Simulation, Fabrication and Characterization of THz Metamaterial Absorbers

Summary

This protocol outlines the simulation, fabrication and characterization of THz metamaterial absorbers. Such absorbers, when coupled with an appropriate sensor, have applications in THz imaging and spectroscopy.

Abstract

Metamaterials (MM), artificial materials engineered to have properties that may not be found in nature, have been widely explored since the first theoretical¹ and experimental demonstration² of their unique properties. MMs can provide a highly controllable electromagnetic response, and to date have been demonstrated in every technologically relevant spectral range including the optical³, near IR⁴, mid IR⁵ , THz⁶ , mm-wave⁷ , microwave⁸ and radio⁹ bands. Applications include perfect lenses¹⁰, sensors¹¹, telecommunications¹², invisibility cloaks¹³ and filters^14,15. We have recently developed single band¹⁶, dual band¹⁷ and broadband¹⁸ THz metamaterial absorber devices capable of greater than 80% absorption at the resonance peak. The concept of a MM absorber is especially important at THz frequencies where it is difficult to find strong frequency selective THz absorbers¹⁹. In our MM absorber the THz radiation is absorbed in a thickness of ~ λ/20, overcoming the thickness limitation of traditional quarter wavelength absorbers. MM absorbers naturally lend themselves to THz detection applications, such as thermal sensors, and if integrated with suitable THz sources (e.g. QCLs), could lead to compact, highly sensitive, low cost, real time THz imaging systems.

Introduction

This protocol describes the simulation, fabrication and characterization of single band and broadband THz MM absorbers. The device, shown in Figure 1, consists of a metal cross and a dielectric layer on top of a metal ground plane. The cross-shaped structure is an example of an electric ring resonator (ERR)^20,21 and couples strongly to uniform electric fields, but negligibly to a magnetic field. By pairing the ERR with a ground plane, the magnetic component of the incident THz wave induces a current in the sections of the ERR that are parallel to the direction of the E-field. The electric and magnetic response can then be tuned independently and the impedance of the structure matched to free space by varying the geometry of the ERR and the distance between the two metallic elements. As shown in Figure 1(d), the symmetry of the structure results in a polarization insensitive absorption response.

Protocol

1. Simulation of a Single Band THz Metamaterial Absorber

A 3D view of the simulation set-up is shown in Figure 2.

1. Lumerical FDTD is used to optimize the transmission, reflection and absorption characteristics of the THz metamaterial absorber. All units are given in μm.
2. Define the THz polyimide material properties by left clicking Materials, Add (n,k) material and inputting 1.68 as the n and 0.06 as the k. Double left click on "new material 1" and rename it as "polyimide". Note that if theoretical or experimental refractive index data is available one can "add sampled data" to define the material properties.
3. Draw the geometry of the device, starting with the 0.2 μm thick metal ground plane. In the structures tab select rectangle and edit the properties by pressing the e key. Input "groundplane" in the name window, (0,0,0.1) as the structure centre co-ordinates and (31,31,0.2) as the span region. Move to the material tab and select Perfect Electrical Conductor (PEC). Repeat to define the 3 μm thick polyimide dielectric layer typing "polyimide" in the name window, (0,0,1.7) as the centre co-ordinates and (31,31,3) as the span. Finally define the 0.2 μm thick electric ring resonator by drawing two rectangular Perfect Electrical Conductor (PEC) regions called "ERR arm1" and "ERR arm2" with the same centre co-ordinates of (0,0,3.3) but different span regions of (10,26,0.2) and (26,10,0.2) respectively.
4. Add the simulation region by left clicking on Simulation and press e to edit the properties. In the general tab input 20 psec as the simulation time. In the geometry tab choose (0,0,0) as the centre co-ordinates and (30,30,200) as the span regions. In the mesh settings tab select a mesh accuracy of 3 and keep the other default settings as they are. Set the simulation boundary conditions in the boundary conditions tab choosing "Anti-symmetric" for x min bc and x max bc, "symmetric" for y min bc and y max bc and "PML" for z min bc and z max bc (the "allow symmetry on all boundaries" must be ticked). Include a mesh override region by left clicking again on Simulation and edit by pressing e. In the general tab type 0.5 μm for the dx and dy override and 0.05 μm for the dz override. In the geometry tab enter the centre co-ordinates (0,0,1.7) and span regions (30,30,3.8). Note that a smaller mesh size of e.g. dx, dy 0.1 μm, will increase simulation accuracy though this will come at the expense of significantly increased CPU memory and simulation time. It is best to simulate using a large mesh size until a structure with the desired properties is obtained and then re-simulate using the smaller mesh size.
5. Define the source type by left clicking on the arrow next to sources and choosing plane wave. Press e to edit the source properties and in the general tab change the direction to backward. In the geometry tab enter the centre co-ordinates (0,0,90) and (35,35,0) for the span region. Note that you cannot modify the z span. Set the minimum and maximum frequency of the simulation in the frequency/wavelength tab. Choose a minimum of 1 THz and a maximum of 4 THz and ensure the pulse in the signal versus time graph in the bottom right corner of the window decays to zero well before 20 psec.
6. Left click on the arrow next to Monitors and select frequency-domain field profile. Press e to edit the monitor properties and enter "r95" in the monitor name window. In the geometry tab enter the centre co-ordinates of (0,0,95) and span region (30,30,0). Repeat and create a second frequency-domain field profile monitor called "t95" with centre co-ordinates (0,0,-95) and spans (30,30,0). Left click on the arrow next to Monitors and select global properties. In the frequency/power profile tab enter 100 in the frequency points window. Figure 2 shows the perspective view displayed in Lumerical on completion of steps 1.1-1.6. Check the memory requirements are compatible with your computer by left clicking on the arrow next to the Check icon on the top toolbar and selecting check simulation memory requirements. Save the file giving it an appropriate name such as "Jove.sim".
7. Run the simulation by left clicking on the Run icon.
8. On completion of the simulation enter the following into the script prompt window. Note that one can also enter the following text in a text editor and save the file as a .lsf file. The script can then be run by left clicking on the arrow next to Run, selecting script and then locating the script file saved on your computer. Note that the # symbol indicates a comment.
   

load("Jove_sim"); # loads the simulation file
f = getdata("r95","f"); # gets the reflection data and frequency data from the r95 monitor
R = transmission("r95"); # defines R as a matrix containing the reflection data
A = 1-R; # calculates the absorption
fthz=f/1e12; # converts frequency to THz
plot(fthz,A,R,"Frequency(THz)","Absorption","Reflection"); # plot data on a single graph
legend("Absorption","Reflection");
filename = "Jove_sim.csv"; # export data for excel import
rm(filename); # delete file if it already exists
lambda = c/f; # converts frequency to wavelength
for(i=1:length(lambda)) {
  write(filename,num2str(f(i)) + "," + num2str(fthz(i)) + "," + num2str(R(i)) + "," + num2str(A(i)) + "," );
} # outputs a .csv file in column format of the frequency, reflection and absorption

2. Fabrication of a Single Band THz Metamaterial Absorber

Figure 3 shows the most important fabrication steps.

1. Clean a 15 mm by 15 mm piece of silicon in sequential solutions of warm (50 °C) opticlear, acetone and ispopropanol using ultrasonic agitation after initially heating the beaker containing the solvent for 10 min. Note that this protocol can also be used to fabricate several devices onto a 4 inch diameter wafer.
2. Evaporate a metal bi-layer of 20 nm/100 nm Ti/Au onto the 15 mm by 15 mm using a Plassys 450 MEB electron beam evaporator (Figure 3, step 1). Note that the metal thickness must be greater than the skin depth at the desired operating frequency.
3. Clean the sample as previously described in section 2.1
4. Dispense VM651 primer onto the sample using a pipette and leave to relax for 20 sec. Spin sample at 4,000 rpm for 5 sec and then bake on a contact hotplate at 120 °C for 60 sec.
5. Remove Dupont PI2545 polyimide from the freezer. Allow 20 min for the bottle to reach room temperature. This is essential since opening the bottle directly after removal from the freezer will result in moisture condensing inside the bottle and degrading the polyimide film properties. Dispense PI2545 onto the sample using a pipette and allow 20 sec for it to relax. Spin sample using a 2 stage spin procedure with the following settings - (i) final spin speed 500 rpm, acceleration 100 rpms^-1, final spin time 5 sec (ii) final spin speed 6,000 rpm, acceleration 500 rpms^-1, final spin time 60 sec. Bake sample on a contact hotplate at 140 °C for 5 min (Figure 3, step 2). If a thicker polyimide film is required then either spin multiple layers or reduce the final spin speed. To obtain a polyimide film thickness of 3 μm with minimal edge bead three layers of PI2545 are spun using the above protocol.
6. Cure the polyimide on a contact hotplate at 220 °C for 10 min. After this cure procedure the PI2545 will be impervious to most solvents and acids and can only be removed using oxygen plasma. PI2545 can be spun onto a dummy piece of silicon, cured as above and the thickness of the film measured by scratching the polyimide and using a DEKTAK surface profilometer to measure the step height.
7. Deposit 15% 2010 Poly(methyl methacrylate), known as PMMA, onto the sample. Spin at 5,000 rpm for 60 sec and bake in a convection oven at 180 °C for 30 min. Before baking remove any excess resist that has crept on to the backside of the sample using acetone. Remove sample from the oven and leave to cool to room temperature (~5 min). Deposit 4% 2041 PMMA onto the sample, spin at 5,000 rpm for 60 sec and bake in a convection oven at 180 °C for 60 min (Figure 3, step 3). Remove any excess resist that has crept on to the backside of the sample using acetone before baking.
8. Write the desired job on a Vistec VB6 electron beam writer using a dose of 450 μC/cm². The job file is designed in Tanner L-Edit, fractured into polygons by Layout Beamer and finally submitted to the beam writer using the Java based BELLE software.
9. Develop the sample in a solution of 1:1 MIBK:IPA at a temperature of 23 °C for 60 sec (Figure 3, step 4). Rinse in a beaker of isopropanol. Inspect pattern fidelity on an optical microscope. If features are poorly resolved strip the resist in opticlear, acetone and isopropanol and start again from 2.2.
10. Descum the sample with O₂ using a Gala Plasmaprep₅ barrel asher for 1 min at 0.1 mbar and 50 W RF power. Evaporate 20 nm Ti and 150 nm Au using a Plassys 450 MEB electron beam evaporator (Figure 3, step 5).
11. Insert the sample into a beaker of warm acetone and place the beaker into a hot water bath kept at 50 °C. After 4 hr remove the sample from the water bath and using a pipette suck up some of the warm acetone and spray liberally onto the sample (Figure 3, step 6). Inspect sample by eye to check that metal is lifting off from the areas where PMMA was present. If lift-off is progressing slowly place beaker in the ultrasonic water bath for 2 min. Inspect sample under the optical microscope.
12. The protocol describes the fabrication of a single band THz absorber however multi-level dual band and broadband absorbers can be produced by repeating steps 2.3-2.11 and stacking several crosses on top of polyimide layers.

3. Characterization of a Single Band THz Metamaterial Absorber

Figure 4 shows the basic FTIR instrument layout.

1. Turn on the nitrogen supply to the IFS 66V/S Fourier Transform Infra Red (FTIR) spectrometer. Press the "FIR" button on the front of the spectrometer control unit to turn on the Hg arc lamp. It takes around 15 min for the lamp power to stabilize. Insert the 6 μm multilayer beam splitter into the appropriate slot in the interferometer unit.
2. Vent the sample compartment of the spectrometer and insert the PIKE 30 ° reflection unit. Place the 4 mm aperture on top of the reflection unit aperture and on top of this put a gold mirror. The 4 mm aperture determines the area of the sample that will be interrogated while the gold mirror is necessary to make a background measurement.
3. Evacuate the sample compartment and wait for the pressure to get down to 5 mbar. The spectrometer can be run in a purged nitrogen environment however the signal size typically drops to less than 20% compared to vacuum.
4. Start the OPUS software and load the configuration file (set-up on installation of the unit) for taking measurements in the 30 cm^-1 to 300 cm^-1 range (1-9THz). This file sets numerous spectrometer parameters such as the scanner velocity, source aperture, source type, data collection method and Fourier transform execution mode. Ensure the LED on the front of the detector compartment is flashing green, indicating that the scanner is operating. Check that the shape of the interferogram is as expected.
5. Run 100 background scans to obtain the background spectrum.
6. Vent sample compartment, remove mirror and place sample face down onto the aperture. Ensure the centre of the sample is in the middle of the aperture. Evacuate the sample compartment.
7. Run 1,000 sample scans to obtain the sample spectrum. The sample spectrum will be compared to the background reference spectrum and the final reflection spectrum of the sample obtained. Note that if the signal reaching the detector is low, a greater number of sample scans may be required to reduce the noise (e.g. 10,000 scans). Repeat sample scans should be made to ensure the measured data is reliable and consistent.
8. Data from the completed scan can be converted into a text file and analyzed offline. The continuous ground plane of the sample means that there is no transmission ergo the absorption spectrum can be found by subtracting the reflection from 1.

Results

Figure 5(a) shows the experimentally obtained and simulated absorption spectra for a MM absorber with a 3.1 μm thick polyimide dielectric spacer. This MM structure has a repeat-period of 27 μm and dimensions K = 26 μm, L = 20 μm, M = 10 μm and N = 5 μm. Experimental measurements were also performed on samples with no ERR layer to confirm that absorption was a consequence of the MM structure and not of the dielectric. The 7.5 μm thick polyimide sample with no ERR structure has a maximum abso...

Discussion

This protocol describes the simulation, fabrication and characterization of THz metamaterial absorbers. It is essential such sub-wavelength structures are accurately simulated before any effort is committed to costly fabrication procedures. Lumerical FDTD simulations provide information on not only the MM absorption spectrum but also the location of the absorption, essential knowledge to aid placement of a transducer and obtain the maximum response. In addition the optimization algorithm in Lumerical can be implem...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Lumerical FDTD	Lumerical
Silicon wafer	IDB technologies		Single sided polished
Plassys 450 MEB evaporator	Plassys Bestek
VM651 Primer	Dupont
PI2545	Dupont
Methyl Isobutyl Ketone	Sigma-Aldrich
Isopropanol	Sigma-Aldrich
Plasmaprep5 barrel Asher	Gala Instrumente
VB6 UHR EWF electron beam writer	Vistec
Tanner L-Edit	Tanner Inc.
Layout Beamer	GenISys Inc.
Polymethyl methacrylate (PMMA)	Sigma-Aldrich	293261 Sigma-Aldrich
IFV 66v/s FTIR	Bruker
Pike 30spec reflection unit	Pike Technologies
Hg arc lamp	Bruker
Au mirror	Thor Labs	PF05-03-M01
Leica INM20 Optical Microscope	Leica microsystems
6 mm Mylar Beamsplitter	Bruker