High-T_c Superconducting Josephson Junction Harmonic Mixers with Stub Tuners on Integrated Bowtie Antennas

Abstract

Ordinary mixers can hardly meet the requirements in terahertz (THz) communications due to the low-power and expensive THz sources. Sensitive harmonic mixers have been widely studied to avoid this problem, owing to the fact that the higher the number of harmonics, the lower the local oscillator (LO) frequency, and the lower the cost. High-T_c superconducting (HTS) Josephson junction (JJ) mixers are performing candidates for THz receiver frontends because of the advantages of excellent sensitivity, wide bandwidth, high harmonic number and low LO power requirement. However, the normal-state resistance of HTS JJ is so low that traditional antennas are difficult to match it. In other words, it is quite a challenge to match the input impedance to a low input impedance for traditional antennas, especially for antennas fed by coplanar striplines (CPSs). In this work, based on the structure of bowtie, two types of stub tuners were integrated to decrease the impedance of the bowtie antenna so as to improve the coupling efficiency between the traditional bowtie antenna and the JJ. Furthermore, HTS YBa₂Cu₃O_7-δ (YBCO) JJ harmonic mixers coupled with the proposed structures and fed by CPSs are fabricated and measured. The measurements show that the JJ mixer coupled with a pair of open-end stubs of the bowtie antenna achieves up to 88 harmonics, with a conversion efficiency of −69.6 dB. In contrast, the JJ mixer coupled with a pair of lumped-element stubs of the bowtie antenna only attains to 30 harmonics, with a conversion efficiency of −73.4 dB. Additional numerical simulations indicate that the coupling efficiency is enhanced when the complex impedance of the antenna is explicitly considered. Compared with other coupled traditional antennas, the JJ mixer with bowtie antenna has the largest harmonic number. This work paves the way for the future application of low-frequency and low-cost LO for THz communications.

1. Introduction

Thanks to the considerable absolute bandwidth, terahertz (THz) communication promises to have the advantages of large capacity, high transmission rate, high security, strong directivity and good penetration. However, due to the serious atmospheric attenuation in THz bands [1], the effective detection of ultrasensitive THz receivers is highly demanded. Due to the limitation of low power and high cost of THz source, harmonic mixer is more popular than fundamental mixer. The higher the number of harmonics, the lower the frequency and cost of the local oscillator (LO).

Semiconductor-based THz heterodyne receivers, generally operating at room temperature, have been widely developed using Schottky barrier diodes [2], high-electron-mobility transistors [3], complementary metal-oxide-semiconductor [4] and silicon-germanium [5] technologies. However, the maximum harmonic number up to 20 is from the Schottky barrier diode produced by Virginia Diodes, Inc. (VDI) [6]. Nowadays, high-T_c superconducting (HTS) YBa₂Cu₃O_7-δ (YBCO) Josephson junction (JJ) is becoming the most attractive harmonic mixer for THz heterodyne receiver, caused by the advantages of excellent sensitivity, wide bandwidth, high harmonic number and low LO power requirement [7]. Broadband antennas with complementary structure have been extensively used in superconducting mixers to enhance the THz signal coupling, such as log-periodic and log-spiral antennas [8]. However, the impedances of this kind of antennas are very high (approximately 188.5 Ω with self-complementary structure in free space), while the normal-state resistances of the YBCO JJs are only several ohms, still resulting in the low coupling efficiencies between antennas and JJs. Thus, the maximum harmonic number cannot be improved in the mixing because of the impedance mismatch. Recently, many works have been reported to enhance the mixing performance of YBCO JJ mixers, including the harmonic number in the mixing [9,10,11]. It shows that the maximum harmonic number from YBCO step-edge JJ is around 30, a bit higher than that with a semiconducting THz mixer. Thus, the enhancement of the maximum harmonic number of the YBCO JJ mixer urgently needs to be explored for THz communications.

In reported traditional antennas, slot antennas [12,13,14,15] were the main choices to match the impedance of JJ, such as double-slot antenna [16] and ring-slot antenna [17,18]. However, these kinds of antennas have to be fed by coplanar waveguide (CPW), meaning the shape of the ground has to be changed during the impedance matching. The impedance matching to a low-input impedance based on traditional antennas with coplanar striplines (CPSs) feeding for a JJ mixer is little reported. The influence of ground shape on the antenna impedance would no longer be considered if the differential CPSs were adopted. The bowtie structure was first proposed by George et al. [19] and applied to many THz detectors [20,21,22,23,24]. Because of the simple structure and low cost, it is a good choice to match the impedance with YBCO JJ mixer and feed it by CPSs. Traditional bowtie antennas often have impedances as high as hundreds of ohms.

In this paper, we adopt two types of stub tuners on bowtie antennas to reduce antenna impedances. The performance of YBCO bicrystal JJ harmonic mixers coupled with these two antennas and fed by CPSs are reported, respectively. Since one of the THz windows is located at 0.21 THz [1], we study the maximum harmonic number of mixers at 0.21 THz. Up to the 88th harmonic has been measured in the mixing when one mixer is coupled with a pair of open-end stubs of the bowtie antenna, while the other one, which coupled with a pair of lumped-element stubs of the bowtie antenna, has a maximum harmonic number of 30. Later, numerical simulations are carried out to analyze the reasons for different performance.

2. Materials and Methods

2.1. Silicon Lens for Eliminating Thick Substrate Modes

THz antenna on thick dielectric suffers power loss because of substrate modes, shown in Figure 1a. More than 90% of the radiated power is trapped in the dielectric [25]. If the substrate thickness can be made infinite, the loss in the substrate mode can be eliminated. Additionally, the infinite dielectric can be synthesized by a lens with the same dielectric constant attached to the antenna substrate [26]. The substrate lens can be hemispherical, hyper-hemispherical and elliptical, seen in Figure 1b–d. As hyper-hemispherical lens [27,28] is widely used and easier to design, we focus on the hyper-hemispherical lens in our study.

If a dielectric hemisphere is attached to the back of the substrate with the same relative permittivity as the interface between them, there will be no refraction or reflection. All radiated rays will directly strike the circular surface of the hemisphere without any disturbance, and there will be only loss due to the reflection loss [29]. This type of lens is called hemispherical lens, shown in Figure 1b. By introducing a matching layer of quarter wavelength, this loss can be eliminated or minimized, the layer is called anti-reflection (AR) coating. If the hemisphere lens is extended by adding a cylinder with the same diameter and attached with the antenna then it is called the hyper-hemispherical lens, shown in Figure 1c. The thickness of this cylinder is called the extension length of the lens.

As the superconducting YBCO film was deposited on a bicrystal magnesium oxide (MgO) substrate with the dielectric constant of 9.6, the high-resistivity, float-zone (HRFZ) silicon (Si), whose dielectric constant of 11.9 is close to that of MgO, is chosen to prepare the hyper-hemispherical lens. Furthermore, the loss tangent of HRFZ Si can be ignored in THz band.

$$\tan \delta =\frac{1}{\omega ·{\epsilon }_{\mathrm{v}}·{\epsilon }_{\mathrm{r}}·R}$$

(1)

Loss tangent is calculated according to the Formula (1) [30], where $\omega$ is the circular frequency, ${\epsilon }_{\mathrm{v}}$ is the dielectric constant of vacuum (8.85 $\times {10}^{-12} \mathrm{F}/\mathrm{m}$), ${\epsilon }_{\mathrm{r}}$ is the relative permittivity of Si (11.9), and $R$ is the specific resistance. For example, loss tangent of HRFZ Si with a resistivity of 10 kΩ cm at 1 THz is 1.5 $\times {10}^{-5}$.

$$L_{\mathrm{h}}=R_{\mathrm{L}}/n_{\mathrm{r}}$$

(2)

The hyper-hemispherical lens can be designed by Equation (2) [31], where $L_{\mathrm{h}}$ is the length of the extension, $R_{\mathrm{L}}$ is the radius of the hemisphere and $n_{\mathrm{r}}$ is the refractive index of the lens, which is equal to $\sqrt{{\epsilon }_{\mathrm{r}}}$. In the literature [26], by changing the diameter of the hyper-hemispherical lens from 4 mm to 9 mm, the directivity increases with the increase in diameter in the low-frequency band of THz. Thus, we make the radius of the hyper-hemispherical lens of 4.5 mm. According to Equation (2), the extension length of the lens should be 1.3 mm. However, due to the thickness of the integrated chip being 0.5 mm or 0.6 mm, the extended length of the customized hyper-hemispherical lens is 0.7 mm.

$$n_1=\sqrt{n_2·n_0}$$

(3)

AR coating of the substrate lens should have a thickness of a quarter wavelength (${\lambda }_{\mathrm{air}}$/4), and the refractive index of the coating material meets the Formula (3) [26], where $n_1$, $n_2$ and $n_0$ are the refractive indexes of AR coating, Si and the air, respectively. Thus, the thickness of the AR coating is 357 μm at 0.21 THz, and $n_1$ equals to 1.86.

As the beam pattern is mainly controlled by the lens, a simple bowtie structure (Antenna 1 below) on a hyper-hemispherical lens with above parameters (${\epsilon }_{\mathrm{r}}$ = 11.9, $R_{\mathrm{L}}$ = 4.5 mm, $L_{\mathrm{h}}$ = 1.3 mm, $n_1$ = 1.86, ${\lambda }_{\mathrm{air}}$/4 = 357 μm at 0.21 THz) was modeled and simulated to get the directivity in the electromagnetic simulator Computer Simulation Technology (CST) Microwave Studio (MWS). In order to save simulation time, the number of mesh cells across stubs is 3 or 4 in x or y coordinate direction. A discrete port with 20 Ω is set to feed the bowtie antenna. Time domain solver based on finite integration technique is chosen with the accuracy set of −50 dB. As a result, the model and the radiation pattern are created and shown in Figure 2. The green-colored shape is the AR coating with the thickness of 357 μm and the relative permittivity of 3.45. The simulation shows that the directivity of the Si hyper-hemispherical lens with the above parameters attains 21.48 dBi at 0.21 THz.

2.2. On-Chip Layout Design

The mixer chip often contains direct current (DC) bias lines, electrodes and so on. Figure 3a,b show the presented geometry of the on-chip layout. Stub tuners are loaded at different positions on bowtie antennas, integrated with YBCO bicrystal JJs. The arm length $l$ and width $w$ of the bowtie are 135 μm and 515 μm, respectively. A pair of stubs with length of $l_{\mathrm{s}1}$ = 30 μm, width of $w_{\mathrm{s}1}$ = 30 μm and an interval of 10 μm, acting as lumped elements [32], are put in the middle of the bowtie, which forms as Antenna 1. Another pair of stubs with length of $l_{\mathrm{s}2 }$ = 225 μm, width of $w_{\mathrm{s}2}$= 10 μm and an interval of 10 μm, placed vertically in the middle of another bowtie, have open ends [33]. Thus it forms as Antenna 2. In addition, electrodes, DC bias lines, and choke filters [34] are integrated on a MgO substrate with the dielectric constant of 9.6. The DC bias lines are connected to the part of bowtie with the weakest current distribution to prevent alternating current (AC) power leakage from the antenna. Choke filter with a bandgap structure [35] is applied on the DC bias lines to avoid AC power leakage to the CPSs. The optimized parameters at 0.21THz by CST MWS are as follows: $d$ = 32 μm,$l_0$ = 246 μm,$w_0$ = 15 μm, $l_1$ = 165 $\mathsf{\mu }$m,$w_1$ = 90 μm, $l_2=l_3$ = 90 μm and $l_4=l_5$ = 135 μm. The length of each section of choke filter is ~${\lambda }_{\mathrm{g}}$/4 [36] with

$${\lambda }_{\mathrm{g}}={\lambda }_0/\sqrt{\left(1+{\epsilon }_{\mathrm{r}}\prime \right)/2}$$

(4)

where ${\lambda }_0$ is the wavelength in free space, and ${\epsilon }_{\mathrm{r}}\prime$ is the dielectric constant of the substrate. As seen in Figure 3c, currents leaked from both antennas are effectively blocked by choke filters, respectively. At the other ends of CPSs, four electrodes are applied in the four-terminal measurement to exclude the influence of contact resistance.

2.3. Fabrication and Experimental Setup

The 80 nm-thick YBCO film with a 20 nm in situ Au film on top was deposited on the MgO substrate with a bicrystal misorientation angle of 24° and the thickness of 0.5 mm by pulsed laser deposition. The critical current density J_c of the YBCO film is 2.5 mA cm⁻², and the critical temperature T_c is 85.7 K. HTS YBCO JJ THz mixers were patterned by a standard photolithography and Ar-ion beam etching technologies. The 2 μm-wide YBCO strips across the grain boundary (GB) form JJs were embedded into two antennas, respectively, as seen in the zoomed photo of Figure 4a. Then, the mixer chip was packaged into a sample holder. A Si hyper-hemispherical lens with parameters of ${\epsilon }_{\mathrm{r}}$ = 11.9, $R_{\mathrm{L}}$ = 4.5 mm and the extension length of 0.7 mm is fixed on the back of the mixer chip with cryogenic glue to focus the THz signal on the chip surface where JJ is located. The DC bias lines on the mixer chip are connected to the DC bias pins on the holder through gold wires and silver epoxy. Intermediate frequency (IF) output shares the same path with DC bias lines and is isolated by two capacitors. A radio-frequency (RF) filter module consists of resistors and capacitors and is applied to the DC bias pins to isolate DC and RF signals. LO signal is radiated out by a 1.95 cm-long monopole antenna, 0.8 cm above the holder mounted in the Gifford–McMahon (GM) cryocooler, shown in Figure 4b.

Measurements are carried out in a GM cryocooler at a bath temperature of about 4.5 K. The schematic diagram of the measuring setup for harmonic mixing is shown in Figure 4c. THz signal is generated from commercial VDI-Tx-S140 manufactured by VDI. Two off-axis parabolic mirrors are applied in the quasi-optical system to focus THz radiation on the Si hyper-hemispherical lens. The LO pump is produced from a microwave analog signal generator Agilent N5183A MXG and radiated through a frequency-dependent monopole antenna. Additionally, the radiation efficiency of the monopole antenna has been calibrated by a vector network analyzer. HP 8447D 011 Dual Amplifier, which has a gain of about 50 dB in the 0.1–1300 MHz frequency band, is used to amplify the down-converted IF output signal, finally recorded in an Advantest R4131D spectrum analyzer. In addition, a homemade current source and an automatic acquisition system of I–V characteristics (IVCs) are applied in the measurements.

3. Measurement Results

3.1. DC Characteristics and Coupling Power Estimation

Figure 5 shows the measured and simulated IVCs of the JJ mixers coupled with different antennas with and without the ~0.21 THz radiation. The Mixer 1 coupled with Antenna 1 (bowtie loaded with a pair of lumped-element stubs) has a critical current (I_c) of 550 μA and a normal-state resistance (Rn) of 0.78 Ω. The Mixer 2 coupled with Antenna 2 (bowtie loaded with a pair of open-end stubs) has a I_c of 900 μA and a Rn of 1 Ω. When mixers are pumped by a ~0.21 THz signal, $I_{\mathrm{c}}$ are suppressed to ~110 $\mathsf{\mu }$A and ~275 μA, respectively, but Shapiro steps [37] are located at the same voltages. Obviously, the voltages $V_m$ where the Shapiro steps are located are related to the incident frequency f_THz, consistent with the Josephson voltage–frequency relationship

$$V_m=m{\mathsf{\Phi }}_0 f_{\mathrm{THz}},$$

(5)

where $m$ is an integer, and ${\mathsf{\Phi }}_0$ is the magnetic flux quantum [38],

$$1/{\mathsf{\Phi }}_0\equiv 2e/h=483.6 \mathrm{GHz}/\mathrm{mV}.$$

(6)

As the first Shapiro steps are located at 0.429 mV, the f_THz is estimated at 0.207 THz. According to the measured DC IVCs and resistively shunted junction (RSJ) model [39], the THz power PTHz, which has been coupled into the junctions, can be obtained through numerical simulation by MATLAB software. The circuit equation for this model is

$$I_{\mathrm{DC}}+I_{\mathrm{RF}}cos{\omega }_{\mathrm{RF}}t=\frac{V\left(t\right)}{R_n}+I_{c}sin\varphi \left(t\right),$$

(7)

where the phase difference $\varphi$ is related to the voltage $V$ by the Josephson relation

$$\frac{d\varphi }{dt}=\frac{2\pi }{{\mathsf{\Phi }}_0}V\left(t\right).$$

(8)

In our experiment, $I_{\mathrm{DC}}$= 0 for JJ mixer is performed for zero-bias operation which means that there is no DC bias supply, and thus, there is no heating effect or shot noise in the junction due to DC bias current [40]. $I_{\mathrm{RF}}$ and ${\omega }_{\mathrm{RF}}$ are THz current in the junction and THz pump frequency here. Thus, the THz power P_THz coupled into the junction is

$$P_{\mathrm{THz}}=\frac{1}{2}{I}_{\mathrm{RF}}^2{R}_n.$$

(9)

The fourth-order Runge Kutta algorithm is used to numerically solve the first-order differential equation with a sinusoidal function. When the simulated DC IVCs matches the measured well, P_THz of mixers coupled with Antenna 1 and Antenna 2 are −23.6 dBm and −36 dBm, respectively. Minor errorbetween the simulated and the measured DC IVCs at ~0.4 mV in Figure 5a may be caused by a capacitance in the junction.

3.2. Harmonic Mixing Performance

For a harmonic mixer,

fIF = |fTHz ± nfLO|,

(10)

where n is the harmonic number, especially

fIF = |fTHz − nfLO|

(11)

as in Ref. [17], for the down-conversion mixer in our experiment. In order to detect the maximum harmonic number, we kept LO power P_LO at a higher level of 11 dBm, and adjusted the frequency f_LO from 10 GHz with a decreasing step of 0.002 GHz. Finally, as recorded in Figure 6a, when the mixer was coupled with Antenna 1, the power of IF output P_IF was −47 dBm at 944 MHz, which was generated from the maximum harmonic number of 30 that we could detect in the mixing between f_THz = 0.207 THz and f_LO = 6.932 GHz. If we decreased the P_LO to 5 dBm, the P_IF of −44.6 dBm at 1017 MHz was recorded in Figure 6b, with the maximum harmonic number decreasing to 22. On the other hand, when the mixer was coupled with Antenna 2, the maximum harmonic number attained in the mixing was 88, with the f_LO of 2.36 GHz and the P_LO as low as 4 dBm, shown in Figure 6c. Thus, under a similar level of LO pumping, the maximum harmonic number from Mixer 2 is much higher than that from Mixer 1.

$$\eta =P_{\mathrm{IF}}/(P_{\mathrm{THz}}\cdot G_{\mathrm{IF}})$$

(12)

The conversion efficiency of the HTS JJ THz mixers can be calculated on Equation (12) [10], where G_IF is IF amplifier gain, which is around 50 dB in our experiment. P_IF can be read from the spectrum analyzer directly. Additionally, P_THz has been calculated through numerical simulation. Thus, the conversion efficiency of the mixer coupled with Antenna 1 is −73.4 dB in the 30th harmonic mixing, while the other one, coupled with Antenna 2, is −69.6 dB in the 88th harmonic mixing.

The mixing parameters of HTS JJ mixers coupled with different traditional antennas with the detected maximum harmonic numbers are listed in

Table 1. Performance comparison of HTS JJ mixers coupled with different traditional antennas with the detected maximum harmonic numbers.

Mixing Parameters	Coupled with Traditional Antennas
	Log-Periodic [41]	Double-Slot [16]	Ring-Slot [17]	Bowtie 1
				Antenna 1	Antenna 2
fTHz (GHz)	207	642.24	614.4	207	207
fLO (GHz)	4.5	159.96	19.75	6.932	2.36
fIF (MHz)	499	2400	2150	944	362.2
n	46	4	31	30	88
η (dB)	−71.6	−18.1	-	−73.4	−69.6

¹ In this paper.

. Coupled with traditional antennas, the JJ with bowtie antenna achieves the highest harmonics. Generally, the conversion efficiency increases with the decrease in harmonic number. However, the JJ mixer coupled with the bowtie antenna (described herein) maintains the similar value of conversion efficiency while the harmonic number is nearly twice of that with a log-periodic antenna. The application of stubs on bowtie antenna has been proven to improve the performance of HTS JJ mixer.

4. Discussion

The mixer coupled with Antenna 2 has a larger harmonic number than that of the other mixer when coupled with Antenna 1. Even more, the mixer coupled with Antenna 2 shows a better mixing performance with the conversion efficiency of −69.6 dB in the 88th harmonic mixing, while the other, coupled with Antenna 1, only has a maximum harmonic number of 30 with the conversion efficiency of −73.4 dB. To explore the reasons, we simulated these two microwave circuit models of mixer chips with attached customized Si hyper-hemispherical lens by CST MWS, displayed in Figure 7a. Because the size of the hyper-hemispherical lens is electrically large relative to the structure in the chip, the AR coating is omitted in the model. Simulated input impedances where HTS JJs locate on the mixer chip attached to a Si hyper-hemispherical lens are shown in Figure 7b. The impedance is 74 − j64 Ω when the mixer coupled with Antenna 1. However, the other impedance is 6 + j36 Ω when the mixer coupled with Antenna 2. Giving an impedance Z_m of the JJ mixer, the coupling efficiency of the antenna can be computed with standard antenna theory as

$${\eta }_{\mathrm{c}}=\frac{\mathrm{Re}\left(Z_{\mathrm{m}}\right)}{\sqrt{{\left. [\mathrm{Re}\left(Z_{\mathrm{a}}\right)+\mathrm{Re}\left(Z_{\mathrm{m}}\right)\right]}^2+{\left. [\mathrm{Im}\left(Z_{\mathrm{m}}\right)+\mathrm{Im}\left(Z_{\mathrm{m}}\right)\right]}^2}}$$

(13)

in [42], where Z_a is the impedance of the antenna. Assuming Z_m ≈ R_n [16], when the mixer with the R_n of 0.78 Ω (Mixer 1) is coupled with Antenna 1, the η_c is only 0.79%. However, when the other mixer with the R_n of 1 Ω (Mixer 2) coupled with Antenna 2, the η_c is 2.7%. Therefore, the coupling efficiency of Mixer 2 is higher than that of Mixer 1. Furthermore, looking back at the surface electric current distribution in Figure 3c, the current where JJ is located in Antenna 2 is stronger than that in Antenna 1. More energy has been transmitted into the junction by Antenna 2. Thus, Mixer 2 coupled with Antenna 2 has a better performance and larger harmonic number.

If the antenna matches to the superconducting mixer impedance (a very low normal-state resistance), the radiation efficiency of the antenna will be very low because of the low resistance. Thus, further work can focus on other methods to solve the impedance mismatch between the coupling antenna and the JJ.

5. Conclusions

Based on the traditional bowtie structure, two methods of introduction of the stubs have been presented to decrease the impedance of traditional bowtie antennas from hundreds to tens of ohms. A prepared JJ mixer with the R_n of 1 Ω coupled with a pair of open-end stubs on the bowtie antenna has shown up to 88 harmonics with the conversion efficiency of −69.6 dB. Coupled with traditional antennas, the JJ mixer with bowtie antenna pairing has achieved the highest harmonics. Moreover, the maximum harmonic number of 88 from the superconducting JJ mixer is more than four times higher than the harmonic number of 20 from the semiconducting Schottky diode mixer. The superconducting JJ mixer has the potential to be applied in an ultrasensitive THz receiver for future THz communications.

As the series JJ structure has become another research interest to solve the problem of impedance mismatch between the mixer and the coupling antenna, the impedance of the mixer can be enhanced by cascading multiple JJs, so as to match the traditional antennas. Further work can focus on the integration of the bowtie traveling wave antenna and series JJ mixer. The work in this paper provides a reference and comparison for the future series JJ mixer coupled with the traditional bowtie antenna.