Monolithic Coplanar Stripline Platform

• Monolithic coplanar stripline platforms are planar on‐chip transmission architectures that integrate conductors, loading structures, and active components in a single lithographically patterned substrate.
• They employ symmetric designs and mode engineering to achieve pure odd-mode propagation, reduce parasitic inductance and capacitance, and enable broadband performance from sub-GHz to THz regimes.
• Fabrication leverages precise lithography and material integration—using superconductors, semiconductors, or CMOS processes—to co-design routing, biasing, and readout functions within a compact footprint.

A monolithic coplanar stripline platform is a planar on-chip transmission-line architecture in which the conductors, passive loading structures, and often the active generator, detector, resonator, or gate elements are realized in one lithographically defined device stack on a single substrate (Klotz et al., 2011, Qaderi et al., 2017, Kusyak et al., 28 Jul 2025). In the reported literature, “monolithic” ranges from a single superconducting film pattern on one dielectric substrate, to one continuous metal structure that simultaneously serves as microwave delivery, electrical top gate, and shadow mask, to a fully integrated terahertz circuit with photoconductive switches deposited directly on sapphire (Qaderi et al., 2017, Klotz et al., 2011, Kusyak et al., 28 Jul 2025). Across these realizations, the common objective is to control modal content, minimize parasitic inductance and capacitance, and co-integrate transmission, coupling, and readout functions within a compact planar footprint.

1. Definition, scope, and neighboring line geometries

A coplanar stripline, as used for spin-control structures, consists of two parallel metallic conductors lying in the same plane on an insulating or semiconducting substrate, with no explicit ground plane above or below; the two strips are driven differentially and can be shorted together at the termination (Klotz et al., 2011). In related work, coplanar waveguide variants retain the same planar layout but use a ground–signal–ground arrangement on one substrate face, while buried stripline places a center conductor between two wide ground planes with the intervening region filled by dielectric (Biurrun-Quel et al., 2022, Monarkha et al., 2024).

The term “monolithic” has been used with different but compatible meanings. In the YBCO rf-SQUID platform, it denotes a single superconducting film pattern on a single LaAlO$_3$ substrate, with pick-up loop, input loop, and resonator all defined in one patterned YBCO layer and no multilayer superconducting stack, no vias, and no overlapping superconducting layers (Qaderi et al., 2017). In the quantum-dot CPS platform, it denotes one continuous Ti/Au structure that simultaneously acts as microwave antenna, Schottky top contact, and optical aperture mask (Klotz et al., 2011). In the terahertz CPS platform, it denotes fully monolithic fabrication of metal lines and amorphous-silicon photoconductive switches on the same sapphire chip, so that generation, transmission, and detection all occur on one substrate (Kusyak et al., 28 Jul 2025).

This broad usage places the monolithic coplanar stripline platform within a wider family of planar microwave and terahertz systems rather than restricting it to a single cross-section. A plausible implication is that the defining property is not a specific conductor topology alone, but the co-fabrication of the transmission medium and its functional peripherals in one planar process.

2. Electromagnetic operation and mode engineering

The principal electromagnetic quantities are those of a distributed transmission line. For slow-wave coplanar lines, the characteristic impedance is approximated by

$Z_0 \approx \sqrt{\frac{L'}{C'}}$

the propagation constant is

$\gamma = \alpha + j\beta$

and the phase velocity is

$v_p = \frac{1}{\sqrt{L' C'}}$

with the line quality factor written as

$Q = \frac{\beta}{2\alpha}$

(Hsu et al., 2024). These relations recur across implementations: geometry changes the per-unit-length inductance and capacitance, which in turn set impedance, field confinement, attenuation, and electrical length.

Mode control is central. A symmetric CPS supports odd and even quasi-TEM eigenmodes. In the odd mode, the strip charges are equal and opposite and the electric field is concentrated in the gap between the strips; in the even mode, the fields extend more strongly normal to the plane and into the surrounding space (Kusyak et al., 28 Jul 2025). The terahertz monolithic CPS platform enforced predominantly pure odd-mode propagation by capacitively coupling a central photoconductive generator symmetrically to both strips, rather than ohmically connecting a source to only one conductor. Finite-integration simulations and measurements showed that suppressing parasitic modes improved signal integrity, extended the operational frequency range to $0.05\text{–}1.4~\text{THz}$, and yielded an effective dielectric constant $\varepsilon_{\text{eff}} \approx 5.1$ with $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$ (Kusyak et al., 28 Jul 2025).

At millimeter-wave frequencies, monolithic coplanar platforms face a different modal problem: substrate and parallel-plate modes. Gap-waveguide coplanar lines solve this by placing the CPW on a substrate above an artificial magnetic conductor, creating a PEC–PMC parallel-plate region that suppresses substrate modes when

$h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$

(Biurrun-Quel et al., 2022). The resulting GapCPW and IGCPW geometries retain a coplanar layout while preventing substrate-mode propagation in-band and, in the inverted version, suppressing the odd slotline mode by means of a top metal cover and channel (Biurrun-Quel et al., 2022).

Superconducting monolithic platforms apply the same logic to resonator–sensor coupling. In the YBCO rf-SQUID configuration, resonator quality factor is extracted from $S_{11}$ via

$Z_0 \approx \sqrt{\frac{L'}{C'}}$0

while $Z_0 \approx \sqrt{\frac{L'}{C'}}$1 between a readout port and the SQUID junction port is used as a proxy for coupling to the SQUID (Qaderi et al., 2017). The design target is $Z_0 \approx \sqrt{\frac{L'}{C'}}$2, so the electromagnetic problem is not only resonance placement but simultaneous optimization of modal overlap, coupling coefficient, and loading (Qaderi et al., 2017).

3. Multifunctional integration patterns

A defining feature of monolithic coplanar stripline platforms is multifunctionality within one patterned structure. In the semiconductor quantum-dot implementation, the terminated CPS is simultaneously a broadband microwave delivery line, a Schottky top gate for charge control, and an opaque Au shadow mask containing $Z_0 \approx \sqrt{\frac{L'}{C'}}$3 apertures for single-dot spectroscopy (Klotz et al., 2011). The quantum dots lie approximately $Z_0 \approx \sqrt{\frac{L'}{C'}}$4 below the metal surface, directly beneath the CPS short, where finite-element calculations show strong in-plane $Z_0 \approx \sqrt{\frac{L'}{C'}}$5 components and an electric-field node. Test measurements on hydrogenated amorphous silicon yielded an average magnetic field of $Z_0 \approx \sqrt{\frac{L'}{C'}}$6 at the relevant device position, corresponding to a $Z_0 \approx \sqrt{\frac{L'}{C'}}$7-pulse time of $Z_0 \approx \sqrt{\frac{L'}{C'}}$8 for $Z_0 \approx \sqrt{\frac{L'}{C'}}$9, and the same platform was verified up to at least $\gamma = \alpha + j\beta$0 (Klotz et al., 2011).

The high-$\gamma = \alpha + j\beta$1 superconducting SQUID platform integrates a flux concentrator and resonator in one YBCO film. The chip contains a large square pick-up loop, a smaller circular input loop, and one of several coplanar resonators patterned either between the loops or inside the input loop, with the rf SQUID itself placed in flip-chip position above the monolithic YBCO structure (Qaderi et al., 2017). Three resonator realizations were explored: a long stripline or transmission-line resonator between pick-up and input loops, a complementary split ring resonator inside the input loop, and a multi-turn spiral inside the input loop. Among these, the spiral resonator gave the best combination of loaded $\gamma = \alpha + j\beta$2, resonance below $\gamma = \alpha + j\beta$3, and strong SQUID coupling (Qaderi et al., 2017).

The flexible planar control-line platform for superconducting qubits extends the same monolithic principle into cryogenic wiring. A buried stripline on polyimide with silver conductors integrates attenuators, an $\gamma = \alpha + j\beta$4 low-pass filter, and an infrared filter directly into the line stack, while maintaining $\gamma = \alpha + j\beta$5 characteristic impedance (Monarkha et al., 2024). The embedded attenuators are implemented as multiple $\gamma = \alpha + j\beta$6 cells based on a classical T-type resistive network, and the entire flex is thermally anchored at every refrigerator stage by copper clamps (Monarkha et al., 2024).

The terahertz CPS architecture is the most explicit system-level realization of the concept: a central generator photoconductive switch launches transients into two symmetric CPS branches, each branch carrying a detector photoconductive switch $\gamma = \alpha + j\beta$7 away, so that one side can host a sample and the other can serve as an in situ reference (Kusyak et al., 28 Jul 2025). Generation and detection remain galvanically isolated, yet strongly THz-coupled, and the CPS strips can simultaneously function as electrostatic gates for a device in the gap (Kusyak et al., 28 Jul 2025).

4. Materials, fabrication strategies, and process constraints

The material systems used for monolithic coplanar stripline platforms are diverse, but the process logic is consistent: define the transmission medium and its functional attachments in one planar stack, then exploit lithographic symmetry to manage fields and parasitics.

In the superconducting rf-SQUID platform, the stack is $\gamma = \alpha + j\beta$8 YBCO on a $\gamma = \alpha + j\beta$9 crystalline LaAlO$v_p = \frac{1}{\sqrt{L' C'}}$0 substrate with chip size $v_p = \frac{1}{\sqrt{L' C'}}$1, patterned into flux-concentrator loops and resonators in one layer (Qaderi et al., 2017). Minimum fine-feature linewidth and spacing are $v_p = \frac{1}{\sqrt{L' C'}}$2, used for the CSRR and spiral, while the transformer uses $v_p = \frac{1}{\sqrt{L' C'}}$3 to $v_p = \frac{1}{\sqrt{L' C'}}$4 conductors (Qaderi et al., 2017). The absence of multilayer alignment and via processing is explicitly identified as a fabrication advantage (Qaderi et al., 2017).

In the quantum-dot CPS implementation, the conductors are Ti/Au, typically $v_p = \frac{1}{\sqrt{L' C'}}$5 Ti and $v_p = \frac{1}{\sqrt{L' C'}}$6 Au in the test structure, on top of a semiconductor heterostructure or on hydrogenated amorphous silicon separated by a $v_p = \frac{1}{\sqrt{L' C'}}$7 benzocyclobutene insulating layer where direct gate contact is not needed (Klotz et al., 2011). The active a-Si:H strip in the test structure is $v_p = \frac{1}{\sqrt{L' C'}}$8 thick, $v_p = \frac{1}{\sqrt{L' C'}}$9 long, and $Q = \frac{\beta}{2\alpha}$0 wide (Klotz et al., 2011).

Gap-waveguide coplanar implementations rely on micromachined artificial magnetic conductors. The demonstrated prototypes used a $Q = \frac{\beta}{2\alpha}$1 silicon substrate, a bed of metallic pins with period $Q = \frac{\beta}{2\alpha}$2, pin width $Q = \frac{\beta}{2\alpha}$3, and pin height $Q = \frac{\beta}{2\alpha}$4, fabricated by DRIE Bosch etching and metallized with approximately $Q = \frac{\beta}{2\alpha}$5 Cu and $Q = \frac{\beta}{2\alpha}$6 Au (Biurrun-Quel et al., 2022). For IGCPW, a machined aluminum cover forms the top channel (Biurrun-Quel et al., 2022).

The slow-wave CMOS platform used a standard $Q = \frac{\beta}{2\alpha}$7 CMOS process with six metal layers: top metal $Q = \frac{\beta}{2\alpha}$8 about $Q = \frac{\beta}{2\alpha}$9 thick, lower metals about $0.05\text{–}1.4~\text{THz}$0, and vias about $0.05\text{–}1.4~\text{THz}$1 (Hsu et al., 2024). Its critical design variables were not only the signal and ground widths and gaps, but also the length, spacing, and stacking of periodic substrate shield strips beneath the line (Hsu et al., 2024).

The flexible stripline wiring for qubits used several-micron silver films for the center conductor and ground planes, polyimide as both dielectric and outer protective layer, and embedded planar resistive and filtering components (Monarkha et al., 2024). The monolithic THz CPS platform used Ti/Au conductors $0.05\text{–}1.4~\text{THz}$2 thick on $0.05\text{–}1.4~\text{THz}$3 c-cut sapphire together with amorphous silicon photoconductive switches deposited by electron-beam evaporation (Kusyak et al., 28 Jul 2025). That choice avoided heterogeneous bonding and III–V transfer, while enabling bias fields of at least $0.05\text{–}1.4~\text{THz}$4 at the generator without visible degradation (Kusyak et al., 28 Jul 2025).

5. Representative operating regimes and measured performance

The published record shows that monolithic coplanar stripline platforms are not confined to one frequency decade or one application class. Reported implementations span sub-gigahertz superconducting resonators, multi-gigahertz spin-control lines, $0.05\text{–}1.4~\text{THz}$5 CMOS slow-wave structures, and on-chip terahertz systems (Qaderi et al., 2017, Klotz et al., 2011, Hsu et al., 2024, Kusyak et al., 28 Jul 2025).

Regime	Monolithic configuration	Representative performance
Semiconductor spin control	Terminated Ti/Au CPS serving as microwave delivery, top gate, and shadow mask	$0.05\text{–}1.4~\text{THz}$6 average $0.05\text{–}1.4~\text{THz}$7; $0.05\text{–}1.4~\text{THz}$8 $0.05\text{–}1.4~\text{THz}$9-pulse time; operation up to at least $\varepsilon_{\text{eff}} \approx 5.1$0 (Klotz et al., 2011)
HTS SQUID coupling	One-layer YBCO flux concentrator with spiral resonator inside input loop	$\varepsilon_{\text{eff}} \approx 5.1$1, $\varepsilon_{\text{eff}} \approx 5.1$2, $\varepsilon_{\text{eff}} \approx 5.1$3 (Qaderi et al., 2017)
CMOS slow-wave coplanar line	$\varepsilon_{\text{eff}} \approx 5.1$4 CMOS with periodic substrate shield strips	$\varepsilon_{\text{eff}} \approx 5.1$5 at $\varepsilon_{\text{eff}} \approx 5.1$6; about $\varepsilon_{\text{eff}} \approx 5.1$7 increase in maximum peak $\varepsilon_{\text{eff}} \approx 5.1$8; phase velocity reduced by roughly $\varepsilon_{\text{eff}} \approx 5.1$9 (Hsu et al., 2024)
Cryogenic planar control line	$$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$0 Ag/polyimide stripline with embedded attenuators and filters	Total attenuation of $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$1 close to zero frequency; no measurable effect on qubit coherence compared to coaxial control lines (Monarkha et al., 2024)
On-chip THz spectroscopy	Ti/Au CPS on sapphire with monolithic amorphous-Si generator and detector switches	$$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$2; $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$3; $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$4; on-chip THz fields on the order of $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$5 (Kusyak et al., 28 Jul 2025)

A closely related superconducting stripline resonator platform, while not coplanar, is instructive as a comparator. Pb stripline resonators measured in parallel magnetic field reached maximum $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$6 at $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$7 and zero field, and when a Sn sample replaced one ground plane the quality factor fell to $$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$8, demonstrating how planar resonators can be repurposed as microwave spectroscopy probes for other materials (Ebensperger et al., 2016).

Taken together, these results suggest that “monolithic coplanar stripline platform” is best understood as a scalable design methodology rather than a single device class. The methodology accommodates broadband non-resonant lines, high-$$v_{\text{ph}} \approx 0.44c \approx 132~\mu\text{m/ps}$$9 resonators, slow-wave interconnects, and balanced THz launchers, provided that the line geometry, coupling topology, and integrated peripherals are co-designed.

6. Limitations, misconceptions, and adjacent directions

A common misconception is that “monolithic” requires every active element to reside in the same electrically continuous layer. The YBCO rf-SQUID system shows a narrower definition: the flux transformer and resonator are integrated in one patterned superconducting layer, but the rf SQUID itself is a separate flip-chip component (Qaderi et al., 2017). In other words, monolithic integration can apply to the planar RF platform even when the ultimate sensing element is separately aligned.

Another misconception is that a coplanar layout automatically guarantees single-mode behavior. The evidence argues otherwise. In the THz CPS architecture, conventional DC-coupled launching excited mixed unbalanced even and odd modes with substantial field outside the CPS region, whereas symmetric capacitive coupling enforced predominantly pure odd-mode propagation (Kusyak et al., 28 Jul 2025). In millimeter-wave silicon technology, standard conductor-backed CPW supported TM0 and TM1 substrate modes, and only the introduction of an AMC-based stopband removed those parasitic channels over the operational band (Biurrun-Quel et al., 2022). Coplanarity, by itself, is therefore not sufficient; mode purity is a separate design task.

A third concern is that replacing coaxial wiring with planar stripline or coplanar structures necessarily degrades coherence in superconducting quantum hardware. Repeated transmon measurements over $h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$0 to $h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$1 per run and across four cooldowns found that changing the microwave control lines from semi-rigid coaxial cables to flexible stripline transmission lines did not have a measurable effect on coherence compared to thermal cycling the system or random coherence fluctuations (Monarkha et al., 2024). This does not prove equivalence for every planar interconnect architecture, but it does directly refute the claim for the tested stripline platform.

Adjacent architectures indicate additional directions for the field. A compact bilateral single-conductor surface-wave transmission line converted the QTEM mode of a low-impedance bilateral slotline into the TM mode of a corrugated single-conductor guide, halving the size of conventional transitions between CPW and single-conductor lines and showing $h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$2 below $h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$3 and $h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$4 above $h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$5 over approximately $h_s < \frac{\lambda_0}{4\sqrt{\varepsilon_r}}$6 (Xu et al., 2017). This suggests a route from monolithic coplanar feeds to integrated surface-wave circuits, where the platform remains planar but the guided mode is no longer a conventional coplanar quasi-TEM field.

A plausible overarching implication is that future monolithic coplanar stripline platforms will continue to converge around three design imperatives already visible in the literature: balanced excitation to enforce the intended mode, integrated shielding or slow-wave loading to suppress parasitic substrate participation, and multifunctional patterning so that routing, coupling, biasing, and referencing are achieved within one planar process (Kusyak et al., 28 Jul 2025, Biurrun-Quel et al., 2022, Hsu et al., 2024).