**Nondestructive Testing of Hollowing Deterioration of the Yungang Grottoes Based on THz-TDS**

**Ju Feng 1, Tianhua Meng 2,\*, Yuhe Lu 2, Jianguang Ren 3, Guozhong Zhao 4, Hongmei Liu 2, Jin Yang <sup>1</sup> and Rong Huang <sup>2</sup>**


Received: 24 February 2020; Accepted: 7 April 2020; Published: 9 April 2020

**Abstract:** Terahertz (THz) spectroscopy is an important method in noninvasive detection and diagnosis for historic relics. A new nondestructive testing (NDT) method based on terahertz time-domain spectroscopy (THz-TDS) technology was developed to measure the hollowing deterioration of the Yungang Grottoes in this paper. Hollowing deterioration samples were strictly prepared, and a series of experiments were conducted to ensure the representativeness of the experimental results. A hollowing thickness model was established by the relationship between the thickness of the hollowing deterioration sample and the time difference of the front flaked stone surface and the stone wall surface of the hollowing deterioration samples. The results show that the R-squared value of the model equation reached 0.99795, which implies that this model is reliable. Therefore, the actual hollowing thickness of the Yungang Grottoes can be obtained by substituting the time difference in the proposed thickness hollowing model, where the time difference is obtained from measured THz spectra. The detection method of stone relic hollowing deterioration is easy to apply, which can not only realize qualitative NDT but also quantitative hollowing deterioration thickness determination. This method has crucial practical significance for the repair and strengthening of stone relics similar to the Yungang Grottoes.

**Keywords:** terahertz spectroscopy; open stone relics; hollowing; weathered; preservation of cultural heritage

#### **1. Introduction**

Stone relics are monuments consisting of natural stones, including buildings, grottoes, stone tablets, etc., which have very high historical and artistic values, as well as represent a specific kind of geological engineering requiring long-term preservation. However, with the intensification of environmental pollution and under the influence of natural and human factors, stone relics (especially open stone relics) are being damaged at an alarming rate [1–3]. This damage has endangered the safety of cultural relic preservation and has affected the historical and cultural values of stone relics.

As one of the commonly occurring types of damage, hollowing deterioration destroys the structure and shortens the life of stone relics. Hollowing possesses concealed characteristics that cannot be observed timely and clearly from the stone surface. With the Yungang Grottoes as an example, as shown in Figure 1, the surface of stone relics is corroded, and the internal layered or sheet-like clay mineral and gypsum components produce a high expansion pressure under the action of natural precipitation, such as rain. When a rock formation has low rock strength, a hollowing structure will be produced, which comprises three parts, namely, the front rock wall (flaked stone), the air layer,

and the substrate layer (stone wall). When the air layer in the hollowing structure reaches a certain thickness, the front rock wall may naturally detach, forming new cracks as a result of large temperature fluctuations and an uneven internal force distribution, which significantly endangers stone relics.

**Figure 1.** Schematic illustration of hollowing deterioration of stone relics and the terahertz (THz) wave reflection single-point thickness extraction principle of the hollowing model. E\_{in} is the incident field; E\_{s1}, E\_{s2}, and E\_{s3} are the fields reflected from the front and back flaked stone surfaces and the stone wall surface, respectively; d\_1 and d\_2 are the flaked stone and hollowing sample thicknesses, respectively; θ<sup>i</sup> and θ<sup>t</sup> are the incidence and refraction angles, respectively; and n and n0 are the refractive indexes of the flaked stone sample and air, respectively.

The nondestructive detection technique is an effective method for identifying hidden internal defects and dislocation impurities to estimate and extend the life of the tested object by the use of sound, light, magnetic field, electricity, etc., under the precondition of not damaging the detection target [4–14]. Compared with the conventional methods in the present nondestructive testing (NDT) field, such as magnetic particle testing, penetration testing, eddy current testing, radiographic testing, and ultrasonic testing, the typical wavelength of terahertz (THz) waves (300 μm) is larger than the size of small-scale structures; therefore, THz scattering in most objects occurs far less than for visible and near-infrared light, and the THz wave photon energy is commonly lower than the chemical bond energy, which means that THz waves can better penetrate most nonpolar materials. Furthermore, a THz wave is particularly suitable for NDT, and it allows the development of non-destructive, non-contact, non-ionizing methods that could advantageously replace other evaluation methods based on X-rays, ultrasound, and thermography [15–21].

Terahertz time-domain spectroscopy (THz-TDS) is a new THz spectrum measurement technique based on ultra-short pulse technology developed in recent years, which has been widely applied in the fields of physics, chemistry, biology, etc. [22–27]. The physical and chemical parameters of tested objects, such as the complex dielectric constant, dispersion coefficient, transmission, and absorption, are usually obtained by THz-TDS, and the material composition and structure of the tested objects can then be studied. However, no relevant report is found on characterizing stone relic hollowing deterioration with THz-TDS. In this paper, the hollowing deterioration of Yungang Grotto samples was studied using THz nondestructive testing (THz-NDT) technology based on THz-TDS.

#### **2. Hollowing THz-NDT Theory**

THz-TDS is a coherent detection technology that can simultaneously obtain information about the THz pulse amplitude and phase [28–30]. As such, it relies on THz wave reflection to detect changes in the THz time-domain pulse wave in the sample before and after irradiation, called the reference and sample waveforms, respectively. The THz time-domain spectra of reference and hollowing deterioration samples are shown in Figure 2. The reference wave is the THz wave in the sample without hollowing deterioration, with a corresponding d\_2 value of 0. When the corresponding d\_2 values of the hollowing deterioration sample waves are 1, 2, 3, and 4 mm, the upper right figure shows that the THz time-domain spectra of the reference and hollowing deterioration samples range from 368 to 404 picoseconds. Figure 2 reveals that the different peak positions of the echo waves correspond to various prolonged times of hollowing samples with different thicknesses (d\_2). With increasing hollowing deterioration sample thickness, the delay time of the echo wave increases. The peak positions are reflected from the front and back flaked stone surfaces (S\_1 and S\_2, as shown in Figure 1) corresponding to 314.88 and 374.17 ps, respectively. The peak positions reflected from the stone wall surface (S\_3 and d\_2, as shown in Figure 1) occur at 378.49, 384.45, 389.79, and 396.08 ps, which correspond to d\_2 values of the hollowing deterioration model samples of 1, 2, 3, and 4 mm, respectively.

**Figure 2.** THz time-domain spectra of the reference and hollowing deterioration samples.

#### *2.1. Single-Point Thickness Extraction Hollowing Model*

THz waves are reflected at the interfaces between media with different dielectric constants during propagation, as shown in Figure 1. The THz wave reflection single-point thickness extraction principle of the hollowing model is based on the assumption that flaked stone is homogeneously and isotropically distributed at a scale that is relatively larger compared with the focal spot size of the THz wave.

When the THz wave has an incident angle θi, E\_{s1} is the THz wave reflected by the front flaked stone surface (S\_1), and T\_1 is the peak position of the first wave, E\_{s1}. Similarly, T\_2 and T\_3 are the peak positions of the first wave reflected by the back flaked stone surface (E\_{s2}) and the stone wall surface (E\_{s3}), respectively (as shown in Figure 1). According to the THz wave propagation theory, the thickness was defined in the reflection single-point extraction model as follows [13]:

$$\mathrm{d}\_{-}2 = \frac{\mathrm{c}\sqrt{\mathbf{n}\_{0}^{2} - \mathrm{n}^{2}\sin^{2}\theta\_{\mathrm{t}}}}{2n\_{0}^{2}}(\mathrm{T}\_{-}\mathrm{3} - \mathrm{T}\_{-}\mathrm{1}) - \frac{\sqrt{\mathbf{n}\_{0}^{2} - \mathrm{n}^{2}\sin^{2}\theta\_{\mathrm{t}}}}{\sqrt{\mathbf{n}^{2} - \mathrm{n}\_{0}^{2}\sin^{2}\theta\_{\mathrm{t}}}} \Big(\frac{n^{2}}{n\_{0}^{2}}\mathrm{d}\_{-}\mathrm{1}\Big) \tag{1}$$

When the incident direction of the THz wave is perpendicular to the hollowing deterioration samples, the thickness of the single-point extraction model can be simplified as:

$$\mathbf{d}\_{-}\mathbf{d}\_{-} = \frac{\mathbf{c}}{2n\_{0}}(\mathbf{T}\_{-}\mathbf{3} - \mathbf{T}\_{-}\mathbf{1}) - \frac{n}{n\_{0}}\mathbf{d}\_{-}\mathbf{1}\_{\prime} \tag{2}$$

where d\_1 and d\_2 are the thicknesses of the flaked stone and the hollowing deterioration sample, respectively, T\_1 and T\_3 are the peak positions of the first wave reflected by E\_{s1} and E\_{s3}3, respectively, n and n0 are the refractive indexes of the flaked stone sample and air, respectively, and c is the light propagation velocity in air.

#### *2.2. Simplified Hollowing THz-NDT Model*

The hollowing thickness can be obtained by measuring the THz echo time difference when the refractive index of the flaked stone is known. However, in a general engineering test, the optical parameters of samples are very difficult to extract. However, the THz echo time difference can represent the hollowing thickness, so we simplified the proposed model with reflective thickness correlation coefficients k and b as follows:

$$\mathbf{d\_{-}2} = \mathbf{a} \times (\mathbf{T\_{-}3} - \mathbf{T\_{-}1}) + \mathbf{b} = \mathbf{k} \times \boldsymbol{\Delta T} + \mathbf{b},\tag{3}$$

Currently, irregularly shaped targets cause challenges in hollowing deterioration detection in engineering applications. Therefore, the simplified hollowing thickness model is pre-established by the correlation coefficient method to solve this problem. The actual hollowing thickness of the Yungang Grottoes can be determined by substituting the time difference in the hollowing thickness model, and this difference time can be obtained from measured THz spectra.

#### **3. Experimental Method**

#### *3.1. Nondestructive Testing Using THz Wave Technique*

In this paper, the hollowing deterioration samples are tested with a THz-TDS1008 test system, which is compact, self-contained, and highly integrated, and the optical antenna method is adopted to produce and detect THz pulses. The latter approach relies on a femtosecond laser, THz emission and detection components, and a composite time-delay system. The central wavelength of the laser is 800 nm, the pulse duration is 100 fs, the THz pulse width is 0.05~3.5 THz, and the signal-to-noise ratio (SNR) >65 dB. In addition, the hollowing deterioration model samples were tested at normal temperature (293 K) and 30% relative humidity. The schematic experimental setup is shown as Figure 3.

**Figure 3.** Schematic of the experimental setup. BS: splitter; M: mirror.

#### *3.2. Hollowing Deterioration Sample Preparation and Testing*

Hollowing deterioration is a common stone surface degradation phenomenon, in which surface sheet-like layers experience uplift deformation leading to cavities and cracks. Over time, these layers will detach due to their weight and the environmental changes, such as temperature, humidity, shock, and vibration. The THz-TDS can be effectively applied to the quantitative diagnosis of hollowing deterioration. In this work, we have avoided the inhomogeneous samples so that precise THz spectra

can be obtained. We cut grotto samples into approximately 2-mm stone sheets and 6-mm stone blocks using an angle grinder and then polished them with sandpaper, which were used as the stone flake and stone wall of the hollowing deterioration model. Finally, we overlaid the two stone slices with different thicknesses to form a hollowing deterioration sample, as shown in Figure 4. The hollowing deterioration model samples were tested, and the thickness range of the hollowing deterioration samples was 0 to 4 mm at 0.1-mm intervals.

**Figure 4.** Schematic of the hollowing deterioration sample.

Since the thickness of the front surface of most hollowing deterioration in Yungang Grottoes is about 2 mm, we chose this typical thickness for our study. At the same time, we also tested the time-domain spectra of the flaked stone in the THz reflection and transmission system, as shown in Figure 5. Figure 6 is the refractive index spectrum. As can be seen from Figure 6, the refraction index of flaked stone was 2.11 in the THz band.

**Figure 5.** THz time-domain spectra of the reference and the flaked stone thickness of 2 mm. The time-domain spectra of (**a**) were obtained from the THz reflector system, with the transmission THz system for (**b**).

**Figure 6.** The THz refractive index spectra of the flaked stone thickness of 2 mm.

#### **4. Results and Discussion**

To accurately and reliably obtain the hollowing thickness, we measured THz spectra of the hollowing deterioration samples, where the thickness ranged from 0 to 4 mm at 0.1-mm intervals, and the measured data was used to develop the hollowing detection model. The THz time-domain spectra for all the hollowing deterioration samples are shown in Figure 7. Figure 7a–d are the THz time-domain spectra of the hollowing deterioration samples with different thicknesses. As THz wave is very sensitive to the small changes of the hollowing deterioration samples, the THz time-domain spectra of the different hollowing deterioration samples were different in the terahertz band and could be distinguished. In addition, it should be pointed out that the stone sheet of the hollowing deterioration samples was relatively thin but had a high refractive index. So the oscillating wave mainly resulted from the multiple reflections inside the sample, which is the Fabry–Perot interference effect. THz time-domain spectra revealed significant differences among the hollowing deterioration samples with different thicknesses, which caused the different propagating velocities in sample paths that gave rise to the different time delays. The decrease in terahertz pulse intensity was due to the reflectivity and absorption of the sample and the THz pulse became broad with the dispersion of the sample. Figure 7 indicates that the THz spectra of all samples attenuated quickly with the increasing of time delay in the whole spectral regions. The thickness of hollowing deterioration samples varied linearly with the peak position of the first wave reflected by the stone wall surface of the hollowing deterioration samples (T\_3).

**Figure 7.** *Cont*.

**Figure 7.** THz time-domain spectra of the hollowing deterioration samples. The thickness of the hollowing deterioration samples in (**a**) are 0.1 to 1.0 mm at 0.1-mm intervals. The thickness of the hollowing deterioration samples (**b**) are 1.1 to 2.0 mm at 0.1-mm intervals. The thickness of the hollowing deterioration samples (**c**) are 2.1 to 3.0 mm at 0.1-mm intervals. The thickness of the hollowing deterioration samples (**d**) are 3.1 to 4.0 mm at 0.1-mm intervals.

The peak positions of the THz spectra (T\_3) for all of the different thicknesses were extracted with the hollowing model, and the reflection peak position of the S\_1 surface (T\_1, 314.88 ps) and the S\_2 surface (T\_2, 374.16 ps) was then subtracted to obtain the THz time delay difference (ΔT). As the thickness of the air layer in the hollowing deterioration increased, several close echoes appeared at the same time. Grubbs' test was selected to eliminate the noise value when T\_3 was selected accurately in the measured THz spectra. By Grubbs' table look-up method, we were able to obtain the values of G (*n*0) for use in excluding outliers (for which G is greater than G (*n*0)). G is defined as follows:

$$\mathbf{G} = \left| \frac{\mathbf{\tilde{t}} - \mathbf{t\_n}}{\mathbf{s}} \right| = \left| \frac{\frac{1}{\mathbf{n}} \sum\_{i=1}^{n} \mathbf{t\_i} - \mathbf{t\_n}}{\sqrt{\frac{1}{\mathbf{n} - 1} \sum\_{i=1}^{n} \left( \mathbf{t\_i} - \frac{1}{\mathbf{n}} \sum\_{i=1}^{n} \mathbf{t\_i} \right)^2}} \right| \tag{4}$$

where t is the average of all THz wave time (t) data for every sample, s is the standard deviation, and *n*<sup>0</sup> is the significance level, which was taken to be 5%.

Figure 8 shows the relationship between ΔT and d\_2, and in addition, the experimental data were linearly fitted. The R-squared value was up to 0.99795, which verifies the feasibility and validity of this method. The linear fitting equation for ΔT and d2 can also be described as follows:

$$\mathbf{d\_{-}2} = -9.88215 + 0.17121 \times \Delta \mathbf{T} \tag{5}$$

**Figure 8.** The relation curve between d\_2 and ΔT and the linear fit of d\_2.

By comparing the above linear fitting equation and Equation (3) of the hollowing thickness model, the correlation coefficients b and k of the latter could be determined as 9.88215 and 0.17121, respectively. In a general survey of Yungang Grottoes deterioration, the accurate hollowing thickness can be calculated by substituting actually measured THz spectra in the proposed model, which can provide effective references for repairing and reinforcing ancient relics.

#### **5. Conclusions**

In this work, we established a hollowing deterioration thickness detection model based on THz-TDS single-point experimental measurements. Our analysis suggests that THz technology can be applied to efficiently detect hollowing deterioration, as it reflects the thickness of hollowing deterioration. Even though the refractive index of hollowing deterioration samples is unknown, the model is universal. In the case of the hollowing deterioration samples of Yungang Grottoes, the THz spectra of 40 hollowing deterioration samples were determined, and the linear relationships between the thickness of hollowing deterioration samples and THz wave time-delay differences of the front flaked stone surface and the stone wall surface in samples were investigated. The resulting statistical model R-squared value reached 0.99795, which verified the feasibility and validity of this model. The method of analyzing the hollowing thickness of cultural relics using the THz-TDS method, which has high precision, is simple and nondestructive, and the method can be used for real-time hollowing deterioration detection of the Yungang Grottoes and be extended to other cultural relics. Moreover, the development of miniaturized, integrated, and higher-resolution THz instrumentation will enable this method to be applied in the field of cultural relic detection.

**Author Contributions:** Conceptualization, J.F., T.M., Y.L., G.Z., H.L., and J.Y.; Data curation, J.F., T.M., J.R., and R.H.; Investigation, J.F., T.M., and J.R.; Methodology, J.F., T.M., G.Z., and R.H.; Supervision, Y.L., G.Z., and J.Y.; Validation, J.F. and T.M.; Visualization, J.F., T.M., Y.L., H.L., J.Y., and R.H.; Writing—original draft, J.F. and T.M.; Writing—review and editing, J.F., T.M., G.Z., H.L., and J.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Fund of China under grants 11504212, the Science and Technology Innovation Group of Shanxi Province, China under grants 201805D131006, Important R&D projects of Shanxi Province under grants 201803D121083 and 201803D31014, Applied Basic Research projects of Shanxi Province under grants 201801D121072, and the Ph.D. research startup foundation of Shanxi Datong University under Grant No. 2014B06.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Improved InGaAs and InGaAs**/**InAlAs Photoconductive Antennas Based on (111)-Oriented Substrates**

**Kirill Kuznetsov 1,\*, Aleksey Klochkov 2,\*, Andrey Leontyev 1, Evgeniy Klimov 2, Sergey Pushkarev 2, Galib Galiev <sup>2</sup> and Galiya Kitaeva <sup>1</sup>**


Received: 28 February 2020; Accepted: 14 March 2020; Published: 17 March 2020

**Abstract:** The terahertz wave generation by spiral photoconductive antennas fabricated on low-temperature In0.5Ga0.5As films and In0.5Ga0.5As/In0.5Al0.5As superlattices is studied by the terahertz time-domain spectroscopy method. The structures were obtained by molecular beam epitaxy on GaAs and InP substrates with surface crystallographic orientations of (100) and (111)A. The pump-probe measurements in the transmission geometry and Hall effect measurements are used to characterize the properties of LT-InGaAs and LT-InGaAs/InAlAs structures. It is found that the terahertz radiation power is almost four times higher for LT-InGaAs samples with the (111)A substrate orientation as compared to (100). Adding of LT-InAlAs layers into the structure with (111)A substrate orientation results in two orders of magnitude increase of the structure resistivity. The possibility of creating LT-InGaAs/InAlAs-based photoconductive antennas with high dark resistance without compensating Be doping is demonstrated.

**Keywords:** terahertz wave generation; InGaAs; molecular beam epitaxy; time-domain spectroscopy; photoconductive antenna

#### **1. Introduction**

At the present time terahertz wave radiation is widely used in various application fields related to pharmacology, medicine, security systems, and data transmission. Therefore, a search is underway for the most effective methods for generating and detecting terahertz radiation. In this regard, photoconductive semiconductor antennas (PCAs) have proven themselves as flexible and effective THz devices for use in time-domain spectroscopy (TDS) and imaging systems. Due to the availability of cost-efficient and reliable components from the telecommunication industry, the state-of-the-art TDS systems often utilize optical excitation at 1550 nm [1,2] with Er3<sup>+</sup> fiber laser femtosecond pulses. Recently [3,4], the In0.5Ga0.5As-based semiconductor structures have been investigated as photoconductive materials for THz PCAs due to an appropriate room-temperature optical absorption cut-off wavelength of 1.5 μm. Lately, a significant improvement in the performance of these devices was achieved, mainly with the help of nanotechnology tools such as plasmonic light concentrators, plasmonic contact electrodes, optical nanoantenna arrays, or optical nanocavities [5–7]. Nevertheless, the development of basic photoconductive materials for THz PCAs is still of current interest.

In order to generate fast transient current and to sample the THz pulse accurately in the time domain, THz PCAs require a photoconductor with high dark resistivity and a short carrier lifetime after optical excitation. Additionally, high electron mobility is necessary for THz PCA detectors. The main development challenge with InGaAs-based photoconductors is relatively small bandgap resulting in low breakdown field strength and large dark background conductivity. Several methods for producing ultrafast InGaAs photoconductive structures have been proposed: ion implantation with heavy ions followed by thermal annealing treatment [8,9], epitaxial doping of InGaAs with impurities producing deep electronic traps in the bandgap [10,11], and growth of specially designed heterostructures such as ErAs inclusions in InGaAlAs [12]. The low-temperature (LT) InGaAs-based epitaxial structures are widely used in commercial THz systems. Low substrate temperatures (TG ≈ 200 ◦C) lead to non-stoichiometric growth with the incorporation of excess arsenic in the crystal structure. The most common non-stoichiometry related point defect is arsenic antisite with concentration in the range of 1017–1019 cm−<sup>3</sup> depending on the substrate temperature and arsenic overpressure [13–15]. The fast capture of photogenerated electrons and recombination with holes through antisite centers results in sub-picosecond carrier lifetimes in LT-materials at optimized growth and annealing conditions [16]. LT-InGaAs shows a high room-temperature residual electron concentration of the order of 1017 cm−<sup>3</sup> due to the thermal ionization of antisite defects. To increase the structure resistivity, LT-InAlAs layers are added to the photoconductive material. LT-InAlAs layers have a higher dark resistivity as compared to LT-InGaAs and exhibit deep trap states that are situated energetically below the antisite defect levels of adjacent InGaAs layers. With acceptor doping by beryllium (Be) atoms, LT-InGaAs/InAlAs superlattices demonstrate both low residual electron concentration and short carrier lifetimes in the sub-picosecond range [17–19].

It was shown recently [20–22] that LT-InGaAs and LT-GaAs structures, fabricated on (n11)A-oriented GaAs or InP substrates with or without PCA electrodes, under pulsed laser excitation, can generate THz radiation with higher power as compared to structures obtained on conventional (100) substrates. It was argued that substrate orientation can influence the concentration and the type of defects in low-temperature grown films. The purpose of the present work is further clarification of the nature of this effect by investigating the carrier dynamics in LT-InGaAs-based epitaxial structures grown on (111)A GaAs and InP substrates. Among the structures, for the first time we study the PCA based on LT-InGaAs/InAlAs superlattice fabricated on InP (111)A-oriented substrate.

#### **2. Materials and Methods**

Figure 1 shows the schematic of photoconductive terahertz source, which consists of a spiral antenna fabricated on an epitaxial heterostructure. As the photoconductive heterostructures we investigate undoped In0.53Ga0.47As layers with metamorphic buffer on GaAs substrates [20] and an undoped lattice-matched In0.53Ga0.47As/In0.52Al0.48As superlattice on InP substrate. The In0.53Ga0.47As layers serve as the photo-absorbing active regions. The mole fraction of indium is chosen as 0.53 to provide an optical absorption cut-off wavelength close to the operating wavelength of 1.5 μm. The room temperature absorption coefficient for In0.53Ga0.47As layers lattice matched to InP substrates is 8000–12000 cm-1 in this wavelength range [23,24]. The thickness of LT-In0.53Ga0.47As layers is chosen as 660 nm to be of the order of the excitation light penetration depth. Also, the In0.53Ga0.47As layer is sufficiently thin to minimize the dark conductivity. The In0.52Al0.48As layers in superlattice structures are used to introduce deep defect states and to reduce residual carrier concentration.

The active layers of the photoconductive structures are grown by molecular-beam epitaxy (MBE) at a low growth temperature of 200 ◦C. Two types of structure layer designs on different substrate materials and orientations are investigated. The 660-nm-thick In0.53Ga0.47As layers are grown on GaAs substrates with crystallographic orientations (100) and (111)A. The step-graded metamorphic buffer InxGa1-xAs is used to accommodate the lattice mismatch between the GaAs substrate and the photoconductive layer. The metamorphic buffer consists of eleven 60-nm-thick InxGa1-xAs layers with indium composition increment of Δx = 0.05. The substrate temperature during metamorphic buffer growth is stepwise decreased from 390 ◦C for In0.05Ga0.95As to 320 ◦C for the topmost In0.55Ga0.45As layer. The beam equivalent pressure (BEP) of arsenic molecules As4 is 2.0 <sup>×</sup> 10-5 Torr during growth. The III/V BEP ratio is 29. The 100-period In0.53Ga0.47As (12 nm)/In0.52Al0.48As (8 nm) superlattice is epitaxially grown on the InP (111)A substrate. The BEP of As4 is 1.2 <sup>×</sup> 10-5 Torr and III/V BEP ratio is 30. The samples were in-situ annealed in the growth chamber for 30 min at 590 ◦C. On the surface of heterostructures the spiral antennas with 320 nm-thick Ni/Ge/Au/Ni/Au annealed ohmic electrodes are deposited using standard photolithography. The central photoconductive gap is 20 μm. The Hall mobility and density of charge carriers were measured using the Van der Pauw method at room temperature.

**Figure 1.** Schematic of the investigated photoconductive semiconductor antenna (PCA) THz emitters: (**a**) topology of spiral antenna, (**b**) LT-InGaAs/GaAs (100) and (111)A heterostructures, (**c**) LT-InGaAs/InAlAs/InP (111)A heterostructure.

One of the most common methods for studying the dynamics of relaxation of charge carriers in semiconductor structures is based on the pump-probe technique. This method has sufficient resolution to observe the dynamics of relaxation of charge carriers on a sub-picosecond time scale [17].

Figure 2 shows our experimental setup for frequency-degenerate pump-probe measurements with time resolution. We measure the temporal behavior of the differential transmission (DT) of the samples induced by pump pulses. The optical radiation source (Las) is a femtosecond Er3<sup>+</sup> laser (wavelength 1550 nm, pulse duration 100 fs, pulse repetition rate 70 MHz). The initial laser beam was divided into probe and pump beams. The pump and probe beams were separated on a Glan polarization prism (G) and had orthogonal polarizations. The power ratio between the beams was regulated using a λ/2 plate in front of the Glan prism (G). A pump beam was focused on the sample; it modulated transmittance of the sample due to interband transitions of electrons in a semiconductor film. The time shift between the pulses of pump and probe beams was realized using the corner reflector (C) mounted on the delay line. The shift was changed with the time step Δt = 0.1 ps. The modulation frequency of the pump radiation chopper (Ch) was chosen equal to 2.3 kHz. The mean pump beam power was 40 mW, the probe beam power was 5 mW. The focal length of the lens (L), which focused the both beams on the sample (S), was f = 1.5 cm. An InGaAs-detector (D) by Thorlabs was used to measure the probe differential transmittance. The signal from the detector was recorded using a Lock-in Amplifier (Amp).

**Figure 2.** Schematics of the pump-probe setup for frequency-degenerate differential transmission (DT) measurements.

Figure 3 shows the experimental setup for generation and detection of terahertz radiation. The source of optical radiation was the same femtosecond Er3<sup>+</sup> laser as in pump-probe experiments. After passing through the beam splitter, most of the radiation was directed to a generating photoconductive antenna, and the rest served to illuminate the detector. The pump beam (with a mean power up to 30 mW) was focused by a lens with a focal length of 5 mm onto the studied antennas. For collimation of the generated THz radiation, a matching silicon lens was placed on the output surface of the antenna-generator (PCA1). The refractive index of high-resistive silicon is nSi = 3.14 in the terahertz range. Four parabolic mirrors were used to collect THz radiation and to focus it further on the silicon lens of the antenna-detector (PCA2). The commercial antenna-detector (Menlo Systems) with a symmetrical dipole antenna located on its back surface was used to detect the THz radiation. An instantaneous action of the THz field on an antenna-detector is equivalent to inducing some difference in potentials of its electrodes. However, the corresponding current arises through the antenna only upon irradiation with an optical pulse, which starts the process of generating free charge carriers in a semiconductor wafer. In order to register the temporal dynamics of the THz field, it is necessary to introduce a controlled delay between the pump beam and the probe beam. This is done using a mechanical delay line with a corner reflector installed. Thus, by changing the arrival time of the probe pulse (using a moving delay line), one can measure various instantaneous values of the terahertz field and, thereby, determine its temporal shape of the THz pulse. Detection of the current was performed using a Lock-in Amplifier. For synchronous detection of radiation, a radiation chopper was placed in the optical path, which modulated the laser beam at a frequency f = 2.3 kHz.

**Figure 3.** Schematics of the terahertz time-domain spectroscopy setup.

#### **3. Experimental Results**

The room-temperature Hall data is presented in Table 1. The electron-type conductivity of the investigated samples is much greater than that of the reference samples of thick undoped In0.53Ga0.47As films lattice-matched to InP (100) substrates obtained at normal growth conditions. The typical unintentional background doping of InGaAs layers in our MBE system is (1–2) ··· 1015 cm−3. The increase of the electron concentration at low growth temperature of 200 ◦C corresponds to the incorporation of excess As atoms into the InGaAs lattice. The thermal ionization of antisite As defects leads to the free electron volume concentration of the order of 1017 cm−3. The electron sheet concentration and mobility depend on the substrate orientation and on the heterostructure design. From the comparison of the LT-InGaAs samples it follows that MBE growth on the (100) and (111)A GaAs substrates at identical growth conditions leads to formation of InGaAs layers with different concentration of point defects. It can be concluded that the antisite defect density is greater in the case of

the sample grown on (111)A GaAs substrate. Introduction of InAlAs barrier layers into InGaAs/InAlAs superlattice results in substantial decrease of the sheet electron concentration by an order of magnitude as compared to thick InGaAs layers. The addition of InAlAs layers also leads to reduction of mobility μ. As a result, the dark resistivity of LT-InGaAs/InAlAs (111)A sample is 60 and 130 times greater than that of the LT-InGaAs/GaAs (111)A and (100) samples, correspondingly. The effect of InAlAs layers on the electron transport is associated with the carrier capture by deep traps into InAlAs barriers and with the scattering.


**Table 1.** Electronic mobility μ and sheet concentration *n*<sup>S</sup> in photoconductive heterostructures.

The pump-probe measurements were performed for LT-InGaAs samples grown on GaAs substrates with the surface crystallographic orientations of (100) and (111)A and for the LT-InGaAs/InAlAs superlattice grown on an InP substrate with (111)A orientation. Figure 4 shows graphs of the temporal dependences of the normalized transmittance for the studied samples. It should be noted that on some graphs, in the falling part of the functional dependences, there are regions of local growth of the normalized reflection coefficient function. These areas appear due to re-reflection of the signal from the back side of the samples. Points in these areas (dashed rectangles) were cut out of the dependencies for correct subsequent approximation.

**Figure 4.** Normalized transmission changes detected for: (left) LT-InGaAs/GaAs(100), (middle) LT-InGaAs/GaAs (111)A, (right) LT-InGaAs/InAlAs/InP (111)A.

Figure 5 shows the temporal profiles of terahertz radiation detected from the studied samples. The measurements were carried out at the same input sensitivity of the Lock-in Amplifier. The magnitude of the applied bias voltage in the case of LT-InGaAs samples was 3.7 V. It can be seen that the signal in the sample grown on a (111)A GaAs substrate is 1.9 times higher than that from the sample grown on (100) GaAs substrate. For the LT-InGaAs / InAlAs (InP) (111)A sample, the applied bias voltage was higher almost by an order of magnitude, equal to 25 V. It can be seen that, mostly due to the higher bias voltage, the signal from the InGaAs / InAlAs-based structure is 5-6 times higher. Applying of higher bias voltage turned out to be possible (without breakdown of the sample) due to significantly higher resistance of this antenna and its lower dark current.

**Figure 5.** Detected time-domain signal traces: violet line LT-InGaAs/GaAs(100) Ub = 3.7 V, blue line LT-InGaAs/GaAs (111)A Ub = 3.7 V, red line LT-InGaAs/InAlAs/InP(111)A Ub = 3.7 V, (inset) LT-InGaAs/InAlAs/InP(111)A Ub = 25 V.

Figure 6 shows the normalized spectra obtained by the fast Fourier transform (FFT) processing of the temporal waveforms presented in Figure 5. It can be seen that the maximum of the power spectral distribution is located at the frequency of 0.2 THz, and the total width of each spectrum is about 2 THz. We have not found significant differences in the spectra of terahertz wave radiation from the studied antennas. Apparently, this is due to the limiting effect of the antenna-detector with an upper frequency of the detection band about 2 THz.

**Figure 6.** FFT spectra of antennas: violet line LT-InGaAs/GaAs(100), blue line LT-InGaAs/GaAs (111)A, red line LT-InGaAs/InAlAs/InP (111)A.

#### **4. Discussion**

#### *4.1. Pump-Probe Results.*

Figure 4 shows the experimental temporal dependences of the falling part of the normalized transmittance. Two separated regions (up to 10 ps, after 10 ps) with different slopes of the curve could be clearly distinguished on each of the presented dependencies. Since the curves are plotted on a logarithmic scale, we can assume these regions as two exponential contributions with different characteristic relaxation times. Dependencies are well approximated by a two-exponential decay model. The interpolation was carried out using the least squares method by the following expression:

$$\frac{\Delta T(t)}{T\_0} = A e^{-t/\tau\_1} + B e^{-t/\tau\_2} \tag{1}$$

Here Δ*T* is a DT, *T0* is a maximal difference transmission, τ<sup>1</sup> and τ<sup>2</sup> are the relaxation times, A and B are the fitting constants. Fitting results are presented in Table 2.


**Table 2.** Characteristic relaxation times.

Most likely, the characteristic time τ*<sup>1</sup>* is the time of an electron capture from the conduction band by an anti-structural defect AsGa<sup>+</sup>. The obtained values of τ*<sup>1</sup>* are in a good agreement with the data of experiments performed earlier by other scientific groups [2,16,25]. The time interval τ*<sup>2</sup>* seems to be the recombination time of holes and electrons captured by traps. Its characteristic scale is of the order of tens of picoseconds, which, in order of magnitude, agrees well with the previous experimental values [17]. The origin of the processes that occur with photo-excited electrons at the short capture time τ*<sup>1</sup>* is connected with the excess of arsenic atoms in the InGaAs crystal structure leading to formation of the special-type defects.

As it is known from the theory by Shockley and Read [26], the carrier capture time by traps (τ*1*) is determined by the following expression:

$$
\pi\_1 = \left( N\_{As+} v\_{t\hbar} \sigma\_{As+} \right)^{-1} \tag{2}
$$

Here, *NAs*<sup>+</sup> is concentration of As+ traps in the crystal, σ*As*<sup>+</sup> is cross-section of the electron capture by traps, and *vth* is the thermal velocity of electrons. Based on the obtained data, we can conclude that the number of AsGa<sup>+</sup> defects in the LT-InGaAs/GaAs (111)A and LT-InGaAs/InAlAs/InP (111)A samples is almost two times higher than that in LT-InGaAs / GaAs (100).

#### *4.2. Temporal and Spectral Dependences of the Generated THz Field.*

Terahertz-wave electric field should be approximately proportional to the derivative of the current density. Indeed, in the simple case of a weak pump, neglecting screening effects, quasi-static and near-field terms in the expression for the electric field, one can obtain the terahertz-wave electric field proportional to the derivative of the concentration of the free electrons [27]. In Figure 5, we see that the terahertz signal amplitude from the sample LT-InGaAs/GaAs (111)A is almost two times higher than that from the sample LT-InGaAs/GaAs (100). This can be explained under the assumption that concentration of charged arsenic traps with (111)A substrate orientation is greater than that with (100) orientation. This assumption is in good agreement with the results of our measurements of characteristic electron capture times. Slower dynamics of charge carriers here could be also explained by decrease in the concentration of active defects AsGa+.

It is usually assumed that fast excitation of charge carriers in InGaAs / InAlAs heterostructures occurs in InGaAs layers, whereas the diffused charge carriers are captured in InAlAs layers [28,29]. Since it was shown that the most efficient terahertz radiation was generated in samples grown on substrates with an orientation different from the traditional (100) [20–22], to obtain the most efficient generation, the InGaAs / InAlAs heterostructure was grown straight on InP (111)A substrate. InAlAs layers significantly increase the resulting structure resistance. The resistance of the InGaAs / InAlAs sample on the InP (111)A substrate was 12.8 kΩ, which is significantly higher than the resistance of 30 Ω for all InGaAs samples on GaAs substrates. This made it possible to increase the bias voltage from 3.7 to 25 V without damaging the antenna and to raise the terahertz radiation power by almost 30 times. Since the reflections are present in the waveforms in Figure 5, the resulting spectra in Figure 6 are strongly modulated with a frequency inversely proportional to the delay between the main and reflected pulses. However, the main features of the antennas are clearly seen. The spectrum from the antenna on the LT-InGaAs/InAlAs heterostructure looks more pronounced and less "noisy" at high frequencies above 2 THz than from the LT-InGaAs antennas. Although the total spectral widths of all antennas on the logarithmic scale practically coincide in Figure 6, the total spectrum of the antenna on the heterostructure InGaAs/InAlAs is slightly wider than that of InGaAs. This issue needs a more detailed study using a wide range of radiation detectors to exclude the possible influence of the receiver on the measured spectrum.

For future research directions, we propose using atypically oriented substrates for the manufacture of antennas in order to obtain faster carrier dynamics, larger signals, and wider terahertz radiation spectra.

#### **5. Conclusions**

The characteristics of terahertz wave radiation from photoconductive antennas based on epitaxial films of low-temperature grown InGaAs with orientations of the crystallographic axes of the GaAs substrate (111)A and (100) were studied. It was found that the terahertz radiation power is almost four times higher for samples with the (111)A substrate orientation. The observed increase in the radiation power is associated with an increase in the number of anti-structural defects. THz radiation generated in the LT-InGaAs / InAlAs / InP (111)A heterostructure was 25 times higher than in the LT-InGaAs / GaAs (111)A antenna. The characteristic relaxation times of charge carriers were measured in LT-InGaAs samples on GaAs substrates with (111)A and (100) orientations, as well as in the LT-InGaAs/InAlAs/InP (111)A heterostructure. Obtained values are consistent with previously published data and qualitatively confirm the proposed explanation of the advantages of the non-standard orientation of the antenna substrate.

**Author Contributions:** Conceptualization, G.G.; MBE growth, E.K. and A.K.; Hall effect measurements, A.K.; PCA antenna, S.P.; pump-probe measurements, A.L. and K.K.; TDS measurements, A.L. and K.K.; measurement analysis, G.K.; data fitting, A.L.; writing and editing, K.K. and A.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by RFBR, grants numbers 18-29-20101, 18-32-20207, 19-02-00598.

**Acknowledgments:** The authors thank D.S. Ponomarev for some helpful discussions, D.V. Lopaev for the help with experiments and I.S. Vasil'evskii, A.N. Vinichenko for help with MBE.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Design and Measurement of a 0.67 THz Biased Sub-Harmonic Mixer**

#### **Guangyu Ji 1,2, Dehai Zhang 1,\*, Jin Meng 1, Siyu Liu 1,2 and Changfei Yao <sup>3</sup>**


Received: 20 December 2019; Accepted: 9 January 2020; Published: 15 January 2020

**Abstract:** To effectively reduce the requirement of Local Oscillator (LO) power, this paper presents the design and measurement of a biased sub-harmonic mixer working at the center frequency of 0.67 THz in hybrid integration. Two discrete Schottky diodes were placed across the LO waveguide in anti-series configuration on a 50 μm thick quartz-glass substrate, and chip capacitors were not required. At the driven of 3 mW@335 GHz and 0.35 V, the mixer had a minimum measured Signal Side-Band (SSB) conversion loss of 15.3 dB at the frequency of 667 GHz. The typical conversion loss is 18.2 dB in the band of 650 GHz to 690 GHz.

**Keywords:** bias; sub-harmonic mixer; anti-series; Schottky diode; conversion loss

#### **1. Introduction**

Terahertz usually refers to the frequency band between 0.1 THz to 10 THz. In recent years, there is an urgent demand for receivers operating at terahertz frequency in radio astronomy, planetary exploration, and atmospheric remote sensing [1]. As is well known, it is difficult to produce high Local Oscillator (LO) power in sub-millimeter and Terahertz frequency for lacking power amplifiers [2,3]. Harmonic mixers are widely used in terahertz heterodyne receivers due to the advantage of reducing the LO frequency. Sub-harmonic mixing and fourth harmonic mixing are the most-utilized mixing methods, and conversion loss increases with the number of mixing times [4].

At the frequency below 600 GHz, unbiased sub-harmonic mixers can achieve good noise performance. In Reference [5], sub-harmonic mixers operating at 183 GHz and 366 GHz are designed based on 3.7 μm thick GaAs membrane. The Double Side-Band (DSB) conversion loss and noise temperature of the 183 GHz sub-harmonic mixer are 4.9 dB and 608 K respectively, and the 366 GHz mixer is 6.9 dB and 1220 K. In Reference [6], a sub-harmonic mixer is designed working at 190–240 GHz using a discrete Schottky diode. The DSB noise temperature is lower than 1500 K and the DSB conversion loss is less than 10 dB at the frequency band. In addition, some similar unbiased sub-harmonic mixer designs can be found in Reference [7–10].

The output power of the LO sources decreases with increasing frequency, especially when the operating frequency reaches 0.6 THz and above [11,12]. So, it is urgent to design biased sub-harmonic mixers to reduce the requirement for LO power. At present, biased sub-harmonic mixers working at 585 GHz [13], 874 GHz [14,15], 1.2 THz [16,17], and 1.2 THz [18] are designed and reported based on advanced GaAs membrane film process or frameless architecture. The biased mixers mentioned above are all based on monolithic integration technology, where the on-chip capacitor is required. But, the thickness of the GaAs substrate is less than 5 μm, which is easy to bend and expensive.

It is valuable to research the biased sub-harmonic mixer in hybrid integration to solve practical engineering problems of low LO power. Because of the big size and poor performance of discrete chip capacitors in terahertz frequency, it is unable to achieve good performance to mixers in hybrid integration of anti-parallel configuration. In this paper, the biased hybrid integration scheme is adopted. The scheme is theoretically derived for the first time and compared with the anti-parallel structure to analyze the advantages and disadvantages. Two discrete Schottky diodes are biased by DC voltage and placed across the LO waveguide in anti-series configuration without chip capacitors. The mode of the LO and RF signals are orthogonal in mixing, so the LO and RF ports are highly isolated. The bias voltage is feed from the IF port and separated by a bias-T.

Section 2 illustrates the theoretical analysis and comparison of different mixing topologies. Section 3 presents the detailed architecture, simulation process, and simulation results of the 0.67 THz biased sub-harmonic mixer. The measurement platform and results of the mixer are depicted in Section 3 at the same time. Section 4 gives the discussion and comparison in simulation, measurement results. Finally, the conclusion is presented in Section 5.

#### **2. Comparison and Analysis of Di**ff**erent Mixing Topologies**

Three different mixing topologies are shown in Figure 1. Figure 1a,b presents two anti-parallel circuit topologies that are commonly used in terahertz sub-harmonic mixers, including biased and unbiased mixing. The currents direction of the primary, secondary and tertiary harmonics of the LO and RF signals of the two diodes are illustrated in Figure 1. The total mixing current contains frequency terms *f* = *m fRF* ± *n fLO* listed in Table 1, where m and n is integer. To sub-harmonic mixers, the IF signal is the only concerned frequency which can be expressed as *fIF* = *fRF* <sup>−</sup> <sup>2</sup> *fLO* .

**Figure 1.** (**a**) Topology of biased anti-parallel; (**b**) topology of unbiased anti-parallel; (**c**) the topology of biased anti-series.


**Table 1.** Mixing products of anti-parallel and anti-series diodes configuration.

Sub-harmonic mixers using the topology shown in Figure 1a typically are based on monolithic integration due to the one on-chip capacitor required. It has the same equivalent circuit with the topology in Figure 1b, which is the anti-parallel mixing configuration. The RF and LO signals are feed to diodes in quasi-Transverse Electromagnetic (TEM) mode. In Figure 1a,b, *i*<sup>1</sup> and *i*<sup>2</sup> have the same frequency components. The only output current I can be expressed as *I*<sup>1</sup> = *i*<sup>2</sup> − *i*1. It means that there is output only when *i*<sup>1</sup> and *i*<sup>2</sup> are in the opposite phase. The currents through the diode junctions can be written as

$$\begin{cases} \ i\_1 = I\_s(e^{-\alpha V} - 1) \\ \ i\_2 = I\_s(e^{\alpha V} - 1) \end{cases} \tag{1}$$

where *Is* is the reversed saturation current; <sup>α</sup> is the slope parameter (<sup>α</sup> = *<sup>q</sup> nkT* ), where *k* is the Boltzmann constant, n is the ideality factor, and T is the operating temperature of the diode.

The conductance of each diode junction is

$$\begin{cases} \text{ g}\_1 = \frac{di\_1}{d\mathcal{V}} = -aI\_s e^{-aV} \\ \text{ g}\_2 = \frac{di\_2}{d\mathcal{V}} = aI\_s e^{aV} \end{cases} \tag{2}$$

The mixing current of the two diode junctions is written as

$$\begin{cases} \dot{\mathbf{i}}\_1 = \mathbf{g}\_1(\upsilon\_{RF}\cos\omega\_{RF}\mathbf{t} + \upsilon\_{LO}\cos\omega\_{LO}\mathbf{t})\\ \dot{\mathbf{i}}\_2 = \mathbf{g}\_2(\upsilon\_{RF}\cos\omega\_{RF}\mathbf{t} + \upsilon\_{LO}\cos\omega\_{LO}\mathbf{t}) \end{cases} \tag{3}$$

The total mixing current of the anti-parallel diode pair is

$$\begin{aligned} I\_1 = i\_1 - i\_2 &= 2aI\_5 \text{sinh}(v\_{LO} \cos w\_{LO}t) \ast v\_{RF} \cos w\_{RF} t + 2aI\_5 \cos(v\_{LO} \cos w\_{LO}t) \ast v\_{LO} \cos w\_{LO} t \\ &= A \cos \omega\_{\mathbb{R}F} t + B \cos \omega\_{\mathbb{L}O} t + C \cos 3\omega\_{\mathbb{L}O} t + D \cos 5\omega\_{\mathbb{L}O} t \\ &+ \mathbb{E} \cos(2\omega\_{\mathbb{L}O} t + \omega\_{\mathbb{R}F} t) + F \cos(2\omega\_{\mathbb{L}O} t - \omega\_{\mathbb{R}F} t) \\ &+ \mathbb{G} \cos(4\omega\_{\mathbb{L}O} t + \omega\_{\mathbb{R}F} t) + H \cos(4\omega\_{\mathbb{L}O} t - \omega\_{\mathbb{R}F} t) \\ &+ \dots + X \cos(m\omega\_{\mathbb{L}O} t + m\omega\_{\mathbb{R}F} t) + \dotsb \end{aligned} \tag{4}$$

As listed in Table 1, the total mixing current only contains frequency terms *f* = *m fRF* ± *n fLO*, where *m* + *n* is odd [19]. The anti-parallel configuration can suppress half of the mixed signal called balanced structure.

The topology of the mixer designed in this paper is presented in Figure 1c. Two Schottky diodes are in anti-series across the LO waveguide [20]. Thus, the two diodes are turned on and off alternately along with the LO signal in TE10 mode. The RF signal is applied to diodes in quasi-TEM mode, where the RF probe is used to transfer TE10 mode to quasi-TEM mode. The mixing current *I*<sup>2</sup> along the microstrip line is *I*<sup>2</sup> = *i*<sup>4</sup> − *i*<sup>3</sup> and outputs only when the phase difference of *i*<sup>3</sup> and *i*<sup>4</sup> is π. The output current *I*<sup>2</sup> is expressed as *I*<sup>2</sup> = *i*<sup>4</sup> + *i*3, and output when *i*<sup>3</sup> and *i*<sup>4</sup> are in the same phase.

The currents of junctions can be written as

$$\begin{cases} \ i\_3 = -I\_s(e^{-\alpha V} - 1) \\ \ i\_4 = I\_s(e^{\alpha V} - 1) \end{cases} \tag{5}$$

The time-varying conduction is

$$\begin{cases} \text{ g}\_3 = \frac{di\_3}{dV} = aI\_s e^{-\alpha V} \\ \text{ g}\_4 = \frac{di\_4}{dV} = aI\_s e^{aV} \end{cases} \tag{6}$$

The mixing current of diode junctions is

$$\begin{cases} \text{i}\_3 = \text{g}\_3(v\_{LO}\cos\omega\_{LO}t - v\_{RF}\cos\omega\_{RF}t) \\ \text{i}\_4 = \text{g}\_4(v\_{LO}\cos\omega\_{LO}t + v\_{RF}\cos\omega\_{RF}t) \end{cases} \tag{7}$$

The mixing current along the microstrip line is

$$\begin{aligned} l\_2 = i\_4 - i\_3 &= 2aI\_\\$\cosh(v\_{LO}\cos\omega\_{LO}t) \* v\_{\overline{\mathbb{R}}\overline{\mathbb{R}}}\cos\omega\_{\overline{\mathbb{R}}\overline{\mathbb{R}}}t \\ &+ 2aI\_\circ\sinh(v\_{LO}\cos\omega\_{LO}t) \* v\_{LO}\cos\omega\_{LO}t \end{aligned} \tag{8}$$

The mixing current of along the LO waveguide is

$$\begin{aligned} I\_4 &= i\_4 + i\_3 = 2aI\_s \sinh(v\_{LO} \cos \omega\_{LO} t) \ast v\_{RF} \cos \omega\_{RF} t \\ &+ 2aI\_s \cosh(v\_{LO} \cos \omega\_{LO} t) \ast v\_{LO} \cos \omega\_{LO} t \end{aligned} \tag{9}$$

As listed in Table 1, half of the frequency components can be prevented from output to the microstrip line. However, part of the mixing signal leaks from the LO waveguide and cannot be reused. The leakage results in about 3 dB increment of the conversion loss compared with the anti-parallel mixers in principle. So, the topology is not a balanced structure in Figure 1c.

The advantage of the topology in Figure 1c is that biased mixing can be achieved without using on-chip capacitors, which is a big advantage to sub-harmonic mixers in hybrid integrated in terahertz.

#### **3. Mixer Design**

#### *3.1. Mixer Architecture*

Figure 2 shows the overall passive circuit structure built in a high frequency structure simulator (HFSS) of the 0.67 THz mixer designed. The LO signal is fed by the WR2.8 rectangular waveguide (711 μm × 356 μm) and reduced the height to 150 μm, while the RF is WR1.5 (381 μm × 191 μm) and reduce the height to 120 μm. Two planar channel Schottky diodes are placed in anti-series across the LO waveguide.

**Figure 2.** The overall passive circuit modeled in the high frequency structure simulator (HFSS). -1 Local Oscillator (LO) reduction waveguide. -2 Schottky diode pair with grounded ears. -3 RF waveguide backs short. -4 IF LPF. -5 RF probe. -6 RF reduction waveguide.

The RF probe is used to coupling the RF signal to the microstrip planar circuit which transfers the TE10 mode to quasi-TEM mode. Due to the orthogonality of TE10 mode and TEM mode, the LO port and RF port are highly isolated. Only one IF LPF (low pass filter) is needed to extract the IF signal and reflect additional harmonics to the diode pair. Due to the difference of mode, the diode pair presents parallel to the LO signal and anti-series to the RF signal. The Rogers 5880 substrate is used as the transition between SMA and quartz substrate.

The mixer has been carefully considered in the following aspects:


**Figure 3.** Simulation flow of the 0.67 THz biased mixer.

#### *3.2. Mixer Simulation*

Two single-anode Schottky diodes are utilized which are the SD1G2 series produced by Teratech Components Ltd. The diode is based on planar channel structure and the cut-off frequency is about 14 THz which can fully meet the requirement of the 0.67 THz mixer design. Table 2 lists the relative parameters of the Schottky diode.

**Table 2.** Parameters of the Schottky diode.


The simulation flow of the 0.67 THz sub-harmonic mixer is presented in Figure 3, which combines the HFSS and Advanced Design Software (ADS). Firstly, in the structure shown in Figure 2, the passive circuit of the mixer is divided into 6 parts. The corresponding scatter-parameters are calculated and exported to SNP files. Second, the complete mixer circuit is built in the ADS, and the harmonic balance algorithm is used to calculate the conversion loss and optimize the matching circuit. Third, the 5-ports overall passive circuit is modeled and simulated in the HFSS and combines the nonlinear diode model in the ADS to verify the final performance. The design is an iterative process.

The circuit in ADS is presented in Figure 4, which is based on the overall optimization method. The SNP 1 to SNP 6 is the corresponding S-parameters of parts in Figure 2. The biased T junction is used to separate the DC voltage and the IF signal and has no insertion loss, which is formed by one ideal capacitor and inductor. The mixing principle is based on the nonlinearity of the Schottky junction which is controlled by the LO signal. According to [21], the LO power is about 6 mw to unbiased sub-harmonic mixers at 670 GHz.

**Figure 4.** Overall circuit in Advanced Design Software (ADS).

Figure 5 shows the curve of conversion loss under different LO power and DC voltage when the LO and RF frequencies are set to 335 GHz and 671 GHz, respectively. When the LO power is fixed at 2 mw and bias voltage ranges from 0.1 V to 0.9 V, the minimum conversion loss is achieved around the voltage of 0.35 V. Since the driving power is insufficient in the range of 0 to 0.35 V, the conversion loss decreases with the bias voltage increases. However, conversion loss increases in the interval of 0.35 V to 1 V because of the nonlinearity reduction of diodes with the increasing of the bias voltage. When the LO power changes, the phenomenon is similar to the above. If a combination of lower LO power (<2 mw) and higher bias voltage (>0.35 V) is used, the optimal conversion loss cannot achieve because of the dynamic range of the diode junction caused by the LO signal is low.

Figure 6 shows the simulation results when the LO power is 2 mw and the bias voltage is 0.35 mV. The conversion loss is from 10 dB to 12 dB when the RF frequency is range from 653 GHz to 710 GHz. When the LO frequency is varied from 330 GHz to 340 GHz, the change in conversion loss is less than 1 dB. This indicates that the 0.67 THz biased mixer has good RF and LO bandwidth characteristics.

Figure 7 shows the simulated isolation between the RF, LO, and IF ports. Due to the orthogonality of TE10 mode and TEM mode, the isolation of LO port to the RF port is above −50 dB between 300 GHz to 400 GHz, and the isolation of RF to LO is above −29 dB between 650 GHz to 720 GHz. Due to the IF filter, the RF power cannot leak to the IF port, and its isolation is above −18 dB from 650 GHz to 710 GHz.

**Figure 5.** Conversion loss with different LO power and DC voltage.

**Figure 6.** Conversion loss with different LO frequencies.

**Figure 7.** Simulated isolation of RF, LO, and IF ports.

#### *3.3. Mixer Fabrication and Measurement*

The cavity of the designed 0.67 GHz biased mixer is made of brass material, and the entire surface is gold plated. The mixer integrates two UG387 flanges for LO and RF waveguides and a female SMA connector for the IF signal. To facilitate assembling, the cavity is cut from the center of the E plane of the waveguide into two parts and locked by screws. As shown in Figure 8, the quartz-glass substrate and diodes are fixed by conductive adhesive, and the Rogers 5880 substrate is glued by tin solder.

**Figure 8.** Circuit in the lower block of the mixer; assembled mixer.

Figure 9 shows the test diagram of the mixer. The RF and LO signals are generated by two different links, and the power and spectrum of the IF signal are measured by a spectrum analyzer. An external Bias T is used to separate the DC and IF signals. The LO signal is generated by a multiplier chain which is composed of a signal generator, W band multiplier, W band PA, and 330 GHz doubler. The RF signal is and generated by a signal generator and \* 54 multiplier module produced by VDI.

**Figure 9.** Test bench and measurement diagram of the mixer.

Before measuring the conversion loss, the respective output power of the LO and RF chains needs to be measured and calibrated by a PM4 power meter. The maximum LO power generated by the LO chain is about 13 mW between 330 GHz and 340 GHz. The RF signal power is between −18 dBm to −15 dBm from 600 GHz to 700 GHz.

Figure 10 presents the Signal Side-Band (SSB) conversion loss versus RF frequency when the LO is fixed at 2 mw@335 GHz. The conversion loss shown has been corrected for attenuation of cables and the insertion loss of the Biased T. The best measured SSB conversion loss is 15.3 dB@667 GHz. In the RF band of 650 GHz–690 GHz, the conversion loss is below 20 dB, besides the frequency of 679 GHz and 685 GHz. The typical SSB conversion loss is 18.2 dB.

**Figure 10.** Measured Signal Side-Band (SSB) conversion loss.

#### **4. Discussion**

As shown in Figure 10, the curve of the SSB conversion loss has a large jitter in the band of 670 GHz to 690 GHz than in 650 GHz to 670 GHz. The phenomenon can be explained as follows. First, the RF power is measured by the PM4 power meter which is a thermal power meter that calculates the total power of input signals. While the output RF power ranges from −20 dBm (10 mW) to −18 dBm (15.8 mW) in 670 GHz to 690 GHz, which cannot be measured accurately. The 3 mW to 5 mW measurement error of the PM4 power meter is normal which may lead conversion loss error of 2 dB. Second, the RF source utilized is a frequency multiplier module (\* 54) which has many harmonic components that affect the RF power.

As can be seen from Figures 6 and 10, there is a conversion loss gap between simulation and measurement. The gap is caused by the following reasons. First, the nonlinear model of the Schottky diode junction utilized in simulation is provided by the ADS software, which is a P-N junction model but not Schottky diode junction (metal-semiconductor junction). When the working frequency reaches 0.6 THz and above, the current saturation in the diode junction and planar structure can increase the conversion loss [21]. It is urgent to modify the diode junction model in the simulation. Second, the assembling error of Schottky diodes and the substrate deteriorates the performance, which is caused by the thickness of conductive adhesive and the alignment of the diodes. In the assembling, the alignment error between the two diodes is about 20 μm, which leads to unbalanced mixing and deteriorate the conversion loss. Besides, the conductivity of conductive adhesive is not ideal and cannot be accurately characterized in simulation, as the conductive adhesive is the self-made mixture of epoxy and silver.

Table 3 shows several reported sub-harmonic mixers and receivers working around 600 GHz. The mixer reported in Reference [10,22] are all based on anti-parallel Schottky diode pair and hybrid integration. Thus, the LO power is higher than the mixer designed in this paper. The 0.67 THz

biased sub-harmonic mixer has better conversion loss than the mixer in [21]. The mixer reported in Reference [13] is based on advanced membrane monolithic integration technology and anti-parallel architecture. Thus, it has better conversion loss than the mixer design.


**Table 3.** Summary of published terahertz mixer working around 600 GHz.

Compared with those mixers, the 0.67 THz biased sub-harmonic mixer has disadvantages and advantages as follows. In terms of conversion loss, the anti-series topology utilized has intrinsically defective in suppressing harmonics compared with anti-parallel topology, as analyzed in Section 2. But the anti-series topology can be used to biased mixers in the hybrid integration that effectively reduce the LO power. The performance can be improved in two ways in simulation. First, the Voltage Standing Wave Ratio (VSWR) of the LO port needs to be further improved to reduce the LO power. Second, the anti-series Schottky diode pair can be used to replace the two discrete diodes. The diode pair can eliminate the alignment error of the discrete diodes in assembling.

#### **5. Conclusions**

A 0.67 THz biased sub-harmonic mixer in hybrid integration has been designed and measured based on an anti-series Schottky diode placed across the LO waveguide. The circuit topology utilized is detailed, analyzed and compared with traditional anti-parallel configurations. The mixer design can realize the biased mixing structure without using discrete chip capacitors, and high isolation between RF, LO, and IF ports. The measured data shows the optimum SSB conversion loss is 15.3 dB at 667 GHz. In the RF frequency band of 650 GHz to 690 GHz, the typical value of conversion loss is 18.2 dB. The mixer design effectively decreased the LO power in the hybrid integrated Schottky diode-based sub-harmonic mixer. At the same time, the 0.67 THz biased sub-harmonic mixer has great prospects in ice cloud detection and planetary exploration.

**Author Contributions:** Conceptualization, methodology, software, and writing, G.J., D.Z., J.M., and C.Y.; investigation, S.L.; visualization, G.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Correction of Optical Delay Line Errors in Terahertz Time-Domain Spectroscopy**

**Alexander Mamrashev 1,\*, Fedor Minakov 1,2, Lev Maximov 1,2, Nazar Nikolaev <sup>1</sup> and Pavel Chapovsky 2,3**


Received: 24 October 2019; Accepted: 22 November 2019; Published: 26 November 2019 -

**Abstract:** One of the key elements of terahertz time-domain spectrometers is the optical delay line. Usually it consists of a motorized translation stage and a corner reflector mounted on its top. Errors in the positioning of the translation stage lead to various distortions of the measured waveform of terahertz pulses and, therefore, terahertz spectra. In this paper, the accuracy of position measurements is improved by using an optical encoder. Three types of systematic errors are found: Increasing and periodic offsets of the translation stage position, as well as a drift of its initial position in a series of consecutive measurements. The influence of the detected errors on the measured terahertz spectra is studied and correction methods are proposed.

**Keywords:** terahertz spectroscopy; optical delay line; correction; optical encoder; terahertz spectra; terahertz metrology

#### **1. Introduction**

Terahertz time-domain spectroscopy (THz-TDS) has become one of the most common methods for studying optical and dielectric properties of materials in the frequency range of 0.1–10 THz with the development of femtosecond laser technology [1,2]. This method is used to study nonlinear optical crystals [3,4], nuclear spin isomers [5], complex biomolecules [6], and charge carriers in solids [7,8].

The principle of operation of terahertz time-domain spectrometers is based on the generation of terahertz pulses and measurement of their electric field waveform. An optical delay line allows changing of the path difference between generation and detection optical channels of the spectrometer. This enables point-by-point sampling of the terahertz pulse waveform. Digital Fourier transform is used to calculate the spectra of the measured signal that contain information on the absorption coefficient and the refractive index of the media under study. Details of the spectrometer operation will be discussed later.

Various elements of spectrometers exhibit random and systematic errors, leading to distortion of terahertz pulses and, therefore, terahertz spectra [9–13]. The errors in the amplitude of terahertz pulses are mainly determined by random fluctuations and the long-term drift of the THz generation system, which consists of a femtosecond pump laser and an optical-to-terahertz converter. Errors in the positioning of the optical delay line lead to more complex distortions. In [14], the effect of a drift of the initial position of the delay line in a series of sequentially measured terahertz pulses was considered. It was shown that it led to error proportional to the THz signal shifted by a quarter cycle. Spectroscopy of thin films and attenuated total internal reflection spectroscopy are especially sensitive

to such error [15]. In [16], random errors of optical delay line positioning were considered. It was shown by Monte Carlo modeling that the terahertz spectrum was impaired by spectrally independent additive noise, which was directly proportional to the noise in the time domain and the square root of the sampling time steps of THz pulses. It was shown in [17] that periodic sampling error results in the presence of spurious mirror copies of the main pulse spectra, in which frequency and amplitude depend on the period and amplitude of the error, respectively.

Optical delay lines in THz spectrometers are usually based on corner reflectors on mechanical translation stages driven by voice coils or stepper motors. There are also conceptually different non-mechanical approaches for shifting time delay between generation and detection optical channels such as ECOPS and ASOPS techniques [18,19]. Imperfections in mechanical translation stages lead to positioning errors that are usually not considered by THz-TDS operators. However, these errors can be eliminated by software or hardware solutions. Algorithms are used to correct the time shift in a series of measured THz pulses [20,21]. Interferometers are used to more accurately measure the delay line position [22]. However, they require additional laser, optical elements and electronics making overall setup more expensive and difficult to operate.

In this paper, we propose a simple and cost-effective method to improve the accuracy of optical delay line positioning by using an optical encoder. We detect systematic positioning errors, study their effects on the measured terahertz spectra, and propose correction methods. The studies are conducted on a custom-made THz spectrometer with a delay line based on a motorized translation stage upgraded with the optical encoder.

#### **2. Experimental Setup and Measurement Procedure**

#### *2.1. THz Spectrometer*

To study the random and systematic errors of the optical delay line and the effect of these errors on the measured terahertz spectra, experiments were carried out on a THz spectrometer created in the Institute of Automation and Electrometry of Siberian Branch of Russian Academy of Sciences. The experimental setup is a standard terahertz time-domain spectrometer (Figure 1). The source of the femtosecond pump and probe pulses is an Er-doped fiber laser with a second harmonic generation module FFS-SHG (Toptica Photonics AG, Munich, Germany) providing radiation with the following parameters: Central wavelength—775 nm, pulse duration—130 fs, and mean power—80 mW. A photoconductive antenna iPCA-21-05-300-800-h with microlense array and interdigitated electrodes on semi-insulating GaAs substrate (Batop GmbH, Jena, Germany) serve as a THz generator. The terahertz field is detected by electro-optic sampling in a (110)-cut 2 mm ZnTe crystal. In this method, the probe pulse passes through ZnTe crystal that became birefringent under terahertz electric field and changes polarization. A quarter-wave plate and a Wollaston prism split the probe pulse into two beams with orthogonal linear polarizations. A pair of photodiodes detect the difference between the powers of two beams which is proportional to the electric field of the terahertz radiation. The differential signal is measured by a lock-in amplifier SR830 (Stanford Research Systems, Sunnyvale, CA, USA) tuned to the frequency of ~8 kHz provided by an iPCA voltage generator.

**Figure 1.** Scheme of the custom-made terahertz time-domain spectrometer.

The optical path lengths of generation and detection arms are equal so that the terahertz pulse and probe laser pulse synchronously arrive at the detection crystal. The optical delay line allows changing of the optical path length of the detection arm and sampling of the terahertz pulse waveform. The Fourier transform of the measured waveform gives its spectrum. The delay line is a motorized translation stage 8MT173-50-20 (Standa Ltd., Vilnius, Lithuania) with a corner reflector mounted on its top. For such setup movement of the translation stage by a distance of Δ*l* corresponds to a time delay of Δ*t* = 2·Δ*l*/*c*, where *c* is the speed of light.

#### *2.2. Upgraded Optical Delay Line*

The leadscrew of the translation stage 8MT173-50-20 is driven by a stepper motor operated by an 8SMC1-USBhF motion controller. Full step resolution of the motor is Δ*l* = 1.25 μm which corresponds to a time delay of Δ*t* = 8.34 fs. The controller provides resolution down to 1/8 of the step, speed up to 5 mm/s, long-range movements with programmable acceleration and deceleration. One revolution of the screw corresponds to a movement of Δ*l*<sup>1</sup> = 250 μm, i.e., Δ*t*<sup>1</sup> = 1.67 ps in the time domain. The full movement range is *L* = 50 mm, i.e., *T* = 334 ps. The controller of the stage measures only its relative position (there are no absolute data) by counting the number of steps done by a stepper motor.

To study random and systematic errors of the optical delay line, a Resolute RL32BAT001B50 optical encoder with an absolute scale RTLA (Renishaw, Gloucestershire, United Kingdom) was installed on the translation stage (Figure 2). The readhead of the optical encoder scans the scale with a code allowing determination of the absolute position of the readhead relative to the scale. The scale is a low-profile stainless-steel tape. The accuracy of the scale is ± 5 μm/m, the coefficient of thermal expansion at the temperature of 20 ◦C is 10.1 ± 0.2 μm/m/ ◦C. The resolution and sub-divisional error of the position measurements are 1 nm and ± 40 nm, respectively. For our task, a scale segment of 10 cm is cut, hence its absolute positioning accuracy is 0.5 μm, and the coefficient of thermal expansion is 1.01 μm/ ◦C. These values correspond to the time domain absolute accuracy of ± 3.34 fs and random error of ± 0.27 fs. The readhead and its communication protocol support the sampling rate up to 25 kHz.

**Figure 2.** Upgraded optical delay line consisting of a translation stage (1), a corner reflector (2), an optical encoder readhead (3), and a scale (4).

The design of the mounting of the optical encoder and the scale allows us quick exchange between four analogous translation stages for testing of their accuracies. The design also allows us to adjust the readhead inclination and its position in two axes and set the encoder to the optimal reading state. After adjustment, the readhead is fixed, and the scale mounted on the translation stage platform moves relative to the readhead.

#### *2.3. Measurement Procedure*

The measurements of the translation stage position were performed in a point-by-point manner. The translation stage speed was set to a default value of 0.78 mm/s. The measurements were performed with the step of 12.5 μm in the range of 45 mm. The step size of 12.5 um contained integer number of stepper motor full steps. When moving the translation stage, we recorded two sets of data: The position of the translation stage measured by counting stepper motor steps (*L*st) and the position obtained from the optical encoder (*L*en). Values measured at the initial position of the translation stage were used as a reference (zero) position. A comparison of the *L*st and *L*en positions was carried out for four analogous translation stages 8MT173-50-20 that are used in our terahertz spectrometer A comparison of the positions was carried out when the translation stages moved both in the positive and in the negative directions. No significant differences were found in these cases; therefore, further results are presented only for positive movement direction.

To assess the repeatability of the results an additional series of measurements for one of the translation stages positions was carried out. In this series, after each measurement, the translation stage returned to the zero starting position according to the value of *L*st. The translation stage position was measured together with the terahertz pulse waveform. The lock-in amplifier time constant was set to 100 ms. We waited the amount of time required for the signal settlement at each point before saving the terahertz field measurement.

#### **3. Results**

Figure 3 shows the difference between the optical encoder measurements *L*en and the positions of the four translation stages *L*st. All of them exhibit similar behavior. Two types of systematic errors can be seen in the figure: An increasing position difference and a periodic error. There are also sharp jumps in position due to scratches, damages, and other mechanical defects of the translation stage screw. Figure 3a shows an increasing offset of position relative to the more accurate data from the optical encoder for all four translation stages. Over the entire range, this offset has a magnitude of the order of tens of micrometers that significantly exceeds the encoder accuracy of 0.5 μm. As we zoom in (see Figure 3b) we can see some periodic position mismatch. The amplitude of the oscillations varies from 0.4 to 1 μm for different translation stages. The oscillation period is 250 μm, which corresponds to the full revolution of the translation stage screw.

**Figure 3.** The difference between the translation stage positions and the optical encoder measurements for four translation stages in the ranges: (**a**) 45 mm; (**b**) 10 mm.

The third type of systematic errors, a drift of the initial position is detected by repeated measurements of the first translation stage. Figure 4 shows the difference between the optical encoder measurements *L*en and the translation stage position *L*st in a series of ten consecutive measurements. In the series, after each measurement, the translation stage was supposed to return to the zero starting position. However, Figure 4 shows that the initial position drifted according to the encoder measurements *L*en. The position shift was about 1 μm (corresponding to the time shift of 6.7 fs) between the first measurements and gradually decreased in the subsequent measurements in the series.

**Figure 4.** The drift of the initial position measured by the optical encoder in a series of ten consecutive measurements (each is depicted with its own color). Sequence of measurements is from top to bottom.

#### **4. The E**ff**ect of Translation Stage Errors on Terahertz Spectra**

For a start, an assessment of the distortions caused by the increasing position offset, i.e., a systematic error of the first type is made. We estimate the effect for one of the stages as an example. It has an offset of 16 μm in the range of 40 mm (see the red line in Figure 3a). The observed offset can be approximated by a straight line with a slope of α = –0.0004. Let *E*(*t*st) denote the amplitude of the terahertz signal. It depends on the time delay corresponding to the position of the translation stage. Time delay measured by the optical encoder *t*en can be expressed with the formula *t*en = *t*st + α*t*st. Therefore, the amplitude of the THz pulse equals *E*(*t*en /(1+α)) = *E*(α1*t*en), where α<sup>1</sup> = 1.0004. We can see that the measured time-domain signal is stretched by the factor of α<sup>1</sup> along the time axis. From the properties of the Fourier transform, it is clear that the spectrum is linearly squeezed along the frequency axis by the same factor. For example, for the frequency of 1 THz the corresponding frequency shift is 400 MHz. Such distortion becomes especially noticeable in spectra with narrow absorption lines.

Let us consider the influence of the second type of systematic error, i.e., oscillating mismatch between the optical encoder measurements and the position of the translation stage (see Figure 3b). According to [17], periodic positioning error leads to the emergence of spurious spectra. These spectra are mirror copies of the true spectrum of the THz pulse emerging around the frequency of the periodic error and its harmonics. In our case, the oscillation period of 250 μm corresponds to 1.67 ps in the time domain, which leads to the appearance of spurious spectra around the frequency of 600 GHz and its harmonics. The amplitude of the spurious spectra is proportional to the amplitude (~5 fs) and the frequency (600 GHz) of the periodic error according to the theoretical estimations in [17]. Thus, the proportionality coefficient can be calculated <sup>≈</sup> 3·10-3. The obtained value is comparable with the signal-to-noise ratio of the THz spectrometer, which makes it difficult to detect.

The third error, the drift of the initial position of the translation stage in a series of measurements, affects averaging over a series of terahertz spectra [14]. In this case, an increase in the number of measurements does not lead to an increase in the signal-to-noise ratio [10].

#### **5. Correction**

More accurate data from the optical encoder can be used to correct systematic errors of the delay line as well as errors due to the mechanical defects in the translation stage screw. For this, the THz electric field sampled at each position of the delay line is associated with the position more accurately measured by the optical encoder. Then by interpolation, the equidistance of the sampling positions is restored. As a result, the corrected waveform of the terahertz pulse is based on the positions measured with the optical encoder and does not contain systematic errors associated with the translation stage. The results of the correction algorithm that eliminates the systematic errors of the first and the second types are presented in Figures 5 and 6, respectively.

**Figure 5.** Terahertz (THz) spectra near two water vapor absorption lines before (black line) and after (red line) applying the correction: (**a**) 0.557 THz (**b**) 1.411 THz.

**Figure 6.** Spectra of THz pulses passed through bandpass filters with the central frequency: (**a**) 224 GHz (black line), 264 GHz (red line), and 312 GHz (blue line), arrows indicate the frequencies of the spurious spectra (**b**) 376 GHz before (black line) and after (red line) correction.

In Figure 5 one can see an example of distortion caused by the error of the first type. We measure terahertz spectrum in the atmosphere containing water vapor that has many rotational absorption lines in the terahertz spectral range [5]. Thus, we can observe the effect of the error by studying THz spectra near two absorption lines of water vapor at 0.557 THz (Figure 5a) and at 1.411 THz (Figure 5b). As expected from the analysis of this error, the spectral shift increases with increasing frequency. It amounts to ~500 MHz for the line at 1.411 THz. Corrected spectra appear to be closer to the tabulated values of water absorption lines in HITRAN database [23] than the uncorrected ones.

We test the influence of the systematic error of the second type by measuring spectra of terahertz pulses passing through high-contrast quasi-optical bandpass filters. The filters are designed as multilayer frequency selective surfaces produced with technologies of photolithography and electroplating [24,25]. They were originally developed for spectro-radiometric applications in electron-beam-plasma experiments on generating high-power sub-terahertz radiation [25,26]. The filters have a bandwidth of 12%–20% and out-of-band transmission of ~10-4. Such filters provide us with an opportunity to clearly observe spurious terahertz spectra since they have a pronounced peak and near-zero out-of-band transmission.

Figure 6a shows the spectra of terahertz pulses passing through high-contrast bandpass filters with the center frequencies of 224, 264, and 312 GHz. It can be seen how the systematic error of the second type leads to the emergence of spurious spectra. The central frequencies of the false spectral features are 600 ± ν where 600 GHz is the frequency of the periodic error and ν is the filter frequency. Figure 6b shows the spectra for 376 GHz filter before and after correction. Its amplitude is ~580 times smaller than the amplitude of the main spectral feature and is practically at the noise level of the spectrometer.

Lastly, we consider the systematic error of the third type. The drift of the initial position by 1 μm measured by the optical encoder (see Figure 4) should correspond to the time shift of 6.7 fs. However, such shift is barely noticeable in the waveforms of consecutively measured terahertz pulses (see Figure 7).

**Figure 7.** Waveforms of ten consecutively measured THz pulses presented in the ranges of 5–40 ps (main figure) and 14–16.5 ps (inset).

For clarity, we compare the initial position drift measured by encoder and time drift of THz pulses on the same scale in Figure 8. The drifts are calculated relative to the first measurement in the series. It can be seen that it takes more than 5 measurements until encoder position drift settles down at –3.5 μm. In contrast, time drift of THz pulses is significant only between the first and the second measurements due to translation stage backlash. Apparently, this discrepancy is associated with the heating of the stepper motor and translation stage platform during operation and the thermal expansion of the optical encoder scale. Heating by 1 ◦C leads to a shift of ~1 μm at the free end of the scale. As a result, setting the initial position based on counting steps of the translation stage stepper motor turns out to be more accurate than based on the optical encoder data. Residual THz time drift can be algorithmically compensated by time shift and interpolation of the signals [20,21].

**Figure 8.** The drift of the initial position measured by the optical encoder (black squares) and measured based on the time shift of terahertz pulses (red triangles) relative to the first measurement.

#### **6. Conclusions**

In the work, we upgraded translation-stage-based optical delay line of the terahertz time-domain spectrometer. Additionally, we installed the optical encoder that made it possible to get more accurate information on the position of the translation stage during the terahertz measurements. We were able to study systematic errors associated with the translation stage without the optical encoder. We also used encoder positioning data to programmatically correct these errors. The proposed method is similar to interferometry-aided terahertz spectroscopy. However, the encoder is cheaper, easier to install and operate while having comparable accuracy.

Using the encoder, we detected three different types of systematic errors in the optical delay line. Firstly, an increasing difference in positions measured by the stepper motor of the translation stage and the optical encoder. This error led to a linear distortion of terahertz spectra along the frequency axis, which is especially critical in gas spectroscopy. Secondly, a periodic positioning error associated with the revolution of the translation stage screw was observed. It was shown that this error led to the appearance of spurious spectra having amplitude on the order of ~10-3 compared to the main pulse spectrum near the frequency of 600 GHz. The appearance of the spurious spectrum was demonstrated by studying the transmission of a band-pass filter with a central frequency of 376 GHz. Thirdly, in a series of ten consecutive measurements of terahertz pulses with the same delay line, a shift in the initial position of the translation stage was detected. Apparently, this effect appeared due to the heating of the stepper motor and translation stage platform during operation, which led to the heating of the optical encoder measuring scale.

It was shown that the measurements by the easy-to-use optical encoder can be employed to correct the first two types of positioning errors. In addition, the correction allowed us comprehensive elimination of the influence of scratches, damages, and other mechanical defects of the translation stage screw on the measured position. To correct the error of the initial position and increase the signal-to-noise ratio, it was proposed to use software correction methods.

**Author Contributions:** Conceptualization, P.C. and A.M.; Methodology, P.C. and A.M.; Software, F.M.; Validation, A.M., F.M., and L.M.; Formal analysis, A.M., F.M., and L.M.; Investigation, F.M. and N.N.; Resources, N.N.; Data curation, F.M.; Writing—original draft preparation, F.M. and A.M.; Writing—review and editing, A.M., P.C., and N.N.; Visualization, F.M. and A.M.; Supervision, P.C.; Project administration, P.C.; Funding acquisition, P.C.

**Funding:** This research was funded by the Russian Science Foundation (RSF), grant number 17-12-01418.

**Acknowledgments:** The authors would like to thank Sergey Kuznetsov for providing bandpass terahertz filters for 224, 264, 312, and 376 GHz.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Design of a 335 GHz Frequency Multiplier Source Based on Two Schemes**

**Jin Meng 1,\*, Dehai Zhang 1, Guangyu Ji 1,2, Changfei Yao 3, Changhong Jiang <sup>1</sup> and Siyu Liu 1,2**


Received: 3 July 2019; Accepted: 25 August 2019; Published: 28 August 2019

**Abstract:** Based on a W-band high-power source, two schemes are proposed to realize a 335 GHz frequency multiplier source. The first scheme involves producing a 335 GHz signal with a two-stage doubler. The first doubler adopts two-way power-combined technology and the second stage is a 335 GHz doubler using a balanced circuit to suppress the odd harmonics. The measured output power was about 17.9 and 1.5 dBm at 167.5 and 335 GHz, respectively. The other scheme involves producing a 335 GHz signal with a single-stage quadrupler built on 50 μm thick quartz circuit adopting an unbalanced structure. The advantage of the unbalanced structure is that it can provide bias to the diodes without an on-chip capacitor, which is hard to realize with discrete devices. The measured output power was about 5.8 dBm at 337 GHz when driven with 22.9 dBm. Such 335 GHz frequency multiplier sources are widely used in terahertz imaging, radiometers, and so on.

**Keywords:** cascaded doubler; quadrupler; Schottky varactor; hybrid integrated circuit

#### **1. Introduction**

In recent decades, terahertz technology has been used for a variety of applications such as radio astronomy, remote sensing of the Earth's atmosphere, radar imaging, etc. [1–5]. Furthermore, advances in terahertz sources and detectors have facilitated the development of these terahertz applications. As for terahertz sources, the methods mainly include the extension of microwave electronics towards high frequencies on one side and the development of photonic devices from the optical region towards low frequencies. In general, the frequency multiplier chain is the typical electronic method that can work at room temperature.

Some leading overseas research institutes such as the Jet Propulsion Laboratory (JPL) have been able to realize solid-state frequency multiplier sources above 1 THz, which can produce tens of microwatts of power [6,7]. Furthermore, several competing technologies have been proposed in the semiconductor frequency multiplier field. In comparison, domestic research on frequency multipliers has mainly focused on the hybrid integrated circuits with discrete Schottky diodes, with an operating frequency around 200 GHz [8–10].

Based on a W-band high-power source, detailed in our former research, two schemes are proposed to design a 335 GHz multiplier. The first solution consists of a W-band source, two cascaded 167.5 GHz doublers, and a 335 GHz doubler. Another solution is to replace the two-stage doubler with a single-stage quadrupler. The details of the modules mentioned above are discussed further in this paper.

#### **2. General Scheme**

Increasing the efficiency and power capability of the frequency multiplier is the common way to obtain high output power [11–13]. For the diodes used in this paper, the safe input power was 24 dBm for a single multiplier. Therefore, power-combined technology was adopted to increase the effective input power. Figure 1 shows the diagram of a 335 GHz solid-state source with different schemes.

**Figure 1.** (**a**) Block diagram of the 335 GHz frequency multiplier based on a two-stage doubler. (**b**) Block diagram of the 335 GHz frequency multiplier based on a single-stage quadrupler.

A frequency multiplier of order N converts the input sinusoidal signal of frequency F1 and power P1 to an output sinusoidal signal of frequency FN = N × F1 and power PN. Hence, the conversion efficiency of the frequency multiplier is defined as the ratio of PN to P1. For a chain (×N1×N2) of two cascaded multipliers of respective order N1 and N2, the conversion efficiency of the chain is η (N1, N2). A high-order frequency multiplier of order N3 = N1 × N2 usually has a conversion efficiency η (N3) < η (N1, N2) and η (N1, N2) = η (N1) × η (N2). Therefore, in theory, the efficiency of scheme (a) in Figure 1 is higher than that of scheme (b).

Furthermore, the relation of η (N1, N2) = η(N1) × η(N2) is valid only when there is no reflected power by the second multiplier. Besides, the mismatch of the interface between the cascaded multipliers caused by dimension error and assembly error could lead to a loss of power. Consequently, the efficiency of the chain × N1×N2 is not necessarily more than that of the chain × N3 in practical application.

#### **3. Basic Principle of Schottky Diode**

The Schottky barrier diode is a two-port device that is important to terahertz frequency multipliers. The diode can be divided into two modes based on operating principle: varistor and varactor. In general, the structure of a Schottky varactor is qualitatively the same as that of a varistor diode. However, the epitaxial layer of the varactor is thicker than that of the varistor, which could increase the breakdown voltage to maximize capacitance variation [14]. Figure 2 shows the cross-sectional view of the Schottky diode. The varistor makes use of a nonlinear resistance characteristic for the mixer, and the varactor is used for frequency multipliers by using a nonlinear capacitance characteristic. The upper part of Figure 2 shows the nonlinear curves of the varistor and varactor.

**Figure 2.** Structures and operating principles of the Schottky varistor and varactor.

The diode consists of intrinsic and parasitic parameters. When the frequency increases to the terahertz range, the parasitic parameters of the diode cell caused by its physical structure play an important role in affecting the performance of the frequency multiplier. Hence, the electromagnetic field around the diodes is calculated with full-wave simulation software. As for intrinsic parameters, these primarily include series resistance, zero bias junction capacitance, barrier voltage, and ideal factor. These parameters can be obtained from the IV (Intensity and voltage) or CV (Capacitance and voltage) curve.

#### **4. Design of 335 GHz Source Based on Two-Stage Doubler**

The three-dimensional model of a 335 GHz source with cascaded balanced frequency doublers is presented in Figure 3. As shown in the graph, the frequency multiplier is a split-block waveguide design, and a suspended microstrip circuit based on a 50 μm thick quartz substrate is mounted in the channel between the input and output waveguide. The varactor chips are mounted on the suspended microstrip circuit with silver epoxy.

**Figure 3.** The three-dimensional model of the 335 GHz source based on a two-stage doubler.

#### *4.1. W-Band High-Power Source*

The W-band power source driven by the 167 GHz doubler, which mainly includes a sextupler, a power amplifier, and a four-way power-combining module. The composition block diagram is

shown in Figure 4. The sextupler employs a commercially available GaAs MMIC chip HMC1110 fabricated by Analog Devices Company (Norwood, MA, USA), and the power amplifier uses an MMIC chip MAAP-011106 fabricated by M/A-COM Technology Solutions Inc (Lowell, MA, USA). Finally, the measured results indicate that the output power is more than 25 dBm at 81–86 GHz, and that the output power is about 27.5 dBm at 83 GHz when driven by 3 dBm of input power.

**Figure 4.** The block diagram of the W-band source.

#### *4.2. Two-Way Power-Combined 167 GHz Frequency Multiplying Source*

Considering the technical requirements and cost, the 167 GHz high-power frequency multiplying source adopts a two-way power-combined scheme. As depicted in Figure 5, the power source includes a power divider/combiner and two identical doublers.

**Figure 5.** The structure of the 167 GHz doubler based on the two-way power-combined technology.

The power divider used in the 167 GHz high-power frequency multiplying source is a Y-type waveguide divider and the phase difference between the two output signals is zero. Furthermore, the second harmonic produced by the doublers has the same phase, and can be combined by using a Y-type waveguide combiner at the output ports. Figure 5 shows the phase relationship of each part in the two branches using the red arrow. Actually, the Y-type power combiner can be regarded as a combination of two-phase shifters and an E–T-type combiner, and the function of the phase shifter is to change the phase of the two-way signal from the same direction to the reverse direction for the T-type combiner.

Generally, the frequency doubler is designed to convert a pump microwave signal to its second harmonic based on the nonlinear voltage-dependence of the diode junction capacitance of the Schottky varactor. To suppress the odd harmonics, the diode array adopted has an anti-series type configuration. The incident signal with the dominant mode of the input rectangular waveguide (TE10) feeds the anti-series diode array. In contrast, the second harmonic would propagate along the suspended microstrip line in an unbalanced mode (TEM). In the 167 GHz doubler design, a 5VA40-13 diode chip provided by Advanced Compound Semiconductor Technologies (Hanau, Germany) was selected, which comprises a linear array of three Schottky junctions. The dimension of the chip is 240 × 60 μm (length and width, respectively) and the semi-insulating GaAs substrate is 35 μm thick.

The equivalent circuit of the balanced doubler is described at the top right of Figure 5. Based on the IV characteristic of the Schottky diode, the output current i can be expressed as [15]:

$$\mathbf{i} = \mathbf{i}\_1 + \mathbf{i}\_2 = -\mathbf{i}\_\theta (\mathbf{e}^{-\alpha V\_{\text{in}}} - 1) - \mathbf{i}\_\theta (\mathbf{e}^{\alpha V\_{\text{in}}} - 1) = -2\mathbf{i}\_\theta [\cos \mathbf{h}(\alpha V\_{\text{in}}) - 1] \tag{1}$$

where is represents the reverse saturation current and Vin represents the junction voltage across the Schottky contact. By using Fourier expansion, Formula (1) is decomposed as follows:

$$\mathbf{i} = \mathbf{i}\_6[2\mathrm{I}\_0(\alpha \mathbf{V}\_{\mathrm{in}}) - 2] + 4\mathbf{i}\_3[\mathrm{I}\_2(\alpha \mathbf{V}\_{\mathrm{in}})\cos\left(2\omega\mathbf{u}\mathbf{v}\right) + \mathbf{I}\_4(\alpha \mathbf{V}\_{\mathrm{in}})\cos\left(4\omega\mathbf{u}\mathbf{v}\right) + \cdots] \tag{2}$$

where In (αVin) is the Bessel function of the first kind. Similar to the computational method of the output current, the current in the loop can be expressed as:

$$\mathbf{i}\_{\rm loop} = \mathbf{i}\_1 - \mathbf{i}\_2 = 4\mathbf{i}\_6 [\mathbf{I}\_1(\alpha \mathbf{V}\_{\rm in}) \cos \left(\omega \mathbf{u} \mathbf{t}\right) + \mathbf{I} \mathbf{j} \left(\alpha \mathbf{V}\_{\rm in}\right) \cos \left(\mathbf{3} \omega \mathbf{u} \mathbf{t}\right) + \cdots]. \tag{3}$$

From the calculated results, it can be seen that the odd harmonics are suppressed in the output circuit, and thus the second harmonic can be obtained at the output waveguide by using the matching circuit.

#### *4.3. 335 GHz Doubler Based on Discrete Schottky Varactor*

Considering the rise of working frequency, the varactor used in the 335 GHz doubler requires a smaller zero bias junction capacitance, and therefore obtains higher cut-off frequency. At the same time, the dimension of the diode chip must be reduced to match the width of the waveguide channel. Finally, the diode chip 137C from Virginia Diodes Inc (Charlottesville, VA, USA). with four anodes in anti-series configuration was applied in the design. To improve the performance of RF ground, the flip-chip mounted method was adopted. The diode chip was glued on the ground points, which are two gold belts on either side of the quartz substrate.

The design process of the 335 GHz balanced doubler is shown in Figure 6. First of all, the impedances of the diode at fundamental and second harmonic are optimized by using source and load-pull under ideal conditions. The diode optimum impedance was found to be Zsource = 33 − j37 Ω and Zload = 16 − j23 Ω. To improve the accuracy of simulation, the field-circuit method is applied in the design process [16,17]. Hence, the doubler is divided into two parts: a linear network, which is analyzed using the finite element method in consideration of the parasitic effects, and the nonlinear behavior of the varactor solved by the harmonic balance method. To reduce the complexity of the problem, the linear part is broken up into three sections: input transition at fundamental and second frequency, output transition, and matching circuit. The signal is coupled through a waveguide-microstrip structure, and the locations of Schottky diodes junction are inserted based on the port impedances (at fundamental frequency) acquired from step 1. Generally, the length of the reduced-height waveguide and location of the input back-short are optimized to achieve a small return loss in the input port. The second harmonic passes through the region between the diodes and input back-short and then is coupled into the output line by matching circuit. Another probe located in the output circuit couples the second harmonic to the standard output waveguide. The abovementioned design process refers to steps 2–5. In the next step, the generated SNP files are imported to the Advanced Design System (ADS) circuit and the characteristic of the diode is added in the nonlinear circuit. Furthermore, the optimization procedure is achieved based on harmonic balance analysis. Finally, the three-dimensional model of the doubler is built according to the optimized results and the calculated S parameter of the complete circuit is exported to the ADS. Now, the doubler model is regarded as a 7-port network. The simulated result of a doubler working at 335 GHz is described at the right side of Figure 6. It clear that the odd harmonics are suppressed in simulation, and that the results coincide with those obtained by Equations (1)–(3).

**Figure 6.** Design process of a 335 GHz balanced doubler with the field-circuit method.

#### **5. Design of 335 GHz Source Based on Single-Stage Quadrupler**

If varactor currents are allowed only at the input and output frequencies, a Schottky diode with ideal CV characteristics cannot generate harmonics higher than the second harmonic. To generate higher harmonics, it is necessary to allow idler currents to flow in the varactor, which could be produced by frequency doubling or frequency mixing.

For a quadrupler, one way to obtain higher harmonics is by doubling and then producing a fourth harmonic by doubling again. Another way is by mixing the second harmonic idler with the fundamental to produce the third harmonic idler first, and by continuing to mix to produce the fourth harmonic output. Actually, the high-order multipliers are most efficient when idler circuits are provided at all idler frequencies. Therefore, the use of idlers could increase the output power and efficiency of reactive frequency multipliers.

The quadrupler has a suspended microstrip circuit based on a 50 μm thick quartz substrate mounted in the channel with silver epoxy. The input and output ports of the quadrupler are standard full-height WR-12 and WR-2.8 waveguides with waveguide dimensions of 3.1 <sup>×</sup> 1.65 mm<sup>2</sup> and 0.71 <sup>×</sup> 0.355 mm2, respectively. As described in Figure 7, a compact suspended microstrip resonator (CSMR) low-pass filter follows an input conversion structure (the simulated return loss is below −20 dB from 75 to 90 GHz), and hence the fourth harmonic produced by varactors could prevent leaking from the input port. Compared with the step impedance filter, the CSMR filter has a compacted structure and wide stop band [18]. The simulated result of the CSMR filter in the band of 30–350 GHz are shown in Figure 7. It can be seen from the graph that the insert loss is lower than 0.3 dB in the pass band, while the side rejection is better than 20 dB from 160 to 350 GHz. Finally, another probe located in the output circuit couples the fourth harmonic to the standard output waveguide, and the simulated return loss is better than 15 dB in the frequency range of 320–360 GHz. All passive networks, such as the low-pass filter, input and output waveguide-to-microstrip transition, and diode passive part, are analyzed by EM simulators. When the sub-circuits are optimized, the complete quadrupler circuit is simulated. The nine port S-parameters of this simulation are extracted and then combined with a nonlinear diode to model the multiply efficiency in the circuit simulator. This process is usually repeated for the further optimization of the quadrupler multiply efficiency.

#### **6. Measurements and Discussion**

The block diagram of the measurement setup is illustrated in Figure 8. An Agilent analog signal generator E8257D (Santa Clara, CA, USA) is followed by the W-band power source to generate the signal in the 81–86 GHz band. The output power of the frequency multipliers is measured by a PM4 power meter (Charlottesville, VA, USA). Moreover, a Sub-Miniature-A (SMA) (type KFD55(Xi'an, China)) is connected to the main transmission circuit using gold wire bonding and an external sliding rheostat connected to the SMA port so as to bias the varactor.

**Figure 8.** (**a**) Photo of the assembled 335 GHz source with two cascaded doublers. (**b**) Photo of the assembled 335 GHz source with a single-stage quadrupler.

Figure 9a shows the measured results of the W-band source. The measured output power is more than 310 mW from 81 GHz to 86 GHz, and the maximum power is about 560 mW at 83 GHz. In the measurement of the quadrupler, the input power is about 200 mW to make sure the diodes work safely, and hence an attenuator is added. The measured output power of the 167 GHz power-combined doubler is shown in Figure 9b. It was found that the power is more than 45 mW at 164–172 GHz, and the highest output power is 62 mW at 167.5 GHz.

**Figure 9.** (**a**) Measured output power of the W-band source. (**b**) Measured output power of the 167 GHz high-power source. (**c**) Measured input and output power of the 335 GHz source based on a two-stage doubler. (**d**) Measured input and output power of the 335 GHz source based on a single-stage quadrupler.

The measured results of the 335 GHz source based on two cascaded doublers are shown in Figure 9c. The measured output power of the 335 GHz doubler is more than 0.5 mW at 328–337 GHz and the maximum output power is about 1.4 mW at 333 GHz. The relation of the single-stage quadrupler 335 GHz source output versus pumping power is described in Figure 9d. The measured typical output power is 2.5 mW at 332–344 GHz, and the highest measured output power of 3.8 mW is measured at 337 GHz with an input power of 198 mW.

Tables 1 and 2 illustrate a comparison of some reported multipliers. A recent development of terahertz solid circuits in China caused a regression in advanced semiconductor technology such as Schottky diode technology, membrane technology, transferred substrate technology, and so on. The result is that an integrated circuit is difficult to realize and the design of the frequency multiplier needs to use a discrete circuit with a higher loss transmission line. The performance of the frequency multipliers presented in this paper reached the same level as that achieved by research institutions abroad, and has a leading position at home. Furthermore, the design using discrete diodes is easy to realize and the cost is relatively low.




**Table 2.** Performance comparison of the frequency multipliers above 300 GHz.

To ensure that the 167 GHz doubler is working safely, the input power produced by the W-band source is controlled below 280 mW and the typical output power of the doubler is, accordingly, 55 mW. Hence the typical efficiency of the 167 GHz doubler is about 20%. The typical efficiency of the 335 GHz doubler is 2% with typical input and output power values of 55 and 1.1 mW, respectively. To summarize, the efficiency of the frequency multiplier chain is about 0.4%. In contrast, the typical input and output power values of a single-stage quadrupler are 190 mW and 2.8 mW, and said quadrupler has a higher efficiency of about 1.5%. However, it is difficult to say whether it is better to realize a high-order multiplier via a single-stage process or by a cascade of two or more low-order multipliers. The decision could be made in accordance with specific conditions.

#### **7. Conclusions**

A solid-state frequency multiplier chain based on two schemes has been designed and tested in this paper. For the first option, the measured highest output power was about 1.4 mW at 333 GHz and more than 0.5 mW at 328–337 GHz. For the second option, the measured typical output power was 2.5 mW at 332–344 GHz, and the highest measured output power was 3.8 mW at 337 GHz. The research content provides the means to generate a terahertz signal above 300 GHz. Our future work will aim at the design of a G-band, higher output power source, and at the increased efficiency of the frequency multiplier working in the sub-millimeter region.

**Author Contributions:** Conceptualization, methodology, software, and writing, J.M., D.Z., and G.J.; formal analysis, C.Y. and C.J.; visualization, J.M. and S.L.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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