High-power in-phase and anti-phase mode emission from linear arrays of resonant-tunneling-diode oscillators in the 0.4-to-0.8-THz frequency range

The terahertz (THz) spectrum occupies a unique frequency range between microwave and infrared waves. This spectral region overlaps with both millimeter waves and far-infrared light, offering diverse opportunities for exploration and application. The THz wave holds significant potential across a myriad of research and practical applications, including non-destructive monitoring/inspection, security, and imaging. Moreover, as the demand for high communication data rates and capacities continues to escalate, wireless communication is increasingly migrating toward THz frequencies. Despite decades of intensive investigation into THz technology, a significant gap persists in the development of high-power, chip-based, and cost-effective THz emitters.^1–3 

Oscillators based on resonant tunneling diodes (RTDs) are room-temperature-operated electronic THz emitters that have reached, among the solid-state electronic THz emitters, the highest radiation frequency.^4–6 This makes RTD oscillators a prominent candidate for bridging the so-called “THz gap.” On the downside, the reported output power of single RTD oscillators remains low⁷ and the phase noise of the RTD oscillator tends to be large.⁸ Substantial efforts have been devoted to the increase of the output power.⁹ One natural progression is to aggregate the output power of an array of RTD oscillators through either incoherent power combining or coherent coupling.¹⁰ The latter approach not only amplifies the emitted power but also mitigates phase noise.¹¹ Recently, there have been several reports on coherent emission of RTD oscillators. A notable milestone was reached with the coherent coupling of 36 RTD oscillators, resulting in an output power exceeding 10 mW at 0.45 THz.¹² Some of the authors of this paper have proposed a planar coherent coupling strategy for slot antennae and verified in experiments that coherent coupling can be achieved via common (shared) stabilization resistors. It is usually assumed that the linear array opts to oscillate in the anti-phase mode, where the phase difference of the oscillations in neighboring slots is π and the radiation destructively interferes in a perpendicular direction in the far field. In order to achieve high-power emission in that direction, a zig-zag structure was proposed to create a net in-plane dipole moment,¹³ and coherent vertical emission from six RTD oscillators arranged in such a zig-zag structure was reported.¹⁴ An additional important development for the enhancement of the emitted power was the introduction of offset-fed slot antennae, both as single devices or utilized in arrays.¹⁵ They exhibit a higher radiation conductance and hence a higher output power than center-fed antennae. However, understanding the mode coupling among a large number of coupled RTD oscillators remains a significant challenge, and in-phase oscillation of RTD oscillators in linear arrays has not been reported yet. Substantial progress is still required to achieve high-power vertical emission from arrays. Overcoming these challenges will be pivotal in unlocking the full potential of RTD-based THz emitters for applications.

In this paper, we propose a novel structure to achieve coherent emission from RTD oscillators based on offset-fed slot antennae arranged in a linear array. By circuit simulations, we show that this kind of array supports both in-phase and anti-phase coupled modes, with the dominating mode being determined by the area of the RTD mesa. The anti-phase mode prevails for large mesa areas and oscillates at low frequencies, while the in-phase mode—running at higher frequencies—dominates for smaller mesa areas. We fabricated linear arrays comprising 11 RTDs and conducted measurements that validated the theoretical predictions. Specifically, when the area of the RTD mesa is large, the anti-phase mode oscillation yields a power of ∼0.7 mW at around 450 GHz. Conversely, for smaller mesa areas, the in-phase mode oscillates at ∼750 GHz and generates a power of about 1 mW. Both the anti-phase and in-phase modes exhibit constructive interference in the far field at distinct radiation angles. For certain mesa areas (around 1.25 μm²), the RTD array can oscillate in either of two frequency bands—with emission in different directions—corresponding to two distinct modes, with bias-controlled switching between them. Moreover, during bidirectional bias sweeping, the switching bias for the anti-phase and in-phase modes displays hysteresis. A similar bias-controlled mode-switching phenomenon was previously observed in stand-alone travelling-wave RTD oscillators.¹⁶ 

The proposed linear RTD oscillator array incorporates asymmetric offset-fed slots. For a fixed antenna length, the offset-fed slot antenna increases both the oscillation frequency and the output power compared to the common center-fed slots.¹⁵ In particular, the short part of the slot lowers the inductance, while the long part determines its radiation conductance. We investigated the possible oscillation modes in linear arrays of such slot antennae via simulations. It is instructive to first consider just a pair of oscillators coupled by a common resistor, as shown in Fig. 1(a). In the following, we call this structure a “two-element array.” In the simulations, we considered slots with a length of 120 μm each, with an offset of the feed-point by 47 μm (40%) from the slot center, the slot being 5 μm wide, and the common stabilization resistor having a width of 2 μm. Such resistors also terminate both ends of the two-element array. In the practical realization discussed in the following, all stabilization resistors were fabricated by etching of the 1-μm-thick n⁺-InP layer, which was employed as the bottom conducting layer. Its conductivity is ∼240 000 S/m, corresponding to the sheet resistance of ∼5 Ω/sq, as measured by using the transmission line method (TLM).¹⁷ This conductivity value was also used in the simulations. With these numbers, one estimates the resistance of each stabilization resistor to be 10.4 Ω.

Our analysis is based on calculations in the framework of an equivalent circuit model for RTD oscillators. Such models have been employed before to predict the oscillation frequency and radiated power of a single RTD integrated in a slot antenna.^18–20 Similar to Ref. 13, the model can be extended in the case of the two-element array considered here. Details are presented in the supplementary material.

In the circuit model, each RTD is represented by two important parameters: G_RTD, the absolute value of the negative differential conductance (NDC), expressing the gain of the oscillator, and C_RTD, the capacitance of the RTD. From the circuit model, one derives two oscillation conditions for the RTD oscillator which must be fulfilled simultaneously: $ωCRTD+I(Ya)=0$ and $GRTD−R(Ya)>0$⁠. Here, Y_a is the complex-valued admittance of the array of two coupled slot antennae (while G_RTD and C_RTD are for the single RTDs). The former condition requires that the total susceptance of the circuit equals zero, and the latter condition expresses that the gain of the RTD must be larger than the circuit loss that is expressed by the real part of the antenna admittance $(R(Ya))$⁠. It is known that the RTD NDC (G_RTD(ω)) rolls off with frequency, the rate of the roll-off being dependent on the specific details of the particular RTD.^21–23 For the sake of the conceptual discussion here, we assumed G_RTD to be constant. The gain per RTD area G_RTD/μm² was obtained by the polynomial fitting of the measured current-voltage curve, resulting in a value of 0.016 S/μm². C_RTD was estimated from the area of the RTD mesa and the dielectric constant of the RTD semiconductors at THz frequencies, yielding a capacitance per area C_RTD/μm² of 3.3 fF/μm².¹⁷ The voltage dependence of the capacitance was not taken into account.

For the determination of the antenna admittance Y_a of the two-element array, we utilized the electromagnetic solver CST Studio Suite (vendor: Dassault Syst$è$mes) and employed the method proposed in Ref. 13. A 2 × 2 antenna admittance (Y_a) matrix can be derived from the CST simulation $y11y12y21y22$⁠, where y₁₂ = y₂₁. Diagonalizing the Y_a matrix yields $γ100γ2$⁠, where γ₁ and γ₂ are the admittances of the two eigenmodes. In small-signal analysis, the components of the corresponding eigenvectors specify the amplitude and phase distribution of that mode. Under the assumption of near-equal gain over the relevant frequency range, as determined by the NDC, the device tends to oscillate in the mode that possesses the lower value of the conductance (the real part $R(γi)$ of the admittance), as it implies a lower loss, which is easier to compensate by the gain.

Based on the derived eigenmodes of the antenna, we calculated the oscillation frequency against the mesa area, as shown in Fig. 1(b), showcasing anti-phase and in-phase modes. The oscillation frequency exhibits an increase with decreasing mesa area, attributed to the reduction in the capacitance of the RTD mesa. There are several salient features. (i) The oscillation frequencies of the in-phase and anti-phase modes lie in two frequency bands: a low-frequency regime below 400 GHz and a high-frequency regime above 550 GHz. (ii) For mesa areas smaller than 1 μm², only the in-phase mode oscillates. This occurs at frequencies $>$0.6 THz in this set of simulations. (iii) For mesa areas larger than 1 μm², both in-phase and anti-phase modes can oscillate. The loss of the modes (expressed in terms of the $R(γi)$ values, see above) determines which mode prevails.

We explore this more in an exemplary fashion for a device with a mesa area of 1.3 μm² [marked by the dashed line shown in Fig. 1(b)]. We plot the real and imaginary parts of γ_i for both the in-phase and anti-phase modes shown in Fig. 1(c). The conductance G_RTD and the susceptance −ωC_RTD of the RTD are also plotted as a function of frequency as magenta and black solid lines. When the curves of $I(γi)$ and −ωC_RTD cross each other, the total susceptance of the circuit equals zero, thus fulfilling the first oscillation condition. In order to fulfill the second condition, it is necessary that $GRTD−R(γi)>0$ at the respective crossing frequency. If both conditions are met, the circuit will oscillate at this particular frequency.

From Fig. 1(c), one finds several crossing frequencies for both the in-phase and the anti-phase mode. In the case of the anti-phase mode, the circuit losses $(R(γi))$ are smaller than the RTD NDC (G_RTD) at 0.375 and 0.56 THz, and the device can, in principle, oscillate at both frequencies, as the losses are nearly equal. However, in real devices, the RTD NDC rolls off with the frequency in Refs. 21–23, and this should probably make the anti-phase mode more unstable at the lower frequency of 0.375 THz.

In the case of the in-phase mode, only the crossing frequency at 0.6 THz fulfills the two oscillation conditions, and the device will oscillate at this frequency. These frequencies of the dominant modes (one for each mode) are the ones shown in Fig. 1(b). Comparing the oscillation frequencies of the in-phase and anti-phase modes, the loss of the in-phase mode (at 0.6 THz) is smaller than that of the anti-phase mode (at 0.375 THz); the two-element array is expected to preferentially oscillate at 0.6 THz in the in-phase mode.

For a mesa area larger than 1.5 µm², we find that both the anti-phase and the in-phase modes oscillate in the lower frequency band and that the anti-phase mode tends to have a lower loss and will hence dominate. For a mesa area smaller than 1.2 μm², both modes lie in the higher frequency band. For a mesa area below 1.0 μm², only the in-phase mode fulfills the first oscillation condition.

The prevailing assumption for multi-element linear RTD arrays, as we consider them here, is that the ohmic loss in the stabilization resistors is the dominant loss mechanism and determines which mode will oscillate.¹³ We can confirm and elaborate on this aspect with the help of Fig. 2, and again for the two-element array shown in Fig. 1(a) with a mesa area of 1.3 μm². The figure plots a snapshot of the y component of the electric field for the anti-phase mode at 0.375 THz (upper panel of Fig. 2) and for the in-phase mode at 0.6 THz (bottom panel of Fig. 2). In the anti-phase mode, the electric field exhibits only one maximum of the field amplitude in each slot, and the field lobes are separated from each other by a field node at the common resistor. As the alternating current (AC) through the common resistor is correspondingly weak, the total loss in the system is comparatively low. The other (in-phase) mode at 0.375 THz does not exhibit a field node at the common resistor (not shown), which leads to enhanced conductor losses. Therefore, the RTD array is made to oscillate in the anti-phase mode.¹³ In contrast, at high frequency (here 0.6 THz), each slot typically exhibits two maxima of the electric field amplitude. In this scenario, one obtains an electric field node at the common resistor for the in-phase mode (as shown in Fig. 2), but not for the anti-phase mode (not shown). This leads to the preferred oscillation of the in-phase mode as it experiences lower loss. This loss argument qualitatively explains why the anti-phase mode dominates at low frequency and the in-phase mode—as a higher-order mode—is preferred at a high frequency for such linear two-element RTD oscillator arrays.

In Sec. III of the supplementary material, we present the amplitude field pattern |E_y| for all four modes (in-phase and anti-phase mode, each at 0.375 and 0.6 THz, respectively). The field patterns substantiate the statements made above: at 0.375 THz, the anti-phase mode has a lower field amplitude in the area of the common resistor compared to the in-phase mode, while at 0.6 THz, the situation is reversed.

We fabricated individual RTDs and linear arrays starting from epitaxial AlAs/InGaAs-on-InP wafers. The details of the epitaxial structure are the same as those reported in Ref. 17. The fabrication sequence is described in Sec. I of the supplementary material. With the individual RTDs, we measured the following properties: the peak current density J_p was 12 mA/μm²; the voltage width ΔV of the NDC region was 0.6 V; and the peak-to-valley current ratio (PVCR) of the current-voltage curve was found to be 2.5.

A microscope image of a finished device block is shown in Fig. 3(a). The block consists of 20 rows of 1 × 11 slot arrays, allowing for independent biasing of each row. The choice of the number of 11 RTDs in a row is arbitrary. We wanted the number to be high in order to obtain as much power as possible, but we also wanted to limit the risk of thermal destruction of the array by the heating resulting from the strong current. The inset of Fig. 3(a) shows a magnified view of two oscillators. The antenna length L is 120 μm and the RTD offset is 47 μm, both as in the simulations. The peak current density of the RTDs was measured to be 12 mA/μm², with a peak-to-valley current ratio (PVCR) of 2 and a voltage swing in the NDC region of 0.7 V.

We employed Fourier-transform infrared spectroscopy (FTIR) for the measurements of the emission spectra. During the measurements, the RTD devices were positioned atop an Si substrate lens with a diameter of 3 cm and biased using needle probes. For the measurements of the radiation power, a pyroelectric detector was utilized. Further details of the experimental setups are provided in Sec. IV of the supplementary material.

The red solid curve in Fig. 3(b) shows a typical emission spectrum of a single RTD oscillator with a mesa area of 1.0 μm². The emission occurs mainly at a frequency of 0.354 THz, with a second harmonic emission at 0.705 THz. The blue solid curve in Fig. 3(b) shows a typical spectrum emitted from a row of RTD oscillators with a mesa area of 0.9 μm². There is only one peak in the emission spectrum at a substantially higher frequency, and we interpret this as evidence for coherent coupling of the RTDs in the row.

Figure 4(a) shows the emission frequencies of single RTD oscillators (magenta double crosses) and 11-element linear arrays thereof (red triangles) as a function of the RTD mesa area. One notices that the single RTD oscillators emit at frequencies below 0.4 THz, whereas the radiation frequency of the arrays depends on the mesa area: For small mesas, the emission occurs at a high frequency of around 0.73 THz, and for large mesas, at low frequency of around 0.45 THz. The measured oscillation frequencies of the arrays as a function of mesa area are very similar to the predictions shown in Fig. 1(b). Guided by the simulation results, we assign the high-frequency emission in the experiments to the in-phase mode and the low-frequency emission to the anti-phase mode. The crossover occurs at a mesa area of (1.2-)1.33 μm², where the oscillation frequency can be switched by the applied current. We will discuss the bistability of the oscillation in Sec. IV B.

In order to determine the total emitted power values and the radiation patterns, we measured the far-field radiation using a pyroelectric detector. The emitter was mounted on a hemispherical Si substrate lens. Details of the measurements are provided in Sec. IV of the supplementary material (see Fig. 3 there for the setup). Figure 4(b) shows the far-field emission pattern for the array with a mesa area of 1.33 μm² (we note that the air bridge of the left-most RTD in each row of this block of linear arrays was disconnected, as shown in Fig. 5 of Sec. VI in the supplementary material). The array was biased at high current (0.8 A), where it oscillates at the high-frequency mode. The main lobe of the emission pattern is oriented perpendicular to the substrate’s surface. This confirms the prediction for the in-phase mode oscillation. Figure 4(c) shows the far-field emission pattern for the same array when biased at a current of 0.75 A where it oscillates in the low-frequency mode at 0.45 THz. The main lobe of the emission points sideways at an angle of θ = 48° from the surface normal. With Eq. (1) and taking for n the average refractive index of Si (n = 3.41) and of InP (n = 3.5), one calculates the theoretical emission angle of θ = 53°. The small difference between the theoretical and measured angles could arise from a slight vertical displacement of the emitter from the center of the substrate lens by the thickness of the InP substrate of 0.6 mm. Such an offset leads to refraction of the wave cone toward the optical axis of the lens and reduces the value of θ. In Sec. V of the supplementary material, we present simulations of the far-field radiation patterns calculated with the CST Studio Suite. The simulations largely reproduce the measured results for both the in-phase and anti-phase modes.

Integrating over the measured far-field patterns, we could estimate the total power emitted by the RTD devices. Figure 5(a) shows the estimated power as a function of emission frequency. For the single RTD oscillators, the emission power is in the range of several tens of μW. The emitted power from the 11-RTD-oscillator arrays is significantly higher: for the anti-phase mode at around 0.45 THz, the power reaches up to 700 μW, and for the in-phase mode at around 0.75 THz, it reaches up to about 1.0 mW. Remarkably, the power obtained from the oscillator arrays is larger than the power measured for the single RTD oscillators multiplied by the number of oscillators in the array. It is quite possible that not all the radiation from the single oscillators was captured, given their large emission cones. There are two reasons, however, to assume that the emission efficiency of the arrays is indeed better than that of the single oscillators. First, the conductor losses in the stabilization resistors are lower per antenna in the array than for the single oscillators. This follows from the consideration of the ohmic losses in the discussion of Fig. 2 (and of Fig. 2 in the supplementary material). Second, one notes that the single oscillators all emit radiation below 0.4 THz. There, the radiation conductance is lower than at higher frequency. This also manifests in the higher power emitted from the arrays when they oscillate in the in-phase mode (at around 0.75 THz) compared to the emission for anti-phase-mode operation (at around 0.45 THz).

Figure 5(b) shows both the calibrated power and the bias voltage (U) as a function of the current (I) through an array with an RTD mesa area of 1.2 μm². From the U(I) curve, one identifies the NDC region (shaded in light green color). The NDC region starts at 0.67 A (1.2 V) and ends at 0.83 A (1.57 V). This is also the region of strong emission by the array. Above the NDC region, the detected power is weak and is of thermal origin due to heating by the strong current. The estimated DC to AC power conversion efficiency at the peak of the emission curve at I = 0.78 A is about 0.08%.

As mentioned in Sec. IV A, if the mesa area is around 1.3 μm², the RTD oscillator array is voltage-switchable between two oscillation modes. For the array with the mesa area of 1.2 μm², the dual-frequency operation was only observed for one row of RTD oscillators, where six RTD mesas could not be biased (as the air-bridge fabrication for these had failed). For the other intact rows of RTD oscillators, only one mode was observed. This is different for the linear array of RTDs with a mesa area of 1.33 μm². Here, the bistable operation was always observed.

Figure 6 shows the measured power and emission frequency of such an array as a function of bias current. Dependent on the bias current, the RTD array oscillates in either one of two modes: At low bias current, it emits in the range from 0.425 up to 0.452 THz, with a tuning range of 27 GHz [see the inset of Fig. 6(b)]. The emitted power reaches up to 450 mW. The emission is attributed to the anti-phase mode. Raising the bias current, the emission abruptly jumps to a frequency of about 0.71 THz, and the emitted power leaps to values of around 800 μW. In this regime, the RTD array oscillates in the in-phase mode, with a tuning range of 10 GHz. Changing the direction of the bias sweep, one observes a pronounced hysteresis in the switching behavior, as indicated by the arrows and the coloring of the data points shown in Figs. 6(a) and 6(b) (the black arrow and data points representing up-sweeps and the red arrow and data points down-sweeps).

Continuous frequency tuning by the bias current was reported before for a single RTD oscillator with a slot antenna,²⁴ and the increase in the oscillation frequency with the current was attributed to a concomitant decrease in the capacitance of RTDs. Our work shows that the change of capacitance is pronounced enough to even induce mode hopping in the RTD array (see related findings for a traveling-wave-based RTD oscillator in Ref. 16). This mode transition is accompanied by a jump of the emission direction (data not shown), showcasing interesting beam-steering capabilities whose speed is the subject of future studies.

Hysteretic switching behavior of RTDs at the edges of the NDC bias region is known to occur due to the nonlinear properties of the RTDs.^25,26

In conclusion, our study presents a novel linear arrangement of 11 coupled RTD slot oscillators, with which we achieve coherent emission at hundreds of GHz with a radiation power approaching 1 mW. Depending on the area of the RTD mesas, the linear arrays support either anti-phase or in-phase mode oscillations. The in-phase mode, composed of hybridized fundamental modes of the individual offset-fed slot oscillators, emits coherently at a lower frequency and at a tilt angle. The anti-phase mode, in contrast, composed of hybridized second-order modes of the individual oscillators, emits coherently at a higher frequency, higher power, and perpendicular to the substrate surface. At an intermediate RTD mesa size, one observes hysteretic bistable operation. Switching between the two modes is achieved by tuning the bias current. Interestingly, this is accompanied by a change in the emission direction, opening the potential for all-electronic beam-steering applications.

Clearly, this achievement calls for an extension of the coupling concept to a larger number of RTDs, also extending the scheme from linear to two-dimensional arrays. This way of coherent power combination promises power levels and beam qualities of the emitted radiation, which are useful for many applications in THz photonics.

The supporting simulation, experimental data, and additional analysis are provided in the supplementary material.

F.M., J.H., and H.G.R. acknowledge financial support from DFG Project Nos. RO 770/46-1 and RO 770/50-1 [the latter being part of the DFG-Schwerpunkt “Integrierte Terahertz-Systeme mit neuartiger Funktionalität (INTEREST)”]. P.O. and M.F. acknowledge the financial support from the FWF Project No. P30892N30. T.Z. and S.S. acknowledge a scientific grant-in-aid (Grant No. 24H00031) from JSPS and CREST (Grant No. JPMJCR21C4) from JST.

The authors thank Feifan Han for his assistance in the experiments and simulations. The authors also thank Professor Masahiro Asada for insightful discussions.

The authors have no conflicts to disclose.

Fanqi Meng: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Zhenling Tang: Data curation (equal); Investigation (equal); Methodology (equal); Software (equal); Writing – review & editing (equal). Petr Ourednik: Data curation (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Jahnabi Hazarika: Data curation (equal); Investigation (equal); Methodology (equal). Michael Feiginov: Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Safumi Suzuki: Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal). Hartmut G. Roskos: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

Raw data were generated at the Zenodo data repository large scale facility Ref. 27. Derived data supporting the findings of this study are available from the corresponding author upon reasonable request.