ABSTRACT
We present a novel approach for the fabrication of terahertz (THz) metamaterial structures utilizing PolyMUMPs, a foundry process commonly used in the fabrication of microelectricalmechanical systems (MEMS) devices. The structure has an alternating composition consisting of three polysilicon layers and two silicon dioxide layers each with a unique thickness. A split ring resonator (SRR) structure was fabricated with dimensions to support resonance around 5 THz. The structures were arrayed to cover a 1 cm2 area. The backside of the samples was polished to improve the transmission characteristics of the material during Fourier transform spectroscopy measurements. The data indicates a transmission null around 3.7 THz due to the periodic arrangement of the SRR structures. These results are encouraging for future use of PolyMUMPs in terahertz metamaterial designs which is ideal for the repeatability the manufacturing process lends to the design.
Keywords: metamaterial, negative refractive index, fabrication, terahertz
INTRODUCTION
Metamaterials are engineered materials designed to exhibit electromagnetic responses that do not occur naturally. A metamaterial is created by patterning materials, typically dielectrics, metals, or semiconductor substrates, in a periodic array of resonators of a particular size depending on the wavelength of the incident radiation. The structured materials are considered an effective medium and are therefore governed by Maxwell’s macroscopic equations and described by their effective electric permittivity and effective magnetic permeability. Tailoring structures to take advantage of the electromagnetic properties of materials enables the possibility of fabricating negative refractive index materials [1-2], the perfect lens [3], and cloaking materials [4].
Metamaterials are a composite material of a metallic structure (of specific shape and size) immersed on a host medium, usually a dielectric or semiconductor. Metamaterials, operating from radio to terahertz (RF to THz), are generally designed with sub-wavelength resonators, such as split ring resonators (SRRs). Pendry was the first to propose the use of the SRR as a means of creating a negative magnetic permeability [5]. The resonators collectively respond to the incident electromagnetic field altering the behavior of the radiation. The SRR has a fixed narrow resonant frequency based on the dimensions of the SRR capacitive gap and the self-inductance from the metal trace. The material will only exhibit a negative permeability just above resonance [6].
Through scaling of the resonators, metamaterials that function in the near visible and the radio frequency range of the electromagnetic spectrum have been demonstrated. Recently, strides have been made to develop metamaterials in the terahertz (THz) regime since most natural materials do not have a response to THz radiation. The lack of natural materials has created what is known as the THz gap. Metamaterials tailored towards THz frequencies provide a means for developing THz devices, such as filters, modulators, amplifiers, transistors, and resonators [7]. For THz generation, resonator structures need to be fabricated with dimensions on the order of 30 pm.
The aforementioned THz gap covers from 100 GHz to 4 THz of the electromagnetic spectrum, which lies just above microwaves and below infrared waves. Developing THz technology has been on the forefront of research as scientist try to close this gap. Thus far, development of THz sources and detectors has resulted in THz imagers, semiconductor characterization, and new methods for chemical and biological sensing [8]. Many THz applications (communications, security, imaging, and chemical and biological sensing) have been identified and are currently being researched [9]. However, there is still a great deal of advancement required to fully exploit this region of the electromagnetic spectrum. These applications would undoubtedly benefit from materials that enhance our ability to manipulate, control, and detect THz radiation.
Metamaterials have played an increasingly important role in the development of THz devices [10]. For instance, planar arrays fabricated on various semiconductor and insulator substrates have shown a response to THz radiation both electrically [8, 11] and magnetically [12-13]. Based on current research, metamaterials are ideal candidates for THz devices because they can be scaled and show a resonant frequency response that can be tunable by design.
This work focuses on the modeling, design, and fabrication of SRRs fabricated from PolyMUMPs to operate around 5 THz. The PolyMUMPs process is a commonly used foundry process used to fabricate microelectronics [14]. Taking advantage of a foundry process allows for increased reliability and repeatability in the design of the THz structures.
MODEL, DESIGN, AND FABRICATION
The design for the SRRs was initially laid out in L-Edit ©, a subset circuit layout editor program of the MEMS Pro software suite, the design is based on MatLab calculations to determine the resonant frequency considering the design parameters. Once the design was complete it was transferred to the PolyMUMPs foundry who then fabricated the devices given our design specifications.
The MatLab code was written to aid in choosing the SRR dimensions. The dimensions of the SRR are determined by first deciding on a target resonant frequency. The main two contributing factors to the resonance are the structures inductance and capacitance, as shown in Equation 1
where L in the self inductance from the metal trace and C is the overall capacitance , however since the gap in the SRR is the dominating source of capacitance it is the only capacitance that is considered. The inductance of the trace and the gap capacitance are given by
where fi0 is the vacuum permeability, l is the length of the side of the SRR, t is the thickness of the material, e0 is the permittivity of free space, er is relative permittivity, w is the width of the trace, and g is the gap separation. Note the resonant frequency is not a function of the sample thickness. The parameter having the most affect on the resonant frequency will be the length of the SRR, which has a linear relationship with the resonant frequency. The resonance will be inversely proportional to the gap separation and proportional to the square root of the width of the trace and the relative dielectric constant. While these parameters will still affect the resonant frequency their contributions are minimal compared to altering the size of the SRR. Considerations must be made to ensure the design dimensions do not exceed the qualifications of the effective medium theory.
Based on the polysilicon and silicon dioxide material, the dimensions of the single split ring resonators were chosen to support a resonate frequency of approximately 5 THz. A layout of the SRR structures and its dimensions are shown in Figure 1. The SRRs have a square shape with a height and length of 40 ^m. The width of the trace is 10 ^m on all sides. The capacitive gap opening is 17 ^m, such that the length of the trace on either side of the gap is 11.5 ^m.
Fig. 1 A schematic of a top down view of a single unit SRR with the dimensions indicated.
The SRR structures were arranged such that there were four to a unit cell as shown in Figure 2. The lattice period is 80 ^m. The PolyMUMPs structures were arrayed to cover a 1 cm2 area to make the design large enough for characteization. The resonance frequency for the SRR shown in Figure 1 using the dielectric constant of silicon dioxide (3.9) was calculated to be 5 THz.
Fig. 2 3D diagram of a unit cell of the patterned metamaterial shows the 3 polysilicon and 2 silicon dioxide alternating layers grown on a silicon wafer with a thin silicon nitride buffer layer.
The SRRs for this study were fabricated with the PolyMUMPs process which uses polysilicon and silicon dioxide in alternating layers. The polysilicon layers act as a metallic structure and the silicon dioxide layers are used as a dielectric. These materials were chosen due to the high plasma frequency of the polysilicon and the dielectric constant of the silicon dioxide. The PolyMUMPs samples consist of alternating polysilicon and silicon dioxide layers grown on top of a single side polished crystalline silicon wafer with a small nitride buffer layer. At the foundry, the alternating layers are capped with a thin layer of chromium followed by a thin layer of gold. The layout of the material layers along with each layer thickness are shown in Figure 3. The gold and chromium layers were removed with a wet etch prior to the metamaterial testing. A detail review of the PolyMUMPs fabrication process can be found on their website [14].
Fig. 3 A schematic illustrating the layers and their corresponding dimensions used in the PolyMUMPs process.
RESULTS
Fourier transform spectroscopy (FTS) was conducted on 3 metamaterial samples and 1 sample with no SRR structures. The transmission was captured by a Fourier transform spectrometer equipped with THz optics at a resolution of 4 cm-1. The measurements were performed in a vacuum at room temperature. The transmission was calculated from the ratio of the reference spectrum and the sample spectrum. Three samples were measured all with identical structures but with varying degrees of surface quality sample 1 having the worst quality while sample 3 has the best. The varying degree of surface quality is a result of the residual gold and chromium that remains on the surface following the wet etch removal.
The FTS transmission spectrum for the sample without SRRs, shown in Figure 4, has 0% transmission in the frequency range investigated. This is expected considering silicon dioxide is not transparent in the far IR. The transmission spectra of all three structured samples shown in Figure 5, have an off resonance transmission of about 25 % which drops off at the resonant frequencies. The spectra for all three samples have a small resonance around 3.7 THz due to the LC response of the SRRs where the transmission drops to approximately 15%. Also present in all the spectra is a resonance at 18.4 THz where the transmission decreases to 5% or 10% depending on the sample surface quality. The resonance null deepens as the surface quality of the material improves.
The MatLab calculations determined the resonant frequency would be around 5 GHz using a dielectric constant of 3.9 for silicon dioxide. The material stacks also contain a thin layer of silicon nitride which may affect the dielectric properties of the material. Calculating the resonance using a dielectric constant of 7.8 for silicon nitride yields a resonant frequency of 3.5 THz, which is much closer to that measured with FTS. The layered materials and different dielectric constants make it difficult to predict the resonant frequency of the samples.
The overall low transmission amplitude is most likely a result of the layered material. Layered materials are known to cause a decrease in the transmission and to broaden the resonance however the resonant frequency remains constant [15]. The weak resonance could also be a result of the substrate used in the fabrication process. The samples are grown on single side polished crystalline silicon. The unpolished backside of the samples resulted in too much scatter for measurements to be obtained. The following transmission spectrum was only obtained after the backside of the samples was polished to a highly reflective surface.
Fig. 4 Transmission spectra of the PolyMUMPs material without the SRRs showing zero transmission across the measured frequency range.
Fig. 5 Transmission spectra of the PolyMUMPs samples fabricated with SRRs showing a transmission of about 25% and a resonance at 3.7 and 18.4 THz
CONCLUSION
We demonstrated a quasi three dimensional metamaterial by fabricating SRRs from alternating layers of polysilicon and silicon dioxide. This is the first use of a foundry process, to our knowledge. All the fabricated PolyMUMPs samples show a resonant response around 3.7 THz and another resonance at 18.4 THz. These results show that a polyMUMPs fabrication approach can be used to produce 3D metamaterials with minimal alterations. However, further research needs to be conducted to determine the overall dielectric constant of the material stacks.
