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Abstract
Complex terahertz (THz) System-on-Chip (TSoC) circuits require ultra-wideband low-loss low-dispersion interconnections between building-block components of various dimensions and characteristics. Tapered transmission lines, which enable the gradual transformation of both physical dimensions and characteristic impedance, are a convenient basis for these interconnections. In this paper, we quantify both experimentally and through simulation, the efficacy of transmission-line tapers connecting two different coplanar-strip transmission-line configurations, for frequencies up to 2.0 THz and with 25 GHz spectral resolution. We demonstrate tapers that enable transitioning from a small device-constrained transmission-line dimension (10 μm line width) to a lower-loss (20-40 μm line width) dimension, as a method to reduce the overall attenuation, and outline design constraints for tapered sections that have minimal detrimental impact on THz pulse propagation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) technology continues to mature, with advances in technology and applications [1]. One important research direction has been guided-wave THz systems, as a means to replace the traditional free-space systems with more robust, compact and ultimately cost-effective systems, and to enable more advanced functions in spectroscopy [2–4] and communications [5]. Researchers have struggled with challenges of waveguide or transmission-line (TLine) fabrication, inclusion of active devices for sources and detectors, and performance (loss and dispersion) [6–10]. Planar TLine technologies, such as microstrip (MS), provide compatibility with surface-mount technology, but limitations are caused by the loss and dispersion of the substrate materials at THz frequencies [11]. Attempts to use low-density materials as a substrate [12] are promising, but fabrication and performance issues remain.
Recently, following the lead of previous work [13–15], we demonstrated a platform for the design and fabrication of a wide variety of THz system-on-chip (TSoC) circuits [16]. This TSoC platform consists of coplanar-strip (CPS) TLines on a thin (less than 1 ${\rm \mu}$m) Si$_3$N$_4$ membrane. The thin membrane allows a quasi-TEM mode to propagate along the metallic TLine with close to zero overlap with the dielectric, resulting in close to zero dielectric loss and dispersion. Conductor features and Si$_3$N$_4$ membrane windows are defined precisely with photolithography, limited in length by wafer size and TLine loss to a few cm, and active devices are surface mounted. Recently, we tested a wide selection of components including filters [17], power dividers [18], capacitors, inductors, Bragg gratings, and combinations of components that are routine at microwave frequencies, but novel at THz frequencies.
Each TSoC circuit design requires low-loss interconnections between various components. For example [16], in coupling from a photoconductive switch (PCS) to a membrane-based CPS, a strip width of 10 ${\rm \mu}$m is desirable to minimize radiation. However, in minimizing TLine loss, a strip width of 40 ${\rm \mu}$m is preferable. Hence a transition between these two TLine sizes is required. Historically tapered structures have primarily been used for field enhancement [19–22], near-field probing [23], and as antennas [24–26]. Our prior work [10] illustrates the reduction of attenuation with tapers, but the usage of bulky metallic slit waveguides significantly limits system integration feasibility (photolithography is not possible). To the authors knowledge, there is limited (or no) prior work which illustrates the ultra-wideband behaviour of lithographically-defined TLine tapers for the purpose of loss reduction into the THz region.
The goal of this paper is to clearly show that tapered CPS TLines provide a simple low-loss and ultra-wideband method to interconnect different THz-bandwidth components or devices. We quantify both experimentally and through simulation the tapered transition from a small device-constrained TLine (10 ${\rm \mu}$m line width) to lower-loss (20-40 ${\rm \mu}$m line width) TLines, as a method to reduce the overall attenuation, and provide design guidelines for tapers that have minimal impact on THz pulse propagation. The key points of novelty are: (1) Experimental confirmation that linear CPS TLine tapering does not induce significant longitudinal oscillations in a propagating THz-bandwidth pulse, (2) Combination of tapers and TLines can reduce the overall loss in a cascaded TSoC device, (3) Demonstration of the furthest distance ($\approx$100$\times$ the spatial pulse length) transmission of an ultra-wideband pulses ($\approx$2 THz bandwidth at −40 dB dynamic range) using a lithographically-defined TLine.
2. Background
A CPS TLine (Fig. 1) consists of two planar metallic conductors of width, W, separated by distance, S, on a substrate of thickness, H. Special consideration must be given to the substrate thickness for CPS TLines to operate into the THz region [14]. Ideally a CPS TLine is fabricated on a substrate which does not significantly confine the TE$_0$ substrate mode in order to minimize dispersion and loss. There are no established design criteria regarding acceptable substrate thickness, thus we define acceptable operating frequency to be a fraction of the next higher-order modes cutoff frequency $f<$ 1/10 $f_c^{TE_1}$ which is given by:
where $c_0$ is the speed of light. For a thin (H = 1 $\mu$m) Si$_3$N$_4$ membrane ($\varepsilon _{r2}$ $\approx$ 7.6 and tan $\delta _2$ $\approx$ 0.0056 [27]), $f_c^{TE_1}$ = 58.4 THz. Thus, by operating below 5.84 THz we can expect minimal confinement of the TE$_0$ mode. Quantification of the mode confinement as a function of transmission line geometry and frequency is outside the scope of this paper.
Fig. 1. Coplanar strip transmission line cross-section. T = 200 nm, H = 1 ${\rm \mu}$m, ${\rm \varepsilon} _{r1} \approx$ 1.0, ${\rm \varepsilon} _{r2} \approx$ 7.6. S = W = 20$\mu$m (for Configuration A), S = W = 40$\mu$m (for Configuration B).
Figure 2 illustrates the taper investigated in this work. The characteristic impedance, $Z_{\mathrm {0}}$, of a CPS TLine is a function of $k$ = S/(S+2W) [28]; thus, if $k$ remains fixed along the tapered section the impedance along its length is also constant and minimal reflections will occur due to Z$_0$ mismatches. If the taper has a simple linear geometric profile given by:
Tapering to larger cross sections after excitation can reduce the overall attenuation. A short taper appears desirable to quickly transition to a low-loss configuration, but if ${\rm L_T}$ is too short then substantial reflections can occur due to field discontinuities. This effect is analyzed via simulations in Section 3.
3. Simulations
In this work we investigate S$_2$ (= W$_2$) = 20 and 40 ${\rm \mu}$m because they have a lower attenuation coefficient than S$_1$(= W$_1$) = 10 ${\rm \mu}$m. The range of L$_\textrm {T}$ was selected to bracket the spatial pulse width. A realistic assumption is that the sub-picosecond THz pulse has a full width at half maximum (FWHM) of $\approx$0.8 ps [14] which corresponds to a spatial pulse width (free-space) of $\Delta x \approx$ 240 $\mu$m. We opted to investigate a wide range around $\Delta x$ and simulated from L$_\textrm {T} \ll \Delta x$ to L$_\textrm {T}\geq \Delta x$, or more specifically, L$_\textrm {T}$ = 5, 50, 250, 500, and 750 $\mu$m. This range of taper lengths is sufficient to illustrate the downside of short tapers, and demonstrate the ultra-wideband characteristics of long tapers.
The simulations performed here use ANSYS HFSS. The simulation material parameters are: $\sigma _{Au}$ = 41 MS/m, $\varepsilon _{r1}$ = 1.0, $\tan \delta _{1}$ = 0.0, $\varepsilon _{r2}$ = 7.6, and $\tan \delta _{2}$ = 0.0056 [27]. The substrate thickness is set to H = 1 $\mu$m in all simulations.
Figure 3 plots the simulated S-parameters for a selection of tapers where S$_1$(= W$_1$) = 10 ${\rm \mu}$m with different values of L$_\textrm {T}$ and S$_2$ (= W$_2$). Port 1 is at the start of the taper (z=0), Port 2 is at the end of the taper (z=L$_\textrm {T}$). A reference (no taper) is included for direct comparison where S$_1$(= W$_1$) = S$_2$(= W$_2$) = 10 ${\rm \mu}$m [Figs. 3(a) and 3(d)]. We desire an ultra-wideband connection (between 0.1 THz and 3.0 THz), therefore we require minimal $|$ S$_{11}$ $|$ and maximal $|$ S$_{21}$ $|$ within the specified bandwidth. From the reference, Fig. 3(a) approximates the numerical noise floor, and Fig. 3(d) illustrates the transmission through various length lossy TLines as a reference. Figures 3(b)–3(c) show that the magnitude of reflections increase with the addition of a taper. For these cases [Figs. 3(b)–3(c)] it should be recognized that long tapers exhibit lower reflections due to smaller field discontinuities. This benefit comes at the cost of higher conductor losses [Fig. 3(d)]. However, if the taper is too short then the substantial reflection reduces the transmission, this is seen in Fig. 3(f) for L$_\textrm {T}$ = 5 and 50 $\mu$m.
Fig. 3. Simulated S-parameters for various taper lengths, L$_\textrm {T}$, with S$_2$ (=W$_2$) = 10, 20, 40 $\mu$m and S$_1$ = W$_1$ = 10 ${\rm \mu}$m.
The purpose of TLine tapers is to provide an ultra-wideband transition region between two different cross-sectional geometries on a physical wafer of limited size. It is possible to examine longer tapers than presented, but this is counterproductive because shorter tapers are desired to optimize wafer usage. As an estimate, we have found performance to be sufficient when the taper length is $\approx$2-3$\times$ longer than the spatial pulse length; e.g., L$_{\mathrm {T}}$ $>$ (2-3)$\Delta x$. We do recommend that simulations are performed for every design prior to fabrication to ensure the return loss is acceptable for the specific application.
As noted earlier, one benefit of tapers relates to reducing the attenuation in a cascaded system (taper and lossy TLine). Figure 4 plots $|$S$_{21}|$ for a cascaded taper and lossy TLine totaling 6 mm. Port 1 is at the start of the taper (z=0), Port 2 is at the end of the taper and TLine (z=L$_\textrm {T}$+L$_\textrm {TLine}$ = 6 mm). For this system $|$S$_{11}|$ is identical to Figs. 3(a)–3(c) since the TLine is terminated in an ideal port. We desire to maximize $|$S$_{21}|$ of the system. This important concept is observed by comparing Figs. 4(b) and 4(c) with 4(a) where it is seen that $|$S$_{21}|$ increases when a taper of sufficient length (L$_\textrm {T}$ $>$ 250 $\mu$m) is present.
Fig. 4. Simulated S-parameters for cascaded taper and transmission line totaling 6 mm. S$_{11}$ is identical to Figs. 3(a)–3(c). S$_2$ (=W$_2$) = 10, 20, 40 $\mu$m and S$_1$ (= W$_1$) = 10 ${\rm \mu}$m.
To demonstrate that linear tapers can function as an ultra-wideband interconnection we need to observe a non-oscillatory spectral response at the receiver. Our primary effort is to demonstrate this concept. For the design and experiment in the following sections we desire minimal reflections (based on simulation), thus we select to use L$_\textrm {T}$ = 750 $\mu$m (or L$_\textrm {T}$ $\approx$ $3\Delta x$).
4. Experiment and design
Figure 5 illustrates the metallization pattern on the Si$_3$N$_4$ membrane used to study cascaded tapers. Figure 6 is a microscope image of a fabricated circuit. Figure 7 is a simplified 3D rendering of the test device. The transmitter and receiver are thin LTG-GaAs films (0.4 $\mu$m thick) which are bonded to the TLine using Van der Waals bonding [15,16,29]. We have found this bonding method to be stable, repeatable, and insensitive to small misalignment. The thin LTG-GaAs devices were fabricated using molecular beam epitaxy (MBE) and photolithography (deposition and etching). To start, a LTG-GaAs layer (0.94 $\mu$m) was grown on-top of an AlAs layer (0.9 $\mu$m) on-top of a semi-insulating GaAs substrate (600 $\mu$m) via MBE. Next, the wafer was then processed via photolithograhy. Gold pads are patterned using physical vapour deposition (RF sputtering), then LTG-GaAs mesa structures are formed using a lithographically-defined citric acid and hydrogen peroxide (4:1) etch. Finally, the LTG-GaAs thin film was separated by submersion in HF acid (10%), then the individual devices were obtained by back-etching the LTG-GaAs (again in citric acid and hydrogen peroxide). The intricate details of this procedure are lengthy and are described in more detail in [15]. Note that we use 0.4 $\mu$m LTG-GaAs thin films, but fabricated a 0.94 $\mu$m layer, this difference originates from the back-etch which separates individual LTG-GaAs devices.
Fig. 5. Circuit used to evaluate the characteristics of the taper (L$_\textrm {T}$) and transmission line (L$_1$). See Table 1 for fabricated dimensions.
Table 1. Design parameters for Fig. 5. Units in $\mathrm {\mu m}$.
The experimental system operates as follows: (1) A DC-bias (25V) is applied to transmitter and a lock-in amplifier connected to receiver, (2) a fs-laser (80 fs) is focused onto the transmitter (optically chopped at 880 Hz) and receiver, (3) a sub-ps pulse is generated at transmitter, travels along TLine0 (Pulse X) and TLine2 (Pulse Y), (4) Pulse X travels directly to the receiver and is used as a reference, (5) Pulse Y travels to the end of TLine2 then reflects ($|\Gamma |$), (6) Pulse Y travels backwards and is detected at the receiver, (7) the difference between Pulse X and Pulse Y is used to measure $|$S$_{11}|$ of taper and TLine2. Note the relation: $| S_{11} | \approx | S_{21} |^2 |\Gamma |$.
The length of L$_{\mathrm {2}}$ was selected to allow of sufficient temporal separation between Pulse X and Pulse Y to achieve reasonable spectral resolution, this can be estimated as:
which is acceptable for characterizing the transmission into the THz region. The length of L$_{\mathrm {0}}$ was selected such that Pulse X reflections between receiver and transmitter could easily be windowed out. A summary of the design parameters is given in Table 1.The characteristic impedance (simulated at f = 1 THz) of the individual CPS TLines are given by: Z$_{0}$(S=W=10$\mu$m) = 190 $\Omega$, Z$_{0}$(S=W=20$\mu$m) = 202 $\Omega$, and Z$_{0}$(S=W=40$\mu$m) = 205 $\Omega$. It is clear that they are not identical. Note that the small differences originate from the presence of a thin substrate. Future work could synthesize a non-linear taper geometry to maintain constant Z$_{0}$; however, the experimental results (later in Section 5) illustrate that this added effort may not be worthwhile due the excellent performance of the linear taper.
Again, longitudinal resonances must be considered when classifying a device to be ultra-wideband. If strong oscillatory behaviour exists in the spectral response at the receiver, then an undesirable cavity exists. In this work we are concerned with the free spectral range (FSR) of a taper which is calculated by: FSR$= c_0/(2 \mathrm {L_T} \mathrm {\sqrt {\varepsilon _{r,eff}}} )$. For $\mathrm {L_T}$ = 750 $\mu$m, FSR $\approx$ 182 GHz. We revisit this in the Section 6.
5. Results
Figures 8(a) and 8(d) plot the measured time-domain THz signals for the two TLine configurations: S$_2$ (= W$_2$) = 20 and 40 $\mu$m. The time-domain traces for Pulse X and Pulse Y were obtained from a single scan, but they are plotted separately to clearly identify the temporal windows used for calculating the Fourier transforms. The magnitude of the Fourier transforms are plotted in Figs. 8(b) and 8(e). Comparing these values [Figs. 8(c) and 8(f)] allows for calculation of $|$S$_{11}|$ for the cascaded taper and TLine similar to the data in Figs. 4(b) and 4(c).
6. Discussion
The results plotted in Fig. 8 characterize $|$S$_{11}|$ for the two CPS TLine configurations. There are some key observations from Fig. 8. First, Pulse X and Pulse Y for both configurations are similar except for the anticipated attenuation and minor temporal broadening. There are no significant resonances at the aforementioned FSR$\approx$182 GHz, thus these tapers are ultra-wideband. As expected Pulse Y for Configuration B has higher $|$S$_{11}|$ (at low frequency), therefore Configuration B has lower loss [Fig. 4(b) and 4(c)]. The high-frequency roll-off for Configuration B is attributed to $|\Gamma |$ (see Fig. 9). This occurs due to radiation because the cross-section at the open-circuit (S+2W = 120 $\mu$m) becomes comparable to $\lambda _0/2$. Future work will investigate a means to mitigate this effect. The simulated traces in Figs. 8(c) and 8(f) are obtained from the complex complex propagation constant of the transmission line. There is excellent agreement up-to the frequency when the end of the transmission line begins radiate ($\approx$ 1.5 THz for Configuration A, and $\approx$ 0.75 THz for Configuration B).
The spectral bandwidth of Pulse X (Fig. 8) dictates the maximum measurable bandwidth of Pulse Y, here that is approximately 3.0 THz with our lock-in amplifier. To measure frequencies beyond 3.0 THz alternative TLine0 configurations should be examined. We find that the attenuation is reasonable for many pulsed THz applications since the inherent roll-off of the broadband pulse is greater than the attenuation added by the TLine.
We can compare the results presented here with other values in literature. In [12] the authors use a similar technique to investigate various CPS TLines on thick low-permittivity substrates. They found that a plastic substrate (Pax, Tsurupica) with S (= W) = 20 $\mu$m resulted in an attenuation coefficient of $\alpha$ $\approx$ 1.7 dB/mm at 1 THz. As a direct comparison we measured $\alpha$ $\approx$ -S$_{11}$/12mm = 11.5 dB/12mm = 0.96 dB/mm at 1 THz which is similar to the value found in [14] ($\alpha$ = 0.9 - 1.0 dB/mm).
To our knowledge, Pulse Y illustrated in Fig. 8(a) demonstrates the furthest an ultra-wideband pulse (with a $\approx$2 THz bandwidth at −40 dB dynamic range) has been transmitted using CPS TLines (total distance of approximately 22 mm, or $\approx$100$\Delta x$).
7. Conclusion
We have shown that TSoC TLine tapers are ultra-wideband devices that can reduce the attenuation of a cascaded taper and transmission line. We did not observe resonant behaviour in the received THz-bandwidth pulse which supports the ultra-wideband claim. These tapered transmission lines will be an important building block in many future devices. Here we investigated the attenuation for a uniform TLine, this technique can be extended to investigate a number of different devices.
Funding
Natural Sciences and Engineering Research Council of Canada.
Acknowledgments
This work made use of the 4D LABS shared facilities supported by the Canada Foundation for Innovation (CFI), British Columbia Knowledge Development Fund (BCKDF), Western Economic Diversification Canada (WD) and Simon Fraser University (SFU).
We would like to acknowledge CMC Microsystems for the provision of products (ANSYS HFSS) and services that facilitated this research.
Disclosures
The authors declare no conflicts of interest.
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