The agricultural and food (agri-food) industry has always attracted significant attention worldwide. In particular, the importance of reliable diagnostic inspection technologies has been growing due to an increasing demand for improving the quality of life. Contamination by foreign bodies, packaging failures and the production of articles with poor characteristics (consistency, appearance) are among the main sources of customer complaints against manufacturing companies, with consequent loss of brand credibility. The food industry is particularly exposed to this problem, especially nowadays that consumers are more aware and pay much more attention to the quality and integrity of the food purchased. Accordingly, huge interest is towards the use of sensing technologies capable of detecting foreign body contamination and packaging failures. Available sensing techniques for food inspection include X-ray imaging [1–3], thermal imaging [4, 5], ultrasonic imaging [6, 7], fluorescence imaging [8] and electromagnetic (EM) systems working at microwave frequencies [9–12]. However, each one of these techniques has advantages and limitations. For example, X-rays systems, which are increasingly used in the food production industry for quality control inspection, provide high resolution images but have difficulties in detecting low density objects such as plastic, glass, wood or insects. Furthermore, the use of ionizing radiation is always related to risks involving both operators and the food itself that could be altered. On the other hand, infrared (IR) technologies have the advantage of being fast and safe but they are limited by a poor penetration capability and strong absorption in water. Instead, fluorescence imaging is effective only when objects with fluorescent compounds are investigated. In this framework, terahertz (THz) imaging appears as an emerging technology, which offers several advantages. THz are electromagnetic waves ranging from 0.1 to 30 THz (wavelength from 3 *mm* to 10 μ*m*), which are currently exploited in various applications, including medical diagnosis [13], pharmaceutical analysis [14], security enhancement [15] and artwork [16]. As microwaves and infrared signals, THz waves are non ionizing radiations thus they allow a safe survey without requiring specific security protocols. Moreover, similar to microwave imaging and differently from X-ray technology, THz systems allow the detection and localization of changes in terms of electromagnetic properties with a high resolution (generally speacking, THz spatial resolution is in the order of some hundred microns while the microwave spatial resolution is typically about centimiters). On the other hand, THz capability of penetrating inside a material is limited to a few millimiters. In addition, THz waves are strongly attenuated by water and suffer the environment humidity conditions. Currently, several studies regarding the detection of both food contaminants [17, 18] and defects in plastic packages [19] have shown the effectiveness of THz imaging technology in the field of food industry. However, the study of THz potential in food inspection is still at an early stage and far to be completely assessed.

This chapter provides an overview of THz imaging for food inspection by summarizing the current state of the technological development and recalling valuable case studies presented in literature. For sake of completeness, the chapter starts with a brief description of the main THz technologies, i.e. THz pulsed and time domain systems as well as continuous wave ones. Then, THz imaging in transmission mode, THz Time of Flight imaging and THz Camera imaging are reviewed and their advantages and drawbacks are discussed. Thereafter, the attention is focused on the employment of THz imaging for food quality control and its potentialities in detecting contaminants and packaging failures. Relevant examples available in literature are described together with some experiments carried out by the authors themselves. Finally, the main open challenges and future perspectives are discussed.

#### **2. THz imaging systems**

Systems for THz imaging can be divided into two main categories based on their operative principle: pulsed and continuous wave systems.

Pulsed or time domain (TD) systems are composed of four principal components: primary source, which is an ultrafast pulsed laser emitting sub 100 *fs* pulses, THz emitter, THz detector and a time delay stage.

There are two major technologies to generate and detect THz pulses: photoconductive antennas (PCAs) and electro-optic crystal (EOC); usually one emitter and one detector are used, even if technologies based on the use of detectors arrays are available [20]. The ultrafast laser beam is divided into pump and probe beams (**Figure 1**). THz pulse is generated by the pump beam that affects the emitter, while the probe beam is used to gate the detector. The probing THz wave is focused onto the sample using polymeric lenses or mirrors. After the interaction with the sample, the THz wave is collimated and refocused on the terahertz detector. The delay stage is used to offset the pump and probe beams and allows the temporal sampling of the THz signal.

*THz Imaging for Food Inspections: A Technology Review and Future Trends DOI: http://dx.doi.org/10.5772/intechopen.97615*

**Figure 1.** *Typical transmission THz imaging system.*

CW or frequency domain systems are based on the beating of two laser wavelengths, whose difference is in the THz region, in a biased semiconductor photomixer [21]. If the photomixer is connected to a properly designed antenna, THz radiation is emitted into the free space. The CW THz radiation is then collimated and guided in the same manner as for pulsed systems [21]. TD and CW THz systems have many differences. TD systems are more complex, expensive and heavy than CW ones but they work in a wide band, usually from 0.1 up to 6 THz for the new generation systems [22]. Moreover, they gather the signal as a function of the time and, thus, allow to reconstruct more information about the investigated samples, provided sophisticated data processing procedures are adopted. Conversely, CW systems are narrow-band and often gather only the intensity of the detected signals, which is stored in a matrix and directly converted to a raster image. Therefore, they are effective in generating THz images almost in real-time but also make inaccessible some information and thus are less flexible. It is worth remarking that TD systems encode depth information as changes in pulse timing, i.e. a variation of the temporal location of the measured peak that indicates a change in the optical path length from the emitter to the sample and from this latter to the detector. CW systems also make possible to obtain this information through the use of additional detectors or by performing additional scans. For instance, by changing the angle between emitter and detector, it is possible to measure the scattered wave instead of the specular reflection. Hence, by performing measurements at different angles it is possible to record intensity data accounting for scattering and reflection

**Figure 2.** *THz setup. (a) Reflection mode. (b) Transmission mode.*

phenomenon occurring at different depths and, thus, to image features of each layer of the measured sample [23].

The choice between TD or CW systems depends on the application of interest. Focusing on food inspections, a preferable choice is a TD system, when the goal is the non-destructive inspection devoted to detect defects or foreign bodies, because it provides more complete information and make possible a 3D visualization of the investigated sample. However, a CW system is sufficient when a 2D image is enough to satisfy the survey finality, as it happens, e.g., when the control of packaging is considered.

Finally, it is worth recalling that both TD and CW systems can be used in reflection or transmission mode as sketched in **Figure 2a** and **b**, respectively.

#### **3. THz imaging modalities**

#### **3.1 THz imaging in transmission mode**

When working in transmission mode, the THz radiation propagates through the material to be inspected from the emitter to the detector. Hence, in this type of setup one places an object at the focus of the THz beam on an x-y moving stage, and measures the waveform passing through the material [24]. By translating the object and measuring the transmitted THz waveform at each position of the object, a pixel by pixel image is built. The transmitted signal is collected as a time-dependent function that contains information regarding the phase and amplitude of the THz field. The recorded signal is digitized and processed by the digital signal processor (DSP) at each pixel to obtain the transmission THz image of a sample [25]. Specifically, several 2D THz images are obtained by plotting, point by point, different features of the measured wave-forms, i.e. their amplitude, phase, maximum or minimum values and so on [26]. Moreover, by means of the Fast Fourier Transform (FFT), frequency-domain information on the samples are also obtained [27]. The transmission mode is effective because many materials strongly absorb THz radiation, while others are transparent. Hence, it is possible to obtain information on the sample by plotting the amplitude of the measured wave-forms and observing its spatial distribution, while taking into account that higher amplitude values correspond to THz transparent materials. However, if the sample is too thick no useful image can be obtained. Further information is obtained by computing the absorption coefficient and refractive index by using the sample *Es*ð Þ*ν* and the reference *Er*ð Þ*ν* spectra. In transmission mode, *Er*ð Þ*ν* is calculated by taking measurements without the sample. Specifically, the transmission function is defined as follows [28, 29]:

$$T(\nu) = \frac{E\_t(\nu)}{E\_r(\nu)} = \frac{4n}{\left(n+1\right)^2} \exp\left[-a\frac{d}{2} + j2\pi\nu(n-1)\frac{d}{c}\right] = A\exp[j\phi(\nu)]\tag{1}$$

where *d* is the sample thickness, *ν* is the radiation frequency, *c* is the speed of light in vacuum, *n* is the refractive index, *α* is the absorption coefficient, *A* is the amplitude ratio between the sample and reference spectra and *ϕ* is the relative phase difference. Hence, it is possible to calculate *n* and *α* for each frequency as:

$$n = 1 + \frac{c\phi}{2\pi\nu d} \tag{2}$$

$$a = \frac{2}{d} \ln \left[ \frac{4nA}{\left(n+1\right)^2} \right] \tag{3}$$

*THz Imaging for Food Inspections: A Technology Review and Future Trends DOI: http://dx.doi.org/10.5772/intechopen.97615*

By taking into account that some materials exhibit strong absorption peaks at specific THz frequencies, once the absorption coefficient and the refractive index have been computed, it is possible to collect information on the structure of the sample and on its materials. THz transmission imaging provides a wealth of information by analyzing the 2D images of these indices at different frequencies, but the pixel by pixel scanning procedure is time consuming and often suffers from poor spatial resolution because the spatial offset used to move mechanically the sample is often comparable or larger than the wavelength of the THz radiation [30].

#### **3.2 THz time of flight imaging (TOF)**

THz time-of-flight imaging (TOF) also known as THz pulsed imaging (TPI) has the unique property of providing a 3D "map" of the object by exploiting data collected in reflection mode [31]. This technique was used for the first time by Mittleman and coworkers to produce the internal structure of a 3.5 inch floppy disk [24]. The apparatus used for reflection imaging is quite similar to the transmission one, except for the change regarding the THz beam path (see **Figure 2**) [32]. In brief, the object is probed by a pulse signal and the reflected waveform is collected as a time-dependent function in a certain observation time window using a THz-TDS configuration. The temporal delay of the reflected pulses reveals the internal structure of the sample (if the object is nonmetallic). By collecting data along a line, moving emitter and receiver along a straight trajectory and plotting the gathered wave-forms, a space–time image is obtained. In particular, the data can be represented in the form of a THz *radargram* (see **Figures 7** and **8** in Section 4.1), that is a two-dimensional image, wherein the horizontal axis is the spatial coordinate and represents the measurement line, while the vertical axis is the temporal coordinate and represents the time of flight, that is, the time *T* that the waveform employs to propagate from the emitter to an electromagnetic discontinuity and to go back to the receiver (see **Figure 3**). The time of flight *T* is related to the distance *d* between THz probes and the detected discontinuities as:

$$T = \frac{2d}{v} \tag{4}$$

*v* being the electromagnetic wave propagation velocity into the object. Therefore, a THz radargram provides a cross-sectional representation of the

**Figure 3.** *Time of flight sensing principle.*

inner features of the object, which gives information about position and thickness of possible inner discontinuities. A 3D characterization is obtained by collecting radargrams along parallel profiles and visualizing the stored data all together.

Reflection mode is effective because different materials exhibit different behavior when illuminated by THz radiation. In principle, as in transmission mode, the spatial distribution of the refractive index can be retrieved, since amplitude and phase of the reflected signals are available by means of the Fourier transform, even if it is quite complex to define the reference signal and this makes the calculation of the reflectivity more complex. On the other hand, it is important to take into account that the reflectivity of an object depends not only on its refractive index, but also on the surface roughness, polarization of incident THz radiation and other geometric factors [15]. In addition, noise is a crucial problem in this case and advanced filtering and signal processing approaches are required. In fact, the intensity of the signal measured in reflection mode is generally lower than in transmission mode. In this respect, noise filtering and deconvolution procedures are commonly applied to improve the final image quality [33].

#### **3.3 THz camera imaging system**

An important research topic regards the development of THz cameras similar to the optical ones. Although active and passive THz cameras have been proposed, THz cameras are mainly designed as an active sensor, being the natural emission of THz wavelength extremely weak. Therefore, an appropriate source has to be used to illuminate the scene. Two main types of THz cameras are available in literature: thermal cameras and FET cameras [34]; they are briefly described in the following.

Thermal cameras record an image based on the heat generated by the THz radiation and exploit three types of thermal detectors: Golay cell, Pyroelectric sensors and bolometers. Golay cells transfer the generated heat to an expanding gas cell and measure the increased pressure optically by means of moving mirrors [35]. Being based on the mechanical movement of a membrane, Golay cells are slow detectors and are difficult to be integrated into dense arrays of detectors. Consequently, THz imaging with Golay cells is often done in a single-pixel detection scheme. Pyroelectric sensors detect changes in terms of the electrical polarizability of certain crystals, which is generated by a temperature growth [36]. Unlike Golay cells, pyroelectric cameras based on an array of detectors are commercially available but are characterized by a low sensitivity and this issue makes them less effective for THz imaging. Bolometers detect the change in a temperature-dependent resistance and are often based on the well-known infrared imaging technology adapted to THz frequencies [37]. Currently, microbolometers (i.e arrays of bolometers mounted onto read-out integrated circuits fabricated with CMOS process technology) are specifically designed to operate at THz frequencies and make possible to reach a sensitivity level suitable for industrial imaging applications, thanks to the inclusion of a Fabry–Perot cavity, antennas, and metamaterials to increase the absorbed THz radiation [38].

THz FET-based cameras measure a rectified voltage after interaction of the THz radiation with a plasma wave in a transistor channel [39]. This approach based on antenna-coupled FETs for THz detection have been implemented in standard CMOS technology [40]. Their production does not require different procedures with respect to standard CMOS technology, which provides the benefit of high maturity in terms of fabrication yield and pixel uniformity. On the other hand, to perform a successful THz imaging, the source beams must be expanded and in

*THz Imaging for Food Inspections: A Technology Review and Future Trends DOI: http://dx.doi.org/10.5772/intechopen.97615*

several standard setup [41] such an expansion is realized by means of parabolic mirrors without any absorption.

Generally specking, the operating principle of a THz camera does not differ so much from that described in the previous paragraphs: a source illuminates the object under test and the reflected (or transmitted) signal is collected by the camera. Moreover, between the object under test and the camera there are often lenses devoted to focus the THz beam on the camera. The main difference with the THz imaging system described in 3.1 and 3.2 is that the THz cameras provide nondiscriminatory intensity-based imaging. It is worth pointing out that, at the current state of the technological development, THz cameras appear suitable to a possible industrial application even if there are still issues related to the requirements to be satisfied. First, the cameras manufacturing process should be compatible with existing manufacturing techniques, such as CMOS technology, which enables the development of high resolution image arrays, in order to reduce the costs. THz cameras must be able to operate at room temperature while still retaining high sensitivity and should be characterized by contained size, weight and energy consumption in order to facilitate integration into industrial imaging systems. Furthermore, it is crucial to assure that data acquisition and processing time are compliant with the time of a production line [42, 43].

#### **4. Applications of THz imaging in food industry**

This paragraph provides an overview of the potentialities offered by THz imaging in the frame of food inspections by presenting examples available in literature as well as experiments carried out by the authors themselves. Specifically, two kind of inspections are considered: 1) the detection of defect and foreign bodies; 2) the packaging quality control.

It is worth pointing out that non-polar and non-metallic substances, such as plastic, cardboard, wood and other common packaging materials, are transparent to THz radiation and show very weak interaction with THz waves. This makes THz imaging attractive tools for the inspections of packaged products. Consequently, the use of THz waves allows us to detect unwanted objects that compromise the safety of the product as well as to check defects of the sample under test by controlling its integrity. In this way, defects such as irregular shape, breaking and even absence of the product itself inside the package can be detected.

#### **4.1 Defect and foreign body detection**

The presence of defects and foreign bodies in food is one of the major concerns of the food industry. Usually, the term 'foreign body' refers to unwanted objects in food products and it accounts for contaminants originated both by food products themselves (e.g bone in meat; fruit stones) and by manufacturing or packaging processes (e.g metal, plastic, glass pieces and small stones) as well as for warms and insects. In the last years, several research groups have focused their activities on THz surveys devoted to detect and localize undesired hidden objects and to verify the quality of food products. For this purpose, both CW systems and pulsed ones have been employed.

The employment of THz systems for the detection of contaminants such as small stones, glass, plastic and metal has been considered to investigate flour [44], milk powder [45], wheat grain [46] and chocolate bars [47]. It is worth reporting, as an example, the THz inspection of chocolate bars [17], that represents a promising field of THz imaging application. In [17], THz imaging was performed in

transmission mode with the aim of detecting contaminants such as stones, glass and metal screws in chocolate bars and a THz-TDS working in the frequency range from 50 GHz to 2.5 THz was used. The 2D images were obtained by scanning the samples perpendicularly to the THz beam. In all the analyzed cases, contaminants were clearly localized in THz images due to the lower intensity of the transmitted THz radiation when the foreign body were present. In fact, glass and stone absorbed part of the signal decreasing its intensity, while metal reflected all THz radiation. THz transmission imaging allowed to identify foreign bodies in the chocolate sample both in the presence and absence of the plastic foil packaging. In [17], it has been also demonstrated that is sufficient to record only some key points of the THz waveform in order to collect all the necessary information thus decreasing the amount of data and the measurement time and bringing the scanning speeds to 0.55 *m=s*. Furthermore, THz technology has been exploited to detect undesired hidden insects such us crickets, mealworms and grasshoppers in flour [48], milk powdered [18], noodle [49–51] and chocolate bars [47]. These studies have been referred to laboratory prepared contaminated samples and have provided a preliminary assessment of THz capabilities to detect insects in food.

The possibility to check the quality of red ginseng and walnuts has been investigated in [52], where a sub wavelength transmission imaging system based on Bessel–Gauss beam focusing in the 140 GHz frequency band has been used. Information about the quality of the analyzed product was obtained since THz images showed that high quality samples have a relatively uniform internal structure. It has been demonstrated that red ginseng and walnuts with thicknesses of 20–30 *mm* could be inspected without causing damage and the internal structure of these objects was observed non destructively. Finally, already commercially available THz imaging system [53], has been used to check the presence (or the absence) of chocolate bars inside their package, preventing any complaints due to an incorrect number of bars.

In this context, the potentialities offered by THz imaging has been assessed by the authors themselves and two test cases involving chocolate cream are herein presented. The results have been obtained by means of the Zomega THz FiCo system available at the Institute for Electromagnetic Sensing of the Environment - National Research Council of Italy (IREA-CNR). The adopted THz system is equipped with an ad hoc designed imaging module, which allows an automatic planar scan (see **Figure 4**) and collects data in normal reflection mode in the effective frequency range from 40 GHz to 1.16 THz. For a more precise description of the system see [16, 54]. The collected data have been processed by means of a two-step filtering procedure: a band pass filter designed to select the effective spectrum of the signal [54] followed by a singular value decomposition (SVD) procedure [16].

**Figure 5** shows the chocolate laboratory-prepared samples that are made by a plastic support filled with a chocolate cream: in the first case there is a surface defect consisting of a piece of pistachio peel (see 5a), in the second case metal has hidden 1 *mm* deep inside the chocolate cream, mimicking the foreign body (see 5b). Falsecolor THz images are shown in **Figure 6**, and have been obtained by plotting, point by point, the maximum amplitude of the processed data collected by the system. **Figure 6** demostrates the THz imaging ability to detect pistachio peel on the surface of the chocolate cream (see 6a) and the presence of the metal inside the sample (see 6b). **Figure 7** shows filtered data, referred to the sample in **Figure 5a**, that have been represented in the form of a THz radargram as described in Sec 3.2. The data have been gathered with a 0.25 *mm* spatial step along the x-axis, for *y* = 14 *mm* and *y* = 20 *mm*, which correspond to lines where the surface defect is present and absent, respectively. By observing 7a, it is possible to note that the extent of the

*THz Imaging for Food Inspections: A Technology Review and Future Trends DOI: http://dx.doi.org/10.5772/intechopen.97615*

#### **Figure 4.** *Zomega FiCO system: Imaging module.*

#### **Figure 5.**

**Figure 6.** *False color THz images. (a) Surface defect detection. (b) Foreign body detection.*

**Figure 7.**

*THz Radargrams referred to 5a. (a) y = 14 mm - the extent of the surface defect ranges from 10 mm to 22 mm. (b) y = 20 mm - No defect.*

defect ranges from 10 *mm* to 22 *mm*. **Figure 8** shows THz radargram, referred to the sample in **Figure 5b**, gathered with a 0.25 *mm* spatial step along the *x*-axis, for *y* = 20 *mm*, that corresponds to an area where the contaminant is present. By observing **Figure 8**, it is possible to distinguish two reflections due to occurrence of different materials. In particular, the first reflection is related to the air-chocolate interface, while the second reflection represents the interface between the chocolate and the metal layer. Based on the obtained results, one can state that THz waves allow us not only to image the surface defect on the food samples, but also to detect and localize hidden objects that may be dangerous for human life.

#### **4.2 Packaging quality control**

The detection of production defects in plastic or paper packaging is a potential area of application for THz imaging. The possibility to check the integrity of plastic welded joints using THz waves has been explored in [55] where a THz - TDS system in transmission mode with a frequency range from 50 GHz to 2.5 THz has been used. Several sheets of high-density polyethylene welded into a lap joint with

#### **Figure 8.**

*THz Radargram referred to 5b - y = 11 mm. It is possible to distinguish two reflections due to occurrence of different materials.*

*THz Imaging for Food Inspections: A Technology Review and Future Trends DOI: http://dx.doi.org/10.5772/intechopen.97615*

#### **Figure 9.**

*Sugar bags. (a) Standard packaging. (b) Defect packaging highlighted in the box.*

#### **Figure 10.**

*False color THz images. (a) Standard packaging. (b) Defect packaging.*

different welds imperfections have been studied. The results obtained showed that the contamination of metal or sand within the weld joint of two plastic sheets could be clearly identified. Furthermore, THz-TDS allowed to distinguish between welded and non-welded material.

Analysis regarding paper packaging defects have been carried out by the authors of this chapter using THz FiCo system introduced in Section 4.1. The experiments have regarded non destructive testing of sugar bags with and without packaging defects. A standard packaging is reported in **Figure 9a**, while the sachet of sugar in **Figure 9b** is characterized by a surface defect of about 10 *mm*. The data has been gathered with a 0.4 *mm* spatial resolution along the *x* and *y* axes. **Figure 10** indicates the ability of THz imaging to represent accurately the surface of the packaging. In particular, the defect of the package has been successfully checked guaranteeing an effective control of quality as **Figure 10b** shows. These results allow us to appreciate the diagnostic capabilities of THz technology of detecting packaging defect that could compromise the quality of the food.

#### **5. Challenges and perspectives**

THz imaging has interesting features that make it particularly attractive for food quality control. However, there are several issues to be faced in order to move from laboratories and academic environments to a widespread industrial use. In this frame, main issues are:

Thanks to technological advancements regarding the development of laser sources, integrated optics and industrial-grade THz hardware, a significant cost reduction has been registered in the last years and it is expected in the future, thus the availability of low-cost and high performance THz imaging systems appears as a reachable goal.  In this regard, the use of 2D arrays of emitters and detectors is worth to be considered in order to avoid mechanical movement of the sample. Alternatively, single-pixel detection combined with compressive sensing techniques can be employed [56]. There are also challenges related to attenuation, penetration depth and scattering effect of THz radiation to be considered. THz waves suffer a strong absorption by water and appears not effective to inspect high humidity products with a thickness greater than 1 *mm*. In this respect, broadband systems or systems working in the low-frequency THz region are subject of research activities [57]. On the other hand, it is important to study THz interaction with food materials and how it depends on the water type and its level. On the other hand, THz waves exhibit a low penetration depth especially when measuring high-moisture foods (e.g meat; fruit). The penetration depth depends on several factors such as properties of the food material, thickness of the sample, power of THz source, probing wavelength, view and observation angles under which the food is surveyed [58]. Modern THz systems mitigate this problem enhancing the power of the THz radiation [59]. The scattering effect affects both transmission and reflection THz imaging and it is ascribable to in-homogeneity of food, the presence of particles having irregular shape and size comparable to the probing wavelength [25]. This challenges can be faced by using data processing algorithms exploiting an advanced modeling of the interaction between THz radiation and food [25].

Finally, it is worth pointing out that, due to the diversity of samples to be analyzed, most of the high-speed THz systems are application-specific. In fact, in order to improve the performances of THz system in a manufacturing and processing line, the system must be specifically optimized for that particular product and purpose. This process is usually long and labor-intensive.

#### **6. Conclusions and future trends**

We presented an overview of the instruments and sensing principles used for THz imaging and its application for food quality inspection. This chapter has begun by presenting the main adopted THz systems and imaging modalities. In particular, we focus our attention on THz imaging in trasmission mode, THz Time of Flight imaging and THz Camera. Then, examples have been summarized briefly in order to show THz imaging applications to different food samples. It emerged that, THz

*THz Imaging for Food Inspections: A Technology Review and Future Trends DOI: http://dx.doi.org/10.5772/intechopen.97615*

waves are characterized by the ability to pass through a wide variety of packaging materials allowing us to control the quality of the products packaged in glass, plastic, paper and cardboard. On the other hand, THz waves are able to detect low density material hidden in food products through a non-destructive monitoring. Although the effectiveness of THz imaging has been demonstrated for a large number of issues in food quality control, it is clear that there is still a long way to go before this technology can be applied in industrial processes. In fact, the costs of THz instrumentation are still very high, there are limits in the penetration depth that can be investigated and the process is time consuming. So future research is needed to develop fast and economical THz systems through the implementation of compact and more efficient instrumentation. Another important goal to be achieved is the introduction of a database library for the main food component that can simplify the prediction and detection processes. Despite the limitations, THz imaging is establishing itself as a powerful tool for non-destructive inspection in the food industry and for the next future its use is expected to be considered in a wide range of surveys and become more and more consolidated.

#### **Acknowledgements**

This work has been supported by PRIN BEST-Food - Broadband Electromagnetic Sensing Technologies for Food quality and security assessment (grant n. 20179*FLH*4*A*).

#### **Author details**

Sonia Zappia1,2, Lorenzo Crocco1 and Ilaria Catapano<sup>1</sup> \*

1 Institute for the Electromagnetic Sensing of the Environment, National Research Council of Italy, Naples, Italy

2 Department of Electrical Engineering and Information Technology, "Federico II" University of Naples, Italy

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 6**

## Terahertz Sensing Based on Photonic Crystal Fibers

*Md. Ahasan Habib, Md. Shamim Anower and Md. Nazmul Islam*

#### **Abstract**

Photonic-crystal-fiber (PCF) based sensors in the terahertz spectrum have been immensely studied and implemented due to their unique advantages and high sensitivity. At an early stage, conventional and hybrid structured porous core PCF-based sensors were proposed, but the sensitivity was not so high. With the advancement of PCF fabrication technology, hybrid structured hollow-core PCFs have been reported and offer superior sensing characteristics than the previous types. In this chapter, both porous core and hollow-core PCF-based THz sensors are analyzed and the propagation characteristics are explained using terahertz spectrum. Finally, some promising terahertz sensors are studied and compared at the end of this chapter.

**Keywords:** terahertz, photonic crystal fiber, relative sensitivity, porous & hollow-core PCF

#### **1. Introduction**

The electromagnetic signal whose frequency ranges between 0.1 and 10 THz is termed the terahertz radiation band [1–4]. This radiation band has been effectively used in numerous applications, such as sensing, medical imaging, biotechnology, and genetic engineering, security, chemical spectroscopy, diagnosis of different cancerous cells, radar, and astronomy [5–10]. Due to the massive advancement in the optoelectronics sector, numerous types of terahertz sources and terahertz detectors (photoconductive antennas, bolometers, *etc*.) are already available on the market [11–13]. On the contrary, efficient and favorable terahertz waveguides are still under research. The major barrier for the expansion of terahertz waveguides in different applications is the selection of waveguide base material. Metallic waveguides are suitable for microwave signal propagation, but they offer high ohmic loss for higher frequency signals. A circular-shaped metallic waveguide [14] was proposed in 1999, which suffered only ohmic loss for terahertz signals, whereas coplanar and microstrip transmission lines exhibited other types of losses [15]. One of the major drawbacks of this circular waveguide was the strong dispersion near the cutoff frequency. One year later, a rectangular metallic waveguide [16] was demonstrated theoretically and experimentally, which experienced the same type of loss and dispersion problem as the circular metallic waveguide [15]. In 2001, a copperbased parallel plate terahertz waveguide was proposed, which exhibited only ohmic loss but the dispersion was absent for this type of waveguide [17]. After that, Wang and Mittleman first introduced bare metal or Sommerfeld wire as a terahertz waveguide, and they proved that this waveguide offered less loss than the metallic waveguides [18]. However, in metallic waveguides, the ohmic loss was low, but this waveguide experienced fewer light confinement problems for terahertz waves. This problem can be solved by replacing metallic slit waveguides instead of the bare metal waveguide, and it was first introduced in 2007 [19]. Along with the various types of metallic waveguides, some remarkable dielectric waveguides were also proposed by the researchers, which also include those in the terahertz frequency range. The dielectric waveguides were used to transmit higher frequency signals (such as infrared and optical frequencies) as metallic wires experienced higher losses at these frequencies. On the contrary, the dielectric waveguides were subjected to dielectric absorption loss dependent on waveguide frequencies. Dielectric waveguides can be classified into two categories, which are hollow- and solid-core-fiber waveguides. The dielectric waveguides offer better light confinement capability than metallic waveguides, so the dielectric waveguides are more popular for terahertz wave propagation.

#### **2. Photonic crystal fiber**

In hollow-core dielectric waveguide, the light is confined by an omnidirectional mirror and the dielectric material is transparent to a high frequency signal. So that, the hollow-core dielectric waveguide eliminates the limitations existing in silica fiber and hollow metallic waveguide. The light-guiding mechanism in PCFs are exactly similar to the hollow-core dielectric waveguide so that the PCFs can be considered as a dielectric waveguide. The invention of photonic crystal fibers (PCFs) has opened a new door for optoelectronics researchers. However, the selection of the base material for PCF is a tough task as most of the materials experience wavelength-dependent attenuation loss for wide-band signals. In the recent past, a huge number of fused silica-based solid core optical waveguides have been theoretically and experimentally investigated due to some excellent characteristics of this material compared to other glasses or plastics [20]. Fused silica has higher tensile strength, higher transparency to light waves, lower absorption loss, higher availability in nature, high melting point, lower dispersion characteristics, and so on, which increase its popularity as an optical waveguide [21]. However, the silicabased fibers are not suitable for the terahertz spectrum as they offer high absorption loss and modal dispersion to terahertz signals. The most commonly used materials for terahertz dielectric waveguides are TOPAS, Zeonex, Teflon, PMMA, *etc*. due to their lower loss coefficients [15]. Among them, TOPAS and Zeonex offer the lowest loss coefficient and highest transparency towards the terahertz spectrum, so that various application dependent fiber waveguides based on those materials have been proposed [22].

PCFs can be classified into three categories on the basis of the core structure, which are solid core PCF [22], porous core PCF [23, 24], and hollow-core PCF [25]. In addition to wave communication functions, PCFs can also be used for optical sensing. To apply a PCF in sensing applications, the sample under test is filled in the core and after that, the electromagnetic wave is injected through the core [26]. The light interacts with the sample, and after analyzing the received signal, the unknown sample can be identified [26]. However, solid core PCF cannot be used in sensing applications as it is not possible to inject analyte inside of the solid core. So, numerous structures based on hollow-core and porous core dielectric fibers have been proposed as liquid or gas sensors [27–31] using the electromagnetic signal at 1.33 μm or 1.55 μm wavelengths. These proposed PCF-based sensors offer relatively high sensitivity and superior guiding characteristics, which are compared with commonly used mechanical sensors and transducers.

#### **3. PCF waveguide parameters**

In order to claim a PCF as a good sensor, it must satisfy some criteria, including high relative sensitivity, low confinement loss, and high numerical aperture. The mathematical formulas or expressions are shown and explained, which are generally used to calculate the sensing and guiding characteristics of an optical sensor.

Relative sensitivity is the key parameter of any PCF-based sensor, which is an indication of how much change of an analyte can be sensed or detected by the sensor. Higher relative sensitivity is desirable from any sensor, as the higher the relative sensitivity, the smaller the change that can be identified by the sensor. The mathematical expression to calculate the relative sensitivity (*r*) is [27–34],

$$r = \frac{n\_r}{n\_{\text{eff}}} \times P\text{\%} \tag{1}$$

where *nr* and *neff* are the effective refractive index of the actual propagating EM wave through the core and the analytes, respectively. In addition, *P* indicates how much light signal power interacts with the analytes filled in the fiber core. In the case of a PCF-based sensor, the parameter *P* is known as power fraction, and that can be easily calculated from the following mathematical expression [27],

$$P = \frac{\int\_{sample} R\_\epsilon \left(E\_\mathbf{x} H\_\mathbf{y} - E\_\mathbf{y} H\_\mathbf{x}\right) d\mathbf{x} d\mathbf{y}}{\int\_{total} R\_\epsilon \left(E\_\mathbf{x} H\_\mathbf{y} - E\_\mathbf{y} H\_\mathbf{x}\right) d\mathbf{x} d\mathbf{y}} \times 100\tag{2}$$

where *Ex*, *Ey*, *Hx,* and *Hy* stand for x and y polarized electric field and magnetic field, respectively, when the propagation direction of light is in the z direction. The numerator of Eq. (2) integrates the energy that interacts with the sample under test and the denominator does the same for the complete sensor.

Another important propagation parameter for any kind of optical fiber-based waveguide or sensor is confinement loss. This loss parameter determines the actual fiber length as higher confinement loss restricts the actual fiber length. This parameter indicates the amount of power wastage due to the cladding air holes and it is usually calculated by employing the following expressions [27–29],

$$a\_{\rm CL} = 8.686 \times \frac{2\pi f}{c} \text{Im} \left( n\_{\rm eff} \right) \tag{3}$$

where *f* is the operating frequency of the propagating EM signal, *c* is the speed of light in free space, and Im (*neff*) stands for the imaginary part of the effective refractive index. In order to be considered a good sensor, the loss must be low. Till date, no optical sensor with lower confinement loss has been developed.

Along with the confinement loss, another loss is present in all optical sensors, which is called effective material loss (EML), which reflects the information power consumed by the background material of the sensor. However, many authors did not provide this parameter in their articles, but it is very important for the practical implementation or setup of a terahertz sensor. The mathematical equation to quantify the EML of a sensor is [1],

$$\alpha\_{\text{eff}} = \frac{\left(c\_{0}\prime\_{\mu\_{0}}\right)^{1/2} \int\_{A\_{\text{mat}}} n \, |a\_{\text{mat}}| |\mathbf{E}|^{2} d\mathbf{A}}{2 \int\_{S} S\_{Z} d\mathbf{A}} \tag{4}$$

where ε*<sup>0</sup>* and *μ<sup>0</sup>* indicate the relative permittivity and permeability of the vacuum, *n* is the refractive index of the guided light, and *αmat* is the bulk material loss coefficient of the base material of the sensor. Usually, Topas and Zeonex are the most commonly used materials for the terahertz sensor as they provide the lowest loss coefficient in the terahertz regime. However, different terahertz sensors with PMMA, Teflon, *etc*. were also proposed by the researchers in the recent past which offered slightly higher EML than the recently proposed PCF-based sensors.

Another important propagation parameter is birefringence, which is important in the case of sensing applications. Birefringence is the absolute difference between the effective refractive indexes of x and y polarization mode which is expressed by using the following expression [32, 33],

$$B = \left| n\_{\times} - n\_{\gamma} \right| \tag{5}$$

where *nx* and *ny* are the effective refractive indexes in the x and y directions, respectively.

In addition, some other propagation characteristics such as bending loss, numerical aperture, V parameter, spot size, beam divergence, nonlinearity, *etc.* are discussed in [32–45].

#### **4. Photonic-crystal-fiber-based terahertz sensor**

A large number of PCF-based terahertz sensors have been proposed in the recent past for the identification of different types of chemicals [32–34], bane chemicals [41], blood components [48–50], alcohols [36], and so on*.* The prime designing objective of any kind of PCF-based sensor is to propagate the maximum amount of light through the core so that maximum light-analyte interaction takes place. The cross-sectional view of some excellent PCF-based sensors in the terahertz regime is represented in **Figure 1**.

A kagome lattice slotted core fiber is shown in **Figure 1(a)**, which was proposed by Islam *et al*. to detect benzene (*n* = 1.366), ethanol (*n* = 1.354), and water (*n* = 1.33) by using the terahertz spectrum [33]. The kagome structure in **Figure 1(a)** offers high confinement of light through the core due to the compact structure in the cladding. That's the reason why the proposed sensor in **Figure 1(a)** has high relative sensitivity in **Figure 2(a)** and **(b)** for the x and y polarization mode. As the core is not symmetrical, the power distribution in both polarization is unequal.

Another hybrid structured PCF with all rectangular holes is proposed by Islam *et al*. in order to detect three different liquids [37]. Its cross-section is shown in **Figure 1(b)** with an enlarged view of the core section. **Figure 1(b)** shows that the structure is not symmetric, performing birefringence and unequal power distribution in two polarization directions. The relative sensitivity is shown in **Figure 2(c)** and **(d)** for two different core dimensions. As the W value is larger than the H value, more light travels with the x-polarization mode. The sensitivity of a x-polarization mode is thus high. Similarly, **Figure 2(d)** shows the relative sensitivity increases as enlarging the fiber core.

Habib *et al*. proposed a simple hollow-core PCF-based chemical detector [40] using terahertz spectrum and the two-dimensional view is represented in

*Terahertz Sensing Based on Photonic Crystal Fibers DOI: http://dx.doi.org/10.5772/intechopen.101732*

**Figure 1.**

*Cross-sectional view of (a) kagome structured slotted core chemical sensor [33], (b) hybrid structured hollowcore chemical sensor [37], (c) hybrid structured rectangular hollow-core chemical sensor [40], (d) hexagonal structured rectangular porous core alcohol sensor [36], (e) hybrid structured polygonal hollow-core cholesterol sensor [45] and (f) hybrid structured rectangular hollow-core blood component sensor [48] in the terahertz regime.*

**Figure 1(c)**. One rectangular air hole is introduced in the core region to be injected by analytes. Due to asymmetric structure, this sensor also has birefringence and the relative sensitivity for both polarization modes are presented in **Figure 2(e)** and **(f)**. This sensor has extremely high sensitivity around 90% at 1.9 THz for the y-polarization mode.

A very simple hollow-core chemical sensor [36] was proposed in 2018 in **Figure 1(d)**. Due to the asymmetric core, the relative sensitivity of that sensor for both polarization modes is reported in **Figure 2(g)** and **(h)**. **Figure 1(d)** indicates that there are considerable amounts of high indexed solid material in the core region. This proposed sensor, therefore, extracts a small fractional THz signal for sensing and results in lower sensitivity. The maximum relative sensitivity is around 73% at 1 THz.

**Figure 1(e)** represents a hybrid structured hollow-core PCF [45] for the identification of cholesterol present in human blood and fruits. The proposed sensor offered a very high relative sensitivity of 98% at optimum conditions for two main reasons. Firstly, the hollow-core permits maximum light to travel through the core,

#### **Figure 2.**

*Relative sensitivity of (a)-(b) kagome structured slotted core chemical sensor [33], (c)-(d) hybrid structured rectangular porous core chemical sensor [37], (e)-(f) hybrid structured rectangular hollow-core chemical sensor [40], (g)-(h) hexagonal structured rectangular porous core alcohol sensor [36], (i) hybrid structured polygonal hollow-core cholesterol sensor [45] for different operating frequencies in the terahertz regime.*

#### *Terahertz Sensing Based on Photonic Crystal Fibers DOI: http://dx.doi.org/10.5772/intechopen.101732*

which increases the power fraction, and finally, the higher refractive index cholesterol (*n* = 1.525) attracts more light to interact with itself. So that, according to the data of **Table 1**, the relative sensitivity of this cholesterol sensor is maximum and the graphical representation of the variation of relative sensitivity is shown in **Figure 2(g)**. This figure also shows the relationship between the core dimension and sensitivity. For example, the maximum core dimension has the highest relative sensitivity than at 1.2 THz when the enlarged core has strong light-analyte interaction.

Few PCF-based sensors can identify different components of human blood [48–50]. In 2019, Ahmed *et al*. proposed a hollow-core Zeonex-based blood component sensor in the terahertz spectrum [48], whose cross-sectional view is represented in **Figure 1(f)**. The relative sensitivity of red blood cells (RBCs), hemoglobin, white blood cells (WBCs), plasma, and water for different operating frequencies is shown in **Figure 3(a)** and **(b)**. From the above discussion, it is clear that the relative sensitivity of the terahertz sensors is higher than the silica-based sensors using IR spectrum [27–31]. In addition, hollow-core terahertz sensors offer higher sensitivity (**Figure 2(c)**–**(f), (i)**) than that of porous core sensors (**Figure 2(a), (b), (g), (h)**).

Now, the loss characteristics of different types of terahertz PCF sensors are discussed below. To reduce the confinement loss and the effective material loss, numerous types of core and cladding structured PCFs were presented [26, 32–35]. However, the light confinement inside the core is largely dependent on the geometric structure of PCF. Now, the variation of confinement loss of PCF-based sensors (**Figure 1**) for different THz frequencies is shown in **Figure 4(a)**–**(f)**. The first three figures (**Figure 4(a)**–**(c)**) represent the confinement loss characteristics at certain PCF structures for sensing benzene, ethanol, and water [33, 37, 40]. At high THz frequency, the confinement loss is lower for all analytes because a few fractional THz wave at high frequency travels through the cladding air holes. The confinement loss of benzene is lowest than the other two samples due to the highest refractive index. The sensing results of **Figure 1(d)** and **(e)** are represented in **Figure 4(d)** and **(e)** respectively. The two figures inform that the loss is inversely proportional to the core dimension of the PCFs. Finally, **Figure 4(f)** shows the confinement loss for sensing blood samples [48]. The confinement loss is low at the high THz frequency and high refractive index conditions. THz waves with high frequencies have the tendency to travel through the high indexed zone, so less fractional power propagates through the cladding. The confinement loss is low at high THz frequencies for all PCF-based sensors. The confinement loss is minimum for the cholesterol sensor (**Figure 1(e)**).

Now, the THz wave loss characteristics of different PCF-based sensors in the terahertz regime are investigated. The THz loss spectra are represented in **Figure 5** for different proposed terahertz sensors shown in **Figure 1(a)**–**(f)**. This loss comes from the solid materials around the core. The THz wave loss characteristics of benzene, ethanol, and water sensors in **Figure 1(b)** and **(c)** are shown in **Figure 5(a)** and **(b)** for different operating frequencies. However, according to **Figure 5(a)** and **(b)**, it is clear that the loss shows an upward trend with the increase of operating frequency. Because THz waves at higher frequency can travel through high indexed solid material, the material more absorbs THz wave energy. **Figure 5(c)** and **(d)** represent THz wave loss characteristics of PCF-based sensors in **Figure 1(d)** and **(e)** for different structural conditions. **Figure 5(c)** shows that THz wave loss is lower for increasing the width of elliptical air holes (**Figure 1(e)**). **Figure 5(d)** shows that the THz wave loss is lowest for the largest core dimension. This structure in **Figure 5(d)** performs the lowest loss among **Figure 5(a)**–**(d)**.

*Terahertz Sensing Based on Photonic Crystal Fibers DOI: http://dx.doi.org/10.5772/intechopen.101732*

#### **Table 1.**

*Comparison of different guiding and sensing parameters for numerous types of remarkable terahertz sensors.*

The following comparison shows the guiding characteristics for hybrid structured sensors [34, 35, 40, 42, 46, 48] and conventional structured sensors [33, 36–39, 41, 43–45, 47, 49–51] in terahertz regime.

The most interesting characteristic of PCF-based sensors is that the guiding or sensing properties are highly dependent on the geometry or structure of the PCFs. However, from **Table 1**, it is quite clear that the relative sensitivity and loss profile is lower for nonconventional structured PCF than regular structured one. For example, the conventional structured liquid sensor in Ref. [44] offered the highest sensitivity of 82.26% among regular structured PCFs but the core loss is high (>10 dB<sup>8</sup> dB/m). On the other hand, a maximum of 93.5% relative sensitivity with

**Figure 3.**

*Relative sensitivity as a function of frequency for different blood components in terahertz regime from (a)-(b) in ref. [48].*

#### **Figure 4.**

*Confinement loss as a function of frequency of (a) Figure 1(a) ref. [33], (b) Figure 1(b) ref. [37], (c) Figure 1(c) ref. [40], (d) Figure 1(d) ref. [36], (e) Figure 1(e) ref. [45] and (f) Figure 1(f) ref. [48] for different PCF based sensors.*

lower confinement loss (< 10 dB<sup>9</sup> dB/m) can be achieved from PCF-based sensor in Ref. [46]. Moreover, the relative sensitivity and loss are also dependent on the test sample also. In **Table 1** the highest relative sensitivity (98.75%) and lowest loss *Terahertz Sensing Based on Photonic Crystal Fibers DOI: http://dx.doi.org/10.5772/intechopen.101732*

**Figure 5.**

*Effective material loss variation of numerous structured terahertz sensorsas a function of frequency of (a) Figure 1(b) ref. [37], (b) Figure 1(c) ref. [40], (c) Figure 1(d) ref. [36], (d) Figure 1(e) ref. [45].*

(core loss = 1.34 10 dB<sup>17</sup> dB/m and THz wave loss = 0.008 cm<sup>1</sup> ) was reported in Ref. [45] as the refractive index of cholesterol (refractive index = 1.525) is maximum than any other samples reported in **Table 1**.

#### **5. Conclusion**

In this chapter, different types of PCF-based terahertz sensors were discussed and compared for numerous chemicals, toxic agents, and blood components identification. In addition, a brief discussion about terahertz technology and different terahertz waveguides are included in this chapter. The sensing and guiding parameters of numerous terahertz sensors are numerically discussed and graphically represented for a better understanding of the readers. However, efficient application-specific terahertz sensors are still under research and we hope this chapter will help the optoelectronics researchers to propose new sensors.

*Terahertz Technology*

#### **Author details**

Md. Ahasan Habib<sup>1</sup> \*, Md. Shamim Anower<sup>1</sup> and Md. Nazmul Islam<sup>2</sup>

1 Department of Electrical and Electronic Engineering, Rajshahi University of Engineering and Technology, Rajshahi, Bangladesh

2 Department of Electrical and Electronic Engineering, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, Bangladesh

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Terahertz Sensing Based on Photonic Crystal Fibers DOI: http://dx.doi.org/10.5772/intechopen.101732*

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### Section 3

## Terahertz Optoelectronic Technology

**Chapter 7**

## Optical Heterodyne Measurement of Terahertz Wave

*Shin'ichiro Hayashi and Norihiko Sekine*

#### **Abstract**

One of the most notable frequency regions in terms of research currently lies in the 'frequency gap' region between microwaves and infrared: terahertz wave. Although new methods for generating and detecting terahertz wave have been developed, few detectors operating at room temperature are able to capture lowenergy terahertz beams. Here we introduce the optical heterodyne measurement (nonlinear frequency up-conversion detection) of terahertz wave using parametric wavelength conversion in a nonlinear crystal; this has better sensitivity than many commonly used thermal detectors such as pyroelectric detectors. Additionally, optical heterodyne techniques allow the beams of terahertz wave to be visualized and their frequency and intensity determined directly as visible light. These are very promising for extending applied researches into the terahertz region, and we expect that these will open new research fields such as wireless information communications or non-destructive inspection in the terahertz region.

**Keywords:** terahertz wave, nonlinear optics, parametric wavelength conversion

#### **1. Introduction**

Terahertz (10^12 Hz) wave region are important not only in the basic sciences, such as molecular optics, molecular spectroscopy, electron acceleration, plasma measurement, and radio astronomy, but also in numerous applications, such as broadband wireless information communication, non-destructive inspection, high precision radar, and global environmental measurement, since they have higher directivity in the atmosphere than microwaves and higher transmittances in soft materials than infrared. Therefore, sensitive, wideband, coherent detectors for terahertz wave that could be widely used in such applications are required. The terahertz wave region is relatively unexplored because of the lack of the commercially available sources, detectors, and optics which have resulted in what is known as the frequency gap [1–3]. Over the past two decades, there has been remarkable growth in the fields of science and engineering using terahertz wave region, which has become a vibrant, international, cross-disciplinary research activity [4]. An effective method for generating and detecting coherent terahertz waves is wavelength conversion in nonlinear optical materials owing to the high conversion efficiency, wide bandwidth, and room-temperature operation. The large figure of merit (FOM) of LiNbO3 at room temperature makes this well-known nonlinear crystal ideal for such applications; terahertz wave parametric generation and detection in LiNbO3 are realized by stimulated polariton scattering via transverse optical phonons [5–10]. In this paper, we introduce the measurement method of terahertz

wave by up-conversion. Terahertz wave is generally measured using thermal detectors, such as Si-bolometers, pyroelectric detectors or Gollay cells. Although these detectors can measure the average power, the frequency and the phase information are lost. Furthermore, high sensitivity bolometers require ultralow temperature and show slow response. Thus, there is a critical need for frequency and phase measurements, sensitive and fast detectors that work at room temperature, so that terahertz-wave can be used more widely in a variety of important applications.

#### **2. Terahertz wave parametric wavelength conversion**

When a strong electric field, such as that of a Q-switched laser pulse, is incident upon a nonlinear optical crystal, the transverse photon and phonon wave fields become coupled and behave as new mixed photon–phonon states, called polaritons. Broadband terahertz wave generation results from efficient parametric wavelength conversion of laser beam via polaritons [5, 6]. The polaritons exhibit phonon-like behavior in the resonant frequency region (near the transverse optical (TO) phonon frequency ωTO), however, they behave like photons in the non-resonant low-frequency region, as shown in **Figure 1**. Detecting terahertz wave can be achieved by injecting a "seed" for the broadband terahertz wave. Spectroscopic measurement is accomplished simply by observing the propagation direction of idler beams depending on the angle between the incident pumping beam and the wavelength of the seeding terahertz wave. In the parametric wavelength conversion process, a photon of terahertz wave and a photon of near-infrared idler beam are created parametrically from a photon of near-infrared pumping beam, according to the energy conservation law *ω*p *= ω*T *+ ω*i (where ω indicates frequency, and p, T, and i denote the pumping beam, terahertz wave, and idler beam, respectively) and the momentum conservation law *kp = ki + kT* (noncollinear phase-matching condition). This condition leads to the angle-dispersive characteristics of the idler beams and the terahertz waves. Thus, broadband terahertz waves can be detected depending on the phase-matching angle, as shown in **Figure 2**.

**Figure 1.** *Dispersion relation of the polariton.*

*Optical Heterodyne Measurement of Terahertz Wave DOI: http://dx.doi.org/10.5772/intechopen.99168*

#### **Figure 2.**

*Noncollinear phase-matching condition.*

In our experiment, we used LiNbO3 as nonlinear crystals. The bandwidth of the terahertz wave parametric wavelength conversion is decided by the parametric gain and absorption coefficients in the terahertz region. **Figure 3** shows the calculated gain and the absorption coefficient at the pumping intensity of 0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 GW/cm2 [11]. As the intensity of pumping beam increases, the gain coefficient also increases in whole frequency region, and peak of the gain curve moves towards higher frequencies. All gain curves have a broad bandwidth with a dip appearing at around 2.6 THz because the low frequency modes of doped MgO in the LiNbO3 work as a crystal lattice defects. The effective parametric gain curve depends on the pumping beam intensity and diameter in noncollinear phasematching conditions. The idler and terahertz wave are parametrically amplified while propagating coaxially with respect to the pumping wave.

#### **Figure 3.**

*Calculated gain and absorption coefficient using MgO:LiNbO3 pumped by Nd:YAG laser for several pumping intensities, 0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 GW/cm<sup>2</sup> .*

#### **3. Experiment**

The experimental apparatus for terahertz wave spectroscopic measurement shown in **Figure 4** consists of a nonlinear crystal (MgO:LiNbO3) with a Silicon prism and a laser beam visualizer. The terahertz wave was focused onto the MgO:LiNbO3 crystal via Silicon prism input coupler. The incident angle between the terahertz wave and the pumping beam from Nd:YAG based MOPA system satisfies the noncollinear phase-matching conditions in the MgO:LiNbO3 crystal. Mixing the pumping beam with the incident terahertz wave created a seeded, up-converted (difference-frequency) signal, which was parametrically amplified by the optical parametric amplifier in the MgO:LiNbO3. The up-converted signals were visualized using an infrared laser visualizer (10VIZ-35, Standa Corp.) as visible lights; the frequency and intensity was determined from the position and the intensity.

**Figure 5** shows pictures of the up-converted signals on the laser beam visualizer when the input frequency of terahertz wave of 1.0, 1.3, 1.6, 1.9 and 2.2 THz. The scales at the bottom show the calculated distance from the pumping beam. The position and the intensity of the up-converted signal depend on the frequency and the energy of the input terahertz wave respectively. As the frequency of the input terahertz wave increases, the position depending on noncollinear phasematching angle between the pumping beam and up-converted beam also increases,

**Figure 4.** *Experimental apparatus for terahertz wave spectroscopic measurement.*

#### **Figure 5.**

*Pictures of the up-converted signals on the laser beam visualizer when the input frequency of terahertz wave of 1.0, 1.3, 1.6, 1.9 and 2.2 THz.*

which shifts the position of up-converted beam. The energy of up-converted beam also depends on the intensity of input terahertz wave, which changes the intensity of the light spot. These make it easy to identify the frequency and intensity of the input terahertz wave from the position and intensity of the up-converted signal. This is in good agreement with the calculation.

**Figure 6** shows the input (terahertz wave) – output (up-converted beam) characteristics of optical heterodyne at 1.8 THz when the pumping energy was 10 mJ/ pulse. Horizontal axis is input energy of terahertz waves, vertical axis is output energy of the up-converted signals. These colors in the figure represent operating ranges of thermal detectors. The green represents pyroelectric detector at room temperature. The orange represents standard 4 K Si-bolometer. As the input energy of terahertz wave was decreased, the output energy of up-converted signal was also

**Figure 6.** *Output energy of up-converted signals as a function of the input energy of the terahertz wave.*

decreased. The maximum energy of up-converted signal was >1 mJ/pulse when the input energy of terahertz-wave was ~1 μJ/pulse. This is easily visualized by laser beam visualizer. The minimum detectable energy of terahertz-wave was less than 100 aJ/pulse. This has higher sensitivity than standard 4 K Si-bolometer. Further, dynamic range reached more than 100 dB.

**Figure 7** shows our experimental setup for phase measurement. We used an injection seeded parametric generator (is-TPG) as a terahertz wave source. The terahertz wave from an is-TPG was collimated, passed through a delay line (a rooftop mirror on a mechanical stage). The terahertz wave separated by a wire grid polarizer focused to the MgO:LiNbO3 crystal for up-conversion detection. The incident angle between the pumping beam, the seeded idler beam, and the input terahertz wave satisfy the noncollinear phase-matching conditions in the MgO:LiNbO3 crystal. Mixing the intense pumping beam and the seeded idler beam with the terahertz wave created an up-converted signal. In this case, the intensity of up-converted signal depends on the phase difference between the seeded idler beam and the terahertz wave.

**Figure 8** shows the energy of up-converted signals as a function of path length difference between the terahertz wave and the seeded idler wave when the input energy of the pumping beam, the terahertz wave and the idler beam were 10 mJ/ pulse, 1 μJ/pulse and 1 μJ/pulse, respectively. As the optical pass length difference increases, we observed blinking of up-converted signals due to the interference between the seeded idler beam and the terahertz wave. The intervals of fringe represent the wavelength of input terahertz-wave. The observed intervals of fringe corresponding to the wavelength of terahertz wave are 200 μm. These show excellent agreement with the wavelength of input terahertz wave from the is-TPG.

**Figure 7.** *Experimental apparatus for terahertz wave phase measurement.*

**Figure 8.** *Phase measurement of terahertz wave by up-conversion.*

#### **4. Conclusion**

We have introduced here spectroscopic, sensitive, coherent, wideband terahertz wave optical heterodyne detection via wavelength conversion in MgO:LiNbO3. The coherent detection is very important for the calibration of terahertz wave frequency. In general, the radiation frequency calibration is based on absorption lines of molecular gases as a traceable standard, but there is no radiation frequency standard in the terahertz region [12]. In the case, the spectroscopic information of terahertz wave is measured by well-developed optical measurement methods as a traceable standard. Under the experimental conditions, the observed minimum energy of terahertz wave is less than 100 aJ/pulse. This is much higher sensitivity than many cryogenic thermal detectors. Furthermore, the sensitivity depending on parametric gain of the terahertz wave in LiNbO3 could be higher by cooling the crystal [13]. The conversion efficiency improves by a factor of at least ten at liquid nitrogen temperatures. The sensitive detection of terahertz wave is also essential for many applications. A number of applications require sensitive, spectroscopic and wideband terahertz wave detector such as wireless communication and nondestructive inspection. In the future, we will endeavor to produce high sensitivity and wide bands for applied researches. This system could be powerful tools not only for solving fundamental physics but also real world problems such as manipulation or alteration of atoms, molecules, chemical materials, proteins, cells, chemical reactions, and biological processes, and real-time spectroscopic imaging, remote sensing, 3D-fabrication.

#### **Acknowledgements**

The authors would like to thank Dr. Minamide, Dr. Nawata, Dr. Taira. Prof. Ito of RIKEN, Prof. Kawase of Nagoya University. This work was partially supported by JSPS KAKENHI Grant Number 18H01908, and Tohoku University - NICT Matching.

*Terahertz Technology*

#### **Author details**

Shin'ichiro Hayashi\* and Norihiko Sekine National Institute of Information and Communications Technology, Tokyo, Japan

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Optical Heterodyne Measurement of Terahertz Wave DOI: http://dx.doi.org/10.5772/intechopen.99168*

#### **References**

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[7] K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett., vol. 68, no. 18, pp. 2483- 2485, (1996).

[8] S. Hayashi et al., "Ultrabright continuously tunable terahertz-wave generation at room temperature," *Sci. Rep.*, vol. 4, Art. No. 5045, (2014).

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[10] Kosuke Murate, Shin'ichiro Hayashi, Kodo Kawase, "Multi-wavelength terahertz-wave parametric generator for one-pulse spectroscopy," *Applied Physics Express*, vol. 9, pp. 082401 (2016).

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**Chapter 8**

## A Novel Approach for Room-Temperature Intersubband Transition in GaN HEMT for Terahertz Applications

*Rakesh Kaneriya, Gunjan Rastogi, Palash Basu, Rajesh Upadhyay and Apurba Bhattacharya*

### **Abstract**

Terahertz (THz) technology has attracted tremendous attention recently due to its promising applications in various domains such as medical, biological, industrial imaging, broadband, safety, communication, radar, space science, and so on. Due to non-availability of powerful sources and highly sensitive and efficient detectors, the so-called THz gap remains largely unfilled. Despite seamless efforts from electronics and photonics technology researchers, the desired level of technology development to fill the THz gap still remains a challenge. GaN-based HEMT structures have been investigated as potential THz sources and detectors by a number of researchers. This chapter presents a very new and versatile mechanism for electrical tuning of intersubband transitions (ISBT) GaN high electron mobility transition (HEMT) devices. ISBT phenomena are usually demonstrated in photonic devices like a quantum cascade laser (QCL). Here we explore ISBT in an electronic GaN HEMT device. Conventional photonic devices like a QCL are operated at cryogenic temperature to minimize thermal effect. Tuning the conduction band through external gate bias is an advantage of an HEMT device for room temperature (RT) THz applications. This chapter demonstrates the theoretical and experimental novel ISBT phenomenon in GaN HEMT is for potential ambient applications in the THz range.

**Keywords:** GaN HEMT, terahertz device, Intersubband transition, Plasmonic Metamaterials, quantum well

#### **1. Introduction**

Terahertz (THz) radiation is a small portion of the electromagnetic spectrum lying between the microwave and infrared regions. There is no precise range defining THz band, but it is most often –considered as frequencies in the range of 0.3–3.0 THz. Although sometimes it refers to 0.1–10 THz as well. The THz spectral range has drawn tremendous attention recently due to its promising applications in various domains. For example, in the field of biomedicine, THz radiation has been explored to detect various biomaterials like nucleic acids, proteins, cells and tissue applications [1, 2]. In the field of medical applications, the THz system has been demonstrated as a highly effective technique in cancer imaging, particularly for skin cancer [3, 4]. A portable real-time THz imaging system could be used to assist early detection of diseases during routine health checkups. Since many non-metallic, nonpolar materials are transparent to THz radiation, scanning of humans is feasible with no health hazards. Due to this, THz radiation is widely used for security and public safety applications. THz radiation can detect concealed weapons, explosives (e.g., C-4, HMX, RDX and TNT), illicit drugs (e.g., methamphetamine and heroin), and more [1]. THz imaging has become a valuable characterization tool for non-destructive testing, process control and quality inspection for inspection of silicon solar cells, nanocomposites, polymer films and dielectric films [1, 5, 6]. Space- and ground-based THz instruments have been explored significantly in the field of astronomy. For example, the THz system is extensively used to study the origin of the universe, formation of stars and galaxies, composition of planets and planetary atmospheres, the climate and environmental balance of our planet Earth, and more [7, 8].

Despite these tremendous potential applications, the so-called THz Gap is not fulfilled to the required level due to technology requirements of high-power sources and efficient and sensitive detectors in the THz range. Semiconductor devices and circuits like transistor and frequency multipliers work well towards the low end of THz frequency, but their power level drops off precipitously as the frequency increases. These devices can be operated up to 1 THz with very low power. Conversely, semiconductor photonic devices like lasers can be utilized in the highfrequency THz range. Again, lasers are limited due to the non-availability of lower bandgap semiconductor materials towards low-frequency THz. The THz quantum cascade lasers (QCLs) showed promising results to fill this THz gap from 1 to 10 THz. However, QCLs required bulky cooling requirements, and reported maximum operating temperature is in the range of 150–200 K, which is too low for general applications [9, 10]. The demand for a compact, efficient and high-speed THz detector and source operating at room temperature has increased drastically. The non-availability of a room-temperature THz source and detector is a prime limitation of the modern THz system.

In this chapter, novel theoretical models and experimental techniques for the intersubband transitions (ISBT) phenomenon are illustrated for ambient THz applications. Section 2 covers the theoretical models and simulations based upon plasmonic metamaterials-assisted ISBT and describes the GaN HEMT response towards the THz spectrum. Section 3 covers the fabrication and measurement of a GaN HEMT device. Section 4 is investigates ambient temperature ISBT in a GaN HEMT device.

#### **2. Theoretical modeling and simulation strategy**

In this section, we present our theoretical model based on ISBT, metamaterial and plasmonic phenomena for GaN HEMT THz applications [11–13]. We proposed a combined plasmonic and metamaterial-driven ISBT phenomenon as one of the possible modes that can extend GaN HEMT operating frequency well beyond its present cut-off frequency to the THz band. ISBT is the prime mechanism to explore as a potential mechanism for THz operation, while metamaterial and plasmonic effects improve the strength of ISBT in a GaN HEMT structure. Theoretical modeling started with the role of polarization in a wurtzite semiconductor followed by the selfconsistent solution of Schrodinger and Poisson equations; k.p model and Fermi Golden rule are used to compute ISBT in the GaN HEMT structure. The size and geometry of an HEMT device act as THz metamaterial (this concept is explored indepth in Section 2.4) and it couples THz radiation to two-dimensional electron gas (2DEG) inside a triangular quantum well. Further, very small gate lengths in the range of 100–250 nm are selected for high-frequency operation of HEMT. This fine

nanometric-sized gate structure of HEMT excites surface plasmon waves at the interface between the gate metallic contact and 2DEG channel in the GaN heterostructure (this concept is explored in-depth in Section 2.5). These combinations (i.e., plasmonic metamaterial-assisted ISBT) govern the THz response of the GaN HEMT device.

#### **2.1 GaN heterostructure and device description**

GaN heterostructure is generally grown on sapphire or silicon carbide (SiC) substrate. **Figure 1(a)** shows the most widely used GaN heterostructure, which consists of a 60-nm AlN nucleation layer, 2-μm thick undoped GaN layer, 1-nm AlN spacer layer, 20 nm-undoped Al0.3Ga0.7N barrier layer, and 3-nm Si3N4 passivation layer. Introducing a thin 1-nm AlN interlayer between AlGaN and GaN plays a crucial role. Better carrier confinement, reduced alloy scattering and enhanced conductivity are achieved by inserting a thin AlN layer [14, 15]. The cross-sectional view of the simulated GaN HEMT device by Silvaco TCAD is shown in **Figure 1(b)**. Computation mesh to simulate the device structure is shown in **Figure 1(c)**. In the regions beneath the gate, at the edges of the source and drain contacts and at the AlGaN/AlN/GaN interface, fine meshing is done to achieve the convergence and accuracy of the calculations. The spacing between different electrodes, namely, source to gate, gate to drain and source to drain are set to 0.9, 2.0 and 3.0 μm, respectively. Gate length is kept as 100 nm. To obtain lower gate resistance, gate geometry is selected as T-gate in simulation as well as in fabrication.

Generally, high-power RF GaN HEMT is fabricated in a multi-finger configuration. Two ground-source-ground (GSG) configurations are shown in **Figure 2**: 2 150 and 8 150. To measure the RF performance of the device GSG configuration is widely used for HEMT fabrication. The 2 150 configuration contains two gate fingers with 150-micron unit gate width of the device. Similarly, the 8 150 configuration contains eight gate fingers with 150-micron unit gate width. To expand the device length for high-power applications, a greater number of gate fingers are used. For example, if the power handling capability of the fabricated GaN HEMT is 5 W/mm, the 2 150 = 0.3-mm device can be used for 1.5 W RF power. Similarly, the 8 150 = 1.2-mm device can be used for 6.0 W RF power. Before further discussion on plasmonic metamaterial-assisted ISBT, the following section refreshes some fundamentals about polarization in III-N (nitride) semiconductors.

#### **2.2 Polarization in GaN heterostructure**

The nitride semiconductor materials exhibit inherent polarization properties. Having the large ionicity of the nitride bond (Ga–N, Al–N, In–N, etc.), it possesses a

#### **Figure 1.**

*(a) GaN Heterostructure, (b) HEMT cross-sectional view and (c) HEMT mesh structure (reprinted with permission from Ref. [12]).*

**Figure 2.**

*Typical configurations of GaN HEMT (a) 2 gate fingers with 150 micron gate width (2* � *150) (zoom image for gate fingers visualization and (b) 8 gate fingers with 150 micron gate width (8* � *150). Representation 3.0/0.10/8/150 indicates source to drain distance 3.0 μm, 0.1 μm (100 nm) gate length, 8 fingers device with 150 μm gate width.*

piezoelectric polarization (PPE) component, while the absence of the center of inversion symmetry and uniaxial nature of the crystal structure produces spontaneous polarization (PSP). Total polarization (PT) in the nitride semiconductor heterostructure is a combination of spontaneous polarization (PSP) and piezoelectric polarization (PPE), as shown in Eq. (1).

$$P\_T = P\_{\rm SP} + P\_{\rm PE} \tag{1}$$

Furthermore, the strain-induced effect at the interface between two nitride semiconductors enhances piezoelectric polarization in the heterostructure. Piezoelectric polarization of the crystal is generally defined in terms of strain (ɛ) and stress (σ) components. Stress and strain are correlated in a crystal by elastic coefficient ɛij = Cij σij. The piezoelectric polarization in heterostructure grown along the z-axis (0001) is given by,

$$P\_{\rm PE} = E\_{33} \varepsilon\_x + E\_{31} (\varepsilon\_x + \varepsilon\_y) \tag{2}$$

where E33, and E31 are piezoelectric coefficients, and ɛx, ɛ<sup>y</sup> and ɛ<sup>z</sup> are strain in x, y and z-directions, respectively. The crystal edge length and height are represented as a0 and c0 respectively in a hexagonal crystal lattice. The strain along the x, y and z-axis is given by (in-plane strain along x-axis and y-axis are assumed to be isotropic),

$$\mathfrak{c}\_{\mathfrak{x}} = \frac{\mathfrak{c} - \mathfrak{c}\_{0}}{\mathfrak{c}\_{0}}, \mathfrak{c}\_{\mathfrak{x}} = \mathfrak{c}\_{\mathfrak{y}} = \frac{\mathfrak{a} - \mathfrak{a}\_{0}}{\mathfrak{a}\_{0}} \tag{3}$$

where a0 and c0 are the equilibrium or unstrained values of lattice constants and a and c are the strain lattice constant due to growth of heterostructure. For hexagonal lattice crystal, the strain components along ɛ<sup>z</sup> and ɛ<sup>x</sup> are related with elastic coefficients as per the following equation,

$$\mathcal{E}\_x = -2\frac{c\_{13}}{c\_{33}}\mathcal{E}\_x,\ \frac{\mathbf{c} - \mathbf{c}\_0}{c\_0} = -2\frac{c\_{13}}{c\_{33}}\frac{\mathbf{a} - \mathbf{a}\_0}{\mathbf{a}\_0} \tag{4}$$

where C13 and C33 are the elastic constants. Substituting Eqs. (3) and (4) in Eq. (2),

*A Novel Approach for Room-Temperature Intersubband Transition in GaN HEMT… DOI: http://dx.doi.org/10.5772/intechopen.98435*

$$P\_{PE} = 2\frac{a - a\_0}{a\_0} \left( E\_{31} - E\_{33} \frac{c\_{13}}{c\_{33}} \right) \tag{5}$$

The macroscopic piezoelectric polarization is defined by variations of the lattice constants a and c. The microscopic piezoelectric polarization is expressed in terms of an internal parameter u, defined as the anion–cation bond length along the z-axis (0001) [16]. Substituting elastic constant values for AlN and GaN in Eq. (5), one gets piezoelectric polarization of AlN greater than GaN. Spontaneous polarization closely depends upon crystal structure c/a ratio. The ideal c/a ratio in the hexagonal, closed-pack crystal structure is 1.633. The spontaneous polarization is found to be greater in actual crystal structures as the c/a ratio is different from its ideal value [16]. This nonideality of c/a ratio in AlN is also greater than GaN, which leads the greater spontaneous polarization. The spontaneous and piezoelectric polarization for alloy (i.e., AlGaN) is obtained by linear interpolation of the binary constituents (Vegard's law). In summary, the spontaneous and piezoelectric polarizations for AlGaN over the whole range of compositions are larger than that of a GaN buffer layer.

The polarization-induced charge density and sheet density in the heterostructure is given by,

$$
\rho = -\nabla \ast P \tag{6}
$$

$$
\sigma = P\_{T(Layer1)} - P\_{T(Layer2)}
$$

$$
\sigma = \left[ P\_{SP(Layer1)} + P\_{PE(Layer1)} \right] - \left[ P\_{SP(Layer2)} + P\_{PE(Layer2)} \right] \tag{7}
$$

The polarization-induced charge density and sheet density for the case of AlGaN/GaN heterostructure is given by,

$$\sigma = \left[P\_{\text{SP}(GaN)} + P\_{\text{PE}(GaN)}\right] - \left[P\_{\text{SP}(AlGaN)} + P\_{\text{PE}(AlGaN)}\right] \tag{8}$$

Extracted 2DEG concentration, purely due to polarization effects, is the order of �10<sup>13</sup> cm�<sup>2</sup> for nitride heterostructures. Unlike GaAs MODFET heterostructures, no doping is required in nitride heterostructures to generate 2DEG concentration, which is a great advantage of these structures.

The basic equations of physical processes are solved for every grid point in the simulation. These equations include Poisson's equation, continuity equations and transport equations, derived from Maxwell's equations [17]. The computation of 2DEG properties due to spontaneous and piezoelectric polarization effects is performed using a polarization model [18, 19]. An induced, strong polarization field is introduced to calculate band diagrams. To increase the reliability of simulation, measurement-based ohmic contact resistance and Schottky barrier height data were incorporated in the simulation to define source, drain and gate contacts. A low field mobility model is used to account for the temperature-dependent drift of electrons and holes separately [20]. The Shockley–Read–Hall recombination model is used to estimate the statistics of holes and electrons as well as their recombination rate. The traps/defects in the heterostructure play a crucial role in the performance of GaN devices. Accordingly, we also introduced interface traps energy level and density in the modeling. Output results were extracted by solving the basic equations for every grid point with the different biasing conditions. The variation of the drain current with respect to applied drain (Vd) and gate (Vg) biasing voltage is plotted in **Figure 3**. The simulated output characteristics (Id-Vd) and transfer characteristics (Id-Vg) are shown in **Figure 3(a)** and **(b)**, respectively. The extracted transconductance is >350 mS/mm as shown in **Figure 3(c)**. The extracted capacitance-gate

**Figure 3.**

*(a) Output characteristics (id-Vd), (b) transfer characteristics (id-Vg) and (c) Transconductance of the simulated device (reprinted with permission from Ref. [11]).*

#### **Figure 4.**

*Extracted (a) CV profile and (b) 2DEG profile with applied gate voltage (reprinted with permission from Ref. [12]).*

voltage (Vg) and 2DEG density with applied gate bias are depicted in **Figure 4(a)** and **(b)**, respectively.

The current gain cutoff frequency (ft) and maximum frequency of oscillations (fmax) are the two most pertinent parameters for high-speed device application. ft and fmax are extracted from small signal RF simulation. Current gain (h21) and maximum available power gain (Ga) are simulated at bias conditions Vds = 7 V and Vgs = �1.5 V and plotted with respect to frequency in **Figure 5**. A summary of simulated DC and RF device parameters is given in **Table 1** that closely matches the corresponding process design kit (PDK) datasheet of renowned international GaN foundries.

The cutoff frequency of field effect transistor (FET) including HEMT is defined by *f <sup>T</sup>* ¼ *<sup>υ</sup>=*<sup>2</sup>*π<sup>L</sup>* ¼ <sup>1</sup>*=*<sup>2</sup>*πτ*, where υ is carrier velocity, L is gate length and τ is electron transit time under the gate. For very small gate length of 30 nm, up to 300–350 GHz cut-off frequency operation has been demonstrated [21]. However, beyond conventional transit-time limitations, these FET devices can be operated at much higher frequencies up to THz. Dyakonov–Shur proposed the plasma wave theory to describe THz behavior in FET devices [22, 23]. The basis of plasma wave theory is the instability of 2DEG, which has a resonant response to incident electromagnetic radiation in short-channel FET. The size and shape of the FET channel are used to govern the resonant response of plasma frequency to electromagnetic radiation. The tuning of plasmon frequency by external biasing has been used for detectors, mixers and multipliers [23]. There are several reports available in which the plasma wave theory is used to describe the THz behavior of devices. The plasma wave theory concept has been widely demonstrated in conventional semiconductors like Si [24], GaAs [22], GaN [25], and InP [26] as well as in new two-dimensional

*A Novel Approach for Room-Temperature Intersubband Transition in GaN HEMT… DOI: http://dx.doi.org/10.5772/intechopen.98435*

#### **Figure 5.**

*Current gain and power gain of the simulated device (reprinted with permission from Ref. [11]).*

#### **Table 1.**

*Summary of extracted DC and RF device parameters.*

materials systems like graphene [27], black phosphorus [28], and more. There are a few papers available in which a working GaN HEMT mechanism is explained through plasma wave theory [25, 29–32]. Based on our simulation and experimental investigations, we have demonstrated for the first time that an ISBT mechanism, in addition to established plasma wave theory, can describe the THz behavior of a GaN HEMT device. ISBT theory is based on carrier transitions within a conduction band, which is entirely different from plasma wave theory. The fundamentals of this theory are explained below.

#### **2.3 Quantum confinement in GaN heterostructure**

The interaction between photons and electrons in the semiconductor can be expressed by the Hamiltonian,

$$H = \frac{1}{2m\_0}(\mathbf{p} - \mathbf{e}\mathbf{A})^2 + V(r) \tag{9}$$

where mo is the free electron mass, V(r) is the periodic crystal potential (in the present case it is the triangular potential function given by, V(z) = eFz), e is charge of electron, Fz is electric field, and A is vector potential of applied electromagnetic field. Hamilton can be expanded into,

$$H = \frac{p^2}{2m\_0} + V(r) - \frac{e}{2m\_0}(\mathbf{p} \cdot \mathbf{A} + \mathbf{A} \cdot \mathbf{p}) + \frac{e^2 \mathbf{A}^2}{2m\_0} \tag{10}$$

$$H \approx H\_0 + H'$$

Here H0 is unperturbed Hamiltonian and H<sup>0</sup> is perturbed Hamiltonian due to the interaction of the electromagnetic wave.

Consideration of the strain effects for extraction of effective-mass Hamiltonian is of prime importance for wurtzite semiconductors. This Hamiltonian is used to derive the electronic band structures of bulk and quantum-well wurtzite semiconductors. Kane's model is applied to derive the band-edge energies and the optical momentum-matrix elements for strained wurtzite semiconductors. We then derive the effective-mass Hamiltonian by using the k.p perturbation theory. The developed k.p model is applied to our heterostructures structures, especially quantum well via the envelope function approximation (EFA) method [33, 34]. An envelope function model is derived for electrons in a semiconductor heterostructure. The materials-dependent Hamiltonian extraction by EFA method is most suitable for abrupt semiconductor junction [35]. The finite element method [36] is used to solve the coupled multi-band Schrödinger Poison's equation [37] numerically.

Under triangular quantum well, the solution of the wave function is given by [38, 39],

$$\Psi'(\mathbf{z}) = Ai\left[\frac{2m\_\pi \,^\*eF\_\mathbf{z}}{\hbar^2}\left(\mathbf{z} - \frac{E\_i}{eF\_\mathbf{z}}\right)\right] \tag{11}$$

where mz\* is the effective mass of electron in the GaN, Fz is the electric field in the z-direction, Ei is the eigenvalues of energy with i = 0,1,2, … . for the ground state, 1st excited state and so on. Airy (Ai) function is given by

$$Ai(z) = \frac{1}{\pi} \int\_0^\infty \cos\left(\frac{t^3}{3} + zt\right) dt$$

The eigen value is given by [37, 38],

$$E\_i \approx \left(\frac{\hbar^2}{2m\_x}\right)^{1/3} \left[\frac{3\pi e F\_x}{2}\left(i + \frac{3}{4}\right)\right]^{2/3} \tag{12}$$

When an incident THz radiation illuminates the GaN HEMT, electrons may absorb the photon energy and jump to a higher energy subband. Carriers below Fermi energy levels were collected by drain electrode when we applied voltage between source and drain. Using Fermi's golden rule for the transition from i state to j state, we can calculate the absorption coefficient by [34, 40],

$$\mathcal{W}\_{\vec{\eta}} = \frac{2\pi}{\hbar} < \Psi\_i |H'|\Psi\_j >^2 \delta(E\_j - E\_i - \hbar \alpha).$$

where H<sup>0</sup> is interaction Hamiltonian as per Eq. (10). By applying the dipole approximation, we obtain [34, 40],

$$\mathcal{W}\_{\vec{\eta}} = \frac{2\pi}{\hbar} \frac{e^2 E\_0^2}{4m\_\pi^2 \alpha^2} < i|e.p|j > ^2\delta(E\_j - E\_i - \hbar\alpha) \tag{13}$$

*A Novel Approach for Room-Temperature Intersubband Transition in GaN HEMT… DOI: http://dx.doi.org/10.5772/intechopen.98435*

The matrix element in the above equation can be expanded in terms of interband and ISBT as follows,

$$ = e.+e.$$

Applying the envelope function matrix element in the z-direction can be written as

$$ = \int \Psi\_i^\*(z)p\_x\Psi\_j(z)dz$$

The dimensionless optical field strength between the two-energy state is given by [33, 38],

$$\|f\_{\vec{\eta}} = \frac{2}{m\_x \ast \hbar o\_{\vec{\eta}}} < i \|p\_x\|j >^2 = \frac{2m\_0 \ast o\_{\vec{\eta}}}{\hbar} < i \|\mathbf{z}\|j >^2 \tag{14}$$

where ω*ij* ¼ *E <sup>j</sup>* � *Ei* � �*=*2 <i/z/j > can be expressed as,

$$ = z\_{ji} = \frac{2L}{\left(t\_i - t\_j\right)^2} \tag{15}$$

with, ti and L are electric length expressed as,

$$t\_i = \left[\frac{3\Pi}{2}\left(i + \frac{3}{4}\right)\right]^{2/3} \tag{16}$$

$$\mathcal{L} = \left(\frac{\hbar^2}{2m\_x \, ^\circ eF\_x}\right)^3 \tag{17}$$

By substituting Eqs. (15)–(17) in Eq. (14) we get,

$$f\_{\vec{\eta}} = \frac{8.32}{\left(t\_i - t\_j\right)^4} \left(\frac{\Pi}{2}\right)^{2/3} \left[ \left(j + \frac{3}{4}\right)^{2/3} - \left(i + \frac{3}{4}\right)^{2/3} \right] \tag{18}$$

By substituting i = 0 and j = 1,2,3, … oscillation strength for transition can be calculated as f01 = 0.73, f02 = 0.12, f03 = 0.045, and so on. The oscillator strength of all the transitions is sum up to 1. Calculated transition indicates that the probability for higher-level transitions is very weak.

The gradual pinning of Fermi level inside the quantum well is possible by increasing gate voltage. When gate voltage is sufficiently negative (0 > Vt > Vg), the conduction band is above the Fermi level. In this case, the channel is completely depleted of 2DEG. When the gate voltage is greater than the threshold voltage (Vg > Vt), charges start filling the channel. As the gate voltage increases, the Fermi level gradually pins inside the quantum well and 2DEG carriers are filled among allowed subbands in the channel. When gate voltage is sufficiently higher (Vg > 0 > Vt), the carrier occupies all allowed subband below the Fermi energy level. For this case, total 2DEG charges are distributed in the allowed energy subband and take participation in channel conduction. The triangular quantum-well conduction band energy profile for GaN HEMT with different gate biasing conditions is shown in **Figure 6(a)**. Fermi energy level pinning inside the subbands of triangular quantum well with different applied gate biasing is shown in

#### **Figure 6.**

*Conduction band energy profile with different applied gate voltage and Fermi energy level with filled subband inside triangular quantum well with different applied gate biasing (b) Vg > 0 > Vt, (c) Vg = 0 > Vt and (d) 0 > Vt > Vg (reprinted with permission from Ref. [12]).*

**Figure 6(b)**–**(d)**. The spacing and charge filing inside the subband strongly depends upon gate-biasing voltage. In other words, the gate biasing-assisted tuning of intersubband resonance (ISR) frequency is possible in the HEMT structure.

In the simulation, we extracted up to four ISB energy levels inside the triangular quantum well. The ISR frequency as a function of applied gate-biasing field is calculated using Eq. (12) and by solving self-consistency Schrodinger–Poison solver for different gate-biasing voltage. The same are shown in **Figure 7(a)** and **(b)**. The ISB tuning is one order higher in asymmetric triangular well potential as compared to the conventional square well potential. Moreover, 2DEG carrier concentration inside the GaN HEMT channel also depends upon Al composition and AlGaN barrier layer thickness. **Figure 8(a)** and **(b)** show the simulated 2DEG carrier concentration variation with AlGaN thickness and Al composition, respectively. It clearly indicates that increment in barrier layer thickness, and Al composition enhances the 2DEG density inside the channel. It further implies that manipulation in ISR is possible in GaN HEMT devices based on variation in 2DEG density, which provide tuning in the THz region.

#### **2.4 Metamaterial-embedded ISBT**

The combination of ISBT in semiconductor quantum wells with metamaterials shows great potential in the THz region [41–47]. There are large numbers of metamaterial structures that have been employed and demonstrated enhanced performance in the THz region. In the present modeling work, we report that the standard GSG device geometry of HEMT itself acts as a metamaterial structure. The enhancement of THz interaction with 2DEG inside the triangular quantum well is

#### **Figure 7.**

*Intersubband resonance frequency as a function of the applied field (a) calculated using Eq. (12), (b) by solving self-consistency Schrodinger-Poisson solver. (reprinted with permission from Ref. [12]).*

*A Novel Approach for Room-Temperature Intersubband Transition in GaN HEMT… DOI: http://dx.doi.org/10.5772/intechopen.98435*

**Figure 8.**

*2DEG carrier concentration of AlGaN/AlN/GaN heterostructure for (a) different AlGaN thickness, (b) different Al composition in AlGaN layer (reprinted with permission from Ref. [12]).*

reported for GaN HEMT. The resonance mode in metamaterial structure is dynamically manipulating the carrier distribution inside the quantum well.

For the metamaterial modeling work, the GaN heterostructure and device geometry are kept identical, as shown in **Figure 1**. A finite difference frequency domain CST Microwave Studio simulator has been used to simulate the entire device configuration, which acts as THz metamaterial. Standard GSG configuration along with 50- to 150-micron gate width has been used for 3D electromagnetic modeling as shown in **Figure 9(a)**–**(c)**. Very fine localized tetrahedral sub-meshing has been used in the active source to drain region to enhance the accuracy of calculations as shown in **Figure 9(d)**. THz radiation (0.3–3 THz) is illuminated on the entire GSG device configuration, which includes the active GaN HEMT region as well. **Table 2** shows the dimensions used in 3D EM simulation work. Three different geometries, 2 50, 2 100 and 2 150, have been used in the present study. The E-field of the incident THz plane wave is kept at 1 V/m for all three devices.

The wavelength corresponding to the entire THz spectrum (0.3 to 10 THz) is about 30–1000 micron. If the device dimension is of the order of incident radiation, it acts as an antenna. Antenna size and shape largely determine the frequency it can handle. Antenna-coupled THz source and detector show a potential advantage in the performance of devices for the THz region [48–52]. The dimensions of the devices as listed in **Table 2** are of the order of illuminated THz radiation wavelength. These devices act as antennas, which leads to convergence of incident radiations towards the active channel region. The resultant electric field intensity inside the active channel region between source and drain is greatly enhanced. The enhancement of the field due to illumination strongly depends on the frequency of incident radiation and device dimension. For example, the electric field intensity distribution for 0.4 THz incident radiation is shown in **Figure 10** (a)–(c) for three different GaN HEMT devices. Each device structure has a unique resonance response towards incident THz radiation. Similarly, the resonance response of a 2 100 GaN HEMT device towards incident THz radiations, namely 0.3, 0.7 and 1.75 THz, is shown in **Figure 10(d)–(f)**. Moreover, the illumination-dependent enhancement of the field is not distributed uniformly throughout the channel. The highest field distribution found at the center of a 2 100 device for 1.75 THz illuminations is shown in **Figure 10(f)**. The summary for average field enhancement inside the channel region due to illumination is illustrated in **Figure 11**. The GaN HEMT device itself acts as metamaterial, which further influences the overall THz performance of the GaN HEMT device.

#### **Figure 9.**

*Three different configuration (a) 2 50, (b) 2 100 and (c) 2 150 of GaN HEMT and (d) GaN HEMT meshing (reprinted with permission from URSI RCRS 2020, IEEE Xplore).*

**Table 2.**

*Different device configurations used in simulations.*

#### **2.5 Plasmonic-assisted ISBT**

A plasmonic nanostructure provides unique opportunities for manipulating electromagnetic waves in the THz range. Recently many novel plasmonic nanostructure-based devices such as photoconductor antennas [52, 53], detectors [31], and plasmonic photomixers [54], QCLs [55] showed significant improvement in device performance.

For plasmonic structure simulation, the finite element frequency domain COMSOL Multiphysics numerical method has been used to solve Maxwell's equation to predict electromagnetic interaction in each layer of the semiconductor

*A Novel Approach for Room-Temperature Intersubband Transition in GaN HEMT… DOI: http://dx.doi.org/10.5772/intechopen.98435*

#### **Figure 10.**

*Electrical field enhancement for 0.4 THz incident radiation on (a) 2 50, (b) 2 100 and (c) 2 150 of GaN HEMT devices. Electrical field enhancement for 2 100 GaN HEMT device at (d) 0.3°THz, (e) 0.7° THz and (f) 1.75°THz incident radiation (reprinted with permission from URSI RCRS 2020, IEEE Xplore).*