Vacuum Voltage Gap: Principles & Applications

• Vacuum voltage gap is a vacuum separation in devices where electrical behavior is determined by geometry and boundary conditions rather than bulk dielectric properties.
• It underpins diverse functions such as tunneling barriers in Au-vacuum-Au junctions, free-space emission in nano vacuum electronics, and insulation in high-voltage feedthroughs.
• Optimized vacuum-gap designs reduce dielectric loss in superconducting circuits while enabling precise control over tunneling, space-charge dynamics, and breakdown phenomena.

Searching arXiv for the cited papers to ground the article in current arXiv records. arXiv search query: "Vacuum-gap transmon qubits realized using flip-chip technology" A vacuum voltage gap is a vacuum separation across which voltage, electric field, transport, or stored energy is set primarily by geometry and boundary conditions rather than by a bulk dielectric medium. In the cited literature, the same basic construct appears in several distinct forms: a shunt capacitor gap in superconducting circuits, a tunneling barrier in Au–vacuum–Au junctions, a free-space emitter–collector channel in planar nano vacuum electronics, a high-voltage insulation region in feedthroughs and arc studies, an internally sealed optical path in Fabry–Pérot cavities, and an extreme-near-field separation in which phonon transmission arises through intersurface coupling (Li et al., 2021, Trouwborst et al., 2011, Turchetti et al., 2022, Liu et al., 2024, Tokunaga et al., 2021).

1. Geometric meaning across device classes

The defining parameter is the vacuum separation itself, but its physical role depends strongly on scale. In superconducting microwave components, the gap is a compact parallel-plate region intended to confine electric field in vacuum rather than in amorphous dielectrics (0810.1976). In nano vacuum electronics, the gap sets the local field through the usual scaling $E \sim V/d$, thereby controlling turn-on voltage, emission regime, and space-charge effects (Turchetti et al., 2022). In high-voltage systems, the gap must prevent flashover or vacuum breakdown while maintaining acceptable field stress near metal edges and triple-junction-like regions (Sterling et al., 2012, Gicala et al., 2021). In precision optics, the vacuum gap becomes the sealed internal environment of the cavity itself rather than the external package (Liu et al., 2024).

Context	Gap or scale	Reported function
Flip-chip transmon (“flipmon”)	$5 \pm 0.4~\mu\text{m}$	Shunt capacitor gap
Planar nano vacuum emitters	$\sim 10$–20 nm	Free-space emission channel
Vacuum microdiodes	order of $1~\mu\text{m}$; also $18$ nm and $500$ nm cases	THz self-bunching gap
Microfabricated flashover structures	3–15 $\mu$m	Surface flashover path
Triode ecton/spark experiment	1 mm cathode–gate spacing	Breakdown threshold control

A recurring implication is that “vacuum gap” does not denote a single regime. The same term can refer to a nominally insulating region, a field-emission channel, a tunneling barrier, or a low-loss electromagnetic energy-storage region, depending on length scale and electrode or surface structure.

2. Electrostatics, field participation, and geometric optimization

In low-loss superconducting capacitors, the idealized design follows the parallel-plate relation

$C=\varepsilon_0 \frac{A}{d},$

with the field intended to be “confined mostly within the vacuum gap” (0810.1976). This design motivation is explicit in vacuum-gap capacitors (VGCs), where replacing amorphous dielectrics with vacuum suppresses two-level-system-related dielectric loss in superconducting resonators (0810.1976, 0910.5252).

The flip-chip transmon implementation makes the same electrostatic logic explicit at the qubit level. In the “flipmon,” one capacitor pad and the single Josephson junction are placed on the bottom chip, the other pad on the top chip, and the two chips are bonded face-to-face by indium bumps. The vacuum gap is the chip-to-chip spacing set by the bump height and stop-bump bonding scheme, with an average gap of about $5~\mu\text{m}$ and sample-to-sample deviations below $0.5~\mu\text{m}$ (Li et al., 2021). Simulations reported an energy participation ratio of $5 \pm 0.4~\mu\text{m}$0 in the vacuum-gap/air region, compared with about $5 \pm 0.4~\mu\text{m}$1 in air for a traditional planar transmon, while the indium-bump surface participation was $5 \pm 0.4~\mu\text{m}$2 (Li et al., 2021). The same simulations indicated that the metal-air interface participation rises substantially and may dominate decoherence, even though the vacuum gap itself should reduce dielectric loss (Li et al., 2021).

At much higher voltages, electrostatic optimization becomes a holdoff problem rather than a loss problem. For a coaxial feedthrough fully described by a layered dielectric model, the center-conductor surface field is written as

$5 \pm 0.4~\mu\text{m}$3

with optimum radius

$5 \pm 0.4~\mu\text{m}$4

(Si et al., 8 Jun 2026). For the commercial 100 kV CF-flange feedthrough studied there, the analytical optimum was $5 \pm 0.4~\mu\text{m}$5 mm in vacuum and $5 \pm 0.4~\mu\text{m}$6 mm in LXe, whereas the original center conductor radius was $5 \pm 0.4~\mu\text{m}$7 mm. Finite-element analysis found a minimum near $5 \pm 0.4~\mu\text{m}$8 mm, reducing the peak field from $5 \pm 0.4~\mu\text{m}$9 to $\sim 10$0 in vacuum and from $\sim 10$1 to $\sim 10$2 in LXe (Si et al., 8 Jun 2026). This directly illustrates that vacuum-gap engineering is often a problem of field shaping, not only of nominal spacing.

3. Tunneling, emission, and space-charge regimes

In Au–vacuum–Au junctions, the vacuum gap acts as a clean tunneling barrier used to benchmark Transition Voltage Spectroscopy (TVS). TVS employs the Fowler–Nordheim representation $\sim 10$3 versus $\sim 10$4, and the minimum defines the transition voltage $\sim 10$5 (Trouwborst et al., 2011). In cryogenic mechanically controllable break junctions at $\sim 10$6 K, $\sim 10$7 was typically above $\sim 10$8 V and often around $\sim 10$9–$1~\mu\text{m}$0 V for a given junction. However, the measured $1~\mu\text{m}$1 was only weakly distance dependent, nonmonotonic, and not proportional to $1~\mu\text{m}$2; it also depended on polarity and local tip structure (Trouwborst et al., 2011). A central conclusion was therefore that the distance dependence $1~\mu\text{m}$3 alone cannot distinguish molecular junctions from vacuum tunneling junctions (Trouwborst et al., 2011).

In planar nano vacuum emitters, the same vacuum gap functions as a free-space emission channel with regime changes visible in the $1~\mu\text{m}$4–$1~\mu\text{m}$5 characteristics. The studied pNVC bow-tie diodes used sub-20 nm gaps, specifically $1~\mu\text{m}$6–20 nm, and could turn on at low voltages below 10 V (Turchetti et al., 2022). Three regimes were isolated in a single device class: Schottky, Fowler–Nordheim, and saturation. Schottky emission appears linear in a $1~\mu\text{m}$7 versus $1~\mu\text{m}$8 plot, FN emission in a $1~\mu\text{m}$9 versus $18$0 plot with negative slope, and saturation was attributed to Child–Langmuir space-charge limitation (Turchetti et al., 2022). Au devices were interpreted as Schottky-like over the measured range, whereas TiN devices showed Schottky-like behavior at about $18$1–10 V, FN-like behavior at about $18$2–13 V, and saturation above about $18$3 V (Turchetti et al., 2022). A key caution was that quasi-linearity in FN coordinates does not by itself prove FN dominance, since Schottky emission can mimic FN behavior over limited ranges (Turchetti et al., 2022).

Space-charge effects dominate even more explicitly in vacuum microdiodes. Simulations showed regular modulation for gap sizes on the order of $18$4 and accelerating voltage on the order of $18$5 V, producing THz-frequency bunching (Ilkov et al., 2014). The mechanism is self-bunching: emitted charge builds up in the gap, suppresses further emission, and then relaxes as the bunch accelerates away, allowing a new bunch to form. Frequency grows with applied field and decreases with emitter area, and coupling between neighboring emitters was approximated as

$18$6

with $18$7 (Ilkov et al., 2014). The same work showed that arrays can outperform a single emitter of equal total area because synchronized oscillators can provide coherent addition, with in-phase power scaling up to $18$8 rather than $18$9 (Ilkov et al., 2014).

4. Breakdown, flashover, and conditioning

At high field, the vacuum gap ceases to be a passive spacer and becomes the site of discharge initiation. Nanosecond-resolved imaging of vacuum arc formation in a tip-to-plane copper gap showed that breakdown occurs when the local electric field at the cathode tip reaches approximately $500$0 (Zhou et al., 2019). The observed sequence was cathode radiance first, then delayed anode glow, and finally decay. For a 3 mm gap, the cathode-radiance stage lasted about 150 ns before significant anode activity developed (Zhou et al., 2019). The study concluded that the conductive channel is built by cathodic plasma long before the anode glow becomes important, and that anode illumination is a secondary effect caused by cathode-generated electrons heating the anode (Zhou et al., 2019).

In microfabricated devices, the limiting process is often not bulk vacuum breakdown but surface flashover along a dielectric. The cited model expresses the flashover voltage as

$500$1

with $500$2 absorbing poorly known surface and desorption parameters (Sterling et al., 2012). Using this framework, the reported fabrication changes produced a more than $500$3 increase in flashover voltage, and in the best silicon-nitride case a $500$4 improvement relative to an amorphous silicon dioxide baseline (Sterling et al., 2012). The same work also found that a conductive substrate or buried conductor beneath the dielectric reduced flashover voltage by about $500$5, consistent with field-line crowding near the triple point (Sterling et al., 2012).

Conditioning history is itself a control parameter. In pulsed-dc copper-electrode experiments at fields up to about $500$6 across a $500$7 gap, longer idle time between pulses increased the probability that the next pulse would produce a breakdown (Saressalo et al., 2020). Secondary breakdowns were concentrated during voltage recovery after a breakdown, particularly when recovery involved stepwise ramps and pauses of about 20 s after voltage changes (Saressalo et al., 2020). The best recovery strategy in that system was a linear increase with minimal idle time, which reduced power losses due to secondary breakdown events (Saressalo et al., 2020).

Feedthrough design embodies the same principles at device scale. A coaxial vacuum-tight feedthrough for cryogenic detectors used a grounded outer sheath embedded into polyurethane resin so that no conductor was exposed to the outside, thereby confining the potential drop inside the dielectric-coaxial structure and suppressing dark/glow discharges in the gas phase above the liquid (Kreslo et al., 2010). It operated down to 77 K, carried up to 30 kV, and showed no leak at a helium leak-detector sensitivity of $500$8 (Kreslo et al., 2010). A different high-voltage approach replaced alumina with UHMWPE in a custom feedthrough for a DC femtosecond electron diffractometer; after gas and voltage conditioning, it achieved 180 kV and $500$9 Torr, while the maximum calculated surface field at $\mu$0 kV was $\mu$1, below the empirically cited vacuum-breakdown level of about $\mu$2 for conditioned surfaces (Gicala et al., 2021).

5. Vacuum gaps in low-loss superconducting circuits and ultrastable cavities

Vacuum-gap superconducting components were introduced specifically to remove amorphous dielectrics from high-field regions. In VGCs fabricated by optical lithography and micromachining, plate separations of 200 nm and 500 nm were realized, with vacuum-volume to post-volume ratios as high as 0.99 and stable geometries scalable above 100 pF (0810.1976). Resonance measurements at 50 mK on LC circuits incorporating these capacitors gave low-power loss tangents as low as $\mu$3, significantly below dielectric-filled capacitors (0810.1976).

The subsequent “vacuum-gap technology” integrated both VGCs and vacuum-gap wiring crossovers (VGXs) into multiplexed resonators and phase qubits. These circuits showed internal quality factors in the range $\mu$4 at 50 mK, and resonators with VGCs as large as 180 pF confirmed single-mode behavior (0910.5252). The same paper attributed residual loss not to the vacuum gap itself but likely to amorphous native oxides on the inner Al surfaces (0910.5252). This is consistent with the broader pattern that vacuum regions remove bulk dielectric TLS participation, but not necessarily surface-related loss channels.

The flip-chip transmon extends the same logic to qubit layout. Its principal motivation was reduced footprint and compatibility with flexible 3D wiring, while moving a large share of the electric-field energy into the vacuum-gap capacitor region (Li et al., 2021). Measured coherence times were in the 30–60 $\mu$5s range, comparable to similarly fabricated planar devices, and no evidence indicated that indium bumps inside the qubit caused significant decoherence (Li et al., 2021). The likely dominant loss channel was instead the increased metal-air interface participation (Li et al., 2021). A common misconception is therefore that merely introducing a vacuum gap guarantees a coherence improvement; the cited measurements suggest that surface participation can remain decisive even when substrate dielectric participation is reduced.

A formally different but conceptually related implementation appears in ultrastable Fabry–Pérot cavities. There, optical-contact bonding performed under vacuum seals the cavity internals themselves, so the cavity can be operated in air without a vacuum enclosure (Liu et al., 2024). For the 9.7 mL cavity at 1550 nm, the measured Allan deviation was $\mu$6 at 1 s, phase noise was thermal-noise-limited from 0.1 Hz to 10 kHz, and the phase noise reached about $\mu$7 at 10 kHz offset (Liu et al., 2024). No observed degradation in cavity stability was reported for over 1 year after bonding (Liu et al., 2024). A 0.5 mL microfabricated version reached about $\mu$8 at 10 kHz offset frequency (Liu et al., 2024). In this context, the vacuum gap is not a voltage-insulation region but an internally preserved low-index reference volume.

6. Extreme-near-field coupling and transient over-acceleration

At nanometer and sub-nanometer separations, a vacuum gap need not eliminate all energy transfer. One continuum treatment considered phonon-mediated heat transfer across a vacuum gap through van der Waals coupling between two closely spaced solids (Sasihithlu et al., 2016). The central result was that sinusoidal surface deformation introduces a modified-Bessel-function factor $\mu$9, giving an exponential suppression of large in-plane wavevector contributions for $C=\varepsilon_0 \frac{A}{d},$0 (Sasihithlu et al., 2016). In that treatment, phonon transfer across vacuum for polymer surfaces became comparable to air conduction at a gap of about 1 nm (Sasihithlu et al., 2016).

A first-principles treatment of intrinsic Si–vacuum–Si structures refined the mechanism. There, overlap of electron wave functions across the vacuum gap created weak covalent interaction between the silicon surfaces, generating finite interatomic force constants and a phonon pathway (Tokunaga et al., 2021). The computed phonon heat transfer coefficient increased steeply as the gap decreased, exceeded near-field radiation below about 1 nm, and in the range $C=\varepsilon_0 \frac{A}{d},$1 to $C=\varepsilon_0 \frac{A}{d},$2 nm followed approximately

$C=\varepsilon_0 \frac{A}{d},$3

without vdW correction (Tokunaga et al., 2021). Acoustic modes dominated the transfer, accounting for more than $C=\varepsilon_0 \frac{A}{d},$4 in the vacuum-gap regime (Tokunaga et al., 2021). This directly contradicts the simple intuition that vacuum necessarily blocks phonon heat transport.

Fast-pulsed high-voltage diodes show another nonclassical effect. In nanosecond and subnanosecond gas-filled and vacuum diodes, electrons with kinetic energies nominally exceeding $C=\varepsilon_0 \frac{A}{d},$5 were reconstructed from foil-attenuation data using regularized inverse methods supported by deep machine learning (Tarasenko et al., 26 Jun 2026). In the gas-filled 6.5 mm gap case, about $C=\varepsilon_0 \frac{A}{d},$6 of beam electrons had $C=\varepsilon_0 \frac{A}{d},$7; in the 4 mm vacuum diode at about 230 kV, the corresponding fraction was approximately $C=\varepsilon_0 \frac{A}{d},$8; in a long-pulse 12 cm vacuum-gap control experiment, the anomalous-energy fraction above 150 keV was only $C=\varepsilon_0 \frac{A}{d},$9 (Tarasenko et al., 26 Jun 2026). The proposed mechanism in vacuum was spatio-temporal synchronism of fast electrons with a space-charge-enhanced field forming in the gap (Tarasenko et al., 26 Jun 2026). This suggests that, under sufficiently fast excitation, the effective accelerating structure of a vacuum gap is determined by transient self-consistent field formation rather than by the static applied voltage alone.

Taken together, these results show that a vacuum voltage gap is not reducible to an empty insulating interval. Depending on scale and operating regime, it can redistribute electromagnetic participation to reduce dielectric loss, define tunneling and field-emission barriers, localize or suppress breakdown, preserve an optical reference path, or even support phonon transfer and transient over-acceleration through intersurface coupling and space-charge dynamics. The literature consistently indicates that geometry, surfaces, interfaces, and temporal excitation history are as important as nominal gap size.