What is the temperature dependence of the NIRCam sensor's responsivity?

[Devin-M]

I've read the NIRCam instrument uses HgCdTe imaging sensors...

"JWST NIRCam has ten 2K × 2K HgCdTe detectors"
https://jwst-docs.stsci.edu/jwst-ne...rcam-instrumentation/nircam-detector-overview

I found this chart which displays the relative sensitivity of the NIRCam sensor for different filters and wavelengths:

From the wikipedia article on Mercury Cadmium Telluride (HgCdTe) detectors:

"In HgCdTe, detection occurs when an infrared photon of sufficient energy kicks an electron from the valence band to the conduction band."

I tried to find a chart showing the "current responsivity" at different temperatures for the actual NIRCam sensor, but I couldn't locate one, so I pulled this chart from a paper written on a different HgCdTe photodiode which shows 1.6 amps per watt of 3.5 micron light incident on the sensor while the sensor is 300 Kelvin (would've posted the actual NIRCam specs if I could find them):

https://www.researchgate.net/publication/343856156_Higher_Operating_Temperature_IR_Detectors_of_the_MOCVD_Grown_HgCdTe_Heterostructures

https://www.speakev.com/cdn-cgi/image/format=auto,onerror=redirect,width=1920,height=1920,fit=scale-down/https://www.speakev.com/attachments/5000b9e5-011d-4ef0-af59-bedb15ff822e-jpeg.156575/

My question is this:

Considering that the 2nd Law of Thermodynamics is inviolable, and so the sensor shouldn't be able to "detect" an object which is colder than the imaging sensor, if the sensor above from figure 12 were used in NIRCam (since I can't find the actual NIRCam responsivity specs), what physical effect would prevent a 3.5 micron photon from kicking an electron from the valence band to the conduction band in the 300k sensor, if the photon were emitted as black body radiation from a 299k object? In other words, how would a valence electron in the sensor determine the temperature of the emitting object from the arriving 3.5 micron photon's characteristics such as wavelength before either being kicked or not kicked to the conduction band, in order to remain consistent with the 2nd Law?

 

[phyzguy]

The near-infrared instruments (NIRCam, NIRSpec, FGS-NIRISS) have now reached their target range from 34 to 39 K by cooling passively.

 

[Devin-M]

Does anyone have access to the engineering "current responsivity" charts for the actual NIRCam sensors at different operating temps?

For the 300k sensor data shown above, to maintain consistency with the 2nd Law how does the 300k HgDcTe valence electron "measure" whether an incoming 3.5 micron photon comes from a 299k object or 301k object? To satisfy the (assumed inviolable) 2nd Law, all the "299k" 3.5 micron photons must be blocked or prevented from elevating internal photoemission electrons from valence to conduction.

https://www.hindawi.com/journals/aoe/2016/1832097/

 

[Oldman too]

Does anyone have access to the engineering "current responsivity" charts for the actual NIRCam sensors at different operating temps?

Not I, however browsing NTRS could point you in the right direction.
https://ntrs.nasa.gov/search?q=NIRcam&page={"size":25,"from":0}
https://ntrs.nasa.gov/search?q=NIRcam engineering
NIRcam was a product of U of Arizona https://www.as.arizona.edu/nircam and
https://www.lockheedmartin.com/en-us/news/features/2021/NIRcam-see-universe-in-new-light.html It's probably worth shaking down those sites for info.This claims to be a technical page for detailed instrument info.
https://jwst-docs.stsci.edu/x/sQTXBQ

The sensors were supplied by https://www.teledyne.com/en-us/news...ed-aboard-the-james-webb-space-telescope.aspx
That might be useful also.

 

[Spinnor]

View attachment 304031
View attachment 304030
View attachment 304029
View attachment 304032

Link for the above images (?), https://stsci-opo.org/STScI-01G7DDBW5NNXTJV8PGHB0465QP.png

 

[Devin-M]

Not I, however browsing NTRS could point you in the right direction.
https://ntrs.nasa.gov/search?q=NIRcam&page={"size":25,"from":0}
https://ntrs.nasa.gov/search?q=NIRcam engineering
NIRcam was a product of U of Arizona https://www.as.arizona.edu/nircam and
https://www.lockheedmartin.com/en-us/news/features/2021/NIRcam-see-universe-in-new-light.html It's probably worth shaking down those sites for info.This claims to be a technical page for detailed instrument info.
https://jwst-docs.stsci.edu/x/sQTXBQ

The sensors were supplied by https://www.teledyne.com/en-us/news...ed-aboard-the-james-webb-space-telescope.aspx
That might be useful also.

Thanks for those links. I did find what appears to be a product page for the NIRCam imaging sensors here:

http://www.teledyne-si.com/products/Documents/TSI-0855 H2RG Brochure-25Feb2022.pdf

The page mentions a quantum efficiency for 3500nm (3.5 micron) light equal to or greater than 70% though it doesn’t mention what temperature the sensor was operating at when it achieved that efficiency.

Also found this:

https://core.ac.uk/download/pdf/10569376.pdf

 

[pinball1970]

The instrument has been at a steady 39K since about day 90 or so according to Where's Webb.

If that helps

 

[Devin-M]

The instrument has been at a steady 39K since about day 90 or so according to Where's Webb.

If that helps

View attachment 304129

View attachment 304130

My question was really about the photons themselves—

What is the physical difference between a 3.5 micron photon from a 299k object versus a 3.5 micron photon from a 301k object?

The reason I ask is there exists a IR imaging sensor made from a similar HgCdTe material to the NIRCam sensor which has a non-zero quantum efficiency for 3.5 micron photons when the sensor’s operating temperature is 300k. Since I assume the 2nd Law of Thermodynamics is inviolable the 3.5 micron photon from the 301k object’s black body spectrum should be detectable while the 299k object’s 3.5 micron black body photon shouldn’t as the 299k black body is colder than the sensor. So essentially the question boils down to what is the difference between these two photons that have the same wavelength such that one should be detectable and the other shouldn’t?

 

[phyzguy]

My question was really about the photons themselves—

What is the physical difference between a 3.5 micron photon from a 299k object versus a 3.5 micron photon from a 301k object?

The reason I ask is there exists a IR imaging sensor made from a similar HgCdTe material to the NIRCam sensor which has a non-zero quantum efficiency for 3.5 micron photons when the sensor’s operating temperature is 300k. Since I assume the 2nd Law of Thermodynamics is inviolable the 3.5 micron photon from the 301k object’s black body spectrum should be detectable while the 299k object’s 3.5 micron black body photon shouldn’t as the 299k black body is colder than the sensor. So essentially the question boils down to what is the difference between these two photons that have the same wavelength such that one should be detectable and the other shouldn’t?

I'm completely lost as to your question. A 3.5 micron photon is a 3.5 micron photon. The detector doesn't care where it came from. Why should the temperature of the body that it came from make any difference? If the photon has enough energy and creates an electron-hole pair in the sensor it gets detected. Otherwise it doesn't.

 

[DrDu]

The question is not so much about detection of electron hole pairs as about the statistics of this process. If the detector has the same temperature or a higher one than the object whose radiation you want to detect, you will not be able to distinguish the signal due to your star from the thermal noise of your detector.

 

[pinball1970]

The question is not so much about detection of electron hole pairs as about the statistics of this process. If the detector has the same temperature or a higher one than the object whose radiation you want to detect, you will not be able to distinguish the signal due to your star from the thermal noise of your detector.

The noise from the instruments should be low. They cooled the kit down via passive radiation to 40 Kelvin then used the cryo for MIRI, 6K. I'm just looking in detail now as all the materials and mechanisms is so complex.
It is just crazy material science and physics.
How did they test all this stuff? To behave where it is now? Vacuum chamber plus extreme low temperature?
Crazy.

 

[Devin-M]

I'm completely lost as to your question. A 3.5 micron photon is a 3.5 micron photon. The detector doesn't care where it came from. Why should the temperature of the body that it came from make any difference? If the photon has enough energy and creates an electron-hole pair in the sensor it gets detected. Otherwise it doesn't.

The question is not so much about detection of electron hole pairs as about the statistics of this process. If the detector has the same temperature or a higher one than the object whose radiation you want to detect, you will not be able to distinguish the signal due to your star from the thermal noise of your detector.

I’m a bit surprised by these answers as I am fully assuming the 2nd Law of Thermodynamic is inviolable and also that it forbids obtaining “useful work” by transferring energy from a cold reservoir to a hot one.

So if we have a shaded-from-the-sun 299k object emitting some 3.5 micron black body radiation, if any electron hole pairs were produced in a 300k detector with non-zero quantum efficiency for 3.5 microns at that operating temperature, wouldn’t that be forbidden? That’s why I asked earlier about the difference between 3.5 micron photons from a 299k source vs 3.5 micron photons from a 301k source.

On the sensor, the photodiodes are wired to charge a small capacitor at each pixel site, & it takes work to charge a capacitor because one obtains useful work when that capacitor discharges.

Considering the diagram below of a photodiode operating with zero bias voltage wired to charge a capacitor, won’t the 2nd Law forbid creating any electron hole pairs which would in turn charge that capacitor, if the 299k emitter emits 3.5 micron black body radiation and the 300k photodiode has non-zero quantum efficiency for 3.5 micron light at that operating temperature? I thought the 3.5 micron black body photon emitter would need to be at least 301k to charge a 300k photodiode which is wired up as shown below, in order to satisfy all the requirements of the 2nd Law.

Wouldn’t the Carnot efficiency for a 300k cold side and a 300k hot side be exactly 0%?

Diagram from: https://www.pantechsolutions.net/characteristics-of-optical-photo-diode-in-zero-bias/amp

 

[DrDu]

By the Fluctuation-Dissipation theorem,
https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem
Both the diode and the resistor will constantly generate a fluctuating current. If the object you want to detect is in thermal equilibrium with your electronic device, you won't be able to detect a change in this fluctuating current, although some of the current will be due to the object. If the temperature of the object is less than that of the device, you might in principle detect that the temperature of you device (and fluctuating current) goes down, but usually the heat capacity of your device is usually to large for this to be detectable. If the temperature of the object is higher, you will be able to detect a signal above the random fluctuation. The smaller the temperature difference, the longer your measuring time will have to be to detect the signal above the thermal noise.

 

[phyzguy]

I’m a bit surprised by these answers as I am fully assuming the 2nd Law of Thermodynamic is inviolable and also that it forbids obtaining “useful work” by transferring energy from a cold reservoir to a hot one.

The second law of thermodynamics works on the average of a large number of events. It doesn't apply to individual photons. Suppose I have an object at 299K next to a detector at 300K. Both objects are radiating. Slightly more energy flows from the 300K detector to the 299K object than flows back the other way. But radiation is still traveling in both directions, and photons flowing from the 299K object to the 300K detector can still be detected.

But as I and others have pointed out, this is not really relevant for the JWST. The NIR detectors are operating at ~40K and the MIRI detectors at 6K.

 

[Devin-M]

By the Fluctuation-Dissipation theorem,
https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem
Both the diode and the resistor will constantly generate a fluctuating current. If the object you want to detect is in thermal equilibrium with your electronic device, you won't be able to detect a change in this fluctuating current, although some of the current will be due to the object. If the temperature of the object is less than that of the device, you might in principle detect that the temperature of you device (and fluctuating current) goes down, but usually the heat capacity of your device is usually to large for this to be detectable. If the temperature of the object is higher, you will be able to detect a signal above the random fluctuation. The smaller the temperature difference, the longer your measuring time will have to be to detect the signal above the thermal noise.

Do you have an article on the Fluctuation Dissipation theorem that mentions diodes? I scanned through the article and there isn’t single a reference to a circuit with a diode incorporated. Aren’t diodes supposed to only allow current to flow in one direction in most cases?

““Resistance and Johnson noiseIf electric current is running through a wire loop with a resistor in it, the current will rapidly go to zero because of the resistance. Resistance dissipates electrical energy, turning it into heat (Joule heating). The corresponding fluctuation is Johnson noise. A wire loop with a resistor in it does not actually have zero current, it has a small and rapidly-fluctuating current caused by the thermal fluctuations of the electrons and atoms in the resistor.”

https://en.m.wikipedia.org/wiki/Fluctuation-dissipation_theorem

“The most common function of a diode is to allow an electric current to pass in one direction (called the diode's forward direction), while blocking it in the opposite direction (the reverse direction).”
https://en.m.wikipedia.org/wiki/Diode

The second law of thermodynamics works on the average of a large number of events. It doesn't apply to individual photons. Suppose I have an object at 299K next to a detector at 300K. Both objects are radiating. Slightly more energy flows from the 300K detector to the 299K object than flows back the other way. But radiation is still traveling in both directions, and photons flowing from the 299K object to the 300K detector can still be detected.

So once any amount of charge gets stored in the capacitor, how can it radiate back out to statistically satisfy the 2nd Law, which I assume is inviolable, considering the diode is only supposed to allow electrical current to flow in one direction?

 

[DrDu]

considering the diode is only supposed to allow electrical current to flow in one direction?

Because this is an oversimplified model of a diode.

 

[Devin-M]

Because this is an oversimplified model of a diode.

So if I understand you correctly, you’re saying the “reverse leakage current” through the diode will always be equal to the forward current generated by any production of electron-hole pairs from photon absorption on average, such that no net voltage develops on the capacitor when the 3.5 micron black body emitter is a lower temperature than the photodiode (such as 299k emitter -> 300k diode). A net voltage can only develop across the capacitor when the 3.5 micron black body emitter is a greater temperature than the photodiode (301k emitter -> 300k diode).

https://en.m.wikipedia.org/wiki/Reverse_leakage_current

 

[Devin-M]

@DrDu Any comment about this page claims adding a 2nd diode stops the capacitor from discharging back into the photodiode?

it says “The simplest solar-powered circuit to charge a supercapacitor is made by just connecting the capacitor to the solar panels. The only other important component is a diode to stop the supercapacitor from discharging back into the solar panels.”

See diagram below, photodiode labeled SC1 Solar_Cell, Capacitor to be charged labeled C1, additional diode to stop the backflow into photodiode labeled D1, Positive terminal to power load from the capacitor labeled VCC and negative terminal to power the load from capacitor labeled GND:

http://www.bitbanging.space/posts/solar-charged-supercapacitos

 

[DrDu]

@DrDu Any comment about this page claims adding a 2nd diode stops the capacitor from discharging back into the photodiode?

it says “The simplest solar-powered circuit to charge a supercapacitor is made by just connecting the capacitor to the solar panels. The only other important component is a diode to stop the supercapacitor from discharging back into the solar panels.”

See diagram below, photodiode labeled SC1 Solar_Cell, Capacitor to be charged labeled C1, additional diode to stop the backflow into photodiode labeled D1, Positive terminal to power load from the capacitor labeled VCC and negative terminal to power the load from capacitor labeled GND:

View attachment 304180
http://www.bitbanging.space/posts/solar-charged-supercapacitos

You think this describes a near thermal equilibrium situation?

 

[Devin-M]

You think this describes a near thermal equilibrium situation?

Well I know when the photodiode detector is 300k, then the Carnot efficiency is 0% for a 300k emitting object and 0.33% for a 301k emitting object.

So I had wondered what is the difference between a 3.5 micron photon from a 300k object vs a 3.5 micron photon from a 301k object since they both have the same wavelength.

I was trying to understand what distinguishes the two types of photons such that the 301k sourced 3.5 micron photons can usefully charge a capacitor with a 300k detector while the 300k sourced 3.5 micron photons can’t charge a capacitor when the detector is 300k, according to the 2nd Law which I assume is inviolable, while both photons have identical wavelengths and energies.

 

[Grinkle]

Well I know when the photodiode detector is 300k, then the Carnot efficiency is 0% for a 300k emitting object and 0.33% for a 301k emitting object.

So I had wondered what is the difference between a 3.5 micron photon from a 300k object vs a 3.5 micron photon from a 301k object since they both have the same wavelength.

I was trying to understand what distinguishes the two types of photons such that the 301k sourced 3.5 micron photons can usefully charge a capacitor with a 300k detector while the 300k sourced 3.5 micron photons can’t charge a capacitor when the detector is 300k, according to the 2nd Law which I assume is inviolable, while both photons have identical wavelengths and energies.

The 2nd law says that as a closed system evolves towards thermal equilibrium, the entropy of that closed system must increase. What is your closed system here?

You will get great discussion of this question I expect, if you post it stand-alone in its own thread.

 

[russ_watters]

Split from the JWST thread.

 

[DrDu]

Thanks Jim for splitting this off!
I think it is easier to consider instead of a diode a pure semiconductor crystal, made of e.g. CdTe. A photon with an energy larger than the band gap may produce an electron-hole pair which may be detected by applying a voltage and measuring the current. Now if the photon is from a thermal source, its typical energy will be about kT and this has to be also the band gap of the semiconductor. The problem is, that if the semiconductor is also hold at temperature T, electron-hole pairs will form with high probability also by simple thermal excitation, without any photon. Therefore, there is no possibility to tell whether a detected current is due to the photon from a source or to spontaneous electron-hole pair production. If the detector is cooled much below T of the source, the probability for thermal electron hole pair production falls off exponentially, so that the signal to noise ratio increases.

 

[Devin-M]

Thanks Jim for splitting this off!
I think it is easier to consider instead of a diode a pure semiconductor crystal, made of e.g. CdTe. A photon with an energy larger than the band gap may produce an electron-hole pair which may be detected by applying a voltage and measuring the current. Now if the photon is from a thermal source, its typical energy will be about kT and this has to be also the band gap of the semiconductor. The problem is, that if the semiconductor is also hold at temperature T, electron-hole pairs will form with high probability also by simple thermal excitation, without any photon. Therefore, there is no possibility to tell whether a detected current is due to the photon from a source or to spontaneous electron-hole pair production. If the detector is cooled much below T of the source, the probability for thermal electron hole pair production falls off exponentially, so that the signal to noise ratio increases.

Thanks for that answer. So if we have this circuit, where the photodiode (SC1) is 300k, gets 1.6 amps per watt of 3.5 micron light while operating with zero bias voltage (photovoltaic mode), with a Schottky capacitor to prevent back flow out of the capacitor:

& the HgCdTe photodetector has this measured amps per watt of 3.5 micron light with zero bias voltage while the detector is 300k:

“Current responsivity (RI) of the backside-illumi- nated MWIR n+p+BppN+ HgCdTe detector is pre- sented in Fig. 12. The mesa diameter of the element is about 350 lm. The measurements were per- formed at temperatures of 230 K and 300 K and without the application of bias voltage (Ub = 0 V).”
https://www.researchgate.net/profile/Pawel-Madejczyk-2/publication/343856156_Higher_Operating_Temperature_IR_Detectors_of_the_MOCVD_Grown_HgCdTe_Heterostructures/links/6086b5a62fb9097c0c0d3442/Higher-Operating-Temperature-IR-Detectors-of-the-MOCVD-Grown-HgCdTe-Heterostructures.pdf?origin=publication_detail

& we consider this reference:

“Photovoltaic
In photovoltaic mode the photodiode is zero biased. The flow of current out of the device is restricted and a voltage builds up. This mode of operation exploits the photovoltaic effect, which is the basis for solar cells. The amount of dark current is kept at a minimum when operating in photovoltaic mode.

Photoconductive
In photoconductive mode, an external reverse bias is applied, which is the basis for our DET series detectors. The current measured through the circuit indicates illumination of the device; the measured output current is linearly proportional to the input optical power. Applying a reverse bias increases the width of the depletion junction producing an increased responsivity with a decrease in junction capacitance and produces a very linear response. Operating under these conditions does tend to produce a larger dark current, but this can be limited based upon the photodiode material. (Note: Our DET detectors are reverse biased and cannot be operated under a forward bias.)

Dark Current
Dark current is leakage current that flows when a bias voltage is applied to a photodiode. When operating in a photoconductive mode, there tends to be a higher dark current that varies directly with temperature. Dark current approximately doubles for every 10 °C increase in temperature, and shunt resistance tends to double for every 6 °C rise. Of course, applying a higher bias will decrease the junction capacitance but will increase the amount of dark current present.”

https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=9020

Do you still have significant thermal leakage current if there is no bias voltage (ie in photovoltaic mode)? If we consider the 300k detector as a single temperature reservoir wouldn’t the 2nd Law which I assume is inviolable forbid the production of electron-hole pairs from internal thermal excitations and also forbid electron-hole pair production from 3.5 micron photons from objects colder that 300k? What changes occur in the circuit with the capacitor & the Schottky diode when the temperature of the black body emitter increases from 299k to 301k such that 301k 3.5 micron emitter can store energy in the capacitor but the 300k emitter can’t? The Carnot efficiency for the 300k emitter is 0% and 0.33% for the 301k emitter, but the 3.5 micron black body photons from both emitters have the same energy and wavelength.

 

[Grinkle]

the 2nd Law which I assume is inviolable forbid the production of electron-hole pairs from internal thermal excitations and also forbid electron-hole pair production from 3.5 micron photons from objects colder that 300k

I don't think specific micro states are excluded by the 2nd law.

 

[DrDu]

Photovoltaic mode, as you say, means, that there is no bias voltage, i.e., the diode is operated in short circuit (with a current meter). A dark current can also flow in zero bias mode. As there is no voltage difference, any dark current, due to the thermal generation of electron hole pairs won't do work. So there is no violation of the second law.

 

[Devin-M]

Photovoltaic mode, as you say, means, that there is no bias voltage, i.e., the diode is operated in short circuit (with a current meter). A dark current can also flow in zero bias mode. As there is no voltage difference, any dark current, due to the thermal generation of electron hole pairs won't do work. So there is no violation of the second law.

So then I have a little thought experiment. Suppose it’s during the commissioning phase, and I want to predict the outcome of 4 experiments based on observing 2 different temperature portions of the lunar surface with the primary mirror either folded or unfolded…

The telescope detectors are still 300k, operating in photovoltaic mode with a Schottky diode to prevent back flow out of the capacitor (detectors haven’t fully cooled), the primary mirror side wings are still folded (primary mirror isn’t yet full size), and the telescope aims at a 301k patch of the night side of the moon and takes a 1 minute exposure, and in so doing the sensor is exposed to 3.5 micron photons from the night side moon surface…

In this case the Carnot efficiency is 0.33%, so the capacitor can build up a useful charge, so the individual 3.5 micron photons hitting the sensor are doing net work on the capacitor in the sensor, charging it, because a Schottky diode prevents back flow out of the capacitor.

Now the telescope swivels to a 300k patch of the moon for another 1 minute exposure. The carnot efficiency is 0% so the capacitor can’t be charged and the individual 3.5 micron photons hitting the sensor from the moon aren’t doing net work on the capacitor, despite the presence of the Schottky diode.

Then the telescope swivels back to the 301k patch of the moon surface, folds out the side mirror wings so the primary mirror area has increased compared to the 1st observation. The carnot efficiency is back to 0.33% so the individual 3.5 micron photons do net work on the capacitor, and the mirror is larger so more 3.5 micron photons from the moon strike the sensor during the 1 minute exposure so more net work is done in total on the capacitor than the 1st test.

Then the telescope swivels back to the 300k patch of the moon. Since the mirror wings are now folded out, more 3.5 micron photos hit the sensor than during the 1 minute 300k test with folded wings, but since the carnot efficiency is 0% on this test, these individual 3.5 micron photons don’t do net work on the capacitor, despite there being more of them than the wings folded test.

So to summarize my predictions,

1) 300k sensor 301k nightside moon, mirror wings folded, capacitor is charged

2) 300k sensor 300k nightside moon, mirror wings folded, capacitor has no net charge

3) 300k sensor, 301k nightside moon, mirror wings unfolded, capacitor has a larger charge than case 1) due to larger mirror size

4) 300k sensor, 300k nightside moon, mirror wings unfolded, capacitor has no net charge, even though because of the larger mirror more 3.5 micron photons hit the sensor than case 2)

Are the predictions reasonable? The thought experiment was designed so we would have a different # of 3.5 micron photons hitting the sensor during each 1 minute exposure, with 2 tests having a 0.33% Carnot efficiency and 2 tests having a 0% Carnot efficiency.

 

[DrDu]

1. The main point is, that there is no difference in efficiency to detect individual photons. The number of photons reaching the detector from a patch of the moon at 301 K is simply higher than the number of photons from a 300 K patch, see the Planck formula.
2. Then you have to take into account that the diode will also emmit photons of 3.5 mu. In thermal equilibrium as many as it receives from the moon.
3. I am not sure whether your circuit resembles even remotely the one used in the telescope. Even then you will have also in a Schottky diode both diffusion and drift currents and in equilibrium, they will be equal.

 

[Devin-M]

1. The main point is, that there is no difference in efficiency to detect individual photons. The number of photons reaching the detector from a patch of the moon at 301 K is simply higher than the number of photons from a 300 K patch, see the Planck formula.
2. Then you have to take into account that the diode will also emmit photons of 3.5 mu. In thermal equilibrium as many as it receives from the moon.
3. I am not sure whether your circuit resembles even remotely the one used in the telescope. Even then you will have also in a Schottky diode both diffusion and drift currents and in equilibrium, they will be equal.

Folding out the mirrors in case 4) while observing the 300k portion of the moon gives 50% greater incoming 3.5 micron photons (12 segments -> 18 segments) compared to observing the 300k portion of the moon with mirror folded (12 segments) in case 2) and the Carnot efficiency is 0% in both cases.

Observing the 301k portion with 12 segments as in case 1) increases the 3.5 micron photon count much less than 50% compared to case 2) observing the 300k portion with 12 segments, and yet case 1) has greater Carnot efficiency than 4).

In other words, a greater # of 3.5 micron photons hit the 300k sensor observing the 300k section of the moon with 18 mirror segments (Carnot efficiency = 0%) than observing the 301k section of the moon with 12 segments (Carnot efficiency = 0.33%), so in the latter case, less 3.5 micron photons hitting the sensor actually is associated with higher Carnot efficiency in this instance, correct?

 

[DrDu]

Folding out the mirrors in case 4) while observing the 300k portion of the moon gives 50% greater incoming 3.5 micron photons (12 segments -> 18 segments)

You are loosing also 50% more of the photons emitted by the sensor which otherwise would have been reflected back onto the sensor or onto some part in thermal equilibrium with the detector.

 

[Devin-M]

You are loosing also 50% more of the photons emitted by the sensor which otherwise would have been reflected back onto the sensor or onto some part in thermal equilibrium with the detector.

I calculated the surface area for one of the JWST sensors is approximately 12.9cm^2.
http://www.teledyne-si.com/products/Documents/TSI-0855 H2RG Brochure-25Feb2022.pdf

I used the Planck radiation formula for a 300k black body, 0.95 emissivity, 12.9cm^2 and a radiation wavelength range from 3400nm to 3600nm and get 0.00019W of radiated power for that wavelength range which is 0.034% of the total radiated power.
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html

I calculated the spectral responsivity of a 300k HgCdTe panel from figure 12 in this paper is 0.0003 amps from 0.00019W of 3.5 micron light.
https://www.researchgate.net/profile/Pawel-Madejczyk-2/publication/343856156_Higher_Operating_Temperature_IR_Detectors_of_the_MOCVD_Grown_HgCdTe_Heterostructures/links/6086b5a62fb9097c0c0d3442/Higher-Operating-Temperature-IR-Detectors-of-the-MOCVD-Grown-HgCdTe-Heterostructures.pdf?origin=publication_detail

I found the typical reverse leakage current of a particular Schottky diode is 0.00000065 amps with 5 reverse volts at 298K from this datasheet:
https://www.st.com/resource/en/datasheet/bat20j.pdf

When I subtract the max expected 0.00000065 amps reverse current through the Schottky diode from the 0.0003 amps forward current into the capacitor from the spectral responsivity of the HgCdTe panel from the 0.00019W of 3.5 micron photons from the 12.9cm^2 300k black body in close proximity of the 300k 12.9cm^2 HgCdTe photovoltaic panel, I calculate a net current into the capacitor of 0.00029 amps.

I assume this is a mistake since the Carnot efficiency for the setup is 0%. On which step did I mess up the calculations?

Circuit diagram for reference:

 

[WernerQH]

I’m a bit surprised by these answers as I am fully assuming the 2nd Law of Thermodynamic is inviolable and also that it forbids obtaining “useful work” by transferring energy from a cold reservoir to a hot one.

It is not helpful to think of the JWST detectors as heat engines, as photovoltaic cells designed to harvest energy from distant galaxies in the form of infrared radiation. On the contrary, much free energy is expended to amplify the weak signals. The second graph in your post #1 is quite remarkable: For a source flux of ${\rm 10~nJy = 10^{-34}~W~m^{-2}~Hz^{-1} }$ and a mirror size of $25~{\rm m}^2$ I estimate a photon flux of only $0.38~{\rm s^{-1}}$ (at frequency $10^{14}~{\rm Hz}$ and bandwith $10^{13}~{\rm Hz}$). This corresponds to a rather small photocurrent of only $6×10^{-20}~{\rm A}$. This requires a lot of amplification and an integration time of 10000 seconds to turn it into a signal!

Well I know when the photodiode detector is 300k, then the Carnot efficiency is 0% for a 300k emitting object and 0.33% for a 301k emitting object.

I find this a very strange argument. Do you think that radio transmission requires that the sender's antenna must be hotter than the receiver's?

 

[Devin-M]

It is not helpful to think of the JWST detectors as heat engines

Do you think that radio transmission requires that the sender's antenna must be hotter than the receiver's?

Well when I read about photodiodes & the internal photoemission process I learned that individual photons with the appropriate wavelength/energy kick individual electrons from valence to conduction, one by one, and that’s how the photocurrent is produced in photodiodes operating in zero bias photovoltaic mode.

When I used the Planck radiation formula for a 300k black body, 0.95 emissivity, 12.9cm^2 (same size as the JWST sensor) and a radiation wavelength range from 3400nm to 3600nm, I get 0.00019W.

I calculated the spectral responsivity of a 300k HgCdTe panel in zero bias photovoltaic mode from figure 12 in this paper is 0.0003 amps from 0.00019W of 3.5 micron light.
https://www.researchgate.net/profile/Pawel-Madejczyk-2/publication/343856156_Higher_Operating_Temperature_IR_Detectors_of_the_MOCVD_Grown_HgCdTe_Heterostructures/links/6086b5a62fb9097c0c0d3442/Higher-Operating-Temperature-IR-Detectors-of-the-MOCVD-Grown-HgCdTe-Heterostructures.pdf?origin=publication_detail

But when I recently sat down with the head of the physics department at one of the California state universities and asked if any photocurrent would be produced in a 300k detector from photons from a 300k black body, he assured me it wouldn’t, because the Carnot efficiency of a 300k black body and a 300k detector is 0%… which led me to wonder what is different about the individual 3.5 micron photons from a 299k object vs a 301k object, such that the 301k sourced 3.5 micron photons can produce some useful photocurrent in a 300k detector while the 299k sourced 3.5 micron photons can’t.

He was very busy at the time and refused to go into a discussion about quantum mechanics so I was left with some unanswered questions.

 

[Devin-M]

Mod note: posts regarding sensors and the second law of thermo split -- again.

The noise from the telescope's internal IR swamped these long wavelength observations with too much noise to get useful images.

I’m confused on this point. Useful images aside, my understanding is the 2nd Law of Thermodynamics (which I assume is inviolable) forbids obtaining useful energy from a single temperature reservoir. The “noise” prior to readout consists of a net charge forming in the in-pixel capacitor. Useful work can be done from a net charge in a capacitor. If one considers the telescope that has run out of coolant to be a single temperature reservoir, how does the net “noise” charge form in the in-pixel capacitor considering the 2nd Law and the assumed impossibility of obtaining useful work from said single temperature reservoir?

 

[Drakkith]

I’m confused on this point. Useful images aside, my understanding is the 2nd Law of Thermodynamics (which I assume is inviolable) forbids obtaining useful energy from a single temperature reservoir.

I believe the target is one reservoir, the rest of the universe is the other reservoir.