A THz Coupler based on Graphene Patterns with SU-8 Photoresist Dielectric Layer


 Leveraging both method and concept, a novel multi-layer structure based on Graphene patterns and SU-8 photoresist dielectric is proposed at THz frequency range. By considering reflection and transmission channels as outputs, a simple THz coupler is provided. The structure is described exploiting equivalent circuit model while results are verified by full wave simulations. According to simulation results, the proposed device is able to reflect and transmit THz waves with high sensitivity versus gate biasing. The operation involves five bands in entire THz spectrum while the structure behavior can be adjusted by external gate biasing. Such a tunable device is in great demand to realize optical sensors and systems in several fields from indoor communications, security and medical imaging.


Introduction:
The terahertz (THz) band is the frequency band between the upper limit of electronics and the lower limit of photonics. This band has been intensively considered by researchers from several fields due to speedier operations compared to RF electronics while reduces the risks of high frequency in the photonics [1][2][3]. For instance, medical imaging can be performed via THz radiation to reduce hazardous effects on body organs. Now, to realize applications in the THz spectrum, we need materials with appropriate features. Graphene is a suitable option for implementing THz devices [4]. In 2010, the Nobel Prize in Physics was awarded to successful researches on graphene. These studies have identified graphene as a two-dimensional carbon material, as thick as a single layer of carbon atoms ( 0.32 nm ) and in a honeycomb network [5]. The density of graphene carriers can be adjusted by changing the gate voltage applied to the graphene. The density of carriers can be affected by electrical doping (via gate voltage) and chemical doping. In addition, it has been observed that the experimental results of high-density graphene carriers ( 12 2 10 n cm   ) can well be described as a system with one type of carrier, type n. The electrons in graphene behave like Dirac fermions without mass. Their distribution on the energy level in a system can be described by the Fermi-Dirac distribution function (the Fermi function) as shown by Eq. (1) [6]. (1) Here, the first part of Eq. (8) is known as the intra-band conduction ( σ( ) intra  ), which is the result of the intra-band transfers of electrons. And the second part, which results from the inter-band transfers of electrons, is known as the inter-band conductivity ( σ( ) inter  ). Intraband conduction is obtained from the Drude model and is described as Eq. (9) [10][11][12].
In conclusion:   A significant issue in the above equation is the relationship between the imaginary part of the conductivity and the real part of the electrical permittivity. The real conductivity part is also related to the imaginary part of the graphene electrical permittivity. Since the losses in graphene are modeled with the imaginary part of its electrical permittivity, the above relation shows that the losses in graphene depend on the real part of its conductivity, and we can use the graphene adjustability to form the losses in the form of desirable change.
Knowledge of graphene material and the behavior of electrons in graphene now makes it possible to implement graphene-based devices in the terahertz band. As a result, numerical modeling methods as well as circuit modeling methods paved the way for the design of such devices.
Here in this work, four layers of graphene patterns are attached to three layers of dielectrics to create two channels as output and coupled ports. Next section describes the proposed device and equivalent circuit model with details while section 3 reports simulation results of the proposed structure. Finally, conclusion is brought.

Proposed Device:
As a simple illustration, Fig. 1 shows a typical operation related to a coupler in general view.
According to this description, one input and at least two outputs are defined for a coupler block. In this regard, the radiation (includes full THz spectrum) is considered as input while transmission part of waves is assumed as regular output. Additionally, reflection channel is considered as coupled output. So seems obvious that absorption must be minimized to obtain high performance operation. In this regard, Fig. 2     layer, assures us that the proposed coupler structure is fully sensitive to the wave. This type of metamaterial, coupled with the applicability of SU-8 as a structural material, offers possibilities for quick, simple microfabrication of THz imagers. SU-8, a negative photoresist, is a low-cost material that can quickly be spun onto a substrate at a wide range of thicknesses, and then photolithographically patterned into a variety of structures. It is also transparent to THz radiation and thus a suitable choice for a dielectric spacer in metamaterials. Other choices for dielectric layer is SiO2 and PMMA dielectrics with refractive index 1.45 and 149 in THz band [30].
According to [10] and [14], each pattern can be modeled via a resistor, inductor, and capacitor. These elements are related to some physical constants and geometrical sizes as bellow: (1)  To obtain n q , and 1n q , physical parameter such as , L, a W , and D , must be designed and then referred to Table 2. Table 2. the value of n q and 1n q based on the geometry of the proposed device.  [16]. Also, the dielectric can be modeled via Eq. (15). And the input impedance is calculated as below: where the definition of parameters of Eq. (13) to Eq. (22) are reported in Table 3: Table 3. Definition of parameters.

Definition Parameter
The wave propagation constant in the dielectric substrate.

Simulation Results:
According to Eq. (13), changing gate bias leads to changing chemical potential which forces the device to react differently [17].
Where g V , , 0 , , and are respectively the gate voltage, the permittivity of the dielectric substrate, the permittivity of free space, the thickness of the dielectric substrate, and the Fermi velocity. The values of the parameters of Eq. (23) are given in Table 1.
In this regard, full wave simulation based on Finite Element Method (FEM) is exploited to show device performance. Fig. 5 extracted from CST simulator which shows transmission, reflection and absorption simultaneously.   According to these Fig. 5, Fig. 6, and Fig. 7, variations of the third layer shifts peaks of transmission and reflection considerably while operation is relatively fixed against variations of first-and second-layers thicknesses. This stems from the fact that the third layer thickness is larger than two other layers. Additionally, device performance against chemical potentials variations are reported via Fig. 8, Fig. 9, Fig. 10 and Fig. 11.    Finally, the comparison table is reported in Table 5.

Conclusion:
Using equivalent circuit model and full wave simulations, a multi-layer structure based on graphene patterns is presented. The reflection and transmission channels are considered as outputs while aim is minimizing absorption. Simulations results show both reflection and transmission in entire THz spectrum while ample sensitivity analysis are reported versus geometrical parameters and gate biasing. According to the results, the proposed structure can be considered as an appropriate coupler block in THz spectrum.