Development and Performance Enhancement of MEMS Helix Antenna for THz Applications using 3D HFSS-based Efficient Electromagnetic Optimization

Interest of Micro-Electromechanical System (MEMS) antennas in Terahertz (THz) applications has rapidly expanded in recent years due to the advent of accurate Computer Aided Design (CAD) tools. The very special needs of newly proposed MEMS antennas, especially with a wide bandwidth range, require advanced optimization procedures of enhancing already established designs. This paper provides a compact design of a wideband MEMS helix antenna optimized using tree-dimensional High Frequency Structure Simulator (3D-HFSS) based on Quasi-Newton (Q-N) and Sequential Non Linear Programming (SNLP) techniques to modify the antenna structure with a high accuracy for the selective band of frequencies by training the samples and minimizing the error from Finite Element Method- (FEM) based simulation tool. The helix antenna is presented using MEMS technology and shows high performance demonstrated by very low return losses of less than -20 to -65 dB for a wide range of frequencies from 2.5 to 5 THz. High antenna geometry precision and efficient performance are finally achieved by rectifying and synthesizing various tunable parameters embedded in silicon substrate including both helix form and feeding line parameters.


Introduction
As new applications for the electromagnetic THz field begin to emerge, a new generation of efficient MEMS antennas [1] is developed to meet the specific requirements of these high frequency systems. Many new processes of MEMS technology are just beginning to stimulate interest in this unique spectral and continue to help manufacturing THz antennas, improving their performance and achieving micro-level precision [2]. Focused Ion Beam (FIB) is one of the important processes used for fabricating MEMS antennas, especially helical antennas [3] by implementing silicon wafers that represent a very good solution to enhance the antenna's radiation and performance. MEMS helix antennas employing silicon substrates, have achieved over the past few years interesting characteristics including compact size, high directional gain, and wide bandwidth, thus their implementation into planar forms seems to become easier due to the advanced micromachining techniques [4]. This has provided a new class of THz antennas with numerous wireless access applications thanks to the use of complex simulation tools to bring the CAD for such high frequency structures to its current state of the art. Accordingly, HFSS-based Q-N and SNLP approaches lead to excellent optimization solutions carrying out by replacing repeated electromagnetic simulations whilst still retaining a good accuracy as compared with finite element modeling to improve the accuracy of the existing design models or develop new design models. This procedure requires acceptable simulation time especially for defining the problem that needs reliable and fully functional approximations. This paper proposes for the THz frequency access systems a compact geometrical configuration of a wide MEMS Helix antenna using HFSS software. The MEMS antenna geometry is optimized using both Quasi-Newton and Sequential Non Linear Programming algorithms to offer fitness functions for excellent bandwidth learning and fast configuration evaluating. The antenna occupies a very compact volume of 79×80×152 um (0.960 10-3 mm3) including the silicon substrate having a thickness of 9.3 um and a dielectric constant of 11.9. The explored MEMS helix antenna design is validated by demonstrating optimal results in terms of return loss properties in comparison to the previous optimized structures [3,5]. The antenna with optimized parameters operates in a wide bandwidth from 2.5 to 5 THz and shows very low reflection coefficients with less than -20dB over the entire bandwidth. The compact optimized MEMS antenna is finally simulated by covering an ultra wide range of frequencies of 8.7 THz extending from 1.2 to 9.9 THz and shwos very good performance resulting in a low reflection coefficient of less than -15dB for the entire bandwidth.

Research Method
Electromagnetic THz gap remains one of the least explored regions of the frequency spectrum for diverse applications, for the reason that it claims a deep knowledge of radiofrequency engineering and semiconductor physics. The size of a THz antenna is expected to closely relate to wavelength, which is about 30 um (10 THz) to 3 mm (0.1THz) [6]. Micro-electromechanical systems therefore present a suitable technology for manufacturing compact THz antennas with low profile, wide bandwidth, and large radiation [7]- [9]. Several processes to fabricate THz antennas employing MEMS technology have been reported in recent years, in which the fabrication process is highly precise and antennas with compact size become soft to be integrated with other devices [10]- [11]. FIB process provides a great flexibility to explore such MEMS antennas in micrometer scale and makes possible to fabricate 3D structures with low cost by employing a large irradiation area of FIB on suspended film structures with the advantages of high flexibility, controllability and repeatability [12]- [13]. The proposed MEMS antenna is realized in a single-crystal silicon substrate and can be fabricated using conventional ul micromachining relying on availa le stress -introducing technique . igure illustrates the geometric structure of the MEMS helix antenna proposed for the optimization and development. igure shows the equivalent circuit (a) of the optimized MEMS helix antenna implemented using Advanced Design System (ADS) simulator, the twodimensional cross-section (b) and three-dimensional view (c) of the antenna using HFSS software which clearly indicate that the antenna reaches a high level of precision leading to interesting characteristics including large bandwidth and low reflection coefficient. The proposed structure uses mainly the set of equations demonstrated in [3] to calculate the helix parameters. The antenna is fed with a coplanar waveguide (CPW) and working in transmission mode.

Antenna Optimization and Development
The proposed antenna design is firstly simulated by HFSS software which constitutes an interactive tool for computing basic electromagnetic field quantities and analyzi ng the electromagnetic behavior of the structure within FEM [15] to understand the physical problem to be optimized. Figure 3 presents the simulated return losses of the proposed geometrical configuration for a frequency range from 2.5 to 5 THz. As it is observed, geometric parameters initially proposed for the analysis show acceptable performance which needs to be more enhanced. The structure is then optimized by coupling Q-N and SNLP methods in order to improve the antenna performance, and achieve a high um-level precision of the helix form parameters, CPW feeding characteristics and silicon platform dimensions.

Quasi-Newton Optimization
First, uasi-ewton optimizer is employed to find a minimum or maximum of the cost function which relates three asic parameters in the model including the helix diameter width and silicon thic ness s to the return loss properties. This choice is mainly ased on selecting parameters exhi iting a smooth characteristic and little numerical noise. his technique wor s to approximate locally the optimization parameter values that will e placed ac into the original function and used to calculate a gradient which provides a step direction and size for determining the next est values in the iteration process. owever this approach suffers from two fundamental pro lems he first issue is the possi le presence of local minima; once the -optimizer has located a minimum this technique will locate the ottom and will not search further for other possi le minima and not a good glo al solution to  At some point, the numerical imprecision in the parameter calculations ecomes greater and the solution will oscillate and may never reach convergence. or this to use theoptimizer effectively the starting point of each parameter optimization is chosen close to the expected minimum displayed by the primary simulation ased on the understanding of the physical pro lem eing optimized. heoptimizer egins then to vary the value of the selected parameters on the basis of getting a minimum or maximum of the cost function to overall simulation goals. Figure 4 shows the simulated return losses of the optimized antenna design usingtechnique which shows that the antenna configuration egins to present good performance for the same frequency range with low return losses of less than -15 to -44dB.

Sequential Non Linear Programming Optimization
Next, in order to achieve a high level of performance of the antenna design, Sequential Non Linear Programming optimizer is further added to analyze four additional parameters including the helix pitch (S), helix turn number (N), CPW gap (G), and CPW thickness (T). The antenna height (HA) and the substrate width (Ws) will be automatically optimized relating into these parameters.  The main advantage of SNLP optimizer over Q-N optimizer is that it handles the optimization problem in more depth, and assumes that the optimization variables span a continuous space and take any value within the allowable constraints and within the numerical precision limits of the simulator. The SNLP optimizer estimates the location of improving points with an accurate Finite Element Approximation (FEA) with Response Surfaces (RS) and light evaluation of the cost function. This allows a faster practical convergence speed than that of Q-N optimizer. Another advantage is that SNLP optimizer allows the use of nonlinear constraints, making it much more general than Q-N optimizer. The SNLP optimizer creates the response surface using a polynomial approximation from the FEA simulation results available from past solutions. The response surface is most accurate in the local vicinity. The response surface is used in the optimization loop to determine the gradients and calc ulate the next step direction and distance. The response surface acts as a surrogate for the FEA simulation, reducing the number of FEA simulations required and greatly speeding the problem. Convergence improves as more FEA solutions are created and the response surface approximation improves. As illustrated in Figure 5, the antenna geometry obtained from the SNLP technique presents very low reflection coefficients with less than -18dB to -88dB, resulting in a significantly high performance for the selected band of frequencies. Figure 6. Return loss and radiation pattern graphs of the optimized THz MEMS helix antenna using HFSS-based efficient electromagnetic optimization Figure 6 shows the simulated return losses (a) and radiation patterns (b) of t he optimized antenna design finally obtained using HFSS based on Q-N and SNLP solvers that indicates excellent performance for the developed antenna design interpreted by very low return losses of less than -30 over the central frequency band. Thus, the radiation patterns, both in Eplane (xoz-plane) and H-plane (yoz-plane) of the antenna transmission mode at the central frequency (3.5 THz), keeps good directivity with slightly bending in the side lobes of yoz -plane due to the fine modeling process. This demonstrates the high efficiency of the applied optimization strategy to provide a good geometrical accuracy and excellent electromagnetic response for the developed antenna design for a very wide THz comparing to previous research works. The promising results obtained from the efficient electromagnetic optimization are then compared to the results previously achieved in [3,5]. As shown in figure 7, it is clearly observed that the new THz MEMS helix antenna geometric characterization developed by HFSS based on efficient electromagnetic optimization comes with very low return losses with closely less than -20dB over the entire frequency band, and less than -30dB over the central frequencies from 3.2 to 3.7 THz, and approximately -55dB and -89dB at 3.20 THz and 3.80 THz respectively, this significantly validates the excellent performance for the proposed THz MEMS helix antenna design improved by Q-N and SNLP optimizers comparing to the previous   [dB] Return losses of the antenna [5] Return losses of the antenna [3] Return losses of the optimized antenna Finally, the compact THz antenna design optimized using Q-N and SNLP methods has been tested and simulated covering an ultra wide range of frequencies of 8.7 THz extending from 1.2 to 9.9 THz as presented in Figure 8. The antenna shows very low return losses of closely less than -20dB for the entire bandwidth presenting a great success in finding useful design with very good performance for UWB wireless products. This demonstrates the advantage of HFSS optimization techniques in offering a more degree of freedom in developing new structures, supporting multiple resonance modes distributed across a large THz spectrum, based on the proposed MEMS helix antenna design which presents a potential candidate for different wireless communication applications.

Conclusion
In this paper, a new geometrical configuration of a THz MEMS helix antenna design is developed using HFSS-based Quasi-Newton and Sequential Non Linear Programming optimizers which demonstrate high efficiency and accuracy in achieving excellent performance and high um-level precision. The proposed THz antenna design can be easily developed using micromachining technology based on MEMS processing, and offers very good applications for a wide range of frequencies from 2.5 to 5 THz. These characteristics make the proposed MEMS helix antenna design highly attractive to support several THz systems such as radar, biomedical, sensing, imaging, space, radio astronomy, and spectroscopy systems [16].