Two-Element Tapered Slot Antenna Array for Terahertz Resonant Tunneling Diode Oscillators

Two-element tapered slot antenna (TSA) array for terahertz (THz) resonant tunneling diode (RTD) oscillators is proposed in this paper. The proposed TSA array has the advantages of both the high directivity and high gain at the horizontal direction and hence can facilitate the horizontal communication between the RTD oscillators and other integrated circuit chips. A MIM (metal-insulator-metal) stub with a T-shaped slot is used to reduce the mutual coupling between the TSA elements. The validity and feasibility of the proposed TSA array have been simulated and analyzed by the ANSYS/ANSOFT’s High Frequency Structure Simulator (HFSS). Detailedmodeling approaches and theoretical analysis of the proposed TSA array have been fully addressed.The simulation results show that themutual coupling between the TSA elements is reduced below −40 dB. Furthermore, at 500GHz, the directivity, the gain, and the half power beamwidth (HPBW) at theE-plane of the proposedTSA array are 12.18 dB, 13.09 dB, and 61, respectively. The proposed analytical method and achieved performance are very promising for the antenna array integrated with the RTD oscillators at the THz frequency and could pave the way to the design of the THz antenna array for the RTD oscillators.


Introduction
The terahertz (THz) frequency, ranging from 100 GHz to 10 THz, has recently attracted a large number of interests in lots of applications, such as radio astronomy, biological monitoring, nondestructive evaluation, and information and communications technology (ICT) [1][2][3][4].To realize the applications above, the resonant tunneling diodes (RTDs) have been seen as good candidates for the THz oscillators working at room temperature [5][6][7].In addition, the good antenna is also considered as the key component for THz oscillators, which can improve the sensitivity of the oscillators to one to two orders of magnitude.
Among the various implementations of antennas integrated with the RTD oscillators, the patch antennas including the rectangular patch antenna [8] and the circular patch antenna [9] have the advantage of achieving the oscillation frequency at the THz band without using the Si lens.Besides, the offset-fed slot antenna, introduced by Hinata et al. [10] and implemented by having the feeding point deviated from the center of the slot antenna, has drawn considerable attention due to the fact that the oscillator has a high output power of 200 uW with the potential of oscillating up to 2 THz.The antennas above designed in planar structure have the vertical radiation pattern.However, in some special applications, such as the wireless data transmissions, an antenna with the horizontal radiation pattern applicable to the horizontal communication is preferable.Thus, the tapered slot antennas (TSAs) are ideal options since they can maintain the directivity approximate to horn antennas.At present, most researches on TSAs are concentrated on the millimeter wave band [11][12][13][14].Very recently, the TSA working at 405 GHz was reported in [15], whose directivity is 8.9 dB.However, the main content of [15] is centered on the RTD, and there is little information and theoretical analysis about how the TSA is designed and matched with the RTD.
The output power of the RTD oscillators integrated with the antenna is usually low (∼uW level) [8][9][10][16][17][18][19].To improve the output power, designing antennas with high directivity and high radiation efficiency is one effective way.Furthermore, the design of the antenna array which can achieve the output power combination of the RTD oscillators is another effective method.Recently, the offset-fed slot antenna array for the RTD oscillators is reported in [20], which achieves the individual output powers of 1.9 uW at 329 GHz and 2.6 uW at 332 GHz, respectively.When the two oscillators are driven simultaneously, a single peak output power of 5.1 uW is obtained at 321 GHz, which is little larger than the summation of the individual output power.This outcome is rather significant in obtaining the high output power of the RTD oscillators, which illustrates the feasibility of the design of the oscillators array.However, there is little information about the modeling approaches and simulation results of the antenna array.
In this paper, the detailed modeling approaches and theoretical analysis of a high directivity and high gain TSA array for THz RTD oscillators are proposed.To our knowledge, this is the first time to apply the TSA array integrated with the RTD oscillators.The matching conditions between the RTD and the TSA element have been fully considered and addressed.The MIM (metal-insulator-metal) stub with a T-shaped slot is used to reduce the mutual coupling between the TSA elements.The validity and feasibility of the proposed TSA array have been simulated and analyzed by ANSYS/ANSOFT's High Frequency Structure Simulator (HFSS).The simulation results show that the directivity and the gain of the TSA array have been greatly improved compared with the TSA element.Furthermore, the mutual coupling between the TSA elements has been greatly reduced, and the side lobes of the proposed TSA array have been greatly supressed.The proposed analytical method and achieved performance are very promising for the antenna array integrated with the RTD oscillators at the THz frequency and could pave the way to the design of the THz antenna array for the RTD oscillators.

Theoretical Analysis of the TSA Element
The TSAs belong to the class of directional antennas known as surface-wave antennas, which utilize a traveling wave propagating along the antenna structure with a phase velocity V ph < .The TSAs maintain the advantage of producing symmetric radiation patterns in the planes which are parallel to the substrate (-plane) and perpendicular to the substrate (-plane), though their geometries are completely planar.To work as a surface-wave antenna, the effective substrate thickness ( eff ) of the TSA has to obey the following requirement [21]: where  0 is the free-space wavelength,   is the relative dielectric constant of the substrate,  is the substrate thickness.The beam width will get wider by using a thinner substrate.Thus, it is vital to know the upper limit of the substrate thickness.
A standard TSA consists of a tapered radiating slot used as a transformer to the free space.Among the various types of the TSAs, the most common are the linearly tapered slot antenna (LTSA), the exponential tapered slot antenna (ETSA), and the constant-width tapered slot antenna (CWSA) [22].Usually, the beam width of the CWSA is the narrowest, followed by LTSA and ETSA on the condition of the same substrate with the same length and aperture size.However, the situation described above is opposite for the side lobe level.Thus, the LTSA is an ideal compromise due to considering the beam width and the side lobe level.The radiation of the LTSA is restricted into the slot by the metal surface; thus, the propagation is end-fire.The bandwidth of the LTSA is decided by the maximal and minimal distance of the slot.The directivity can be estimated as where   () and   () are, respectively, the directivity function of the -plane and the -plane.
The schematic structure of the proposed RTD-integrated TSA element is demonstrated in Figure 1, which is not the same proportion as the real size.The whole device is composed of a resonator, a waveguide, and an LTSA.A double-barrier RTD is located in the resonator.The upper and lower electrodes of the TSA element are connected to the correspondent sides of the RTD.For heat sink, the bridge connects the upper edge of the RTD and the upper electrode is designed much larger than the RTD.At one end of the resonator, a 100-nm-thick SiO 2 is inserted between the upper and lower electrodes to prevent short.The waveguide with a slightly larger width is linked to the other end of the resonator; thus, the standing wave is formed since the high frequency electromagnetic waves are reflected at the both edges of the resonator.Finally, the THz wave is radiated horizontally through the waveguide and the LTSA.
The resonator can be equivalent to an offset-fed slot antenna integrated with RTD.For the antenna without offset, the resonant point should satisfy the following conditions [23]: where  is the length of the offset-fed slot antenna,   is the equivalent refractive index, and  is a positive integer.The impedance of the TSA element increases with the increasing of the resonator width, and the resonant frequency decreases with the increasing of the resonator length.The potential profile and characteristics of the RTD are shown in Figure 2; we can observe that the RTD is composed of two heterobarriers and a quantum well.In the current-voltage (I-V) characteristics, the resonance level in the quantum well is close to the conduction band edge of the emitter at the peak current.With the increasing of the voltage above the peak current, a negative differential conductance (NDC) region exists, which corresponds to the negative differential resistance (NDR) region.The oscillation of the RTD integrated with the antenna is obtained in this region [24].Therefore, because of the NDR of the RTD and the positive resistance of the antenna, the conjugate impedance matching condition between the RTD and the antenna is rather difficult.Generally, the matching conditions are analyzed through the equivalent circuit mode.
The oscillation of the RTD oscillators integrated with the antenna can be achieved if the following two conditions are met simultaneously [25]: where  is the total admittance of the antenna and the RTD.The equivalent circuit of the proposed TSA element integrated with RTD without parasitic elements is expressed as shown in Figure 3.The parasitic elements such as the resistance and capacitance of the upper contact of the RTD, the inductance of the RTD mesa, the mesa resistance, and the spreading resistance from the RTD mesa to the lower electrode can be neglected here, which does not affect the Usually, the output power of the RTD oscillators integrated with the antenna is low (∼uW level).By an approximate analysis, the output power is given as [26] where P can be maximized at the condition  ANT =  RTD /2, where  ANT is equal to the  TSA in this paper.Furthermore, if the tunneling time and transit time are neglected, the maximum value of the output power will be obtained as [27]  max = 3 16 ΔΔ, where Δ and Δ are the current and voltage of the NDR region.

Design of the TSA Element
So far, there is no unified standard about the design of the THz antenna for RTD oscillators.Several factors which are rather important for the antenna should be fully considered.First, the antenna should have high directivity and high radiation efficiency for improving the output power of the RTD oscillators, as mentioned above.Furthermore, antennas with broadband are also necessary which can broaden the range of the application for the RTD oscillators.Other factors such as the half power beam width (HPBW) and the front back to ratio are also crucial for designing the antennas for RTDs oscillators.The design specification of the proposed TSA element is shown in Table 1.
The proposed TSA is designed on the semi-insulting (SI) InP substrate.The equivalent refractive index of SI-InP and SiO 2 are 3.48 and 1.97, and their conductances are neglected.The substrate is thinned in order to reduce the radiation loss of the substrate.It is assumed that both electrodes are made of gold ( = 4.52 × 10 7 S/m), and the frequency dependence of the conductivity is neglected.The mesh area of the RTD is 4 m 2 , which is linked to the RTD and the heat sink.Considering the design specification, the parameters of the proposed TSA element are shown in Table 2.By the circuit simulation, the NDC of the RTD is −6.52 mS at 500 GHz and the inherent capacitance C d is 3.8 fF.Thus, theoretically, the admittance of the proposed TSA element is (3.26 −  * 11.84) mS, and the corresponding impedance is (21.6 +  * 78.5) ohm at 500 GHz.
The return loss and the impedance versus frequency of the proposed TSA element are shown in Figures 4 and  5, respectively.We can observe that the bandwidth of the proposed TSA is 254 GHz (from 337 GHz to 591 GHz, S 11 < −10 dB), which yields a rather large relative bandwidth of 54.7%.Furthermore, the impedance of the proposed TSA element is (22.0 +  * 79.8) ohm at 500 GHz, with the corresponding admittance of (3.2− * 11.6) mS, both of which agree very well with the theoretical values.
The radiation pattern and the directivity at the -plane of the proposed TSA element at 500 GHz are shown in Figures 6 and 7, respectively.We can observe that the gain, the directivity, and HPBW at the -plane of the proposed TSA element are 9.58 dB, 10.38 dB, and 59 ∘ , respectively.Furthermore, the first side lobe's gain is −1.89 dB at  = 39 ∘ , the front back to ratio is 11.5 dB, and the radiation efficiency is 83.2%.
From the analysis of the proposed TSA element above, we can obtain that the proposed TSA element enjoys a broadband centered at 500 GHz, high directivity, and high gain at the horizontal direction, which satisfies the design 300.00 350.00 400.00 450.00 500.00550.00 600.00 Frequency (GHz) 0.00

Design and Theoretical Analysis of the TSA Array
The schematic structure of the proposed TSA array integrated with the RTDs is demonstrated in Figure 8. Two TSA elements are designed linearly in a planar.The MIM stub with a T-shaped slot is used to reduce the mutual coupling between the TSA elements.The schematic structure of the coupling part is shown in Figure 9.The coupling part length L5 is 100 m, which is less than a quarter of the wavelength.The slot width w3 is 10 m in the lower electrode, which is used for bias separation.The oscillation modes of the two-element RTD oscillators array can be divided into the even mode and the odd mode when RTD 1 and RTD 2 are operated simultaneously.Two RTDs are assumed to be the same.The oscillation frequency of the even mode  () and the odd mode  () can be obtained as [28]  =  () and  () where  1 is the angular frequency when RTD 1 is operated solely.L is the inductance mainly determined by the antenna and the coupling part, and  12 represents the coupling characteristic.If Im( 12 ) > 0, the frequency of the even mode is lower than the other, and only this mode is stable.
The combined output power of the two-element RTD oscillators array in the even mode and odd mode is proportional to where   is the normalized complex amplitudes, which satisfies |  | 2 = 1, and  is the coupling parameter given as where   is the conductance determined by the antenna and coupling part.It can be seen from ( 8) that the combined output power of the two-element RTD oscillators array is about four times of a single oscillator in the even mode, while zero in the odd mode.The S-parameters versus frequency of the proposed array is shown in Figure 10.We can observe that  means that the MIM stub works very well in reducing the mutual coupling between the TSA elements.The admittance  12 versus frequency of the proposed TSA array is shown in Figure 11.We can observe that the imaginary part of  12 is positive; thus, the two-element RTD oscillators can work in the even mode and achieve the output power combination.
The radiation pattern of the proposed TSA array is shown in Figure 12.We can observe that the gain of the proposed TSA array is 12.18 dB at the horizontal direction, which is 2.6 dB larger than the gain of the TSA element.Furthermore, the first side lobe's gain is 1.1 dB at  = 41 ∘ , and the front back to ratio is 21.3 dB.From the analysis of the radiation pattern of the TSA array, we can obtain that the TSA array enjoys a high gain at the horizontal direction, and the side lobes have been greatly suppressed.The directivity of the proposed TSA array at the -plane at 500 GHz is shown in Figure 13.We can see that the maximum horizontal directivity is 13.09 dB, which is 2.71 dB larger than the directivity of the TSA element.Furthermore, the HPBW at the -plane is 61 ∘ , which changes little compared with the HPBW of the TSA element.However, the beam width of the TSA array becomes narrower at the -plane.Finally, the radiation efficiency of the TSA array is 81.2%, which means that the decrease of the radiation efficiency is quite little compared with the single TSA element.From the analysis of the directivity of the TSA array, we can conclude that the proposed TSA array has a very good directivity at the horizontal direction and hence can achieve the horizontal communication between the RTD oscillators and other integrated circuit chips.

Conclusion
The detailed modeling approaches and theoretical analysis of high directivity and high gain TSA array for THz RTD oscillators are presented in this paper.The MIM stub with a T-shaped slot is used to reduce the mutual coupling between the TSA elements.The simulation results show that the presented TSA element enjoys high directivity and high gain of 10.38 dB and 9.58 dB at the horizontal direction, respectively.When the two TSA elements formed to a linear array, the directivity and gain of the presented TSA array are 13.09dB and 12.18 dB, which are 2.71 dB and 2.6 dB larger than that of the single TSA element, respectively.The  21 of the TSA array is below −40 dB, which means that the mutual coupling between the TSA elements has been greatly reduced.The first side lobe's gain is 1.1 dB; thus, the side lobes of the TSA array have been greatly suppressed.Finally, the radiation efficiency of the TSA array is 81.2%, which means that the decrease of the radiation efficiency is quite little compared with the TSA element.Therefore, the presented TSA array has the advantages of both the high directivity and high gain at the horizontal direction and hence can achieve the horizontal communication between the RTD oscillators and other integrated circuit chips.The presented two-element TSA array can be extended to a multielement array.The presented analytical method and achieved performance are very promising for the antenna array integrated with the RTD oscillators at the THz frequency and could pave the way to the design of the THz antenna array for the RTD oscillators.

2 Figure 1 :
Figure 1: Schematic structure of the proposed TSA element.

Figure 2 :Figure 3 :
Figure 2: Potential profile and characteristics of RTD.

Figure 4 :
Figure 4: Return loss of the proposed TSA element.

Figure 7 :Figure 8 :
Figure 7: Directivity of the proposed TSA element at the -plane at 500 GHz.

Figure 13 :
Figure 13: Directivity of the proposed TSA array at the -plane at 500 GHz.

Table 1 :
Specifications of the proposed TSA element.  is the inherent capacitance of the RTD,  TSA is mainly determined by the TSA element.− RTD is the negative differential conductance (NDC) of the RTD,  TSA is the conductance of the TSA which represents the radiation loss of the TSA element.Oscillation occurs if  RTD >  TSA ; that is, the absolute value of the NDC exceeds the radiation loss of the TSA element.

Table 2 :
Parameters of the proposed TSA element.