On this page, we will calculate the temperature changes in a metamaterial microbolometer sensor as a result of IR absorption.
The main elements of metamaterial microbolometer are an absorber and a thermistor. The absorber is composed of a silicon layer sandwiched between a periodic gold disks and a gold mirror. Under the absorber, there is a thin silicon nitride (Si3N4) film followed by the vanadium oxide (VOx) thermistor layer. The thin silicon nitride layer delivers heat from the absorber to the thermistor layer and serves as electrical insulation. The device is suspended by a Si3N4 bridge for thermal isolation.
Typical design goal for metamaterial microbolometers is to reduce the pixel size without sacrificing detector sensitivity and the thermal time constant. This requires both optical and thermal simulations. We first carried out an optical simulation to calculate the absorption due to IR radiation. Then we take the optical absorption profile and use it as a heat source in the subsequent heat transport simulation in HEAT to calculate the temperature change in the thermistor layer. In addition, because the HEAT solves the coupled system of equations for heat transport and conductive electrical transport, we can also look at the electrothermal effect due to an applied voltage and calculate the IV response for the microbolometer.
Since the absorption is mostly confined in the absorber region, we can consider only this part of the device in optical simulation and ignore the rest of the underlying layer. Assuming that the optical behavior of each pixel is identical , we can further reduce the simulation volume by only including a single unit cell of the array and impose periodic boundary conditions as if there are infinite number of such arrays. This will significantly reduce the simulation time required. If the radiation has a non-uniform distribution and each pixel experiences different amount of absorption, then more unit cells in the device will need to be included in the optical simulation.
When applicable, the simulation time can be further reduced by taking advantage of the symmetry of the structure. As seen in the figure below, a mesh override region is used to resolve the thin layers as the thickness of the dielectric layer is critical to the absorption.
After running the simulation file meta_microbolo.fsp, run the following script to create the reflection, transmission and absoprtion (left).
f = getdata('R','f'); T = -transmission('T'); R = transmission('R'); plot(c/f*1e6,R,T,1-R-T,"Wavelength (um)","R/T/A"); legend('R','T','A');
The cross-sectional electric/magnetic field profiles can be visualized from the 'xz' and 'yz' monitors. The spatial distribution of absorption can be visualized by right-clicking 'pabs' analysis group and selecting 'Pabs'. You can set the 'Parameter' setting as below and use the slicer to get the cross-sectional view at the desired locations. The results show that the magnetic field is confined mainly in the dielectric layer, and this strong magnetic resonance is responsible for the high absorption.
Reflection/transmission/absorption spectra, the magnetic field (Fig 2. (a) and (d) of the referenced paper) and absorption profile at resonance
The absorption resonance of this device can be tailored by changing the radius of the metal disk as shown in the following plot, which can be created by running the meta_microbolo_r.lsf. With a radius of 530 nm, the absorption resonance peaks at around 9.3 um, which corresponds to the human body radiation.
Absorption as a function of radius and wavelength (Fig 2. (b) and (a) of the referenced paper)
Heat transport simulation
For the heat transport simulation, we will be considering the following structure based on the paper by Du, where the metamaterial absorber is rooted on a silicon substrate by two legs. To take advantage of the symmetry for shorter simulation time, only half of the 5x5 pixel structure is simulated in HEAT , as marked by the orange simulation region.
Schematic diagram of integrated microbolometer on substrate and its perspective view in HEAT
The 'pabs' analysis group in the optical simulation saves the absorption profile into a .mat file. This file can be imported into the heat transport simulation by using the 'Import Heat' object and selecting the specified file. Note that because we only included 1 unit cell in the optical simulation, we have to copy heat source into each pixel. One can do this easily with the "copy" or "array" function.
We are going to study both the steady-state and transient characteristics of the system in response to the heat source. In both cases, a fixed temperature of 293.15 K is applied to the two pillars supporting the microbolometer as shown in the following figure.
The boundary condition settings in HEAT
For the steady-state simulation, meta_microbolo_steady.ldev, the solver mode is set to 'steady state' in the Edit Heat Solver window. After running simulation, right-click on the 'HEAT' object and visualize the 'thermal' result. In the visualizer, select 'T' in the attribute. Since the absorbed power is relatively small, the resulting temperature change in the microbolometer is very small and is almost uniform in the absorber region. The plot below shows the change in temperature as a function of pixel size, and one can see that, as expected, dT increases quadratically as a function of pixel size
Steady-state thermal distribution and the temperature change as a function of the pixel size (Fig. 6 (b) of the referenced paper)
For the transient simulation, meta_microbolo_transient.ldev, the solver type is set to 'transient' in the Edit Heat Solver window. The on/off setting of the import source can be adjusted in the 'Transient' tab of the same window. To obtain the transient temperature response, run meta_microbolo_extract.lsf. The following plot was obtained by running optical and heat transfer simulations for pixel sizes of 5 and 10 um. It is worth noting that while a larger pixel size gives a larger temperature change, it take longer to reach a steady state level.
Kaikai Du et al., "Wavelength and thermal distribution selectable microbolometers based on metamaterial absorbers," IEEE Photonics Journal, 7, 6800908 (2015).