MAT-VET-F 20003

Examensarbete 15 hpJuni 2020

Design and Simulation of Terahertz Antenna for Spintronic Applications

Malin BohmanNils EivarssonEmil GrosfilleyAxel 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 forSpintronic Applications

Malin Bohman, Nils Eivarsson, Emil Grosfilley, Axel Lundberg

Spintronics is a spin-electronic field where the electron spinangular momentum, in conjunction with charge, is used to read andwrite 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-20003Examinator: Martin SjödinÄmnesgranskare: Natalia FerrazHandledare: 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 densitycompared 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 examplethe 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 withits charge. These two aspects of the electron are used to read and write information in magnetic sensorsand 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 thewriting of information is done by switching the magnetic state. In analogy to how ones and zeroes arestored as a potential difference in modern day electronic devices, one could use the magnetic state achievethe same result. Magnetic state manipulation can be realized by utilizing THz radiation. In order torealize the ultrafast optical switching of anti-ferromagnetic state for dense device integration, THz signalamplitude should be higher than 50MV/m (2).

Storing data with spintronic devices holds several substantial advantages compared to electronicequivalents. 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 electricalmethods to write and read information, there are fewer heat related energy losses which in turn allowsfor 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 technologydoesn’t have this limitation. This is due to the fact that many antiferromagnetic materials, a necessarycomponent in spintronics, have resonance frequencies in the THz region, and there is no fundamentallimit 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 ultralow-power and ultra-fast operated logic circuits.

In the future, it is likely that spintronics will become the standard tool for storing and accessinginformation. One of the driving factors for making this switch is to lower the energy consumed byinformation and communication technology, the main issue being the electricity required to run datacenters. One prediction shows that, if no advancements are made to lower the energy usage of electronicdevices, 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 generateTHz radiation (5). An STE can be seen in figure 1. When the STE is hit by a laser pulse, spin currentsare induced in the STE which by the reverse spin Hall effect induce charge currents in the non-magneticlayers. This charge current then acts as a source of THz radiation. STEs could be be used for datatransmission 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 bewithout damaging the chip (5).

1.4 Antennas

A potential solution to the limited output power is coupling an antenna to the STE. Antennas arestructures that are used to emit or capture radiation. By changing the structure, antennas may becomemore 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.

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Figure 1: A schematic of an STE (5).

In the application of STE:s, antennas are used to absorb radiation and amplify a desired bandwidthto enable the radiation to be used in data storage. As the STE-antenna will act in the THz range, thestructure will be built in a µm scale. These antennas could also be used on spintronic logic circuits tofurther improve the incoming THz signal.

In the context of this study, antennas are used to amplify the radiation from the STE, and to focus itin a certain bandwidth. The antennas that are to be examined are selected from previous studies. Theh-dipole antenna (5), the Spiral antenna (6), the Bow tie antenna (7) and the Sub THz antenna (8) arechosen 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 ofonly the STE. The aim is to study this improvement by different antennas by examining the amplitude ofthe electric field norm (EFN) on the antennas after being exposed to THz radiation. The goal is to achievea minimum EFN of 50MV/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

2c0ε0E

20 (1)

where I is the intensity, c0 is the speed of light, ε0 is the vacuum permittivity and E0 is the electricfield amplitude. The power carried by the wave through a perpendicular area A (2), is then

P = I ·A =1

2cε0E

20A (2)

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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 turnsconnected to a arm. The antenna in the study had a arm length, la, a width, W , a gap width, Wg, anda thickness of the antenna material, t. The values of these parameters are listed as the default values insection 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 separatedby a gap Wa. The length between the arms was called la and the height of the arms was called h. Thethickness of the antenna was noted ta.

Figure 2: Figures of the antennas and its parameters. (a) shows the spiral antenna, (b) the H-dipoleantenna, (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 infigure 2c. The parameters that were varied were those of the rectangular plates. More specifically, theirheight h, their width W and the gap size Wg. As for the triangular plates, the base and height were keptat 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 platesacting as directors. The geometry of the antenna is described in figure 2d. The default parameter valueswere set to those in table 1 as these were suggested in (8) for the best gain.

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Table 1: Parameters used for the Sub-THz antenna.

w 10µmg 4µmld 115µmlf 35µmlr 280µmld1 150µmd1 135µmd1d 125µmd2 164µm

4.2 COMSOL Multiphysics

The simulation were done using the simulation software COMSOL Multiphysics, a software made forsimulating a multitude of physical problems. It uses a finite element method to solve differential equationsdepending on the simulated physics. In this study the module for electromagnetic waves in the frequencydomain was used. The first part of the simulations was to alter mesh sizes, the simulation space, materialconstants and boundary conditions until the results from the simulation was physically accurate. Afterachieving 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. Theplane of the antenna, as seen in figure 4 is situated in the xy plane, which size is different for everyantenna. For the h-dipole antenna the plane was 315 × 315µm. For the spiral antenna the plane was60×54µm, 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 simulationspace in COMSOL.

On top of the antenna, where the incoming radiation iscoming from, a 100µm space in the z-direction filled withair was simulated. On the bottom of the antenna a 500µmsubstrate was used, except for the sub-THz antenna, wheremultiple substrate thicknesses was simulated.

4.2.2 Mesh

The mesh divides the simulation space into smaller volumeelements, in this cases tetrahedrons was used, and the differ-ential equations are solved for the elements. The size of themesh 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 inreasonable time scales. The mesh is automatically generatedby COMSOL based on the physics used, but can be manu-ally tuned. To ensure the mesh was small enough the meshwas reduced in size until reducing it further did not alterthe results significantly. The mesh sizes of the antennas wasbased on the minimum wavelength, λmin of the simulations.An example mesh of the spiral antenna is shown in figure 4.All simulations used a general maximum mesh size for theentire space of λmin/10. Then the mesh of each antenna wasfine-tuned in specific regions until it was sufficient.

The h-dipole antenna used a maximal mesh-size ofλmin/100 over the antenna. The edges of the gap used amaximal mesh size of λmin/500.

On the entire boundary of the spiral antenna the meshsize was maximally λmin/100 and on the inner and outeredge on the gap in the spiral the mesh size was maximally λmin/500. The mesh size on the corners ofthe antenna was further reduced to λmin/1000.

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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 sizeof λmin/4 while the antenna plates had a maximum mesh size of λmin/35. Along the edges of therectangular plates closest to the gap the maximum mesh size was set to λmin/1000, whereas the areabetween the gap was set to λmin/125.

The Sub-THz antenna used the λmin/20 for the main dipole antenna part. While the directors andreflector 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 withMagnesium-Oxide (MgO) as substrate. The bow tie antenna was also studied with Thulium Orthoferrite(TmFeO3). The substrate material might influence the results. The MgO was simulated with a relativepermittivity of 9.5, and a electrical conductivity of 1S/m. While the TmFeO3 was simulated with arelative permittivity of 1 and an electrical conductivity of 52.239S/m. Both materials had a relativepermeability 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 incidentpower 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 magneticconductor (PMC). The PMC and PEC are chosen like this to have the electric field of the radiationperpendicular to the PEC and the magnetic field perpendicular to the PMC. The antenna itself wastreated as a transition boundary, as the currents in the antenna can be assumed to flow only on thesurface as it is much larger than the depth. This allows for the antennas thickness to be accounted forwithout 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 differentfor 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 frequencythat was chosen was therefore 0.2 - 1 THz. As the peaks are quite thin a high resolution was needed, afrequency of 1 GHz was chosen.

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The spiral antenna from the study was simulated in the range 0.1 - 2 THz. A simulation at thefrequencies 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 therevised antenna was only simulated for the frequencies 0.4 - 1 THz. For each parameter variation thesimulations were first done using a low resolution to find the peak. After finding a rough estimate ofwhere the peak was the simulation was run with a resolution of 1 GHz in a range of 30GHz around thepeak 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 frequencyof 0.65 THz, which is why the frequencies 0.5 - 3 THz were simulated for the TmFeO3 substrate. Forthe MgO substrate the peak is clearly below 2 THz, which is why the frequencies 0.5 - 2 THz weresimulated. 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 thatthese were the relevant frequencies. All simulations were performed with a resolution of 20 GHz or 10GHz.

4.2.6 Plot data

From the simulations there are two types of data considered in the result. EFN and S11-parameter. EFNis the L2-norm of the electric field which is both plotted in specific points on the antennas for varyingfrequencies and in a plane of the simulation space for one specific frequency. The S11-parameter is ameasurement of how much of the electromagnetic radiation sent from the port can be measured at thesame port again. In other words, it is related to the reflection. For the h-dipole, sub-THz, and the bowtie antenna the values were plotted on the corners of the gaps of the antennas. For the spiral antennathe 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. Eachparameters were varied independently, while the other parameters were assigned their default value. Forthe Sub-THz antenna, only the substrate thickness was varied, not the geometry of the antenna.

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Parameters Values DefaultSpiral antenna

Width, W 1.5-2.5 µm 2 µmGap width, Wg 0.8-1.9 µm 1.5 µmArm length, la 16-20 µm 18 µmAntenna thickness, t 50-400 nm 200 nm

H-dipole antennaThickness, ta 5-20 µm 10 µmGap width, Wa 10-20 µm 10 µmArm height, h 150-315 µm 315 µmArm distance, la 100-250 µm 200 µm

Bow tie antennaRectangle width, W 4-6 µm 4 µmGap width, Wg 3.8-5.8 µm 3.5 µmRectangle height, h 10-14 µm 10 µm

Sub THz antennaSubstrate 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 0.2-1THz for every 1 GHz. The EFN for every frequency in the four corners at the middle of the antenna canbe see in figure 6, there is a clear peak at 0.265 THz. In figure 7 the electric field profile in the plane ofthe 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, forthe default h-dipole antenna.

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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 possibleconfiguration of the original and optimal individual parameters were tested. The optimal combinationwas found to be ta = 5µm, Wa = 10µm, h = 315µm and la = 150µm. This altered h-dipole antennawith different size parameters was studied in a similar frequency range, 0.2-1 THz for every 1 GHz. TheEFN for every frequency in the four corners at the middle of the antenna can be seen in figure 8, thereis a clear peak at 0.304 THz. In figure 9 the electric field profile in the plane of the antenna is shown forthis frequency. The highest EFN around the antenna is 0.67 MV/m, which is a 26% increase. Comparedto 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, forthe altered h-dipole antenna.

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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 frequencyrange, 0.5-3 THz. In figure 10 the EFN evaluated in the simulation can be seen. The graph shows thefield norm in 8 points on the inner edge of the spiral, where specifically can be seen in the method insection 4.2.6.

Figure 10: The EFN of eighth points on the inner edge of the spiral for frequencies 0.5-3THz for theantenna 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 beinglocated at 0.68 THz. There is also another wide peak with a slightly smaller EFN around 1.5 THz andmultiple narrow peaks in the higher frequencies. Since the EFN is highest below 1 THz the focus of thesimulations was put there. In figure 11 the field profile in the plane of the antenna for the frequency0.68 THz. A dense EFN can be seen in the corners of the spiral which in some simulations overshadow

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the rest of the field norm and therefore EFNs above 0.35 MV/m have been excluded in the field normprofile.

The parameters mentioned in section 4.3 were varied according to table 2. The antennas weresimulated in a frequency range of 0.4 to 1 THz. For the different parameters the EFN was studied tofind which value of each parameter gave the largest field norm. Figure 12 shows what the largest EFNwas depending on the different parameters and figure 13 show for what frequency gave the largest foreach 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.

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Figure 13: Four graphs of how frequency with the highest EFN depends on four parameters in the spiralantenna.

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 theEFN of the antenna with the default parameters is shown and in figure 15 the EFN of the antenna withthe optimal parameters are shown. The peak EFN value of the optimal antenna was 30% larger thanthe 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 defaultparameters

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Figure 15: The EFN of eighth points on the inner edge of the spiral of the spiral antenna with optimalparameters.

5.3 Bow tie antenna

As mentioned previously, this antenna was simulated with two different substrate materials: TmFeO3

and MgO. The former version was simulated between 0.5 and 3 THz, where a peak in the EFN can befound at around 2 THz. This, as well as a view of the electric field profile in the antenna plane, canbe seen in figure 16. While using MgO as the substrate material the antenna response was simulatedbetween 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 TmFeO3 provides a much smoother curve than MgO in addition to a much larger bandwidth.Both the EFN peak amplitude as well as the frequency for which it occurred were higher for TmFeO3.As for MgO, simulations of the EFN for frequencies larger than 1 THz provide a very unpredictable andtherefore insipid result for the purposes of this study. As for the electric field profile, also seen in figure17, MgO seemed to increase its amplitude at the outer edges of the antenna – a result that was not seenwith TmFeO3 as the substrate material.

Although MgO arguably had the weakest performance it was still used in the posterior simulationsfor a more accurate comparison to the other antennas in this project. These simulations were made toexamine how the EFN amplitude was affected by variations in the antenna’s parameters, namely: thegap 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 peakbetween 8 and 9 THz by a factor of 2, as seen in figure 18a. When varying the height h of the rectangularplates of the antenna from 10µm to 14µm there was no noticeable change in the peak values of the EFNamplitude. However, the values of the EFN at the edges of the antenna, as shown in figure 18b becamemore homogeneous. When varying the width W of the rectangular plates of the antenna from 4µm to6µm the EFN peak increased by a factor of 2, just as it did when the gap size was varied.

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Figure 16: EFN and profile of the bow tie antenna while using TmFeO3 as the substrate material andthe default parameters from table 2. The EFN graph shows the resulting values at each of the four edgesclosest to the gap of the antenna.

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Figure 17: EFN and profile of the bow tie antenna while using MgO as the substrate material and thedefault parameters from table 2. The EFN graph shows the resulting values at each of the four edgesclosest to the gap of the antenna.

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Figure 18: Plots of the EFN at each of the four edges closest to the gap of the bow tie antenna afterchanging the antenna parameters. (a) shows the result after changing the gap size Wg from 3.8µm to5.8µm, (b) the result after changing the rectangle height h from 10µm to 14µm and (c) the result afterchanging 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 valueshad 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 thicknesswas varied with values of 50, 100, 200 and 500 µm. The E-field norm was examined for three pointsalong the antenna gap edge. One on each end, and a third in the middle. The E-Field norm is availablein 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. Thepeak seems to move to a higher frequency as the substrate thickness increases, while no clear peak canbe seen for subt = 500µm.

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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.

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6 Discussion

The software COMSOL multiphysics was used to simulate antenna responses to THz radiation. Theantennas were parametrically varied to study whether the amplitude of the THz radiation could beincreased further with more optimal antennas. The point of using the antenna was to amplify the THzradiation, 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 ofTHz radiation. This is an inaccurate way of measuring the THz radiation, however, comparing the EFNfor 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 severalhours long. This combined with the access to the COMSOL software being time limited resulted innot being able to study each parameter as thoroughly as first intended. Secondly, because the Sub-THzantenna was larger than the other antennas it required a larger simulation space, which in turn requireda more computationally heavy mesh. This led to the computer running out of RAM during simulationsand not being able to be computed with the desired mesh size. The sum effect of these problems is whyno parameters on the sub-THz antenna was studied.

It was also difficult to satisfyingly determine if the results were physically accurate since there wereno completely similar studies, with the same antennas and substrate. The values of the EFN wassignificantly lower than other studies; in one study (6) an EFN of 100MV/m for a similar spiral antennawas achieved while, in this study, the EFN peaked at 0.2MV/m. If this depended on the mesh, theincident radiation or some other factor could not be established.

One important factor when solving partial differential equations are the boundary conditions. In thisstudy PEC and PMC were used which reflect the electric and magnetic field at the boundaries whichcauses interference of these fields. For example, if a perfectly absorbing boundary condition would havebeen used instead, it might lead to a different result, since there is no longer any interference. Despitethe uncertainty of the results in terms of the values of the EFN , the enhancement of the electric fieldby 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 byabout 30% while the bow tie antenna improved by 100%. The exceptionally large increase for the bow tieantenna 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 howto increase the EFN for that antenna. For both the h-dipole and spiral antenna the frequency of the peakwas increased, while the frequency for the bow tie antenna stayed about the same. When comparingthe figures 12 and 13 the frequency dependency and the EFN dependency of the spiral antenna followsimilar trends. For the h-dipole antenna the broadband was halved for the altered version. For the bowtie antenna the version with the TmFeO3 substrate was clearly better, with both a higher maximalEFN, 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 bedrawn about how certain parameters affect the results. It is clear that the substrate makes a verysignificant difference on the EFN, TmFeO3 gave better results, however, this was only tested on oneantenna. Geometrical parameters of the antenna can be tweaked to change the EFN, peak frequencyand broadband, these effects are different for every antenna, furthermore no general conclusions couldbe 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 propertieshad an impact on both the maximum amplitude and which frequencies were amplified. This suggeststhat 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.

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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 thesimulation be able to run with a smaller mesh size and therefore yield more accurate results. Thisimprovement is especially relevant for the Sub-THz antenna.

Futher simulations with different boundary conditions could be done to test their effect on the resultsof the simulations.

Most importantly, none of the antennas in this study reached the desired EFN amplitude of 50MV/mrequired to manipulate the magnetic state of anti-ferromagnetic materials, meaning that they would notbe useful for spintronic applications. However, they did increase the STE output by several orders ofmagnitude 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 antennasthe EFN was increased by 30% and for the bow tie antenna the EFN was increased by 100%. Thesubstrate on which the antenna is placed on also has a significant impact on the EFN and frequencybroadband. The impact of the substrate on the results would be interesting to study further. It was notpossible to reach an EFN of 50MV/m required to manipulate the magnetic state of anti-ferromagneticmaterials. However, the antennas can still be used to increase the output amplitude of an STE.

8 Popularvetenskaplig sammanfattning

Med dagens digitala framfart anvander sig nastan alla, unga som gamla, av elektroniska enheter. I ochmed att allt fler blir uppkopplade och dessutom okar sin anvandning av internet har vi kommit till enpunkt dar det ar dags att ta hansyn till var klimatpaverkan fran var digitala anvandning.

Var internettrafik hanteras och lagras i diverse datacenter. Med okad internetanvandning kravsda saklart fler servrar och dessutom mer energi for att driva dem. Idag gar redan 10% av Sverigeselproduktion at till att driva dessa datacenter. Om tio ar kan den siffran stiga upp till 51% forutsatt attman inte lyckas minska pa elektronikens energiforbrukning.

En avlagsen men valdigt lovande losning skulle vara att ersatta elektronik med s.k. spinntronik.Idag sparas data, som manga vet, i form av ettor och nollor. Rent fysikaliskt avlases detta som narvarorespektive avsaknad av en elektrisk spanning. Denna spanning kraver en konstant tillforsel av energi foratt uppratthallas. I spinntronik kan man istallet utnyttja elektronernas spinn for att spara data. Spinnar en egenskap hos elektroner som gor att de kan betraktas som sma magneter, kompletta med en nord-och sydsida. Detta skulle lika garna kunna anvandas som fysikalisk grund for att lasa av ettor och nollori en lagringsenhet. Spinnen forandras inte av sig sjalv och skulle darfor inte krava samma konstantaenergitillforsel. En fordel med spinntronik ar darav en betydligt mindre energiforbrukning an dagenselektronik. Dessutom skulle spinntronik vara mer platseffektiv, vilket innebar att lagringsminnen kan faplats med mer data.

Ett problem som maste losas innan spinntronik blir en verklighet ar att pa ett effektivt satt kunnavaxla pa spinnen. Den mest prominenta losningen som undersoks ar att utnyttja terahertz-stralning,en viss typ av elektromagnetisk stralning som lampar sig val till detta syfte. Det finns flera satta attgenerera terahertz-stralning och ett av dem ar en annordning som kallas spinntronisk terahertz emitter.Stralningen maste vara tillrackligt for att kunna vaxla elektronens spinn och for att uppna denna styrkakan en antenn kopplas samman med emittern.

I denna studie undersoktes hur fyra olika antenner reagerade pa terahertz-stralning for att se omdessa antenner lampar sig och om de kan goras battre. Detta gjordes genom att simulera antennerna.Flera olika geometriska parametrar varierades for att framstalla en optimalare antenn. Nar dessa un-dersokningar gemfordes kunde inga slutsatser dras om vissa parametrar var battre. Vi testade ocksa attsatta antennen pa ett annat material vilket visade sig ha stor paverkan.

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References

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[2] Ankit Kumar, personal communication.

[3] J. W. Lu, E. Chen, M. Kabir, M. R. Stan, and S. A. Wolf, “Spintronics technology: past, presentand future,” International Materials Reviews, vol. 61, no. 7, pp. 456–472, 2016.

[4] A. S. G. Andrae and T. Edler, “On global electricity usage of communication technology: Trends to2030,” Challenges, vol. 6, no. 1, pp. 117–157, 2015.

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[6] Debanjan Polley et al, “Terahertz magnetic field enhancement in an asymmetric spiral metamaterial,”J. Phys. B: At. Mol. Opt. Phys.., vol. 51, no. 224001, 2018.

[7] Schlauderer, S., Lange, C., Baierl, S. et al., “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature, vol. 569, pp. 383–387, 2019.

[8] Vettikalladi, Hamsakutty and Sethi, Waleed Tariq and Abas, Ahmad Fauzi Bin and Ko, Wonsuk andAlkanhal, Majeed A. and Himdi, Mohamed, “Sub-thz antenna for high-speed wireless communicationsystems,” International Journal of Antennas and Propagation, vol. 2019, no. 9573647, 2019.

[9] C. Nordling and J. Osterman, Physics Handbook for Science and Engineering. No. F.5.3, Studentlit-eratur, 8th ed., 2006.

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