1. Introduction
Thermal detectors’ operation is related to the absorption of incident radiation, among others. This absorption is determined by the spectral-dependent surface absorptance of the detector or absorber material. According to Planck’s law, any object whose temperature is greater than 0 K radiates at thermal equilibrium, and the spectral radiance of this electromagnetic radiation can be expressed by Equation (1).
Here,
= spectral radiant existence,
= temperature,
λ = wavelength,
= Plank’s constant,
= speed of light in the propagating medium, and
= Boltzmann’s constant. When infrared (IR) radiation from an object is absorbed by a detector material, the temperature of the material changes and a measurable change in electrical signal is produced. This change in the electrical properties of the material can be measured. For an object at a temperature of 300 K, the peak emittance occurs around 9.5 µm of wavelength, according to Planck’s law [
1]. So, Planck’s law gives us the feasibility of using a detector operating at room temperature. The typical spectral response for thermal detectors is in the IR region (700 nm–1 mm) [
2,
3].
Microbolometers are thermal detectors in which the resistance changes in the sensing layer because of the absorption of irradiation energy [
4,
5]. This change in resistance is associated with the temperature coefficient of resistance (TCR) of the material, which is defined by Equation (2).
where
R is the resistance of the material, which has a TCR of
when a temperature change of
dT yields a resistance change of
dR. Both the TCR and resistivity are material properties, and materials with a higher TCR would yield microbolometers with higher figures of merit such as responsivity and detectivity. Microbolometers are widely used in many applications, which include defense and security, surveillance, autonomous driving, and many others. As no cooling is required, these detectors are lightweight as compared to their counterparts, such as photon detectors, making them easily portable. The absorption of IR radiation in the sensing material creates a very small change in temperature. Because of this, it is very important to have good thermal isolation so the absorbed radiation can be prevented. Excellent thermal isolation in combination with a material with a high TCR will exhibit a microbolometer with higher figures of merit.
The linear equation relating resistance and temperature change is expressed by Equation (3).
where
is the final resistance of the material when there is a temperature change of
and
is the initial resistance at room temperature. TCR depends on the properties of the material. In the case of semiconductors, the TCR is negative and has an exponential temperature dependence. Because of the negative TCR, the decrease in temperature increases the current flow through the sensing layer, and this could be burned out if we do not have a good model.
The temperature change of a body,
, subjected to IR radiation is defined by Equation (4).
The temperature gradient is defined as the difference in temperature between the detector and the substrate. This temperature change will depend on the heat flux , which is irradiated by the sensor, which has an emissivity of . Here, that is the angular frequency related to the irradiant energy that falls on the sensor, is the thermal time constant, and is the effective thermal conductivity of the microbolometer.
Besides TCR, there are two important figures of merit that are used to analyze the performance of a microbolometer. These are - responsivity and detectivity. Primarily, the values of these figures of merit indicate the fundamental performance limits of thermal detectors.
The voltage responsivity,
of a microbolometer is defined as the amount of output power obtained per unit of radiant optical power input and can be expressed by Equation (5).
where
is the bias current.
Another important figure of merit detectivity is the area normalized signal-to-noise ratio, which is expressed by Equation (6).
where
is the voltage responsivity,
Ad is the detector area,
is the noise-equivalent bandwidth, and
is the total noise.
is related to the heat transfer in solid by conduction (
), convection (
) and radiation (
). For a microbolometer operating in vacuum, the bolometer must be enclosed in vacuum to increase the performance so that we can ignore the convection,
. Therefore, we can calculate this value by considering Equation (7).
A microbolometer is composed of different layers and materials with different thermal conductivities. Therefore, we need to consider these different layers and dimensions between the irradiation and the heat sink to calculate the value of
. For a microbolometer operating in vacuum,
is related to how much of the irradiation energy is absorbed by the microbolometer. The value of this could be calculated by Equation (8).
where
is the Stefan–Boltzmann constant. We can say that this is the only way by which heat can be conducted between the detector and the surrounding area when a microbolometer is operating in vacuum. Other than the detector area, other parameters that affect the value of
are dependent on the material properties.
The thermal conductance of a microbolometer depends on the structure and volume of the arms. A well-designed arm can perfectly balance the heat conduction towards the heat sink and the thermal time constant of the device. The value of thermal conductance has a direct effect on the responsivity of the device and is dependent on the
. This value can be calculated using Equation (9).
where
is the thermal conductivity of the arm,
is the cross-sectional area of the arm, and
is the length of the arm of the microbolometer. This equation can be applied to
numbers of “layers” that make up the arms to calculate the effective thermal conductance. In our model, the thermal conductance depends on two arms made of titanium. The resulting effective thermal conductance can be expressed by Equation (10).
The thermal time constant () is equal to the heat capacity over the thermal conductance. This value represents the time required by the sensor to reach 63% of its possible maximum temperature.
The effect of the heat capacity of the model is considered to evaluate the performance of the device. To calculate the value of the heat capacity of the model, we use Equation (11).
where
,
, and
are the specific heat capacity, density, and volume, respectively, of the materials that constitute the detective membrane. Therefore, we could express Equation (12).
Knowing these two values, we can calculate the value of the thermal time constant of the model using Equation (13).
From Equation (4), it can be seen that lower values of and would yield higher , which would increase the detectivity and responsivity. While TCR is a purely material property, responsivity and detectivity of a microbolometer can be increased by lowering and values through the design. In this work, we studied the change in temperature in the sensing layer as a function of time to study the thermal time response when we modified the dimensions of various layers to obtain higher figures of merit of a microbolometer.
To this day, various microbolometer designs have been mentioned and implemented [
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16]. Each model the scientific and engineering community presents seeks to improve its capabilities. They have been focused on developing the fabrication of dense pixel arrays to improve image quality, leaving aside the sensitivity and detectivity of the pixel. Recently, the discussion of improving these two parameters has been revived with the emergence of new semiconductor alloys and nanomaterials. In this work, we designed a dual-cavity microbolometer that used alloys of germanium, silicon oxygen, and tin (Ge
xSi
ySn
zO
r) as the sensing layer [
17]. This work reports the design, simulation, and performance analysis of the figure of merit of a microbolometer that used Ge
36Si
0.04Sn
11O
43 thin films as the sensing layer.
2. Materials and Methods
We used the finite element method (FEM) utilized by COMSOL Multiphysics software to design the microbolometer and construct the three-dimensional model. We also used the same software to determine the figures of merit of the microbolometer.
COMSOL provides an integrated development environment (IDE) that combines a model builder in 2D and 3D environments and workflows to mix more than one physics phenomenon [
18]. In COMSOL, we can couple many physical phenomena to the model we built to obtain the responses of the devices. COMSOL provides heat transfer with surface-to-surface radiation (HTSSR) Multiphysics coupling to model this phenomenon [
19]. When we added this module to the model builder, it automatically added the heat transfer at the solid interface (HTSI) and surface-to-surface radiation interface (SSRI) [
20]. These two physics are coupled. This combination provides the governing equations and boundary condition nodes necessary to simulate the heat transfer by irradiation using the blackbody theory. Moreover, we used the electric current interface (ECI) to study the effect of heat change on the resistance of the sensing layer [
21].
We studied the heat transfer process in the microbolometer model and observed how this phenomenon affected the electrical resistance of the microbolometer. One of our objectives is to see the effect of applied heat flux on the temperature change of the sensing material and thereby the change in the resistance of the sensing material. The implementation of this computational model helped us understand the thermal heat distribution and electrical response of the microbolometer and determine the figures of merit in detail [
22].
Our current work is based on the design and simulation of a microbolometer using a double sacrificial layer.
Figure 1a shows the side view, while
Figure 1b shows the top view of the microbolometer we designed using two cavities. In this design, two overhanging layers were built on top of the substrate using sacrificial layers. The first layer from the bottom is made of the sensing material, while the top layer represents the absorber. Here, titanium (Ti) was used as the electrode arm layer, while nickel–chromium (Ni
80Cr
20) was used as the absorber layer.
In
Table 1, we show the properties of the nickel–chromium (Nr
80Cr
20) alloy used to build the absorbing layer [
23]. Titanium (Ti) was used to build the post, arms, and contacts [
24], and germanium–silicon–tin–oxide (Ge
36Si
0.
04Sn
11O
43) to build the sensing layer [
17]. The resistivity parameter used in the simulation for the sensing layer was measured using a Linseis thin film analyzer. The measured electrical resistivity value using a four-point probe was
Ωm. Using this value, we computed the device’s resistance using COMSOL. At room temperature, the resistance was found to be 1.049 MΩ.
It was assumed that the device’s initial temperature was 298 K, and a heat flux of 50
was applied to the device to see the effect of irradiation on the sensing layer. We varied the thickness, dimension, and geometry of different layers to see the parametric effect of them on the device’s performance. The design was optimized to see the effect of it on the temperature rise of the sensing material.
Table 2 shows the dimensions of different layers along with the materials we used to optimize the performance of the device. The reason for this is that these parameters have a direct relationship with thermal conductance and the response time of the device. The purpose of varying these parameters is to find a balance between heat capacity and response time.
For the study of heat transfer, we used 1000 ms as the study time in steps of 1 ms for our simulation. This study computes the change in temperature in the microbolometer in this time frame for different arm widths and thicknesses.
One of the biggest challenges of the computer simulation was finding the correct values between the meshing parameters and the “fully couplet” setting values. Many times, the simulation diverges because of an inconsistency in the tolerance value. Therefore, we set the values in the “fully couplet setting” section to improve the convergence. We calculated the responsivity, detectivity, and NEP of the device using equations [
11,
12,
13].
To calculate the thermal time constant of the model, we used the analytical Equation (14); where
is the initial temperature and
is the maximum change in temperature.