energy very well, and the amount of energy exiting through radiation is expected
to be very limited and has been ignored.
The blocks belonging to the column circuits have been slightly modified to avoid
the very small gaps that would otherwise be separating them. Areas of considerably smaller size, compared to their neighbours, will force nearby mesh to be
very dense in order to properly connect to the small mesh elements. Blocks have
been moved slightly or have had their area adjusted to close gaps between blocks.
To minimize errors from this area change the power densities of the blocks are
adjusted as well in order not to change the total amount of energy entering the
system.
30
6.2.3
Simulations and results
Meshing
The whole interconnect layer is meshed on the top surface with a two-dimensional
mesh. The active pixels have a mapped, rectangular mesh. A rectangular mesh is
slightly less accurate than a triangular mesh, but the regularity of the rectangular
mesh provides data points positioned at the same locations in all pixels, making
comparison between columns more accurate.
After some preliminary simulations, it was quickly seen the only noticeable temperature gradients in the active pixel array are found at the edges. To save computation time, the active array is divided into two mesh regions. The first region
being a relatively narrow rim along the edges enclosing the areas with larger temperature gradients. The temperature in the remaining center portion is almost
constant throughout the entire region, justifying the use of a less dense mesh to
reduce simulation time.
Figure 6.5: Mesh of the active pixel array. Note the portions of the two axes that
have a more dense mesh. In order for this figure not to get cluttered the mesh has
been thinned out a bit to give a better view of mesh distribution in the different
regions.
The left and right portions of the active pixel array have more mesh elements per
column since it is interesting to see how heat entering the array from the sides
spread in the x-direction. Row density is reduced to not force the center part to
be too densely meshed since the mesh lines must fit together where the two regions
meet. Figure 6.5 illustrates the mesh across the active pixels.
6.2 Temperature distribution in IR camera chip
31
The reference pixel are meshed with mapped rectangular elements identical to the
most dense parts of the pixel array to provide easy comparison of the two blocks.
The rest of the top surface has a triangular mesh for efficient simulation.
Once the top layer is completely meshed it is swept down through the entire interconnect layer to where the silicon substrate begins. At the intersection between
the layers, the rectangular elements stemming from the active pixels are converted
to triangular elements by having a diagonal line inserted to connect it to the mesh
of the silicon substrate which is meshed using an automatic tetrahedral mesh.
6.2.4
Simulation results
Standard Operating Temperature, 27◦ C
The temperature distribution of the whole chip surface is shown in figure 6.6. The
temperature distribution in the array of the active pixels is not visible in this image
because the temperature does not vary enough to be visible when using such a
large color scale. The hot spot in the upper right corner is due to the I/O pads.
Figure 6.6: Temperature distribution on the chip surface. Note that some areas
have temperatures far outside the color scale. Maximum temperature increase is
230mK, located at the I/O pads in the top right corner. Ambient temperature is
27◦ C.
The results most interesting to extract is the temperature distribution across the
32
Simulations and results
active pixels. The distribution in this area is plotted separately in figure 6.7,
this way it is possible to clearly see how temperature is distributed across the
pixels. Not surprisingly there is a temperature gradient along the edges. The
three hotter portions at each side of the array is due to the chip temperature
sensors being placed just outside pixel array. The most prominent temperature
increase is found in the top right corner. This is due to heat from the relatively
hot I/O pads finding its way into the array.
Figure 6.7: Temperature map of the chip’s active pixels. Ambient temperature is
27◦ C.
The reference pixel column is placed to the left of the active array, on the other
side of the three chip temperature sensors. The sensors does create an uneven
temperature throughout the reference column, as showed in figure 6.8.
The camera generates images by calculating the difference between reference- and
active-bolometers. By plotting this difference it is possible to see where the ROIC
causes image artifacts. Each row of active pixels is compared to the reference pixel
in the same row. The difference is plotted in figure 6.9.
6.2 Temperature distribution in IR camera chip
33
Figure 6.8: Temperature in reference pixels. Simulation performed at 27◦ C.
Figure 6.9: Temperature difference compared to reference pixels. Simulation done
at 27◦ C
34
Simulations and results
Minimum operating temperature, -40◦ C
At lower temperatures, the active temperature compensation in the chip is decreasing the amount of power dissipated in the bias circuit which leads to lower
temperatures across the entire pixel array, as seen in figure 6.10.
The hot spots caused by the I/O pads and the column circuits are not significantly
cooler than in the room temperature simulations. The amount of heat coming from
the I/O pads is nearly the same as at room temperature as power consumption in
the pads does not vary much with temperature.
The reference pixels also become cooler when the ambient temperature is lower,
even though a large number of pixels still experience a temperature increase caused
by the chip temperature sensors. The temperature in the reference pixels can be
seen in figure 6.11.
The difference in temperature between the active pixels and the reference pixels is
plotted in figure 6.12. There is still a difference caused by the uneven temperature
distribution in the reference pixels. In contrast to the simulation at 27◦ C, which
had areas both warmer and cooler compared to the reference column, the active
pixels in this simulation are all cooler than their respective reference pixel.
Figure 6.10: Temperature map of the chip’s active pixels. Ambient temperature
is -40◦ C.
6.2 Temperature distribution in IR camera chip
35
Figure 6.11: Temperature in the reference pixel column. Simulation done at -40◦ C.
Figure 6.12: Temperature difference compared to reference pixels. Simulation
performed at -40◦ C.
36
Simulations and results
Maximum Operating Temperature, 95◦ C
When the bolometer resistance decreases as a consequence to the higher ambient
temperature its power consumption is reduced, redirecting some of the power to
the column bias circuits which now dissipate more heat. All this leads to the pixel
surface being hotter than in the previous simulations, as noted in figure 6.13.
The reference pixels are also hotter than in previous simulations, and the temperature fluctuates more throughout the column. The temperature of the reference
pixels is shown in figure 6.14.
The difference in temperature between the active pixels and the reference pixels
is plotted in figure 6.15. At this higher ambient temperature the difference has
increased noticeably, even though the absolute temperature difference is still very
small.
Figure 6.13: Temperature map of the chip’s active pixels. Ambient temperature
is 95◦ C.
6.2 Temperature distribution in IR camera chip
37
Figure 6.14: Temperature in reference pixels. Simulation performed at 95◦ C.
Figure 6.15: Temperature difference compared to reference pixels. Simulation
done at 95◦ C.
38
6.3
Simulations and results
Row biasing simulation
When dealing with time-dependent simulations it is necessary to consider the increased simulation load. Time-dependent simulations require more complex equations that take more time to solve. Add the fact that all calculations need to be
iterated for all time steps and its easy to see that the model needs to be set up
carefully to balance the computation time against the need for resolution.
6.3.1
Model setup
All physics settings are the same as in the previous steady state simulation, with
the exception of the biasing of bolometer rows.
To ensure having the correct temperature distribution when the simulation starts,
the temperature distribution obtained in the steady state simulation is used as
the model’s initial temperature. This way it is not necessary to do considerable
amounts of time-dependent simulations just waiting for the system to stabilize.
The only heat source not located on the boundary between the silicon substrate and
the interconnect layer is the heat dissipated in the bolometers. Since no bolometers
are present in this model, the heat generated by them is inserted directly onto
the chip’s top surface. While this might be a very significant simplification, the
alternatives besides including a bolometer model are very limited.
As the bolometers are biased one row at a time, the most logical way of creating
heat sources for the bolometer rows is to draw strips on the surface and then bias
one strip at a time. The downside with this approach becomes very clear when
trying to mesh the surface, as all the hundreds of strips are a narrow geometry of
their own, all these areas must have their own mesh elements, causing the mesh
to be very dense. Another problem is that all these strips need to have their own
time-dependent heat source; manually selecting one strip at a time to define its
heat source is an extremely tedious task.
A better approach is to have a single continuous surface across the whole array of
active pixels. This creates a better situation for the mesh to be controlled properly.
The heat is not supposed to be applied uniformly to the surface, but a surface can
only have a single heat function. This means the heat source must be controlled
by a function which inserts heat at the correct row at the correct time, as opposed
to all previous simulations where the heat sources have just applied heat evenly
across the whole surface. The function needs to have both the y-coordinate and
the elapsed time as arguments.
The biasing moves across the pixels in discrete steps, but the movement can also
be though of as a continuous wave moving across the surface. With the help of the
heat wave, a function controlling the biasing can be created. Having the bias time
and pitch for the bolometer rows, the speed of the heat wave travelling across the
6.3 Row biasing simulation
39
surface is easy to obtain. The function evaluates the wave’s position and enables
the heat source at all coordinates placed within the same strip as the wave.
The position of the wave is obtained through equation 6.2.
ywave = t · vwave
pitch
vwave =
bias time
with
where
ywave
vwave
t
pitch
bias time
=
=
=
=
=
(6.2)
Wave position (y-coordinate) [m]
Wave speed [m/s]
Elapsed time [s]
Pixel pitch [m]
Time slot length [s]
After having determined the position of the wave, it is only a matter of testing
whether a coordinate is in the same row as the heat wave. Heat is applied to all
coordinates fulfilling the condition in equation 6.3.
ywave
pitch
ywave
y − y0
<
≤
pitch
pitch
where
ywave
= Wave position (y-coordinate) [m]
y
= Coordinate to test (y-coordinate) [m]
y0
= Starting position (y-coordinate) [m]
pitch
= Pixel pitch [m]
b c rounds down to the closest integer, d e rounds up to the closest integer
(6.3)
40
6.3.2
Simulations and results
Simulation results
Temperature data is extracted from ten adjoining active pixels in the middle of
the pixel array, all belonging to the same column. The temperature from the
corresponding ten reference pixels is also extracted. The internal heating in the
bolometer is causing temperature increases much higher than the pixels’ steady
state temperature, making the choice of which pixels to examine less important.
The biasing does make the temperature increase significantly compared to the
steady state temperature. Temperature on the surface of the pixel is increased by
nearly 600mK, which is about 100mK higher than the reference pixel. The plot
can be seen in figure 6.16.
Figure 6.16: The plot shows the temperature distribution in the ten pixels included
in the bias simulation. The plot shows the temperature distribution at the moment
when the seventh pixel is biased. The grid is representing the width of each pixel.
Simulation performed with an ambient temperature of 27◦ C.
When the same simulation is performed at an ambient temperature of -40◦ C,
the surface temperature is only increased by 100mK. As the reference pixels are
also cooler, the different between the them is reduced to 16mK. The results are
displayed in figure 6.17.
6.3 Row biasing simulation
41
Figure 6.17: Temperature distribution in ten active pixels near a biased pixel. The
plot is showing the temperature distribution when the seventh sampled pixel is
biased. The grid shows the extent of each pixel. Simulation performed at -40◦ C.
The results from the 95◦ C ambient temperature simulation is found in figure 6.18.
There is a little less power being dissipated in the bolometer than in the 27◦ C
simulation, resulting in a slightly lower temperature increase when biased.
Figure 6.18: Temperature distribution in ten active pixels near a biased pixel.
The plot is showing the temperature distribution when the seventh sample pixel
is biased. The grid shows the extent of each pixel. Simulation performed at 95◦ C.
42
6.4
Simulations and results
Heat transfer on pixel level
As previously mentioned, the pixel cells are too complex to be included in chip level
simulations. However, it is possible to simulate a smaller pixel array to investigate
the thermal coupling between pixels. The results can then be compared to the legto-leg coupling that exists in the bolometer model using lumped elements. The
array consist of a 3 by 3 array of pixels, where all pixels have their full metal
wiring still intact.
6.4.1
Model setup
The same amount of power dissipated in a biased bolometer is applied onto the
pads of a center pixel. By measuring the temperature increase in neighbouring
pixels the thermal coupling between them can be obtained. As in all previous
simulations, the outer edges are thermally insulated, meaning no heat can escape
through these surfaces.
In all other simulations a heat sink has been placed on the bottom of the silicon
substrate. In this simulations this method is not practical since the substrate
is about twenty times as thick as the whole interconnect layer. By adding such
a large geometry the model would be much more complex and hard to simulate
successfully. Instead of including the silicon substrate, a condition is applied to the
bottom surface of the interconnect layer governing the amount of heat flux that
exits the system. The amount of heat flux passing through the surface depends on
the difference between surface temperature and ambient temperature as described
in equation 6.4. This approach is equivalent to placing an infinite number of
lumped resistances between the interconnect layer and the heat sink, meaning the
silicon substrate now only conducts heat along the z-axis. The amount of heat
travelling between different parts of the interconnect layer by passing through the
substrate is very limited and will not have any noticeable effect on temperature
distribution.
with
where
φq
T
Tamb
h
ksilicon
∆z
=
=
=
=
=
=
φq = h(T − Tamb )
ksilicon
h =
∆z
Heat flux [W/m2 ]
Temperature [K]
Ambient temperature [K]
Heat flux coefficient [W/m2 K]
Thermal conductivity of silicon[W/m K]
Substrate thickness [m]
(6.4)
6.5 Temperature distribution when using polysilicon resistors
6.4.2
43
Simulation results
Like in the simulations that determined the pixel’s average thermal conductivity,
heat travels a lot easier along the same column compared to the the same row.
This is believed to be caused by a combination of the better conductivity along
columns, but also by the fact that both neighbour pads in the same column have
edges close to the biased pads, as opposed to the neighbours in the same row where
one pad is further away from the warm pixel than the other.
Figure 6.19: Thermal correlation between pixels. The power produced in a biased
bolometer is applied onto the two pads in the center pixel. The bolometer itself is
bonded to the circular portion of the pad.
6.5
Temperature distribution when using polysilicon resistors
The chip has a number of polysilicon resistors placed above the pixel array that
can be used as a substitution to the bolometers to test and verify the chip without
having to mount any bolometers. The first actual temperature measurements of
the chip will likely be carried out on a chip where the bolometers have not been
mounted. By also having a simulated temperature distribution of this scenario, it
is possible to compare the simulation with the measurement before the bolometers
have been mounted. If this simulations is accurate, it reasonable to believe the
other simulations will also be accurate.
44
6.5.1
Simulations and results
Model setup
There is one resistor for every column, each of them having the same electrical
resistance as a bolometer at 27◦ C, making the chip believe it is using the actual
bolometers. The same amount of power previously dissipated in a biased bolometer
row is now applied to the polysilicon resistor area. There is no heat coming from
any active- or reference-bolometers.
6.5.2
Simulation results
The results are displayed in figure 6.20, a slight temperature increase can be seen
in the polysilicon resistor area directly above the active pixels. Other than that the
distribution is nearly identical to the temperature map presented in section 6.2.4
which described chip temperature distribution at 27◦ C.
Figure 6.20: Temperature distribution of the chip surface when using polysilicon
resistors instead of bolometers.
Chapter 7
Discussion
COMSOL Multiphysics seems to be a good tool for simulating temperature distribution in an integrated circuit. It is reasonable easy to get acquainted with and
the user interface is straightforward when setting up simulations and also provides
many intuitive ways of presenting simulation results. The close relationship with
MATLAB makes it easy to transfer functions, parameters and data between the
two. However, the drawing tool lacks a lot of functionalities normally found in
dedicated drawing tools.
The complexity of the thermal model must be balanced well to keep simulation
time and computer requirements on a reasonable level. This is especially true in
time-dependent simulations where time steps adds to simulation load. The most
critical parameters are the number of mesh elements and the number of time steps.
All temperature distribution simulations show temperature gradients in the active
bolometer array caused by the temperature sensors and the I/O pads. Even though
the temperature plots look very dramatic, the temperature only varies by a few
millikelvin. When comparing the temperatures to another similar simulation of the
same chip, the simulations presented here show significantly lower temperatures.
However, the temperature gradient looks similar in both simulations; and it is the
gradient that is the most important output from this model.
It is possible there are weaknesses in the model explaining the low temperature
increases. Power consumption in the blocks is assumed to be accurate as they
have been measured in a prototype chip. The uncertainty lies more in the model’s
thermal conductivity, mainly in how heat flows toward the heat sink. The transition between the silicon and the interconnect layer might be modeled to let heat
through more easily than what is the case in the actual chip. There is a very
thin layer of silicon dioxide separating the two layers, which is not included in
the model. Silicon dioxide is a poor thermal conductor and the layer could, even
though it is very thin, cause more heat to stay in the interconnect layer instead of
being transported toward the heat sink.
45
46
Discussion
It is interesting to see the reference pixels being affected to such a high degree by
the chip temperature sensors. An unwanted temperature increase in the reference
pixels can influence readout in whole rows of active pixels. Therefore additional
effort has to be taken in terms of block placement and power consumption to
minimize the unwanted temperature differences between the reference- and activepixels.
The simulations show a predictable temperature gradient for all three ambient
temperatures. The temperatures does increase when ambient temperature is increased, but the distribution does not change as much as might have been expected.
The results imply the temperature compensation in the chip works well to reduce
thermal gradients caused by changes in ambient temperatures.
Time-dependent row biasing simulations show that there is pixel-to-pixel interference between neighbouring pixels. However, the simulations suffer greatly from
not having a bolometer model. Once the bias power is modeled to come from the
bolometer itself, the temperature interference is expected to decrease. Due to the
large thermal capacitance in the bolometer, the temperature increase in the currently biased bolometer is less likely to be affected by heat from previously biased
bolometers. The model still serves a good purpose as a good foundation for future
models as the biasing function and the chip’s thermal model can still be used in
future simulations.
Chapter 8
Improvements and future
work
As with all models, they need to be compared to actual measurements in order
to be validated. This can hopefully be done quite early in the testing phase as
comparison can be made using the results showing temperature distribution when
using polysilicon, without having to bond any bolometers to the chip. Measuring
chip temperature though is beyond the scope of this thesis.
A thermal model of the bolometer needs to be included to accurately simulate
effects from bolometer biasing. Including the capacitive effects of the bolometers
will generate better results when simulating transient behavior of the bolometer
row biasing.
The layout of the chip with its circuit blocks is not very complicated, but the
unintuitive drawing environment in COMSOL Multiphysics is very frustrating to
use when having rectangles placed inside other rectangles as is the case with the
chip. Whether COMSOL Multiphysics is used as the simulation tool or not, it
would be beneficial to create a script that is able to use the coordinates of the
circuit blocks to create a finished layout that could be imported into the simulation
tool. If practically possible, it would also be very helpful if the scrip could extract
block information directly from the chip’s IC design file. This would make it easy
to update the model’s circuit blocks if they were to change in future versions.
47
Bibliography
[1] T.L. Williams. Thermal imaging cameras: characteristics and performance.
CRC Press, 2009. ISBN 978-1-4200-7186-3.
[2] P. Ericsson. Low cost IR imaging. Aperturen, (1), 2009.
[3] J.L. Tissot, B. Fièque, C. Trouilleau, P. Roberts, A. Crastes, C. Minassian,
O. Legras, J.J. Yon, and A. Arnaud. Uncooled amorphous IRFPAs with 25µm
pixel-pitch. In Ronald G. Driggers and A. David Huckridge, editors, ElectroOptical and Infrared Systems: Technology and Applications III, volume 6395
of Proc. SPIE, 2006.
[4] Y. Tanaka, A. Tanaka, K. Iida, T. Sasaki, S. Tohyama, A Ajisawa, A. Kawahara, S. Kurasina, T. Endoh, K. Kawano, K. Okuyama, K Egashira, H. Aoki,
and N. Oda. Performance of 320x240 uncooled bolometer-type infrared focal
plane arrays. In Bjørn F. Andresen and Gabor F. Fulop, editors, Infrared
Technology and Applications XXIX, volume 5074 of Proc. SPIE, 2003.
[5] W.J. Parrish and J.T Woolway. Improvements in uncooled systems using bias
equalization. In Bjørn F. Andresen and Marija Strojnik, editors, Infrared Technology and Applications XXV, volume 3698 of Proc. SPIE, 1999.
[6] F. Simoens, M. Tchagaspanian, A. Arnaud, P. Imperinetti, G. Chamming’s,
J.J. Yon, and J.L. Tissot. New IRCMOS architecture applied to uncooled microbolometers developed at LETI. In Bjørn F. Andresen, Gabor F. Fulop, and
P.R. Norton, editors, Infrared Technology and Applications XXXIII, volume
6542 of Proc. SPIE, 2007.
[7] H.D. Baehr and K. Stephan. Heat and Mass Transfer. Springer, 1998. ISBN
3-540-63695-1.
[8] G. Bäckström. Fields of Physics by Finite Element Analysis. Studentlitteratur,
1998. ISBN 91-44-00655-1.
[9] C. Nordling and J. Österman. Physics Handbook for Science and Engineering.
Studentlitteratur, eight edition, 2006. ISBN 91-44-04453-4.
49
Upphovsrätt
Detta dokument hålls tillgängligt på Internet — eller dess framtida ersättare —
under 25 år från publiceringsdatum under förutsättning att inga extraordinära
omständigheter uppstår.
Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner,
skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för ickekommersiell forskning och för undervisning. Överföring av upphovsrätten vid en
senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av dokumentet kräver upphovsmannens medgivande. För att garantera äktheten, säkerheten och tillgängligheten finns det lösningar av teknisk och administrativ art.
Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman
i den omfattning som god sed kräver vid användning av dokumentet på ovan beskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådan form
eller i sådant sammanhang som är kränkande för upphovsmannens litterära eller
konstnärliga anseende eller egenart.
För ytterligare information om Linköping University Electronic Press se förlagets hemsida http://www.ep.liu.se/
Copyright
The publishers will keep this document online on the Internet — or its possible replacement — for a period of 25 years from the date of publication barring
exceptional circumstances.
The online availability of the document implies a permanent permission for
anyone to read, to download, to print out single copies for his/her own use and
to use it unchanged for any non-commercial research and educational purpose.
Subsequent transfers of copyright cannot revoke this permission. All other uses of
the document are conditional on the consent of the copyright owner. The publisher
has taken technical and administrative measures to assure authenticity, security
and accessibility.
According to intellectual property law the author has the right to be mentioned
when his/her work is accessed as described above and to be protected against
infringement.
For additional information about the Linköping University Electronic Press
and its procedures for publication and for assurance of document integrity, please
refer to its www home page: http://www.ep.liu.se/
c Stefan Salomonsson