Preliminary calculations suggest it’s feasible to build electrostatic relays out of paper and graphite that operate reliably for millions of cycles at frequencies from DC up to medium-wave RF, at voltages of dozens to hundreds of volts, with individual devices that can be clearly seen with the naked eye. Actually this is so absurdly good on paper that surely someone has tried it and the scheme has some hidden fatal flaw I’m not seeing. Details follow.
I was reading about electrostatic relays the other day. MEMS relays are made using nanophotolithography techniques, just like CMOS, but have significantly different performance characteristics; they turn on and off more slowly than MOSFETs do, but once they’re active, they pass signals with lower resistance and thus higher speed; and they don’t have a linear region the way MOSFETs do, having near-infinite gain at their transition point. Careful circuit design can get circuits with comparable performance.
The idea of an electrostatic relay might seem paradoxical: wouldn’t you need a higher “gate voltage” to turn it on and off than what it can switch? The solution taken by the MEMS designs is very simple: the contact area is small, and the signal conductor is narrow, while the gate area is large. (They are insulated from one another with a layer of amorphous silicon dioxide.) Because the contact area is small, the electrostatic force generated by the signal being switched is proportionally small, perhaps two orders of magnitude smaller than the force generated by the larger-area gate.
Other solutions are possible, involving things like leverage to allow a smaller electrostatic force to outwrestle a larger one, but just using larger and smaller plate areas is simple enough.
It occurred to me that you could build such devices macroscopically, or mesoscopically (with, say, a characteristic dimension of 100μm to 1mm rather than 10mm or 1μm) out of paper and foil. The most obvious conductors to use, aluminum and copper, are not very suitable for relay contacts for operation in air — sparks at the contacts will produce hard, nonconductive oxide layers which will make the relays unreliable in short order. Reasonable alternative contact materials include gold (reduces its oxide), silver (has a conductive oxide), graphite (has gaseous oxide), tin (has a semiconducting oxide), and lead (has conductive metallic dioxide).
Typical electromagnetic relays are good to only about 10k to 100k operations, although high-reliability mercury-wetted reed relays sometimes advertise a million. These electrostatic relays should be able to last many times longer through the use of more appropriate materials, much lower circuit inductance, and much lower currents. But this is speculative.
Spring materials might be trickier. Paper might work okay at least for prototypes, but ideally you’d like something that doesn’t creep or fatigue over time, such as glass foil or foils of other metal oxides. Alternatively, instead of relying on the insulator to provide a spring force, we could rely on the conductor — metallic conductors such as copper, silver, gold, or even iron should be immune to creep and fatigue at these temperatures, deformations, and thicknesses, and a thin film of some insulator could be deposited onto the surface of the gate conductor to separate the gate from a later-deposited channel.
A 3mm×3mm paper foil relay might consist of a 100μm-thick square of aluminum foil on the gate side (this is conservative; common household foil is 22μm, while ribbon-microphone aluminum-leaf is 0.6–2μm), attracted toward a 100-μm-thick square on a substrate paper, which has a 100-μm-thick insulating paper layer (again, conservative; ordinary 80 g/m² office paper is this thick, but 80-μm 60 g/m² paper is easily available) separating it from the traces being bridged, which might each have a 1mm×1mm contact area. Actually you probably only need one such area, but let’s keep it simple. The moving gate might move by 100μm to bring the contacts into contact.
Our 3mm × 3mm sheet works out to be more like 5mm × 5mm including quiet zones around it:
EE EE EE EE EE
EE AA AA AA EE
DD BB CC BB DD
EE AA AA AA EE
EE EE EE EE EE
Here the different pixels have stacked-up contents as follows when the contacts are open, with “G” being the gate electrode, “.” being air, “I” being insulating paper, “C” being the contact material, “N” being the channel conductor (for example, copper), and “S” being the substrate electrode, which can be aluminum or copper or whatever.
AA: BB: CC: DD: EE:
GGGG GGGG GGGG .... ....
IIII IIII IIII .... ....
.... CCCC NNNN .... ....
.... .... .... .... ....
.... CCCC .... NNNN ....
IIII IIII IIII IIII IIII
SSSS SSSS SSSS .... ....
If each of these layers is 100μm thick, which seems plausible, we have 500μm between the gate and the substrate at the point where we want to activate the thing. The total moving mass is about 0.9 mm³ of aluminum gate (about 2.4 mg) plus a similar volume of paper (about 0.9 mg) plus 0.3 mm³ of channel (say, another 1 mg, depending on what you make it from) for a total of 4.3 mg. You want to somehow hinge or spring it so that the paper spring restoring force is large comparable to the weight of the 4.3 mg (so it won’t fail from being upside down) but not too enormous. How much electrostatic force can we expect?
Say we run the thing on 200V, since it’s an electrostatic device and those have always required a fair amount of EMF to do anything. Coulomb’s law F = k(q₁q₂)/r² tells us that two 1-nanocoulomb point charges 500 μm apart will generate a 36-millinewton force. But how much charge do we have at 200 volts? If our capacitance C = εA/d and our ε is ε₀ — probably a good approximation for paper, and an excellent one for air — our capacitance is 0.160 pF, so we have about 32 picocoulombs on each foil, giving about 1.12 mN, under whose influence the relay will snap shut at initially 259 m/s², about 26 times the acceleration of gravity, which is in the right ballpark. It might even be possible to use lower voltages like 48V or 24V.
https://www.hindawi.com/journals/jchem/2017/4909327/ may be relevant; on a single sheet of notebook paper (probably 80 μm?) the dude got 53 pF/cm², so 0.53 pF/mm² (?), which is in pretty close agreement with what I calculated above for the larger plate separation encountered in an electrostatic relay.
(I think we can neglect the electrostatic force of the channel since, as I said above, we can make it almost arbitrarily narrow.)
Neglecting the spring force, which I think can be substantially smaller than the electrical force, we have in theory an operational speed of around 2 μs, which in theory requires about a 16 μA charging current — though the capacitance will increase by 20% by the time the contacts come into contact, generating additional charging current and electrostatic force.
At currents and voltages like these, resistances below a few hundred kilohms will have no effect, so you might as well use graphite for all the conductors, rather than trickier and heavier metal foils. (Silver’s resistivity ρ is 1.59×10⁻⁸ Ωm, copper’s 1.68×10⁻⁸, gold’s 2.44×10⁻⁸, aluminum’s 2.82×10⁻⁸, lead’s 2.2×10⁻⁷, amorphous carbon’s 5–8×10⁻⁴, and graphite’s 2.5–5.0×10⁻⁶ perpendicular to the basal plane. So a 100μm×1mm×3mm trace of randomly oriented graphite particles in good contact might contribute as much as 10⁻⁵Ωm×3mm/1mm/.1mm = 0.3Ω, six orders of magnitude too small to matter. This suggests in some sense that you could narrow the channel by six orders of magnitude, down to 1nm, before its resistance became important, but that is of course impractical.) Also, you probably want to avoid sharp corners to avoid ionizing the air or the paper.
Actually reaching such high frequencies might require you to extensively perforate the paper (without bridging the contacts on the two sides) or operate the whole device in a vacuum to avoid air resistance.
Andrea Shepard points out that at high frequencies the paper will not behave as a rigid or quasi-rigid object; applying a force to one part of the paper will cause displacement to ripple out from that place as shear waves at a speed of sound in the paper, on the order of 1 km/s, which is to say 1 mm/μs. This would cause great slowness if the gate electrode did not overlap the “channel” and “contact” material, as it does in the above design sketch. Even in the above sketch, there is a distance of some 100 μm between them, and the compressive deformation will take on the order of 100 ns to propagate through it and 1 μs to approximate the behavior of a rigid object again. I hazard a guess that this will not be the limiting factor in the performance of these hypothetical devices.
The perfectly overlapping electrodes are somewhat questionable, though, for a different reason: electric fields can’t normally penetrate conductive masses such as the channel and contact material, because statically speaking the field induces a surface charge sufficient to cancel it. (This also creates a MOSFET-like “charge injection” problem.) So there might be no net force from the overlapping part of the gate, and the shear waves described above might carry almost all of the opening or closing force.
If you scale the device down by a factor N, its area diminishes by N² while its plate separation diminishes by N, so the capacitance, the charge per volt, decreases by N. At the same time, though, the Coulomb force per nanocoulomb increases by N², so the force per volt increases by N. The mass that must be moved decreases by N³, so the acceleration per volt increases by N⁴, so the time to cover a given distance at a given voltage decreases by N². And the contact separation distance also decreases by N, which, with the same acceleration, would give you a √N speedup. So you actually get an N²√N speedup, in a vacuum, at a constant voltage. Maybe more in the real world. Or less.
This suggests that, with crepe paper or Mylar or glass foil or something, you should be able to reach well into the megahertz with devices that are still individually visible to the naked eye, although perhaps a bit tricky to construct by hand.
In the limit you might have to diminish the voltage as the plate separation and radii of corners decrease to keep corona discharge and avalanche breakdown under control. If you decrease the voltage, you get proportionally less force, and need proportionally less charge. This means that the characteristic resistances stay the same, but in some sense the amplification factor drops. Like CMOS, these devices are capacitive loads, though very small ones; they have gain limited only by the leakage current, in this case further potentiated by the additional extremely high factor of gain at the threshold voltage between barely contacting and barely not contacting.
In the above diagram, the vast majority of the area is occupied by the gate electrode; the channel occupies only a small part of the device. It might be worthwhile to run two or three channels across it to amortize the expense of the large gate over more channels. As calculated above, the channel itself doesn’t reach a significant resistance at these voltages and currents until it’s only 1nm wide (and 100μm tall, making it more like a graphite wall than a graphite trace, so maybe reducing it to 30μm × 30μm would be more reasonable). So you could run many channels across, controlling them all with a single gate voltage, and thus get many bits of switching out of a single device.