Jeong JunKyo^{1}
Jeong ByeongJun^{1}
Oh Jae Sub^{2}
Lee GaWon^{1}

(Department of Electronics Engineering, Chungnam National
University, Daejeon, 34134, Korea)

(Development of Global Nanotechnology, National NanoFab Center,
Daejeon, 34141, Korea)
Copyright © The Institute of Electronics and Information Engineers(IEIE)
Index Terms
Uncooled aSi IR microbolometer, infrared sensor, time constant, simulation, downscaling, temperature coefficient of resistance
(TCR)
I. INTRODUCTION
Infrared (IR) detection techniques can sense radiation from an object and measure
the temperature or visualizing the shape of the object in an environment with no visible
light ^{(1}^{3)}. IR detectors are typically classified into two types—uncooled and cooled—depending
on the operating temperature of the detector. A cooled device has high sensitivity
and a fast response but requires a cooling device to operate at very low temperatures
for noise suppression. An uncooled device, in contrast, operates at room temperature
without the need for a cooling system and provides moderate performance at low cost
to meet a broader range of civilian and military applications ^{(4,}^{5)}. The detector system is fabricated by combining with sensing cells and readout integrated
circuits (ROICs) using microelectromechanical system (MEMS) technology, referred
to as a microbolometer. This detector system is widely applied to human body temperature
measurement and motion detection ^{(6}^{8)}.
Fig. 1 illustrates the typical structure of an uncooled IR microbolometer cell. In the cell,
a reflector is deposited on the ROIC substrate to glance back the IR and increase
the absorption rate. IR sensing layer is spaced by an airgap through an anchor forming
a floating structure. The sensing layer is composed of a cantilever, an absorption
layer, a resistance layer, and a passivation layer. The cantilever supports the absorption
and the resistance layer from the airgap. The absorption layer takes in the incident
IR by which the resistance of the resistance layer is changed, and the passivation
layer prevents the deformation of the structure. For the resistance layer, the most
widely used material was vanadium oxide but a more recent microbolometer uses amorphous
silicon (aSi) because it is fully compatible with the standard complementary metaloxidesemiconductor
(CMOS) processing technology required to integrate the cell with ROICs.
Fig. 1. Typical structure of uncooled IR microbolometer cell.
In aSi microbolometer, lowcost and enhancedperformance has become key issues. Especially,
considering that insitu fabrication of sensing layer with ROICs is desirable for
a high speed operation, the response time represented by a (thermal) time constant
of the microbolometer cell ^{(9)} must be considered and engineered in the design level of pixel structure for enlarging
the applications of microbolometerbased cameras. Several studies have reported on
the enhanced performance of the cell experimentally, focusing on the cell structure
^{(10,}^{11)}. However, the time constant when the pixel size is downscaled has not been efficiently
considered. In this study, the change of the time constant due to downscaling of the
pixel size was analyzed based on the COMSOL Multiphysics simulation, which can be
a useful approach to reduce the design costs and improve the productivity.
II. EXPERIMENT
1. Uncooled IR Microbolometer Designs
The aSi uncooled IR sensor was fabricated; Fig. 2 illustrates the (a) top view, (b) crossview, (c) current flow in the top view, and (d) cell array of 35 ${\mathrm{\mu}}$m pixels. The pixel was designed threedimensionally
and simulated. The thicknesses of the cantilever, the a bsorption layer, the resistance
layer, and the passivation layer were 120 nm SiO$_{2}$, 15 nm TiN, 100 nm aSi, and
110 nm SiO$_{2}$, respectively. The cells were arranged in an 80${\times}$80 array
and packaged in a vacuum.
Fig. 2. Uncooled IR microbolometer cell structure (a) Top view, (b) crossview, (c)
current flow in top view, (d) SEM of fabricated 80${\times}$80 cell array with 35
${\mathrm{\mu}}$m pixel. In this study, the length of the resistance layer and width
of the leg were chosen as factors affecting the time constant.
2. Simulation Models
The IR microbolometer measures the current change due to the joule heating by the
driving voltage and the heat of the IR from outside. In this study, temperature increase
by joule heating was simulated where the time constant was extracted. The time constant
indicates how quickly the system can respond to temperature changes ^{(12)}. In the microbolometer, the time to reach 63.2% of the maximum temperature was set
as the time constant. The equation is:
$$\tau =C/G,$$
where ${\tau}$ is the time constant, $\textit{C}$ is the thermal heat capacity, and
$\textit{G}$ is the thermal conductance. Table 1 presents Specific heat capacity and thermal conductance of materials used in the
simulation.
Table 1. Specific heat capacity and thermal conductance of materials used in the simulation
aSi

Specific heat capacity

700 J/(kg·K)

Thermal conductance

130 W/(m·K)

TiN

Specific heat capacity

210 J/(kg·K)

Thermal conductance

19.2 W/(m·K)

The joule heating is simulated using an Electric Currents module, Heat Transfer in
Solids module provided by the COMSOL and the formula is like below ^{(13)}:
$$\rho C_{p}\left(\frac{\delta T}{\delta t}+u_{\textit{trans}}\cdot \nabla T\right)+\nabla
\cdot \left(q+q_{r}\right)= \alpha T\colon \frac{dS}{dt}+Q,$$
where ${\rho}$ is the density of the material, $\textit{C}$$_{p}$ is its heat capacity,
$\textit{T}$ is the temperature, $\textit{u}$$_{trans}$ is the velocity vector of
translational motion, $\textit{q}$ is the heat flux by conduction, $\textit{q}$$_{r}$
is the heat flux by radiation, $\textit{S}$ is the second PiolaKirchhoff stress tensor,
and $\textit{Q}$ is the heat sources. Furthermore, $\textit{q}$ represents the flow
of heat by conduction and is expressed by Fourier’s law as $q= k\nabla T$, where
$\textit{k}$ is thermal conductivity ^{(13)}. $\textit{Q}$ is a term that includes heat generated by other factors and changes
in temperature due to conduction, convection, and radiation, which are heat transfer
methods. Therefore, $\textit{Q}$ represents the current density, and the current density
can be expressed by the following equations ^{(13)}.
$$\begin{equation*}
Q=J\cdot E
\end{equation*}$$
$$J=\left(\sigma +\mathit{\int }_{0}\varepsilon _{r}\frac{\delta }{\delta t}\right)E+J_{e},$$
where J$_{\mathrm{e}}$ is the current density applied externally and defaults to 0.
In the IR microbolometer, the change in the current by the temperature change is detected
and so the ${σ}$ value is set as a parameter related to the temperature. The equation
is ^{(13)}:
$$\sigma =\frac{1}{\rho _{0}\left(1+\alpha \left(T T_{0}\right)\right)},$$
where ${\rho}$$_{0}$ is the specific resistance at $\textit{T}$$_{0}$, ${\alpha}$
is the temperature coefficient of resistance (TCR), $\textit{T}$ is the heated temperature,
and $\textit{T}$$_{0}$ is the reference temperature, usually 20$^{\circ}$C.
The heat transfer in a solid is ^{(13)}:
$$\begin{equation*}
\rho C_{p}\frac{\delta T}{\delta t}=k\nabla \cdot \nabla T+J\cdot E,
\end{equation*}$$
Therefore, when the material eigenvalue is determined as a constant with the applied
voltage from the outside, a differential equation relating to the temperature is obtained,
and the temperature change over time can be calculated.
In addition to determining IR, we calculated the energy of the wavelength of the IR
light absorbed by the IR microbolometer. For the calculation, Wien’s law and StefanBoltzmann’s
law are used. Wien’s law states that the wavelength at which an object emits maximum
radiation energy at a certain temperature is inversely proportional to temperature.
The equation is ^{(14)}:
$$\lambda _{max}=\frac{2898}{T},$$
where ${\lambda}$$_{max}$ is the wavelength representing the maximum radiation intensity.
StefanBoltzmann’s law states that the sum of the light energy of all wavelengths
emitted from a unit surface area of a black body is proportional to the fourth power
of the absolute temperature of the black body ^{(14)}:
$$P=\varepsilon \sigma eT^{4},$$
where ${\sigma}$ is the StefanBoltzmann constant and ${\varepsilon}$ is emissivity.
Emissivity refers to the ratio of the radiant intensity of an object with the same
temperature to the blackbody surface.
3. External Environment Setting
An important factor for accurate time constant simulation is the external energy loss
of the cell. Fig. 3 is a simple schematic diagram of the heat loss that can occur in the cell.
Fig. 3. Heat loss model in IR microbolometer cell. Q$_{\mathrm{Sink}}$ is heat release
by heat transferred to the ROIC substrate through the anchor and Q$_{\mathrm{Convection}}$
is heat release by ambient convection.
If external energy loss is not considered in the simulation, the temperature of the
cell tends to continuously increase during operation because there is no heat emitted
to the outside and the heat energy inside accumulates. Therefore, to extract the time
constant, it is necessary to set the supplied thermal energy and the lost thermal
energy (Q$_{\mathrm{Exernal}}$). The supplied thermal energy is determined by the
sum of the thermal energy by Joule heating (Q$_{\mathrm{Joule heating}}$) and IR (Q$_{\mathrm{IR}}$).
The total heat energy (Q$_{\mathrm{Total}}$) applied to the cell can be expressed
as:
$$Q_{\text {Total }}=\left(Q_{\text {Joule heating }}+Q_{I R}\right)Q_{\text {External
}}$$
where $\textit{Q}$$_{External}$ can be expressed as the sum of the heat release due
to convection to the outside (Q$_{\mathrm{convection}}$) and the heat release to the
ROIC substrate through the anchor (Q$_{\mathrm{Sink}}$):
$$Q_{\text {Extemal}}=Q_{\text {Convection}}+Q_{\operatorname{Sink}}$$
However, the IR microbolometer is vacuumpackaged, so convection with the outside
does not occur. In this study, the boundary condition is set such that there is no
heat flow except where ROIC substrate and anchor are bonded. Accordingly, only Q$_{\mathrm{sink}}$
was considered in this study. For the simulation, Q$_{\mathrm{Sink}}$ and Q$_{\mathrm{IR}}$
are extracted from the fabricated device with values of 6350 W/(m$^{2}$·k) and 976
W/m$^{2}$. Q$_{\mathrm{IR}}$ and Q$_{\mathrm{Sink}}$ were set based on a 35 ${\mathrm{\mu}}$m
pixel, and the values were normalized to the area even if the cell size is changed
by downscaling, the conditions of the simulation are the same.
4. Temperature Coefficient of Resistance (TCR) Setting
Another important factor for accurate time constant analysis is the TCR of aSi. TCR
of aSi is known to be temperaturedependent but in many cases, the TCR is assumed
to be a constant. To improve simulation accuracy, the temperaturedependent TCR of
aSi is used in this study. Fig. 4 illustrates the TCR based on the temperature; the black curve represents the experimental
data presented in a reference paper ^{(14)} while the red curve is fitted to model the TCR values of aSi. In the reference paper,
TCR was extracted based on temperature using the manufactured aSi device. In this
study, TCR was expressed as a function of temperature and applied to the simulation.
Fig. 5 illustrates the simulation results of the cell current according to the time during
the operation considering the factors described above. The applied voltage is 1.8
V in the simulation. Comparing the simulation with the measurement values of the fabricated
35 ${\mathrm{\mu}}$m pixel devices, the two current values are nearly equivalent.
Based on these results, the applied voltages to the standard designed cells of 25
and 17 ${\mathrm{\mu}}$m were set to the current between 1 and 2 ${\mathrm{\mu}}$A
and 1.3 and 1 V. The standard dimensions of the resistance layer and leg for each
pixel size are depicted in Table 2.
Fig. 4. TCR of aSi used in the simulation. The black curve represents experiment
data ^{(15)} and the red curve is fitted to model the TCR.
Fig. 5. Simulation results of the cell current based on the time during the operation
with the measurements in the fabricated 35~${\mathrm{\mu}}$m cell.
Table 2. Standard designed dimensions of the resistance layer and leg for each pixel
size
Pixel size

35 µm

25 µm

17 µm

Length of the resistance layer

1.0 µm

0.7 µm

0.5 µm

Width of the leg

1.0 µm

0.7 µm

0.5 µm

III. SIMULATION RESULTS
In a microbolometer cell, the total resistance is determined by the length of the
resistance layer and width of the leg. As the length of the resistance layer decreases,
the resistance decreases, which increases the influence of Joule heating. Consequently,
the maximum temperature increases and the time constant increases. In the case of
the leg, the resistance increases as the width decreases. Consequently, the maximum
temperature decreases and the time constant decreases. Therefore, in this study, each
pixel was designed to analyze time constants according to length of the resistance
and width of the leg.
Fig. 6 illustrates three types of 35 and 25 ${\mathrm{\mu}}$m pixels. Fig. 6(a) is a general structure, and Fig. 6(b) and (c) are structures with reduced sensing areas; Type 2 has a larger sensing area than
Type 1. Each pixel is designed to analyze the sensing area effect on the time constant.
Table 3 presents the dimensions of the pixels.
Fig. 6. Cell structure with different sensing areas (a) General structure, (b) Type
1, (c) Type 2 with reduced sensing are. Here, Type 2 has a larger sensing area than
Type 1.
Table 3. Dimensions for standard designed 35 and 25 ${\mathrm{\mu}}$m pixels
Pixel size

35 µm

25 µm

Length of the leg

General

21.5 µm



Type 1

16.5 µm

10.5 µm

Type 2

16.5 µm

10.5 µm

Area of absorption layer

General

866 µm$^2$



Type 1

377 µm$^2$

171 µm$^2$

Type 2

468 µm$^2$

202 µm$^2$

Width of resistance layer

General

32.9 µm



Type 1

20.0 µm

13.6 µm

Type 2

24.0 µm

16.0 µm

Area of anchor

16 µm$^2$

9 µm$^2$

Fig. 7(a) and (b) illustrate the simulation results in a 35~${\mathrm{\mu}}$m pixel. As the width of
the resistance layer increases, the time constant decreases while there is little
change according to the leg width. This is because the effect on the overall resistance
is very small when changing the width of the leg. Therefore, the time constant of
Type 2 is longer than Type 1. Fig. 7(c) and (d) illustrate the time constant of the devices downscaled from 35 to 25 ${\mathrm{\mu}}$m.
25 ${\mathrm{\mu}}$m pixels tend to be similar to 35 ${\mathrm{\mu}}$m pixels. Table 4 presents the resistance values and the ratio for the 35 and 25 ${\mathrm{\mu}}$m
pixels.
Fig. 7. Simulation results on time constant based on (a) the length of the resistance
layer and (b) the width of the leg in a 35~${\mathrm{\mu}}$m pixel and based on (c)
the length of the resistance layer and (d) the width of the leg in a 25 ${\mathrm{\mu}}$m
pixel varying cell structure.
Table 4. Resistance value and ratio for standard designed 35 and 25 ${\mathrm{\mu}}$m
pixels
Pixel size

35 µm

25 µm

Total resistance (A)

General

1,392,555 Ω



Type 1

2,211,525 Ω

2,310,217 Ω

Type 2

1,879,509 Ω

1,972,078 Ω

Leg portion resistance (B)

General

140,416 Ω



Type 1

213,926 Ω

198,084 Ω

Type 2

215,458 Ω

198,352 Ω

Absorption layer resistance (C)

General

1,081,665 Ω



Type 1

1,764,277 Ω

1,603,590 Ω

Type 2

1,438,699 Ω

1,352,226 Ω

Ratio of the leg portion resistance to total resistance (B/A)

General

0.101



Type 1

0.096

0.086

Type 2

0.115

0.101

Ratio of absorption layer resistance to total resistance (C/A)

General

0.777



Type 1

0.798

0.694

Type 2

0.765

0.686

When the cell area is scaled down, the leg dimension can affect the total resistance
of cell. Fig. 8 presents three types of 17 ${\mathrm{\mu}}$m pixels with different leg length. Table 5 presents the dimensions by type for the standard designed 17 ${\mathrm{\mu}}$m pixel.
Fig. 8. Cell structures of 17 ${μ}$m pixel (a) Type 3, (b) Type 4, (c) Type 5.
Table 5. Dimensions of standard designed 17 ${\mathrm{\mu}}$m pixel
Pixel size

17 µm

Length of the leg

Type 3

14 µm

Type 4

20 µm

Type 5

27 µm

Area of absorption layer

Type 3

226 µm$^2$

Type 4

189 µm$^2$

Type 5

164 µm$^2$

Width of resistance layer

Type 3

16.5 µm

Type 4

16.1 µm

Type 5

14.1 µm

Area of anchor

1 µm$^2$

Fig. 9 presents the simulation results and the time constant is longer than for 35 and 25
${\mathrm{\mu}}$m pixels because Q$_{\mathrm{sink}}$ decreases as the contact area
between the anchor and ROIC substrate decreases. Furthermore, unlike 35 and 25 ${\mathrm{\mu}}$m
pixels, the time constant increases as the width of the leg increases. As the length
of the leg becomes longer from Type 3 to Type 5, the time constant decreases because,
as the length of the leg increases, the total resistance increases, decreasing the
current and maximum temperature. Table 6 presents the resistance values and ratios of the standard designed 17 ${\mathrm{\mu}}$m
pixel.
Fig. 9. Simulation results of the time constant based on the length of the resistance
layer and width of the leg in 17 ${\mathrm{\mu}}$m pixel with different length of
the leg.
Table 6. Resistance values and ratios of standard designed 17~${\mathrm{\mu}}$m pixel
Pixel size

17 µm

Total resistance (A)

Type 3

1,335,938 Ω

Type 4

1,585,151 Ω

Type 5

2,044,353 Ω

Leg portion resistance (B)

Type 3

376,650 Ω

Type 4

529,878 Ω

Type 5

710,158 Ω

Absorption layer resistance (C)

Type 3

696,043 Ω

Type 4

765,529 Ω

Type 5

994,522 Ω

Ratio of the leg portion resistance to total Resistance (B/A)

Type 3

0.282

Type 4

0.334

Type 5

0.347

Ratio of absorption layer resistance to total Resistance (C/A)

Type 3

0.521

Type 4

0.483

Type 5

0.486

IV. CONCLUSIONS
In this study, the thermal time constant of an uncooled aSi IR microbolometer cell
is simulated according to the cell dimension and structure. Downscaling is a useful
way to increase the competitive price of devices with highresolution images. For
accurate simulation, thermal properties such as Q$_{\mathrm{IR}}$ and Q$_{\mathrm{Sink}}$
are extracted from the real 80${\times}$80 array device with a 35 ${\mathrm{\mu}}$m
pixel, and the temperaturedependent TCR model of aSi is used. In cell component,
the length of the resistance layer and width of the leg is changed for each pixel
size, 35, 25, 17 ${\mathrm{\mu}}$m. The results show that the time constant increases
as the length of the resistance layer becomes narrower for all pixels. In the case
of the leg width, there is little dependence of the time constant for 35 and 25 ${\mathrm{\mu}}$m
pixels. However, for a 17 ${\mathrm{\mu}}$m pixel, the time constant increases. From
these, it is expected that simulation can propose efficiently a downscaling direction
for a highperformance uncooled aSi IR microbolometer.
ACKNOWLEDGMENTS
This work was supported by the National NanoFab
Center (NNFC) grant funded by the Korean Government
(MOTIE) (N0002454, International joint technology
development project (European technology cooperation
project)), and by a National Research Foundation of
Korea (NRF) grant, funded by the Korea government
(MSIP) (2017R1D1A1B03033601).
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Author
JunKyo Jeong received a B.S.
degree in electronic engineering in
2016 and is currently working toward
an integrated Ph.D. program in the
Department of Electronics Engineering
from the Chungnam National
University, Daejeon, Korea.
His
research interests include flash memory, oxide thin film
transistor.
ByungJun Jeong received a B.S.
degree in Physics in 2017 and is
currently working toward an M.S.
degree in the Department of
Electronics Engineering from the
Chungnam National University,
Daejeon, Korea.
His research
interests include Fabrication high performance oxide thin
film transistor.
JaeSub Oh received the B.S
degrees in Metallurgical Engineering
from Jeonbuk National University,
Jeonju, Korea in 1997, the Ph.D.
degrees at the Department of
Electronics Engineering, Chungnam
National University in 2013, Daejeon,
Korea.
From 1997 to 2004, he was with Hynix
Semiconductor Inc. (originally LG Semiconductor Inc.)
Ichon, Korea, where he was involved in the development
of 0.18um, 0.13um, 0.115um CMOS process
technologies. Since 2004, he has been with National
NanoFab Center, Daejeon, Korea, as a Principal
Research Staff in the development area of Nano Process
Technology.
His main research fields are nanoscale
CMOS, IoT device, Sensors and plasma etching
including nonvolatilememory and flexible display
technology.
GaWon Lee received B.S., M.S.,
and Ph.D. degrees in Electrical
Engineering from Korea Advanced
Institute of Science and Technology
(KAIST), Daejeon, Korea, in 1994,
1996, and 1999, respectively.
In 1999,
she joined Hynix Semiconductor Ltd.
(currently SK Hynix Semiconductor Ltd.) as a senior
research engineer, where she was involved in the
development of 0.115Se and 0.09—S DDR II DRAM
technologies.
Since 2005, she has been at Chungnam
National University, Daejeon, Korea, as a Professor with
the Department of Electronics Engineering.
Her main
research fields are flash memory and flexible display
technology including fabrication, electrical analysis, and
modeling.