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Can we harvest Earth's background gamma radiation and put it to good use? Here's my 2 ¢ on the topic.

It's true that gamma rays can be converted to energy, just as visible light photons can by hitting a semiconductor junction with a bandgap similar to the energy of the same photons. However, as with most problems, in this one too, there is a trade off.

Energy: Gamma ray photons are significantly more energetic than visible light, which is at first sight good in the case of a harvesting application. The energy in a 1 MeV gamma ray photon is $1.6 \times 10^{-13}$J. Compared to visible light at e.g. 580 nm, a visible photon has $E = \frac{hc}{\lambda} = 342^{-21}$J. That's a difference of a few orders of magnitude and so a 1 MeV gamma photon is about 467000 times more energetic than a 580 nm (red) photon.

Interaction: Here comes a catch — the matter interaction probability of gamma rays is much much lower compared to visible light photons in the general case. Gamma rays primariliy interact with atomic electrons, therefore their matter interaction mostly depends on the electron density in the sensing material (there are of course other interaction mechanisms such as compton, or pair production which I exclude for simplicity). The ratio between the electron density to the bulk material density for various elements is usually constant and follows: $P = Z . \rho/A$; $Z$ is the element number, $\rho$ is the mass density and $A$ is the atomic mass. For most useful purposes, the most convenient way to harvest gamma rays is through integration with some form of semiconducting material. All useful semiconducting materials are of low Z (e.g. Ge, Si, Ga, B, etc..). There are some heavy element based devices out there, but those are expensive and relatively difficult to produce.

Compared to low-energy gamma rays or visible light, at this stage there are electronic devices offering quantum efficiency in the orders of 80-90 %. The same can not be said about high-energy gamma rays. Beyond 100 keV the QE of silicon drops dramatically to orders of < 1%.

Earth's gamma background: But even so, perhaps we should start optimistically by looking into Earth's natural gamma background and see how much energy there is, here's a plot taken recklessly from the study in [1].

The measurement is energy compensated and performed under a thick lead shielded detector, so I assume that the counts per second reflect the real particle activity due to the energy compensation and detector calibration. We can see that the background gamma follows some sort of a 1/f distribution. There is a distinct peak at 1461 keV which is due to the presence of Potassium 40.

For simplicity we can divide the graph into a few sections such that we can do a ballpark numerical integration.

Energy Range [keV] Activity [cpm]
Mid-energy range (for calculation) [keV]
Photon energy [J]
Total Energy [J/min]
0-500 75 250 40e-15 3e-12
500-1000 11 750 120e-15 1.32e-12
1000-1500 11 1250 200e-15 2.2e-12
1500-2000 3 1750 280e-15 840e-15
2000-2500 2 2250 360e-15 720e-15
2500-3000 1 2750 440e-15 440e-15
TOTAL - - - 8.52e-12

I know that this type of integration simplification is not accurate in its entirity but it gives a rough idea of the collectable energy from background per minute which happens to be 8.5 pJ/min. This may be enough to support some wonderful creations of nature, such as the many Radiotrophic Fungi out there, but in the case of primitive electronics design, even with the most advanced processes that level of energy is by far not enough to cover leakage currents.

Okay, let's assume that we don't rely solely on the background radioactivity, but rather could use some form of safe (?) radioactive source, such as small quantities of Americium 241 — the same isotope used in smoke detectors.

Americium 241 is primarily an alpha emitter with helium particles in the energy range of about 5 MeV, it also emits gamma as it decays, but that's negligible and low-energy ~60 keV. The typical quentity available in smoke detector capsules is about 0.3 micrograms with an activity of about 37 kBq. Here's a picture of one such capsule I'm currently holding in my hands.

Let's assume that with a PIN diode we somehow could collect 5 MeV alpha particles with a quantum efficiency of about 1 %, which is a very bold statement for such high energy range. Knowing the activity, quantum efficiency and energy per particle we can estimate the energy accumulation per second.

$$37 \text{ kBq} = 37000 \text{ particles/second}\\ QE = 0.01\\ 37000 \times 0.01 = 370 \text{ collected particles/second}\\ 5 \text{ MeV} \approx 801.10^{-15} \text{ J/particle}\\ \text{Total Energy Rate} = 801.10^{-15} \times 370 = 296 \text{ pJ/second}$$

An energy rate of 296 pJ/second is not a lot. Especially if you look at it from another perspective. You can divide the total collected particle rate per second by the amount of charge movement necessary to yield an Ampere. Even if you take the all particles, that still brings 12 pA. It may be enough to trigger the Darlington device in a smoke detector, but won't be quite enough to suit power applications.

Finally, to summarize — harvesting background gamma may sound like a crazy idea, but I don't think it's impossible. Especially in environments where that high energy ionizing radiation is abundant i.e. understand space. Here on earth, I think the use of some stronger isotopes would definitely make it possible to harvest with a PIN diode, but there are perhaps more efficient methods which have already been well explored.

Date:Thu Aug 09 22:27:10 EET 2018