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 tekniska högskola
Linköpings universitet Linköpings universitet
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
Avdelning, Institution Division, Department
Information Coding
Department of Electrical Engineering Linköpings universitet
SE-581 83 Linköping, Sweden
Datum Date 2011-02-14 Språk Language Svenska/Swedish Engelska/English Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport
URL för elektronisk version
http://www.icg.isy.liu.se http://www.ep.liu.se ISBN — ISRN LiTH-ISY-EX--11/4421--SE Serietitel och serienummer Title of series, numbering
ISSN —
Titel Title
Simulering av temperaturdistribution i IR-kamerachip Simulation of Temperature Distribution in IR Camera Chip
Författare Author
Stefan Salomonsson
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 an-other similar simulation of the chip, there is reason to believe the simulated tem-perature 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 an-other similar simulation of the chip, there is reason to believe the simulated tem-perature increase is a bit low. The other simulation cannot be used to draw any conclusions about the distribution of temperature.
Sammanfattning
Examensarbetet undersöker den temperaturdistribution som uppkommer i ett chip till en IR-kamera till följd av värmeutvecklingen i dess egna utläsningskretsar. Ge-nom att ha information om temperaturdistributionen är det möjligt att längre fram i utvecklingsprocessen skapa algoritmer som subtraherar bort chippets inter-na värmetillskott från den termiska bilden.
Den simulerade temperaturdistributionen visar att de största temperaturgradien-terna 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 tempera-tursensorerna påverkar även temperaturen i kolumnen med referenspixlar, vilket kan ge upphov till avvikelser i den termiska bilden i höjd med dessa temperatur-sensorer.
Simuleringar av radvis basering av bolometrar utförs för att få information om hur bolometerbiaseringen påverkar temperaturen i angränsade rader. Simulering-arna 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 simu-leringsresultat 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 över-stiger 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.
Contents
1 Introduction 1
1.1 Project background . . . 1
1.2 Problem description . . . 1
1.3 Thermal imaging applications . . . 2
1.4 Method . . . 2
1.5 Limitations . . . 3
2 The IR camera 5 2.1 IR camera description . . . 6
2.2 Read out integrated circuit . . . 7
2.3 Temperature read out . . . 9
3 Heat transfer 11 3.1 Heat transfer theory . . . 11
3.2 Finite Element Method . . . 14
4 Chip thermal conductivity 15 4.1 Silicon substrate . . . 15
4.2 Interconnect layer . . . 15
4.3 Thermal properties of pixel cell . . . 16
5 Thermal modeling using COMSOL Multiphysics 19 5.1 COMSOL Multiphysics introduction . . . 19
5.2 Heat sources . . . 20
5.3 Heat application . . . 21
5.4 Meshing . . . 22
5.4.1 Two-dimensional mesh . . . 22
5.4.2 Three-dimensional mesh . . . 24
6 Simulations and results 25 6.1 Thermal conductivity of pixel cell . . . 25
6.1.1 Model setup . . . 26
6.1.2 Meshing . . . 28
6.1.3 Simulation results . . . 28
6.2 Temperature distribution in IR camera chip . . . 29 ix
x Contents
6.2.1 Temperature dependency . . . 29
6.2.2 Model setup . . . 29
6.2.3 Meshing . . . 30
6.2.4 Simulation results . . . 31
6.3 Row biasing simulation . . . 38
6.3.1 Model setup . . . 38
6.3.2 Simulation results . . . 40
6.4 Heat transfer on pixel level . . . 42
6.4.1 Model setup . . . 42
6.4.2 Simulation results . . . 43
6.5 Temperature distribution when using polysilicon resistors . . . 43
6.5.1 Model setup . . . 44
6.5.2 Simulation results . . . 44
7 Discussion 45
8 Improvements and future work 47
Contents xi
List of Figures
2.1 Light spectrum. . . 5
2.2 Atmospheric transmittance in the infrared spectrum . . . 6
2.3 Illustration of bolometer placement on the chip . . . 7
2.4 Typical layers in an integrated circuit . . . 8
2.5 Placement of the chip’s circuit blocks . . . 9
2.6 Schematic of typical pixel bias circuit . . . 10
5.1 Insertion levels of heat sources in IC model . . . 21
5.2 Illustration of general two-dimensional meshes . . . 23
5.3 Adapting quadrilateral boundary mesh for further meshing . . . . 24
6.1 Rendering of pixel cell . . . 26
6.2 Via outline simplification . . . 26
6.3 Removal of metal layer overlap . . . 27
6.4 Results of pixel cell thermal conductivity simulation . . . 28
6.5 Active pixel array mesh . . . 30
6.6 Temperature map of ROIC contribution (27◦C) . . . 31
6.7 Active pixels temperature map (27◦C) . . . 32
6.8 Temperature in reference pixel column (27◦C) . . . 33
6.9 Temperature difference compared to reference pixels (27◦C) . . . . 33
6.10 Active pixels temperature map (-40◦C) . . . 34
6.11 Temperature in reference pixel column (-40◦C) . . . 35
6.12 Temperature difference compared to reference pixels (-40◦C) . . . . 35
6.13 Active pixels temperature map (95◦C) . . . 36
6.14 Temperature in reference pixel column (95◦C) . . . 37
6.15 Temperature difference compared to reference pixels (95◦C) . . . . 37
6.16 Temperature distribution near biased pixel (27◦C) . . . 40
6.17 Temperature distribution near biased pixel (-40◦C) . . . 41
6.18 Temperature distribution near biased pixel (95◦C) . . . 41
6.19 Thermal correlation between neighbouring pixels . . . 43
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.
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 tem-perature 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. Com-mon areas of use are in law enforcement, surveillance and search and rescue op-erations. 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 3
1.5
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
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 wave-lengths are scattered more easily, greatly decreasing the usable range for applica-tions 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 resis-tance changes dramatically with change in temperature. When a bolometer ab-sorbs 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 ther-mal 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 infor-mation 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 function-ality. 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 tem-perature will vary significantly depending on the ambient temtem-perature. 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 tem-perature is due to chip temtem-perature, 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 gen-erally good thermal conductors. Other materials with low thermal conductivity are considered thermal insulators.
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 simula-tion 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 (3.1)
where
m = Object mass [kg]
ρ = Material density [kg/m3]
V = 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 equiva-lent.
Electrical Thermal
Voltage - U Temperature - T
Current - I Heat flux - φq
Electrical conductivity - G Thermal conductivity - k Capacitance - Cel Heat capacity - Cth
3.1 Heat transfer theory 13
Electrical I = G · ∆U (3.2a)
T hermal φq= k · ∆T (3.2b)
where
I = Current [A]
G = Electric conductance [S] ∆U = Voltage difference [U ]
φq = Heat flux [W ]
k = Thermal conductance [W/K] ∆T = 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 φq = k · l · ∆T (3.3) where φq = Heat flux [W/m] k = Thermal conductivity [W/m K] T = Temperature [K] l = 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. −Q = −ρc dT dt + ∇ · (k∇T ) (3.4) = −ρc dT dt + kx d2T dx2 + ky d2T dy2 + kz d2T dz2 where
k = Thermal conductivity matrix [W/m K]
ρ = Material density [kg/m3]
c = Specific heat capacity [J/kg K]
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) = kx d2T dx2 + ky d2T dy2 + kz d2T dz2 where
k = Thermal conductivity matrix [W/m K]
ρ = Material density [kg/m3]
Q = Inserted heat [W/m3]
3.2
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 proper-ties, presented in table 4.1.
Table 4.1: Thermal properties of silicon.
Thermal conductivity Density Specific heat capacity
W/m K kg/m3 J/kg K
Silicon 163 2330 703
4.2
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
16 Chip thermal conductivity
transformed into a new homogeneous material having thermal properties equiva-lent 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 Density Specific heat capacity
W/m K kg/m3 J/kg K
x y z
Interconnect layer 3.9 8.4 5.6 2600 687
4.3
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]. Thermal Conductivity Density Specific Heat Capacity
W/m K kg/m3 J/kg K
Aluminum 238 2700 903
Copper 400 8700 385
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= Vtot ρtot X i Vi Cthi· ρi !−1 (4.1) where
Cth = Specific heat capacity [J/kg K]
V = Volume [m3]
ρ = Density [kg/m3]
Chapter 5
Thermal modeling using
COMSOL Multiphysics
This chapter describes the general way of setting up thermal models in COM-SOL 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 in-cluded 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
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 trans-fer 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 to-ward 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 ap-plying a mesh to the geometry to be able to perform the calculations. Mesh-ing is an important part of modelMesh-ing 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 de-scribing temperature distribution are common to plot. It also possible to create one- or two-dimensional graphs plotting results from parts of the ge-ometry.
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 ther-mal modeling. For simplicity, all circuit blocks are assumed to produce heat evenly across their geometry. In reality, heat will be produced in the individual transis-tors, 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 intercon-nect 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 consid-ered 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 density W/m2 = block power [W ]
block area [m2] (5.1)
5.4
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 compro-mise 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 compre-hensive 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 bound-ary 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 param-eters. 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 possi-ble 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
5.4 Meshing 23
(a) Triangular mesh (b) Qquadrilateral mesh
(c) Mapped mesh (d) Converted mapped mesh
24 Thermal modeling using COMSOL Multiphysics
5.4.2
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 automat-ically 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.
2A 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 simula-tions 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.
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
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 equa-tion 6.1, an equivalent conductivity for the examined dimension is obtained.
ki= Q li· ∆Ti (6.1) where k = Thermal conductivity [W/m K]
l = Distance between heat source and thermal ground [m]
Q = Applied heat [W ]
∆T = Average temperature difference [K]
28 Simulations and results
6.1.2
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 29
6.2
Temperature distribution in IR camera chip
6.2.1
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 consid-erably 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 Simulations and results
6.2.3
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 tem-perature gradients in the active pixel array are found at the edges. To save com-putation 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 tem-perature gradients. The temtem-perature 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 inter-connect 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.
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 de-creasing 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 temper-ature fluctuates more throughout the column. The tempertemper-ature 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 Simulations and results
6.3
Row biasing simulation
When dealing with time-dependent simulations it is necessary to consider the in-creased simulation load. Time-dependent simulations require more complex equa-tions that take more time to solve. Add the fact that all calculaequa-tions 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 (6.2)
with vwave=
pitch bias time where
ywave = Wave position (y-coordinate) [m]
vwave = Wave speed [m/s]
t = Elapsed time [s]
pitch = Pixel pitch [m]
bias time = 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 ≤ y − y0 pitch < ywave pitch (6.3) where
ywave = Wave position (y-coordinate) [m]
y = Coordinate to test (y-coordinate) [m]
y0 = Starting position (y-coordinate) [m]
pitch = Pixel pitch [m]
40 Simulations and results
6.3.2
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 Simulations and results
6.4
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 leg-to-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. φq = h(T − Tamb) (6.4) with h = ksilicon ∆z where φq = Heat flux [W/m2] T = Temperature [K]
Tamb = Ambient temperature [K]
h = Heat flux coefficient [W/m2K]
ksilicon = Thermal conductivity of silicon[W/m K]
6.5 Temperature distribution when using polysilicon resistors 43
6.4.2
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
polysil-icon 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 Simulations and results
6.5.1
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.
