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| Fig. 1: Diagram of electron-hole pair generation by beta particles. (Image source: Z. Jahan) |
A persistent challenge in engineering is creating energy sources that are able to operate for decades without maintenance or recharging. Chemical batteries are the most common current solution, but they are temperature-sensitive, degrade through charge cycling, and require periodic replacement. In applications where replacement is impractical or impossible, such as implanted medical devices or sealed spacecraft subsystems, these limitations become critical constraints. Betavoltaic batteries address this problem by deriving electricity directly from the radioactive decay of a beta-emitting isotope. Since the energy source is the isotope itself, a betavoltaic device produces power continuously for as long as meaningful decay activity remains, with operational lifetimes ranging from roughly a decade to over a century depending on the isotope chosen. [1]
A betavoltaic cell functions on the same basic principles as a photovoltaic solar cell, with beta particles replacing photons as the energy input. When a radioisotope undergoes decay, it emits beta particles that strike the semiconductor material and generate electron-hole pairs (EHPs) through impact ionization. Fig. 1 shows a simplified diagram of this process. These EHPs diffuse to the depletion region, where the built-in electric field separates electrons and holes, driving them to opposite contacts and producing a current in the external circuit. [2] The key difference from photovoltaics is scale: a single beta particle carries more energy than a visible photon at tens to hundreds of keV of energy, and can generate thousands of EHPs in a single cascade. However, the flux of beta particles from a practical source is orders of magnitude lower than the photon flux from sunlight, so the resulting currents are in the nanoamp-to-microamp range rather than milliamps. [1]
Efficiency is defined as the ratio of maximum electrical output power to the total radioactive decay power deposited in the device. [2] The remainder is lost primarily as heat when EHPs recombine before being collected by the junction. The theoretical ceiling on this efficiency is set by Claude Klein's empirical formula: for each electron-hole pair of energy Eg created, the beta particle expends an average of 2.8Eg + 0.5 eV, with most of the excess going to lattice vibrations. This relationship implies that wider bandgap semiconductors, such as gallium nitride (GaN) and silicon carbide (SiC), waste a smaller fraction of each beta particle's energy, pushing the theoretical maximum toward roughly 35% for the widest practical bandgaps. [1]
In practice, reported efficiencies for fabricated devices span from under 1% to around 6% for conventional semiconductors, and the numbers can seem low without context. [1-4] The key intuition is that decay power, the denominator of the efficiency ratio, is self-renewing on a timescale of years to decades at no ongoing cost or maintenance. [1] A chemical battery converts stored energy to electricity at much higher efficiencies, but it is depleted within months, so a betavoltaic device running at 1% efficiency for twenty years delivers more total energy per gram of device mass than a chemical battery for the same application. For example, the first Betacel pacemaker battery achieved 4% efficiency and produced up to 400 W at the start of its ten-year useful life, which is sufficient to pace a human heart continuously for a decade without any intervention. [1]
The main constraint in choosing a radioisotope for betavoltaic devices is that beta particles energetic enough to displace atoms in the semiconductor lattice will progressively damage the junction, degrading efficiency over the device lifetime. The approximate threshold for atomic displacement in most semiconductor materials is 300 keV. [1] Among all beta-emitting radioisotopes with half-lives long enough to be practically useful, nickel-63 (Ni-63) and tritium (H-3) have maximum beta energies comfortably below the 300 keV displacement threshold.
Ni-63 has a half-life of 101.2 years and a maximum beta energy of 66.9 keV, well below the displacement threshold. [5] This combination makes it the most conservative choice for long-life applications since a device retains over 50% of its initial activity after 100 years, and the low beta energy is fully absorbed within a few micrometers of silicon. The cost of enriched Ni-63 is high at roughly $4,000 per curie, and this has historically limited its deployment, but its stability and longevity make it the reference isotope for research. [1]
H-3 (tritium) has a half-life of 12.3 years and a maximum beta energy of only 18.6 keV. [5] Its low energy means that the beta particles are absorbed within about one micrometer of the source surface (self-absorption), which limits power density if the source geometry is not carefully optimized. At the same time, those same particles are harmless to the semiconductor junction and cannot penetrate even a sheet of paper, making tritium far easier to handle from a regulatory standpoint. [6] Tritium is also the cheapest of the viable isotopes at $3.50 per curie, further making it suitable for commercial use. [1]
Given an isotope, two further design choices determine efficiency: the geometry of the semiconductor junction and the semiconductor material. While these factors operate independently, a good geometry with a poor material choice will underperform a well-matched combination of both. Semiconductor material determines the theoretical ceiling on efficiency through Klein's formula, and choosing a wide-bandgap material is the most direct path toward that ceiling. Silicon, with a bandgap of 1.1 eV, has been the default substrate due to its low cost and mature processing technology, but its relatively narrow bandgap limits maximum efficiency. SiC, with a bandgap of 2.33.3 eV, and GaN, with a bandgap of 3.2 eV, offer higher bandgaps and additional radiation hardness due to their strong atomic bonding, making them less susceptible to the long-term lattice damage that even sub-threshold beta particles cause over decades of irradiation. [2]
Diamond represents the extreme end of these materials, with a bandgap of 5.5 eV, which is the widest of any practical semiconductor. One study measured a diamond Schottky diode under electron-beam irradiation matched to the average energy of Ni-63 and achieved a total conversion efficiency of approximately 3%, with peak efficiency approaching 3.754% at lower beam energies matched to the H-3 average. [3] More significantly, another study found that a diamond p-n junction, which is a more difficult structure than a Schottky diode but has a higher built-in potential, achieved a total conversion efficiency of up to 24%. These are some of the highest values reported for any betavoltaic device. The open-circuit voltage of 4.26 V reflects diamond's high built-in potential of approximately 4.5 V, which is roughly double that of a silicon p-n junction. The practical limitation of diamond, though, is its fabrication difficulty and cost because growing defect-free - type diamond layers of sufficient size is complex, and the output powers in these experiments were in the nanowatt range. [4]
Betavoltaic batteries are the only practical power source capable of delivering continuous microwatt-level electricity for decades without any maintenance, charging, or external energy input. The core physics involves beta particles generating electron-hole pairs in a semiconductor junction, and the fraction converted to electricity depends on the semiconductor bandgap and junction geometry. The 300 keV atomic displacement threshold is the central constraint on isotope selection, restricting practical long-life devices to H-3 and Ni-63. Recent work on diamond p-n junctions has demonstrated semiconductor efficiencies close to the theoretical limit, though scaling these devices to practical source geometries and areas remains an open challenge. [4]
© Zara Jahan. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] L. C. Olsen, P. Cagauy, and B. J. Elkind, "Betavoltaic Power Sources," Physics Today 65, No. 12, 35 (December 2012).
[2] M. B. Naseem et al., "Betavoltaic Nuclear Battery: A Review of Recent Progress and Challenges as an Alternative Energy Source," J. Phys. Chem. 127, 7565 (2023).
[3] V. Grushko et al., "Energy Conversion Efficiency in Betavoltaic Cells Based on the Diamond Schottky Diode with a Thin Drift Layer," Appl. Radiat. Isot. 257, 109017 (2020).
[4] T. Shimaoka et al., "Ultrahigh Conversion Efficiency of Betavoltaic Cell Using Diamond pn Junction," Appl. Phys. Lett. 117, 103902 (2020).
[5] A. S. Bykov et al., "Application of Radioactive Isotopes for Beta-Voltaic Generators," Russ. Microelectron. 46, 527 (2017).
[6] H. Kang et al., "Low Energy Beta Emitter Measurement: A Review," Chemosensors 8, 106 (2020).