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Photocathode Resonates


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Hello you all!

Here, I suggest photocathodes that resonate at the light's frequency like a radiowave antenna to improve the sensitivity. As usual, I didn't check the state of the art, and since antennas for light exist already on solar cells, I could well be late.

To increase the field, the cathode has a sharp tip like at some electron guns, and it shall resonate well, but metals are lossy at visible frequencies. Silver must be the best choice, followed by aluminium if the light isn't blue.


From the CRC Handbook of Chemistry and Physics, section "optical properties of metals", for silver at 2eV = 620nm = 3*1015rad/s:
The extinction coefficient k=4.18 so the current is shallow as compared to the wavelength;
The reflectivity is still 0.944 so an incident wave of 1V/m that induces 5.2mA/m dissipates 150µW/m2;
I deduce a surface resisitivity of 5.4 ohm/square.

The tip needs a different material for emissivity but it conducts nearly no oscillating current.

A cylindrical quarter-wave antenna of 30nm diameter with estimated 400nH/m has then j1,2Gohm/m and ohmic losses of 57Mohm/m hence an intrinsic Q~20, which is the desired improvement. If alone over the ground plane, it has also 36ohm radiation resistance which would much reduce the external Q, but we can spoil the radiation resistance and keep a decent inductance. For instance a reflector does that: wide enough, it adds little resistive losses, and if not too high, it lets the electrons escape. This can exaggerate up to a resonating cavity with a small hole letting the emitting tip through and some coupling for the light, like a small hole to adapt a fibre to the cavity. Dielectrics look less useful as they increase the ohmic losses.

The antenna can have a wider base to reduce a bit the losses, for instance be conical (and longer to stay tuned).

The light's electric field should be roughly parallel to the antenna. Often, flat photocathodes receive light from their normal direction, which I believe is suboptimum; a lens (punched as needed) with big numerical aperture should improve this, or a better orientation.

One single antenna can receive light through a lens or from a fibre or guide; semiconductor processes can make the guide in addition to the antenna. Several antennas permit to cover a wider area; when used without a reflector, such an antenna catches electromagnetic power from a fuzzy area of 0.5*Lambda2/4pi, which tells what spacing is meaningful. Closer spacing broadens the frequency band but won't help the sensitivity.


A resonating photocathode, if better, has about the same uses as a traditional one. Some specific cases:

  • An electron microscope needs an electron gun as brilliant as possible. Maybe a resonating photocathode improves that. I'd try warm sharp LaB6 at the tip. Multiphoton absorption is worth trying here with enough peak power, that is, even if the work function exceeds the photon energy.
  • Future linear electron colliders have similar needs, but I suppose better answers exist already for them.
  • Datacomms transport light on a tiny cross-section and need sensitive receivers.

I already suggested to develop a photomultiplier tube with a small sensitive cathode spot
because photomultiplier tubes have already a small dark signal despite their big photocathode at room temperature. To my opinion, this is an easy research project that has good chances to work and is useful for physics instrumentation and for communications, including single-photon cryptography. The resonating photocathode would combine nicely with such a photomultiplier tube.

Marc Schaefer, aka Enthalpy

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A semiconducting anode would well detect energetic electrons (for instance photoelectrons) whose direct impact creates many carrier pairs. The arrangement is more compact and faster than the many dynodes of a photomultiplier. I had suggested it in 2008 for microscopic vacuum valves, and it is long known for other purposes.

Gallium arsenide has a good hole and electron saturation speed, stopping power, resistance to beta rays, and it can integrate the fast preamplifier. Other semiconductors may be better, especially silicon for slower, thicker detectors. 1µm GaAs takes <10ps to collect the charges and stops >8keV photoelectrons that create 1900 pairs.

This sketch has no scale. Horizontal and vertical dimensions aren't comparable.

160µm vacuum from the cathode to the anode take 6ps to cross, but I didn't check if the mean 50MV/m let the vacuum break down or provoke field emission. Over 1mm, the transit would increase to 37ps, but because the electrons' energy is uniform to better than +-1eV, the transit time would spread by +-300fs only. Operating near the field emission conditions would extend a photocathode's sensitivity to longer wavelengths.

A broad guard ring at the cathode's potential, or even more negative, shall reduce the transverse speed of the emitted electrons. Modelling the field as hemispherical from R=15nm to the R<150nm guard ring, then flat to 160µm distance, the hemispherical part drops ~34V, so 34eV transverse energy let the electrons spread over R=10µm at the anode. A less pessimistic model would bring much.

A D=30µm h=1µm GaAs (er=12.9) PIN diode has 80fF capacitance. A HEMT (transistor) on GaAs with 40fF input capacitance and 50ohm noise equivalent resistance creates 110µV = 13aC = 82q RMS noise over 15GHz bandwidth for 20ps bit duration, or +-11 sigma signal from one 8keV electron. Single photoelectron detection at >50Gb/s! The unpolarized diode adds no dark current, the modulation or pulse detection scheme shall make 1/F noise irrelevant, and 10nA gate leakage adds only 1q noise.

The diode must be passivated and I don't trust an insulator. Maybe thin cobalt is hermetic enough. Additional metals are often needed for an ohmic contact. The passivation and the first electrode don't waste many pairs, as most appear where the incoming electron stops.

If more than one photon created in the passivation or diode (including by radiative recombination) excites the cathode, the mode changes to sustained avalanche. Less convenient for datacomms, sometimes useful for instrumentation. By the way, we still don't have pleasant theories for vacuum breakdown to my knowledge, and this may be one.

Integrating the preamplifier at the same chip and face as the diode reduces the parasitic capacitance hence the noise. A preamp at the rear face is nontrivial, stacked chips are possible. If the circuit must be protected from stray 8keV electrons (I didn't check), then >1.1µm aluminium stops the electrons and converts less than 500ppm of the energy flux in photons. 8keV photons would need the chip's thickness to attenuate by 105, but 1.5keV Auger photons are attenuated by e for every 370nm of cobalt thickness.

If incoming light isn't perfectly concentrated, a carpet of resonating photocathodes, or a broad smooth photocathode, can target one semiconductor anode. A chip or module can integrate many semiconductor diodes and preamplifiers, for instance to make images or receive many parallel data paths.

Marc Schaefer, aka Enthalpy

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A lens to make the light's electric field more perpendicular to the photocathode was already proposed:


An experiment report about vacuum insulation, thanks:
from 1971 but informative. I didn't read all reports, but many try to rescue somehow the disproven emission field model. It seems that Mankind lacks a good theory for vacuum insulation, despite many components rely on it.

Measurements from 0µm through 1µm to 30µm distance, round AgNi electrodes:
observe 6kV breakdown at 30µm distance, so my unsubstantiated 8kV at 100µm look feasible. They may demand a cathode tip round instead of sharp, more so if the material has a low work function.


I suggested on 23 April 2017 that anode fluorescence and cathode photocurrent may cause vacuum breakdown. The linked report for Arpa suggested it already.

A way to test this hypothesis for soft X-rays around 100kV is to deposit the same thin layer on varied anode materials like Al, Cu, Mo, Nd, W. The thin layer would give identical work function, optical properties, cleanliness, while the bulk materials vary the X-rays emission.

Electrochemical means can deposit 5µm nickel. This lets electrons >40keV pass through, and attenuates X-rays >5keV by <2.7.

Semiconductor processes achieve thinner layers of varied materials. For instance 500nm aluminium block visible light, let electrons >6keV pass through, and attenuate X-rays >500eV by <2.7. Thinner is easy.

If different anode materials with identical coating give varied breakdown voltages, we can attribute it to X-rays feedback, and varied layer thicknesses indicate which X-ray energy range acts. If a difference is observed, it also suggests how to improve anodes.


If it hasn't been done yet, take banal cathode and anode materials but free of radioactivity, and observe the time to failure at ground level and in a tunnel or mine.

Marc Schaefer, aka Enthalpy

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A way to test the breakdown by visible and UV photons is to increase the feedback by adding mirrors.


To concentrate light from the anode on the cathode, the left setup bounces it twice on parabolic mirrors, or maybe spherical ones. The right setup bounces light once (smaller losses) on elliptic mirrors, or maybe spherical ones. The right setup eases the insulation at the mirrors, and these can consist of several elements, for instance round ones.

Aluminium offers unbeaten 0.8 reflection at 14eV and 0.6 at 15eV. If accepting 0.20, aluminium stops at 16eV, tungsten extends to 24eV and rhenium to 27eV = 46nm. Maybe the index step at Al2O3, TiO2, ZrO2 outperforms metals but it won't be easy. A combination of ceramics, optionally with metal?

If the breakdown voltage varies with the area or number of mirrors, one could seek a relation with the solid angle exposed to the anode by the mirrors, and compare it with the cathode's one.


Deep UV feedback is compatible with some observations. Smaller electrodes insulate better despite the field concentration, and a little bit of gas improves over vacuum.

Marc Schaefer, aka Enthalpy

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  • 4 years later...

The semiconducting anode of 23 April 2017 achieves fibre datacomms speeds with nontrivial development. A less fast semiconducting anode is easily developed. It can be a first research step and is useful in many science experiments, for instance

If the sensitive area is bigger than a halfwave, the photocathode needs not resonate and can be standard photomultiplier technology like GaAs. Just reducing the area improves the dark current. Cooling the photocathode to 77K would do miracles, and then the semiconducting anode and the amplifier would be cooled too for speed and noise.

I didn't check how long the PIN survives energetic photoelectrons. It's a worry for datacomms, not for an experiment detecting few photons.


A separate amplifier, bonded by wires to the PIN diode, is easier. For instance the FHR20X or NE32400 transistors offer <0.2pF capacitance and low noise as the input of a transconductance amplifier. More time for hole drift enables a thicker PIN diode, like 5µm Ge, that catches more energetic photoelectrons, for instance 24keV producing 8 000 pairs of carriers, while less bandwidth reduces the noise.

5µm Ge needs no external polarisation. Additional 0.2pF allow D=100µm. A window of 0.5µm thin Al can stop stray light, while 10µm Al, for instance a bonding pad, protect the insulators against the photoelectrons.

15 Ohm noise equivalent resistance and 77K create 120pV/sqrt(Hz) noise, so 5GHz noise equivalent bandwidth and 0.2+0.2pF produce 22q rms noise. A threshold discriminates easily the 8000q signal even at 10Gb/s.


Much slower: a TLC081 bicmos op amp builds the transconductance amplifier. 12pF input plus 22pF from the PIN diode widened to D=1mm, combined with 8.5nV/sqrt(Hz) at 300K and 1kHz to 10kHz passband create 170q rms noise, nice overkill again. A threshold at 3500q detects every photoelectron, and 20*sigma fulfil all unreasonable intents and purposes.


The threshold discriminates parasitic currents, especially if using guard rings. I see only electrons travelling through vacuum from the cathode, and other ionizing rays, that can provoque false detections. Clean detector and shielding materials, and a cold photocathode as small as possible, make the dark current extremely small.

Marc Schaefer, aka Enthalpy

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On 4/17/2017 at 6:14 PM, Enthalpy said:

Here, I suggest photocathodes that resonate at the light's frequency like a radiowave antenna to improve the sensitivity. As usual, I didn't check the state of the art

The state of the art is that photocathode quantum efficiencies are typically about 10% to 30% (Lower figures for IR sensors, higher ones at visible and UV wavelengths).


So there's a limit to how much better you can get. You certainly won't do better than a 10 fold improvement.

On the other hand, by selecting a resonant wavelength, you must de-select the other wavelengths.

And since, for many applications, it's better to have a flat frequency response tan a peaked one, I'm not sure this idea is going anywhere.



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The semiconductor anode is known. It's the chapter 11 of this handbook, called "new" in 2007:

The added avalanche section in the semiconductor increases the gain. For many uses, I'd have no avalanche section in the anode:

  • According to my estimates, it isn't needed in counting mode.
  • It lets the gain fluctuate. Just removing its polarisation remedies this.
  • A thin PIN diode is extremely fast, but a thick avalanche section, even unpolarised, makes a slower current decrease.
  • Does Hamamatsu produce the pairs in a low-field region? They better appear in a depleted zone for speed, hence my PIN.

As the primary electron produces most pairs at the end of its path, the PIN region attraction the slower holes, the P, should be there, at least at constant accelerating voltage. So if the I thickness matches the energy, have the N where the primary electron impinges and the P where it stops, for narrower current pulses.

On some uses, I'd add a second electronic threshold to reject pulses too strong, since these can't result from individual photoelectrons but rather from cosmic rays, radioactivity or others. Photoelectrons in a PIN diode make highly repeatable pulses, so this discrimination is very efficient. Successive pulses too near to an other could also be removed if they are improbable in the signal.

========== Noise standard

Avalanche diodes sell as bad noise standards. I propose instead a non-avalanching hybrid photo-detector as noise standards.

Strong noise results from electrons arriving in groups: sqrt(2iQB) where B is the bandwidth and the collective charge Q comprises many electrons. To prove it, I illuminated a wide avalanched diode and observed that the noise decreases, as light provides more seeds and the same current comprises more parcels of smaller Q.

Usual avalanche diodes are very sensitive to temperature that creates avalanche seeds and changes Q. Alas, they also produce much heat.

Instead, a non-avalanching hybrid photo-detector provides extremely constant Q (the number of electrons fluctuates less than its sqrt). Already the acceleration voltage defines it well, so the light source could be regulated for a given output current.

The photoelectron current can be regulated by the light intensity, the pair generation current by the accelerating voltage, to provide an acurate noise density.

Seems even better: thermoionic emission could make the primary electrons (or maybe tunnel emission if it becomes reliable), by some filament or LaB6 spike. Trivial to regulate with additional electrodes.

The primary electrons can be deflected by usual means to spread the damage over the anode for longer life.

I had estimated <10ps charge collection time in 1µm GaAs depleted zone (which can be polarized here). This would provide a noise spectrum decreasing around 50GHz, wow.

The noise density resulting from the primary and the pair generation currents is very accurate, much better than from avalanche diodes.

Marc Schaefer, aka Enthalpy


Hi JC, thanks for your interest! I come back.

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The detector with photoemissive cathode, acceleration voltage and semiconductor anode is excellent to make imagers: the circuit for each pixel is simple, and the detection of individual primary electrons gives outstanding sensitivity and linearity.

If a retina covers much area, the semiconductor anodes can be smaller, and they potential attract the primary electrons.

========== Circuits

The fastest amplifiers must sit at or behind the anode, or just besides, with one amplifier chip per anode. Scanning 1D imagers may afford that.

In the 1ns response time range, 50mm printed lines reach several pixels, and for instance a BGA170 Dram package can host 20 analog inputs and outputs. BF998 performance suffices and is easily integrated. A 2D imager is conceivable.

At 10ns response time, packages with 1500 balls can host 200 channels, and a 2D imager becomes reasonable (which doesn't mean "cheap").

The circuits can add ADC modes to the counters to extend the dynamics, with one or several lower-gain outputs without comparators.

Because the input signals are fragile, I prefer to integrate the comparators on downstream chips with the counters. The amplifiers, comparators and counters can integrate 2* to 4* as many channels in a package of same size. Or rather, the counter chips would have bigger packages.

All channels on a counter chip can share a bus, for instance USB.

========== Particles

Cooled photocathodes exist for the near-infrared.

At visible light, such an imager can have single-photon sensitivity, say for night vision. Would it outperform CCD imagers for astronomy?

With some scintillator or other converter, individual ionizing particles are detected. Sensitivity and speed would make nice Positron Emission Tomography.

Marc Schaefer, aka Enthalpy

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A retina with semiconductor anodes can integrate many (millions of) pixels, if the size is reasonable (optics) and the fast signals reach the circuitry.

Maybe through vias can carry the signals from the diodes to the rear face, and the counters and associated circuits reside there or on a stacked chip. Optionally, a minimum circuit (transconductance amplifier, single transistor...) can be on the front face at each diode, to reduce the input capacitance and send a stronger signal through the via.

But if the fabrication process achieves it, the whole circuits better reside next to the diodes. Digital processes not too old make a 40+ bit counter much smaller than a 4µm*4µm pixel. A 1µm deep Pin diode isn't standard in recent digital circuits, but these diodes need no optimized properties, and fast Mos transistors are good as preamplifiers. Counting 10G/s is reasonable.

The photocathode can reside close to the anodes, like 50µm, and then a few kV give the photoelectrons straight paths.

The pixels could be smaller and more plentiful if the optics is good. The pixels don't interfere, and the dynamic range is far better than a Ccd. I hope cooling lets detect single photons over hours, fantastic for astronomy, better than a Cmos retina.

Many uses need fast reading, but at least the data is digital here. A Gddr interface suffices, few USB too.

Marc Schaefer, aka Enthalpy

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On 6/19/2021 at 1:33 PM, John Cuthber said:

[...] photocathode quantum efficiencies are typically about 10% to 30%. You certainly won't do better than a 10 fold improvement. [...]

Sure. But twice as sensitive would already be fantastic, and many people try very hard to improve less than that.

In a noise-limited experiment, signal *2 means experiment time /4. At a neutrino detector, or at the LHC photon-emitting free fall experiment I propose, this changes everything.

On 6/19/2021 at 1:33 PM, John Cuthber said:

[...] by selecting a resonant wavelength, you must de-select the other wavelengths. [...] for many applications, it's better to have a flat frequency response [...]

In other uses, a narrow frequency response is perfect. It's often the case when the setup produces its own light. If a Led or a laser diode emits narrowband light to measure ranges, detect remote items... a resonating detector would further help the desired filter.

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2 hours ago, Enthalpy said:

Sure. But twice as sensitive would already be fantastic, and many people try very hard to improve less than that.

In a noise-limited experiment, signal *2 means experiment time /4. At a neutrino detector, or at the LHC photon-emitting free fall experiment I propose, this changes everything.

In other uses, a narrow frequency response is perfect. It's often the case when the setup produces its own light. If a Led or a laser diode emits narrowband light to measure ranges, detect remote items... a resonating detector would further help the desired filter.

The trouble is that you don't get to choose either/ or.
The neutrino detector emission  is broad band, so your idea doesn't work.

There are plenty of occasions where a narrow band detector is useful.

But in many, perhaps most, of those, it's useful to be able to tune the detector.

That's easy if the frequency selective element- perhaps something as simple as coloured glass- can be changed, but it's tricky if you have to change the whole detector.
So, yes, if you were looking at something like LIGO where the bandwidth is narrow, that's great.

But they aren't short of sensitivity (on that count) If they were, they could get a brighter laser.


There will be applications, but it's never going to be as useful as a simple photocathode, nor as cheap.

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  • 1 month later...

A small current noise is desired at the proposed detector with accelerated photoelectrons and semiconductor anode, more so without avalanche at the semiconductor. My bias and optionally feedback by photocurrent fit well here.
That's especially useful if few signal events are expected and the input capacitance must be held tiny. Feedback resistors get quickly impractical then, but photocurrents still do the function.

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