Análisis, diseño y simulación multifísica de una antena Fotoconductora Terahertz usando el método de elementos finitos

Introduction

Terahertz photoconductive antennas (PCA) have been rapidly growing as a research field during the last year, due to the vast spectrum of configurations for each of their building parameters. The main research trend has been to optimize their configuration. In this field, each parameter has been investigated independently, so the real challenge appears when all parameters are interacting simultaneously. In this study, we modeled all parameters at the same time to know which configuration yields the best results according the pulse and power of the signal.

A PCA antenna was simulated to improve its power efficiency. To achieve this goal, the COMSOL Multiphysics software was used, in which the Maxwell wave equation for optical interaction, the Poisson equations, and the derivative derivative diffusion of the electrical response were combined to determine a numerical solution.

The paper is organized as follows: section 2 introduces the theory and concept behind the proposed THz-PCA design, as well as defining the computational domain and methodology; section 3 contains a brief state of art; section 4 presents the validation of the model with both computational and experimental work from the literature, and it shows the results of the proposed THz-PCA design with other designs from previous studies; and section 5 summarizes and concludes and presents theconclusions of this research.

Background

In recent years, it has been determined that the interaction between the different properties of matter produces Terahertz radiation. These signals are significantly useful due to the size of the devices that produce them, as well as their frequency and power. The field of telecommunications has shown that the need to generate high-frequency signals involves the challenge of building larger active equipment, which is why most of the infrastructure occupies large spaces, which limits the spectrum of applications. Therefore, the generation of Terahertz radiation from small devices offers a wide variety of potential applications in the fields of health, safety, and images, among others.

Now, the interaction between different materials and techniques in this context has been a matter of research. There are two ways to generate THz radiation: by means of solid and optical state methods, the latter of which was used in this article.

An advantage of the use of the optical state technique is that it can be implemented at room temperature. Optical state techniques can be classified into optical rectification and generation with photoconductive materials, the latter being more efficient when using laser oscillators ^[1].

Thus, PCAs have emerged as conventional devices to emit THz radiation from the excitation of an oscillator laser, which has evolved over the years into powerful laser systems generally based on titanium-sapphire alloys ^[2].

Antenna

A PCA consists of an excitation laser that impinges on a surface in time lapses of the order of femtoseconds (fs). The surface, manufactured with photoconductive material, receives a constant electric potential to polarize the flow of electrons. Two metallic planar electrodes are on the photoconductive material, which can be a semiconductor substrate such as semi-isolated gallium arsenide (SI-GaAs). It is separated by an area with a defined shape, which is the geometry of the antenna, one of the parameters that were modified through modeling in this article.

The substance with which the antenna is manufactured, also called substrate, must comply with picosecond life times for the carriers, which means high mobility and high inverse breaking voltage for the flow of electrons generated in the voltage source connected to the antenna ^[3].

The attenuation in this type of radiation is very high, which is why it is necessary to use highpower sources to propagate the pulse in the air. The use of this type of sources has increased the price of this technology, thus hindering its implementation in small laboratories. Some studies have reported radiation levels of up to 60 THz ^[4]. However, the efficiency of these antennas is 0,1% by default, with an excitation of the lasers of 1-8 mW.

On the other hand, the signal-to-noise ratio and the dynamic range based on photoconductive antennas at the THz frequency is based on the quality and performance of the emitter, specifically on the amount of output power. As mentioned above, the power of the antenna depends on the source of voltage supplied to the system, which implies a high power consumption and a difficulty dissipating the heat produced during this process.

This scenario reveals the need to investigate the requirements for efficiency, as well as to identify topologies and optimal excitation parameters.

The potential applications of these devices have also required the use of different types of substrate, electrode geometry, polarization voltages, and different optical powers, reporting different efficiencies for each case.

Following this line of research, this article seeks to determine the parameters of photoconductive antennas through simulation techniques in order to improve their efficiency. The typical configuration of this concept can be seen in Fig. 1.

Figure 1: THz radiation generation diagram [5]

Plasmonic Light Concentrators

The combination of metal and a dielectric forms a material called plasmons. This material creates electromagnetic waves under the influence of light. The light that hits the metamaterial turns into shallow plasmonic polaritons, which are shorter in wavelength than the incident light. Plasmons are confined waves composed of electrons and plasma that are at the interface between a metal and a dielectric.

The direction of the initiating electromagnetic signal must match the direction of the surface plasmon wave, which can be determined from the metal and dielectric permittivity values. Therefore, modifying the shape of the metal could adjust the direction of both the electromagnetic and the plasmon waves ^[8]. In other words, the process of changing the shape of the metal allows a greater concentration of light near the space where the plasmon waves are located. Thus, the shape parameter, also called the geometry of the antenna, determines its efficiency, thus making the THz pulse power better in comparison to other possible approaches.

Starting from the operational basis of a typical antenna, different approaches are defined for the construction of a nanoantenna. These typical forms can be initially classified in two categories as shown in Fig. 2.

Figure 2: Typical antenna

From this first approach, antennas were built modifying the electrode shapes and their position.

These were PCAs based on plasmonic light concentrators, as shown Figure 3a, in this case, the surfaces where the light beam strikes are con-fined in a small space between the two electrodes. The surface surrounding the electrodes is the metal semi conductor ^[4]. Another approach for building photoconductive antennas is based on plasmonic contact electrodes, as shown in Figures 3b, 3c, and 3d. The main goal of this approach consists of increasing optical absorption near the contact electrodes.

Figure 3: Design PCA based on plasmonic

State of the art

Terahertz radiation has been widely studied in recent years, given its wide field of applications. There are important advances in the construction of photoconductive antennas according to their application. However, building an antenna is a difficult process mainly due to its size, components, and technology barrier. Therefore, computational modeling offers a good alternative to accomplish this process without an increase in costs. The mathematical principles of the steady model with a nonlinear function (Bernoulli) provide great tools to model the physical phenomena ^[9], and this equation was formulated by using COMSOL®.

The generation of frequencies in the THz band through optical processes can be classified into two techniques. The first one is called optical rectification and the second technique is based on photoconductor materials. The latter one is more efficient when using laser oscillators. The geometry of this photoconductor material could affect the THz pulse, which is why some researchers focus on the shape of the antenna.

Plasmonic contact electrodes are a novel design with a more effective separation and acceleration of photocarriers forming grating, with SI-GaAs and LT-GaAs substrates in each gap. This kind of geometry features efficient time-varying dipoles as a response to the laser incident ^[10].

Significant advances have been made in increasing the power efficiency of the THz pulse due to geometries that imply the three dimensions in the contact between electrodes. One of these cases shows that the efficiency of the antenna improved by 7,5% using a geometry with a jagged shape integrated with a logarithmic spiral on a LT-GaAs substrate ^[11].

There is also a different kinds of shape, which is composed of a photoconductor with a gap among both contacts, positive and negative, connected to a bowtie antenna. GaAs (LT-GaAs) is used for the substrate^[(12].

According to the modeling of photoconductive antennas, a great variety of numerical and analytical models have been reported ^[7], ^[13], ^[14], in which it has been possible to distinguish, from the electromagnetic theory or from the transport phenomenon in semiconductors, the parameters involved in improving the efficiency of photoconductive antennas as THz emitters. Analytical models use transport model, to explain the generation of photocurrent in the photoconductive substrate of the antenna, which is responsible for the THz emission ^[15]. The electromagnetic phenomena, models with approximations to Hertzian dipoles have been reported using Maxwell’s equations ^[16], ^[17], and HFSS simulations that are widely used to measure the main parameters of the antennas, such as radiation patterns, input impedances, and efficiencies ^[6].

It is also important to consider that, given the growing interest in this field, the number of research groups has increased worldwide. This includes the THz spectroscopy division of the Helmholtz- Zentrum Dresden- Rossendorf research center in Dresden, Germany and the University of Cambridge’s group of applications in THz. This has led to a better positioning and higher impact of indexed journals on THz technology, such as the “IEEE Transactions on Terahertz Science and Technology” with 4,342 impact factors, ranked in the first quartile according to SCOPUS.

Analysis and design of a PCA

Exploration in the THz band has grown rapidly in recent decades ^[18]- ^[20]. There are ultrafast photoconductive antenna systems excited by laser pulses in times less than picoseconds to achieve the emission of THz waves ^[21]. As mentioned above, some of the advantages of using this technology are: operation at ambient temperature, high signal-to-noise ratio, and precise measurement of the magnitude and phase of the signal, as well as various applications such as pharmaceutical screening of polymorphous and hydrated forms ^[22], ^[23], detection of materials for surveillance and security schemes ^[22], ^[24], monitoring of metal processing and construction ^[2], ^[22], detection of cancerous tissues ^[25], absolute thickness measurements ^[26], and the characterization of materials ^[21], among others.

For the design process, the materials must be correctly selected and prepared depending on their properties. Here, it must be taken into account that they must not be ionizing and have a high water absorption to facilitate high reflectivity and complete opacity. To achieve operation in THz, lasers with pulses in femtoseconds must be used, which are sent to the polarized antenna to generate an excitation that activates the recombination and generation process of the carrier ^[5], ^[21].

Now, by using the equation of the electromagnetic wave in terms of frequency (3) and the incident field (4), the resulting field is obtained by means of (5), thus simulating the optical excitation of the femtosecond pulse and showing the component peaks of the electric field in both spatial and temporal terms. Once this is done, the vector components of the power density and its total flux can be calculated (9), arriving at the generation of the carrier with equation (10) and obtaining the recombination response through (13).

The objective of Table I is to present a compilation of various authors regarding the optical conversion to THz, the geometry of the antenna construction, the type of plasmonic structure, the gap space, the characteristics of the laser, the semiconductor substrate, the polarization voltage, and the dimensions and type of lens, in order to understand what is the response produced by each of the parameters of a PCA and their influence on improving the design and output power.

Table I: Table of construction parameters and design of PCAs

Conventional PCA simulation

Thanks to the development of specialized software to simulate physical phenomena, COMSOL is used in its finite element method (FEM) mode to facilitate troubleshooting and obtain more accurate currents in order to have numerical stability and values closer to reality.With this method, it is easy to couple different physics. Next, Fig. 4 shows each of the parameters included in the COMSOL tool.

Figure 4: PCA parameters in the COMSOL software

As well as the construction of the geometry dimensions, which can be seen in Fig. 5 and the definition of domains and material properties in Fig. 6.

Figure 5: Geometry dimensions of the PCA

Figure 6: Domains and material properties of PCA

Once this has been defined, the work domains, the conditions of impedance and periodicity are assigned, as shown in Figure 7.

Figure 7: Domains and material properties of the PCA

Then, the design of the PCA is simulated, observing the concentration of the electric field in the gap zone of the dipole (Fig. 8a), the concentration of electrons in the gap zone on the semiconductor substrate closest to the dipole anode (Fig. 8b), the concentration of holes with higher gap intensity of the distributed dipole in most of the semiconductor substrate (Fig. 8c), and the concentration of electric potential in the antenna’s anode and the semiconductor substrate given by the incident beam (Fig. 8d).

Figure 8: Conditions of impedance and periodicity of the PCA

Similarly, the resulting amplitude of the electric field (THz radiation vs. time) can also be observed in Figure 9.

Figure 9: Complete view of the photoconductive antenna

Figure 10: Electric field (THz radiation vs. time) of the PCA

Conclusions

In accordance with the proposed objective, it is possible to identify the excitation parameters that allow the generation of THz radiation using PCAs. These parameters were identified based on the state of the art described in this paper.

Similarly, it was also possible to reproduce the theoretical models that describe the behavior of photoconductive antennas, while also identifying the geometric model and the physicochemical behavior to understand the ideal topologies leading to the generation of the desired photocurrents, which are necessary for applications in the industry.

The analytical and mathematical modeling of this design is facilitated by using the COMSOL finite element solver, in which the equations involved are configured. Then, this this tool proceeds to simulate them, depending on the initial parameters that were configured to obtain the photocurrent peak. All the obtained results such as the concentration of electrons and holes in the semiconductor surface, its generated electric field, and, finally, the THz radiation peak, were identified and explained based on a conventional, theory-based photoconductor antenna solution, and it was possible obtain a photocurrent peak of the order of 0,1-1,2 THz, which shows that the application of the theories was satisfactory.