MAT-VET-F 20003
Examensarbete 15 hp Juni 2020
Design and Simulation of Terahertz Antenna for Spintronic Applications
Malin Bohman
Nils Eivarsson
Emil Grosfilley
Axel Lundberg
Teknisk- naturvetenskaplig fakultet UTH-enheten
Besöksadress:
Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0
Postadress:
Box 536 751 21 Uppsala
Telefon:
018 – 471 30 03
Telefax:
018 – 471 30 00
Hemsida:
http://www.teknat.uu.se/student
Abstract
Design and Simulation of Terahertz Antenna for Spintronic Applications
Malin Bohman, Nils Eivarsson, Emil Grosfilley, Axel Lundberg
Spintronics is a spin-electronic field where the electron spin angular momentum, in conjunction with charge, is used to read and write information in magnetic sensors and logic circuits, e.g.
hard disk drive (HDD), magnetic random access memory (MRAM) and broadband TeraHertz (THz) emitters. To realize the THz operations of the spin logic circuits THz manipulation of the magnetic state is pivotal. This THz manipulation of the magnetic state in anti- ferromagnetic magnetic materials can be realized by coupling the materials with THz antennas. On the other hand, these antennas enhance the THz amplitude of spin-electronic THz emitters when coupled with its output. Therefore, these THz antennas can not only be coupled with the input of magnetic logics to improve the efficiency of magnetic sate manipulation in logic devices but also with the output of the spintronic THz emitters to enhance the generated THz signal amplitude. In this project, we have examined four types of antennas: h-dipole, spiral, bow-tie, and a sub-THz antenna. All the antennas are placed on top of a MgO substrate material for simplicity. However, a bow-tie antenna is also fabricated on an antiferromagnetic substrate of TmFeO3 to check this antenna’s reliability to manipulate its magnetic state. We have studied the impact of antenna geometries on the generated electric field amplitude. We have optimized each antenna for maximum electric field norm profile, with an increase of 30% for the h-dipole and spiral antennas, and an increase of 100% for the bow-tie antenna. However, in this project we were not able to find any general conclusions about what geometrical parameters can further amplify the generated electric field. None of the antennas generated a large enough peak-to-peak electric field amplitude to manipulate the magnetic state of anti-ferromagnetic materials.
However, they did successfully amplify the spintronic THz emitter output and could certainly be useful in that regard.
ISSN: 1401-5757, MAT-VET-F-20003 Examinator: Martin Sjödin
Ämnesgranskare: Natalia Ferraz Handledare: Ankit Kumar, Rahul Gupta
1 Introduction
1.1 Terahertz radiation
Terahertz (THz) radiation is electromagnetic radiation of frequencies in the range of 0.1-100 THz.
THz radiation can be used for multiple applications, such as data transmission, spectroscopy, imaging and various sensors (1). One of the interesting aspects of THz radiation is its higher information density compared to GHz that is often used in classical electrical components today.
The primary application of interest for this study is in digital data storage and processing, for example the utilization of THz radiation to optically manipulate the state of a bit at ultrafast speeds.
1.2 Spintronics
Spintronics is the field of research that studies the electron spin angular momentum in combination with its charge. These two aspects of the electron are used to read and write information in magnetic sensors and logic circuits, for example in hard disk drives (HDD), magnetic random access memories (MRAM), and broadband THz emitters. One of the most promising prospects lies within data storage, where the writing of information is done by switching the magnetic state. In analogy to how ones and zeroes are stored as a potential difference in modern day electronic devices, one could use the magnetic state achieve the same result. Magnetic state manipulation can be realized by utilizing THz radiation. In order to realize the ultrafast optical switching of anti-ferromagnetic state for dense device integration, THz signal amplitude should be higher than 50MV/m (2).
Storing data with spintronic devices holds several substantial advantages compared to electronic equivalents. They require much lower power to operate, increase the information density by several or- ders of magnitude and are non-volatile (3). Since spintronics use a combination of optical and electrical methods to write and read information, there are fewer heat related energy losses which in turn allows for denser information storage. In addition to this, semiconductor-based electronics are currently lim- ited to signals in the GHz range due to inter connect speed limitations, whereas spintronics technology doesn’t have this limitation. This is due to the fact that many antiferromagnetic materials, a necessary component in spintronics, have resonance frequencies in the THz region, and there is no fundamental limit associated with spintronic technology as it is with semiconducting technology. However, in spin- tronic technology it is channeling to replace ferromagnetic materials with antiferromagnetic materials.
Spintronic technology has potential to revolutionize the telecommunication industry by providing ultra low-power and ultra-fast operated logic circuits.
In the future, it is likely that spintronics will become the standard tool for storing and accessing information. One of the driving factors for making this switch is to lower the energy consumed by information and communication technology, the main issue being the electricity required to run data centers. One prediction shows that, if no advancements are made to lower the energy usage of electronic devices, communications technology may consume 51% of the electricity produced globally in 2030 (4).
1.3 Spintronic Terahertz Emitter
As mentioned another use of spintronics is a broadband THz emitters called spintronic THz emitter (STE), devices made of a stack of ferromagnetic and non-magnetic metal thin films made to generate THz radiation (5). An STE can be seen in figure 1. When the STE is hit by a laser pulse, spin currents are induced in the STE which by the reverse spin Hall effect induce charge currents in the non-magnetic layers. This charge current then acts as a source of THz radiation. STEs could be be used for data transmission in telecommunication if made economically viable and having an broadband THz range.
They could also be used as THz source to manipulate the magnetic state for spin logic applications.
The power of the THz radiation an STE is able to emit is limited by how strong the laser pulse can be without damaging the chip (5).
1.4 Antennas
A potential solution to the limited output power is coupling an antenna to the STE. Antennas are structures that are used to emit or capture radiation. By changing the structure, antennas may become more sensitive to certain frequencies. This is often done by letting it resonate at those frequencies.
Antennas can also be used to focus radiation in a certain direction.
Figure 1: A schematic of an STE (5).
In the application of STE:s, antennas are used to absorb radiation and amplify a desired bandwidth to enable the radiation to be used in data storage. As the STE-antenna will act in the THz range, the structure will be built in a µm scale. These antennas could also be used on spintronic logic circuits to further improve the incoming THz signal.
In the context of this study, antennas are used to amplify the radiation from the STE, and to focus it in a certain bandwidth. The antennas that are to be examined are selected from previous studies. The h-dipole antenna (5), the Spiral antenna (6), the Bow tie antenna (7) and the Sub THz antenna (8) are chosen as they are all antennas that are effective in the lower end of the THz spectrum.
2 Aim
Coupling antennas to STE:s can yield THz radiation with higher amplitude compared to the output of only the STE. The aim is to study this improvement by different antennas by examining the amplitude of the electric field norm (EFN) on the antennas after being exposed to THz radiation. The goal is to achieve a minimum EFN of 50M V /m and thus allow manipulation of magnetic states in spintronic applications.
This will be done by simulating the antennas in the simulation software COMSOL Multiphysics.
3 Theory: Power of the incident radiation
To calculate the power of the THz radiation sent toward the antennas the formula for the intensity (1) for a plane electromagnetic wave taken from Physics Handbook (9) was used:
I =1
2c00E20 (1)
where I is the intensity, c0 is the speed of light, 0 is the vacuum permittivity and E0 is the electric field amplitude. The power carried by the wave through a perpendicular area A (2), is then
P = I · A = 1
2c0E02A (2)
4 Methodology
4.1 Geometry of the antennas
4.1.1 Spiral Antenna
The geometry of the spiral antenna is shown in figure 2a. The antenna consists of a spiral with two turns connected to a arm. The antenna in the study had a arm length, la, a width, W , a gap width, Wg, and a thickness of the antenna material, t. The values of these parameters are listed as the default values in section 4.3. The same applies for the other antennas as well.
4.1.2 H-Dipole Antenna
The h-dipole antenna, seen in figure 2b consists of two mirrored parts. The two parts were separated by a gap Wa. The length between the arms was called la and the height of the arms was called h. The thickness of the antenna was noted ta.
Figure 2: Figures of the antennas and its parameters. (a) shows the spiral antenna, (b) the H-dipole antenna, (c) the bow tie antenna and (d) the sub THz antenna.
(a) (b)
(c) (d)
4.1.3 Bow tie Antenna
The bow tie antenna consists of two triangular sections, each attached to a rectangular plate as seen in figure 2c. The parameters that were varied were those of the rectangular plates. More specifically, their height h, their width W and the gap size Wg. As for the triangular plates, the base and height were kept at constant values of 60µm and 55µm respectively.
4.1.4 Sub THz Antenna
The Sub THz antenna consists of a driven dipole antenna which makes up the center. There’s a rectan- gular plate below the dipole antenna called a reflector. In addition there are three equally spaced plates acting as directors. The geometry of the antenna is described in figure 2d. The default parameter values were set to those in table 1 as these were suggested in (8) for the best gain.
Table 1: Parameters used for the Sub-THz antenna.
w 10µm
g 4µm
ld 115µm lf 35µm lr 280µm ld1 150µm d1 135µm d1d 125µm d2 164µm
4.2 COMSOL Multiphysics
The simulation were done using the simulation software COMSOL Multiphysics, a software made for simulating a multitude of physical problems. It uses a finite element method to solve differential equations depending on the simulated physics. In this study the module for electromagnetic waves in the frequency domain was used. The first part of the simulations was to alter mesh sizes, the simulation space, material constants and boundary conditions until the results from the simulation was physically accurate. After achieving this the parameters of the antennas were varied and the EFN on the antenna was studied.
4.2.1 Simulation space
The simulation space is a cuboid, divided into two parts by a plane which contained the antenna. The plane of the antenna, as seen in figure 4 is situated in the xy plane, which size is different for every antenna. For the h-dipole antenna the plane was 315 × 315µm. For the spiral antenna the plane was 60×54µm, for the bow tie antenna it was 100×150µm. Figure 3 shows the simulation space in COMSOL, for the bow tie antenna.
Figure 3: A figure showing the simulation space in COMSOL.
On top of the antenna, where the incoming radiation is coming from, a 100µm space in the z-direction filled with air was simulated. On the bottom of the antenna a 500µm substrate was used, except for the sub-THz antenna, where multiple substrate thicknesses was simulated.
4.2.2 Mesh
The mesh divides the simulation space into smaller volume elements, in this cases tetrahedrons was used, and the differ- ential equations are solved for the elements. The size of the mesh need to be small enough to give accurate results, how- ever, a smaller mesh also require more computational power, therefore a balance is required to compute accurate results in reasonable time scales. The mesh is automatically generated by COMSOL based on the physics used, but can be manu- ally tuned. To ensure the mesh was small enough the mesh was reduced in size until reducing it further did not alter the results significantly. The mesh sizes of the antennas was based on the minimum wavelength, λminof the simulations.
An example mesh of the spiral antenna is shown in figure 4.
All simulations used a general maximum mesh size for the entire space of λmin/10. Then the mesh of each antenna was fine-tuned in specific regions until it was sufficient.
The h-dipole antenna used a maximal mesh-size of λmin/100 over the antenna. The edges of the gap used a maximal mesh size of λmin/500.
On the entire boundary of the spiral antenna the mesh size was maximally λmin/100 and on the inner and outer
edge on the gap in the spiral the mesh size was maximally λmin/500. The mesh size on the corners of the antenna was further reduced to λmin/1000.
Figure 4: An example of a mesh used in one of the simulations for the spiral antenna.
As for the bow tie antenna, the boundary surface of the material was set to a maximum mesh size of λmin/4 while the antenna plates had a maximum mesh size of λmin/35. Along the edges of the rectangular plates closest to the gap the maximum mesh size was set to λmin/1000, whereas the area between the gap was set to λmin/125.
The Sub-THz antenna used the λmin/20 for the main dipole antenna part. While the directors and reflector each had a maximum mesh size of λmin/15.
4.2.3 Substrate
The antennas from the studies were placed on a substrate. All of our antennas were studied with Magnesium-Oxide (MgO) as substrate. The bow tie antenna was also studied with Thulium Orthoferrite (T mF eO3). The substrate material might influence the results. The MgO was simulated with a relative permittivity of 9.5, and a electrical conductivity of 1S/m. While the T mF eO3 was simulated with a relative permittivity of 1 and an electrical conductivity of 52.239S/m. Both materials had a relative permeability of 1.
4.2.4 Boundary condition
The surface at the top of the simulation was treated as a port with wave excitation and with an incident power calculated with the equation 2. The incident electric amplitude, E0 was 1000V /m in the x- direction. The surface at the bottom of the simulation was treated as a port without wave excitation.
In the x-direction the surface on the edge of the simulation was treated as a perfect electric conductor (PEC). In the y-direction the surface on the edge of the simulation was treated as a perfect magnetic conductor (PMC). The PMC and PEC are chosen like this to have the electric field of the radiation perpendicular to the PEC and the magnetic field perpendicular to the PMC. The antenna itself was treated as a transition boundary, as the currents in the antenna can be assumed to flow only on the surface as it is much larger than the depth. This allows for the antennas thickness to be accounted for without having to mesh it. The thickness of the antenna in z-direction was specified.
4.2.5 Frequency
The simulation in the frequency domain is chosen from the previously mentioned studies and is different for every antenna.
The h-dipole antenna mentioned in the study seemed to be the most effective between 0.5 - 1.5 THz, however, during simulations it was clear that the peak was at a lower frequency. The final frequency that was chosen was therefore 0.2 - 1 THz. As the peaks are quite thin a high resolution was needed, a frequency of 1 GHz was chosen.
The spiral antenna from the study was simulated in the range 0.1 - 2 THz. A simulation at the frequencies 0.1 - 3 THz was performed, as the results in the study ends in a upward trend. However, there was nothing interesting below 0.5 THz. The frequencies that were chosen to be studied were 0.5 - 3 THz, with a resolution of 10 GHz. As the peak was around 0.68 THz and due to a lack of time the revised antenna was only simulated for the frequencies 0.4 - 1 THz. For each parameter variation the simulations were first done using a low resolution to find the peak. After finding a rough estimate of where the peak was the simulation was run with a resolution of 1 GHz in a range of 30GHz around the peak and 10 GHz elsewhere in the 0.4-1 THz range.
For the bow tie antenna, the study mentions a repetition rate of 3 THz, and a resonant frequency of 0.65 THz, which is why the frequencies 0.5 - 3 THz were simulated for the T mF eO3 substrate. For the M gO substrate the peak is clearly below 2 THz, which is why the frequencies 0.5 - 2 THz were simulated. Both simulations were made with a resolution of 10 GHz.
The sub THz antenna was studied for the frequencies 0.3 - 0.8 THz as test seemed to indicate that these were the relevant frequencies. All simulations were performed with a resolution of 20 GHz or 10 GHz.
4.2.6 Plot data
From the simulations there are two types of data considered in the result. EFN and S11-parameter. EFN is the L2-norm of the electric field which is both plotted in specific points on the antennas for varying frequencies and in a plane of the simulation space for one specific frequency. The S11-parameter is a measurement of how much of the electromagnetic radiation sent from the port can be measured at the same port again. In other words, it is related to the reflection. For the h-dipole, sub-THz, and the bow tie antenna the values were plotted on the corners of the gaps of the antennas. For the spiral antenna the values were plotted in eight points along the inner spiral, seen in figure 5.
Figure 5: A graphic of were the EFN were plotted for the spiral antenna.
4.3 Parameters
The antenna parameters that were varied in this study are listen in table 2, as well as their ranges. Each parameters were varied independently, while the other parameters were assigned their default value. For the Sub-THz antenna, only the substrate thickness was varied, not the geometry of the antenna.
Parameters Values Default Spiral antenna
Width, W 1.5-2.5 µm 2 µm
Gap width, Wg 0.8-1.9 µm 1.5 µm Arm length, la 16-20 µm 18 µm Antenna thickness, t 50-400 nm 200 nm
H-dipole antenna
Thickness, ta 5-20 µm 10 µm
Gap width, Wa 10-20 µm 10 µm Arm height, h 150-315 µm 315 µm Arm distance, la 100-250 µm 200 µm
Bow tie antenna
Rectangle width, W 4-6 µm 4 µm Gap width, Wg 3.8-5.8 µm 3.5 µm Rectangle height, h 10-14 µm 10 µm
Sub THz antenna
Substrate thickness 50-500 µm 500 µm
Table 2: The antenna parameters that were varied in the study.
5 Results
5.1 H-dipole antenna
First a h-dipole antenna with the default parameters as shown in table 2 was simulated in the range 0.2-1 THz for every 1 GHz. The EFN for every frequency in the four corners at the middle of the antenna can be see in figure 6, there is a clear peak at 0.265 THz. In figure 7 the electric field profile in the plane of the antenna is shown for this frequency. The highest EFN around the antenna is 0.52 MV/m.
Figure 6: The EFN for the four corners in the middle of the antenna at the frequency 0.265 THz, for the default h-dipole antenna.
Figure 7: The EFN in the plane of the antenna, for the default h-dipole antenna.
Each parameter mentioned in table 2 was changed while keeping the others constant. Then all possible configuration of the original and optimal individual parameters were tested. The optimal combination was found to be ta = 5µm, Wa = 10µm, h = 315µm and la = 150µm. This altered h-dipole antenna with different size parameters was studied in a similar frequency range, 0.2-1 THz for every 1 GHz. The EFN for every frequency in the four corners at the middle of the antenna can be seen in figure 8, there is a clear peak at 0.304 THz. In figure 9 the electric field profile in the plane of the antenna is shown for this frequency. The highest EFN around the antenna is 0.67 MV/m, which is a 26% increase. Compared to the first h-dipole antenna, the broadband of the peak is narrower.
Figure 8: The EFN for the four corners in the middle of the antenna for the frequency 0.304 THz, for the altered h-dipole antenna.
Figure 9: The EFN in the plane of the antenna, for the altered h-dipole antenna.
5.2 Spiral antenna
First a spiral antenna with the default parameters as shown in table 2 was simulated in a wide frequency range, 0.5-3 THz. In figure 10 the EFN evaluated in the simulation can be seen. The graph shows the field norm in 8 points on the inner edge of the spiral, where specifically can be seen in the method in section 4.2.6.
Figure 10: The EFN of eighth points on the inner edge of the spiral for frequencies 0.5-3THz for the antenna with the default parameters as shown in table 2.
There is one wide peak below 1 THz where the field norm is the largest with the peak value being located at 0.68 THz. There is also another wide peak with a slightly smaller EFN around 1.5 THz and multiple narrow peaks in the higher frequencies. Since the EFN is highest below 1 THz the focus of the simulations was put there. In figure 11 the field profile in the plane of the antenna for the frequency 0.68 THz. A dense EFN can be seen in the corners of the spiral which in some simulations overshadow
the rest of the field norm and therefore EFNs above 0.35 MV/m have been excluded in the field norm profile.
The parameters mentioned in section 4.3 were varied according to table 2. The antennas were simulated in a frequency range of 0.4 to 1 THz. For the different parameters the EFN was studied to find which value of each parameter gave the largest field norm. Figure 12 shows what the largest EFN was depending on the different parameters and figure 13 show for what frequency gave the largest for each parameter.
Figure 11: The EFN in the plane of the antenna for the frequency 0.68THz.
Figure 12: Four graphs of how the EFN depends on four parameters in the spiral antenna.
Figure 13: Four graphs of how frequency with the highest EFN depends on four parameters in the spiral antenna.
After simulating the parameters an antenna with each optimal parameter was modeled and simulated.
The optimal parameters were la = 20µm, W = 1.5µm, Wg = 1.0µm and t = 300nm. In figure 14 the EFN of the antenna with the default parameters is shown and in figure 15 the EFN of the antenna with the optimal parameters are shown. The peak EFN value of the optimal antenna was 30% larger than the peak of the previously studied antenna.
Figure 14: The EFN of eighth points on the inner edge of the spiral of the spiral antenna with default parameters
Figure 15: The EFN of eighth points on the inner edge of the spiral of the spiral antenna with optimal parameters.
5.3 Bow tie antenna
As mentioned previously, this antenna was simulated with two different substrate materials: T mF eO3
and M gO. The former version was simulated between 0.5 and 3 THz, where a peak in the EFN can be found at around 2 THz. This, as well as a view of the electric field profile in the antenna plane, can be seen in figure 16. While using M gO as the substrate material the antenna response was simulated between 0.5 and 2 THz. As shown in figure 17, there is a peak in the EFN between 0.8 and 0.9 THz.
The most noticeable difference between the two substrate materials is easily spotted in the EFN plots, where T mF eO3 provides a much smoother curve than M gO in addition to a much larger bandwidth.
Both the EFN peak amplitude as well as the frequency for which it occurred were higher for T mF eO3. As for M gO, simulations of the EFN for frequencies larger than 1 THz provide a very unpredictable and therefore insipid result for the purposes of this study. As for the electric field profile, also seen in figure 17, M gO seemed to increase its amplitude at the outer edges of the antenna – a result that was not seen with T mF eO3 as the substrate material.
Although M gO arguably had the weakest performance it was still used in the posterior simulations for a more accurate comparison to the other antennas in this project. These simulations were made to examine how the EFN amplitude was affected by variations in the antenna’s parameters, namely: the gap width as well as the width and the height of the rectangular sections closest to the gap.
As seen in table 2, the gap width Wg was varied from 3.8µm to 5.8µm which increased EFN peak between 8 and 9 THz by a factor of 2, as seen in figure 18a. When varying the height h of the rectangular plates of the antenna from 10µm to 14µm there was no noticeable change in the peak values of the EFN amplitude. However, the values of the EFN at the edges of the antenna, as shown in figure 18b became more homogeneous. When varying the width W of the rectangular plates of the antenna from 4µm to 6µm the EFN peak increased by a factor of 2, just as it did when the gap size was varied.
Figure 16: EFN and profile of the bow tie antenna while using T mF eO3 as the substrate material and the default parameters from table 2. The EFN graph shows the resulting values at each of the four edges closest to the gap of the antenna.
Figure 17: EFN and profile of the bow tie antenna while using M gO as the substrate material and the default parameters from table 2. The EFN graph shows the resulting values at each of the four edges closest to the gap of the antenna.
Figure 18: Plots of the EFN at each of the four edges closest to the gap of the bow tie antenna after changing the antenna parameters. (a) shows the result after changing the gap size Wg from 3.8µm to 5.8µm, (b) the result after changing the rectangle height h from 10µm to 14µm and (c) the result after changing the rectangle width W from 4µm to 6µm.
(a)
(b) (c)
5.4 Sub THz antenna with directors
When running the simulations for the Sub THz antenna, COMSOL Multiphysics often ran out of memory.
This put a constrain on which values for mesh sizes and substrate thickness could be used, as those values had a big impact on the number of elements that the simulation had to consider.
The antenna was examined for frequencies between 300 GHz and 800 GHz. The substrate thickness was varied with values of 50, 100, 200 and 500 µm. The E-field norm was examined for three points along the antenna gap edge. One on each end, and a third in the middle. The E-Field norm is available in figure 19. A specific peak where the antenna resonates is hard to determine. The S11 parameters (reflection coefficient) is plotted in figure 20. There seem to be some kind of peak around 550 GHz. The peak seems to move to a higher frequency as the substrate thickness increases, while no clear peak can be seen for subt= 500µm.
Figure 19: EFN for various substrate thicknesses for the Sub-Thz antenna.
Figure 20: S11 parameter for various substrate thicknesses for the Sub-Thz antenna.
6 Discussion
The software COMSOL multiphysics was used to simulate antenna responses to THz radiation. The antennas were parametrically varied to study whether the amplitude of the THz radiation could be increased further with more optimal antennas. The point of using the antenna was to amplify the THz radiation, however, the attempts of simulating THz radiation in COMSOL were inconclusive. Therefore, the EFN was considered instead, to get indications of which antenna will emit the highest amplitude of THz radiation. This is an inaccurate way of measuring the THz radiation, however, comparing the EFN for different antennas could indicate which antenna will be better or worse at emitting THz radiation.
This could be used as a basis for choosing which antennas to use in future studies.
6.1 Problems with COMSOL
To acquire accurate results the mesh was required to be small and therefore requiring substantial com- puting power. This led to two problems: first of, the computing time for each simulation was several hours long. This combined with the access to the COMSOL software being time limited resulted in not being able to study each parameter as thoroughly as first intended. Secondly, because the Sub-THz antenna was larger than the other antennas it required a larger simulation space, which in turn required a more computationally heavy mesh. This led to the computer running out of RAM during simulations and not being able to be computed with the desired mesh size. The sum effect of these problems is why no parameters on the sub-THz antenna was studied.
It was also difficult to satisfyingly determine if the results were physically accurate since there were no completely similar studies, with the same antennas and substrate. The values of the EFN was significantly lower than other studies; in one study (6) an EFN of 100M V /m for a similar spiral antenna was achieved while, in this study, the EFN peaked at 0.2M V /m. If this depended on the mesh, the incident radiation or some other factor could not be established.
One important factor when solving partial differential equations are the boundary conditions. In this study PEC and PMC were used which reflect the electric and magnetic field at the boundaries which causes interference of these fields. For example, if a perfectly absorbing boundary condition would have been used instead, it might lead to a different result, since there is no longer any interference. Despite the uncertainty of the results in terms of the values of the EFN , the enhancement of the electric field by varying the parameters can still give insight into how the antennas can be improved.
6.2 Field enhancement by parameter variations
The best geometrically altered h-dipole and spiral antennas managed to improve the maximal EFN by about 30% while the bow tie antenna improved by 100%. The exceptionally large increase for the bow tie antenna might be because of the version from the original study being optimised for another substrate.
No parameters were varied for the Sub-THz antenna and therefore no conclusions could be made on how to increase the EFN for that antenna. For both the h-dipole and spiral antenna the frequency of the peak was increased, while the frequency for the bow tie antenna stayed about the same. When comparing the figures 12 and 13 the frequency dependency and the EFN dependency of the spiral antenna follow similar trends. For the h-dipole antenna the broadband was halved for the altered version. For the bow tie antenna the version with the T mF eO3 substrate was clearly better, with both a higher maximal EFN, a higher peak frequency and a much larger broadband.
As previously mentioned, it is difficult to compare these antennas with other studies. For this reason, comparisons with antennas from other studies are inconsequential. However, conclusions can still be drawn about how certain parameters affect the results. It is clear that the substrate makes a very significant difference on the EFN, T mF eO3 gave better results, however, this was only tested on one antenna. Geometrical parameters of the antenna can be tweaked to change the EFN, peak frequency and broadband, these effects are different for every antenna, furthermore no general conclusions could be drawn about which parameters are generally more effective.
6.3 Future improvements
The results for the Bow tie antenna varied depending on the substrate material. The material properties had an impact on both the maximum amplitude and which frequencies were amplified. This suggests that when design an antenna, the material can be chosen to attain desired antenna properties. Therefore, the impact of material properties might be an interesting area to study further.
A substantial improvement would be to run the simulations on a computer with more working memory, or design the simulation in such a way that it requires less working memory. As this would let the simulation be able to run with a smaller mesh size and therefore yield more accurate results. This improvement is especially relevant for the Sub-THz antenna.
Futher simulations with different boundary conditions could be done to test their effect on the results of the simulations.
Most importantly, none of the antennas in this study reached the desired EFN amplitude of 50M V /m required to manipulate the magnetic state of anti-ferromagnetic materials, meaning that they would not be useful for spintronic applications. However, they did increase the STE output by several orders of magnitude and could therefore be useful for such purposes.
7 Conclusion
It was possible to increase the EFN of the antennas by altering some parameters of the antennas geometry.
However, this also changed for which frequencies the EFN peaks. For the spiral and h-dipole antennas the EFN was increased by 30% and for the bow tie antenna the EFN was increased by 100%. The substrate on which the antenna is placed on also has a significant impact on the EFN and frequency broadband. The impact of the substrate on the results would be interesting to study further. It was not possible to reach an EFN of 50M V /m required to manipulate the magnetic state of anti-ferromagnetic materials. However, the antennas can still be used to increase the output amplitude of an STE.
8 Popul¨ arvetenskaplig sammanfattning
Med dagens digitala framfart anv¨ander sig n¨astan alla, unga som gamla, av elektroniska enheter. I och med att allt fler blir uppkopplade och dessutom ¨okar sin anv¨andning av internet har vi kommit till en punkt d¨ar det ¨ar dags att ta h¨ansyn till v˚ar klimatp˚averkan fr˚an v˚ar digitala anv¨andning.
V˚ar internettrafik hanteras och lagras i diverse datacenter. Med ¨okad internetanv¨andning kr¨avs d˚a s˚aklart fler servrar och dessutom mer energi f¨or att driva dem. Idag g˚ar redan 10% av Sveriges elproduktion ˚at till att driva dessa datacenter. Om tio ˚ar kan den siffran stiga upp till 51% f¨orutsatt att man inte lyckas minska p˚a elektronikens energif¨orbrukning.
En avl¨agsen men v¨aldigt lovande l¨osning skulle vara att ers¨atta elektronik med s.k. spinntronik.
Idag sparas data, som m˚anga vet, i form av ettor och nollor. Rent fysikaliskt avl¨ases detta som n¨arvaro respektive avsaknad av en elektrisk sp¨anning. Denna sp¨anning kr¨aver en konstant tillf¨orsel av energi f¨or att uppr¨atth˚allas. I spinntronik kan man ist¨allet utnyttja elektronernas spinn f¨or att spara data. Spinn
¨
ar en egenskap hos elektroner som g¨or att de kan betraktas som sm˚a magneter, kompletta med en nord- och sydsida. Detta skulle lika g¨arna kunna anv¨andas som fysikalisk grund f¨or att l¨asa av ettor och nollor i en lagringsenhet. Spinnen f¨or¨andras inte av sig sj¨alv och skulle d¨arf¨or inte kr¨ava samma konstanta energitillf¨orsel. En f¨ordel med spinntronik ¨ar d¨arav en betydligt mindre energif¨orbrukning ¨an dagens elektronik. Dessutom skulle spinntronik vara mer platseffektiv, vilket inneb¨ar att lagringsminnen kan f˚a plats med mer data.
Ett problem som m˚aste l¨osas innan spinntronik blir en verklighet ¨ar att p˚a ett effektivt s¨att kunna v¨axla p˚a spinnen. Den mest prominenta l¨osningen som unders¨oks ¨ar att utnyttja terahertz-str˚alning, en viss typ av elektromagnetisk str˚alning som l¨ampar sig v¨al till detta syfte. Det finns flera s¨atta att generera terahertz-str˚alning och ett av dem ¨ar en annordning som kallas spinntronisk terahertz emitter.
Str˚alningen m˚aste vara tillr¨ackligt f¨or att kunna v¨axla elektronens spinn och f¨or att uppn˚a denna styrka kan en antenn kopplas samman med emittern.
I denna studie unders¨oktes hur fyra olika antenner reagerade p˚a terahertz-str˚alning f¨or att se om dessa antenner l¨ampar sig och om de kan g¨oras b¨attre. Detta gjordes genom att simulera antennerna.
Flera olika geometriska parametrar varierades f¨or att framst¨alla en optimalare antenn. N¨ar dessa un- ders¨okningar gemf¨ordes kunde inga slutsatser dras om vissa parametrar var b¨attre. Vi testade ocks˚a att s¨atta antennen p˚a ett annat material vilket visade sig ha stor p˚averkan.
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