First principles study on the time-related properties of 4H-32SiC as an energy converting material of betavoltaic batteries

The radioactive 4H-32SiC is applied as an energy converting material to fabricate high performance betavoltaic batteries. The time-related component change is considered, and the structural, stability and electrical property changes are calculated by density functional theory. As time goes by, the number of 32Si atoms decrease exponentially while the concentration of 32S increases gradually. The Si63PC64 configurations have smaller lattice constants, while the lattices of Si62PSC64 configurations are larger. All Si63PC64 and Si62PSC64 configurations have very small bandgaps indicating the metallic behavior. This suggests that the betavoltaic battery with 4H-32SiC is likely to transform into a Schottky diode over time.

The radioactive 4H- 32 SiC is applied as an energy converting material to fabricate high performance betavoltaic batteries.The time-related component change is considered, and the structural, stability and electrical property changes are calculated by density functional theory.As time goes by, the number of 32 Si atoms decrease exponentially while the concentration of 32 S increases gradually.The Si 63 PC 64 configurations have smaller lattice constants, while the lattices of Si 62 PSC 64 configurations are larger.All Si 63 PC 64 and Si 62 PSC 64 configurations have very small bandgaps indicating the metallic behavior.This suggests that the betavoltaic battery with 4H- 32 SiC is likely to transform into a Schottky diode over time.© 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd Supplementary material for this article is available online B etavoltaic batteries have become a promising lowpower supply due to their small size, stable output, high power density and long service life. 1,2)[5] Compared with betavoltaic batteries based on Si 6) or GaAs, 7) they have a higher open-circuit voltage, conversion efficiency and radiation damage resistance. 8)Specifically, SiC (silicon carbide) is a wide bandgap semiconductor with high thermal capability, high carrier mobility, high breakdown field strength and excellent radiation resistance. 9,10)Moreover, the n-type and p-type doping of SiC can be controlled in a wide range, 11) which is a great advantage over many other wide bandgap semiconductors with doping asymmetry problems. 12)As a result, SiC is commonly used to fabricate electronic components, 11) and the 4H-SiC is much preferred because of its higher bandgap and mobility. 13)[20][21][22] For SiC, the main radioactive isotopes with pure beta emission are 32 Si and 14 C, which are heavier than the relative stable isotopes (i.e., 28 Si, 29 Si, 30 Si, 12 C, and 13 C). 32Si is a cosmic ray produced beta emitting isotope with a half-life of about 153 years. 23)By emitting beta particles with average and maximum energies of 69.55 and 227.2 keV, 32 Si nuclear decays into 32 P nuclear.Subsequently, the daughter nuclear 32 P decays into stable 32 S nuclear with a half-life of 14.3 days, 24) and the average and maximum beta energies are 695.03keV and 1710.66 keV, respectively.In recent years, 32 Si can be produced by proton-irradiation of vanadium, KCl or other radioactive nuclides, 23) which broadens its potential applications.This paper focuses on the structural and electrical properties of radioactive 4H-32 SiC, and the density functional theory (DFT) is employed due to the lack of experimental results.
All calculations are performed by employing the Vienna ab-initio Simulation Package (VASP). 25)The pseudo potential and exchange-correlation functional are projector augmented plane wave (PAW) 26) and Perdew-Burke-Ehrenzorf (PBE), 27) respectively, and the plane wave cut-off energy is 700 eV.All forces are less than 0.01 eV/Å in primary cells calculation, and the Brillion zone is sampled with a 7 × 7 × 7 Monkhorst-Pack k-point mesh. 28)The high symmetry path is obtained by SeeK-path method. 29)n order to obtain the properties after decay, a 2 × 2 × 2 4H-SiC supercell with 64 atoms is employed.The k-point is 4 × 4 × 3 Monkhorst-Pack mesh.In this work, the decayed 4H-32 SiC is treated as a defected system D, and the overall charge is neglected.
The stability of all decayed configurations is evaluated by the formation energy E D , f ( ) which is calculated by the following equations: 30) where i is the type of the defect, E D tot ( ) is the total energy of defected supercell, E pure tot ( ) is the total energy of n ondefected supercell, n i is the quantity of defect and μ i is the chemical potential of atoms.
The number of 32 Si, 32 P and 32 S nuclei can be obtained by series decay equations: where N 1 , N 2 and N 3 are the number of 32 Si, 32 P and 32 S nuclei, N 0 1 ( ) is the initial number of 32 Si, t is the time.l 1 and l 2 are decay constants of 32 Si and 32 P. By applying l = A N, the radioactivity of 32 Si, 32 P and total radioactivity can be obtained as follows: where A t 1 ( ) and A t 2 ( ) are radioactivities of 32 Si and 32 P, respectively.The total radioactivity A t t ( ) is the sum of A t 1 ( ) and A t 2 ( ) because 32 S is a stable isotope.The initial radioactivity is assumed as 3.7 × 10 9 Bq.
As time goes by, the proportion of 32 Si, 32 P, and 32 S changes continuously.The time-related component change is shown in Fig. 1.The number of 32 Si nuclei decrease exponentially, while the component of 32 S increases gradually [shown in Fig. 1(a)].The component change of 32 P [shown in Fig. 1(b)] is more complex.At the beginning of the decay process, more and more 32 P nuclei generates due to the decay of 32 Si.Since 32 P is an unstable isotope with very short half-life, it soon decays and the component decreases drastically.The full process can be divided into three stages: 1) N Si >N P >N s .This stage is from the beginning of the decay process to about 90 days (at which the content of 32 P and 32 S is the same).2) N Si >N s >N P .At about 0.466 a, the mixture has the highest amount of 32 P. 3) N s >N Si >N P .The content of 32 Si and 32 S is the same at about 153 a. Finally, the mixture will become pure 32 S and lose its radioactivity.The radioactivity changes are shown in Fig. 2. As time goes by, the radioactivity of 32 Si follows the exponential decay pattern [shown in Fig. 2(b)], while the total and 32 P radioactivies initially rises, and then decreases exponentially [shown in Fig. 2(a)].The maximum of total radioactivity and 32 P radioactivity appears at about 0.428 and 0.466 a, respectively.When 32 S becomes the main component of the 32 Si-32 P-32 S mixture, the system has a relatively low radioactivity, resulting in a loss of efficacy for the betavoltaic battery.Therefore, the first two stages are selected to perform a DFT calculation.One representative structure is presented for each stage in this work, which is labeled as Si 63 PC 64 (where one P atom substitutes for one Si atom in the SiC supercell) and Si 62 PSC 64 (where one P atom and one S atom substitutes for two Si atoms in the SiC supercell).
After the decay of 32 Si, one 32 Si nucleus changes into 32 P nucleus and emits one electron and one anti-neutrino.Since the position of the decayed nucleus is uncertain, nine different configurations are selected to investigate the structural, stability and band properties of Si 63 PC 64 (shown in Fig. 3).The decayed atom can be located either at the edges, or in the planes, or inside the supercell.
The lattice parameters of different Si 63 PC 64 configurations are listed in Table I.Compared with the non-defected SiC supercell, all Si 63 PC 64 configurations have smaller lattice constants and volumes.In configuration No. 8 and 9, the lattice is no longer hexagonal.
Table II shows the total and formation energy of each configuration.The chemical potentials of P atom and Si atom are −1.87617 and −0.04931 eV, respectively.Among all configurations, No. 8 has the lowest formation energy, indicating that it is the most stable configuration.Nos. 3, 4, 5 and 9 are relatively unstable because their formation energies are significantly higher.
The bandgap of all Si 63 PC 64 configurations ranges from 0.0001 to 0.0047 eV, indicating the metallic behavior, rather than the indirect bandgap semiconductor behavior of SiC.The fermi levels range from 10.5128 to 10.5567 eV, which is significantly higher than that of pure SiC supercell (8.3313 eV).For each configuration, the CBM and VBM are not at the same point in the K-space.Take the band structure of No. 8 configuration as an example (shown in Fig. 4), one can see the conduct and valence band moved downwards.
All Si 62 PSC 64 configurations are formed based on No.8 Si 63 PC 64 configuration, which is the most stable one among all Si 63 PC 64 configurations.These configurations have different distances between the phosphorus and sulfur atoms (which is marked as P-S length).The relative lattice constants are shown in Table III.It can be seen that all Si 62 PSC 64 configurations have slightly larger lattice constants and volumes than those of original Si 63 PC 64 configuration, and the lattices derivate from the hexagonal crystal system.
The chemical potential of the S atom is −0.03158 eV, and the formation energies of different Si 62 PSC 64 configurations are listed in Table IV.It can be seen that the No. 1 041001-2 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd configuration with the shortest P-S length is the most unstable configuration, while the No. 4 configuration with moderate P-S length is the most stable one.Generally, configurations with short P-S lengths are relatively unstable, and longer P-S lengths lead to better stability.Unlike SiC and Si 63 PC 64 configurations, most of the Si 62 PSC 64 configurations have magnetic moments (shown in Table IV) because of the presence of the S atom.Therefore, the spin-polarization should be taken into consideration, and the spin-up and spin-down band structures are different from each other.All bands have very small bandgaps (E g < 0.01 eV) which indicates the metallic behavior.The ranges of bandgap and Fermi Level are 0.0003 ∼ 0.0074 eV and 9.7331 ∼ 10.082 eV, respectively, and the CBM and VBM are at the different points in K-space.In summary, these configurations all have metallic behavior.
The planar 32 SiC-SiC (both materials exhibit a 4H structure) integrated betavoltaic battery prototype is shown in Fig. 5.As mentioned before, SiC can be easily doped as either n-type or p-type, whereas Si 63 PC 64 and Si 62 PSC 64 exhibit metallic behaviors.Therefore, if the 32 SiC-SiC device functions as a pn-junction at the beginning, it is likely to transition to a Schottky diode over time.
However, due to the existence of series decay, the electrical properties of decayed 32 SiC may be more complex than what has been stated.For example, a configuration of Si 62 P 2 C 64 (where two P atoms substitute two Si atoms in the SiC supercell) is an indirect bandgap semiconductor with a bandgap of 0.6114 eV.This could lead to further   © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd changes in the performance of the betavoltaic battery, and there are still more situations that need to be calculated and discussed.
In this work, 4H-32 SiC is intended to be used both as the beta source and the energy converting material of betavoltaic battery.Several time-related changes of 4H-32 SiC are investigated including component, structural, stability and band structure.As time goes by, 32 Si atoms decrease exponentially while 32 S increases gradually.The content of 32 P reaches its peak value at 0.466 a.The Si 63 PC 64 configurations have smaller lattice constants than 4H-SiC supercell, while the lattices of Si 62 PSC 64 configurations are larger and derivate from the hexagonal crystal system.All Si 63 PC 64 and Si 62 PSC 64 configurations calculated in this work have metallic behavior with very small bandgaps, indicating that the betavoltaic battery with 4H-32 SiC is more likely to become a Schottky diode over time.The quantitative change of phosphorus and sulfur atoms may lead to different structural and electrical properties, and other situations are remained to be explored.041001-4 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd

Fig. 1 .
Fig. 1.Time-related component change of 32 Si source.(a) Changes of 32 Si, 32 P and 32 S. (b) The long-term change of 32 P.

Fig. 2 .
Fig. 2. Time-related radioactivity change of 32 Si source.(a) Total radioactivity (shown in solid line) and the radioactivity of 32 P (shown as a red dotted line).(b) Radioactivity change of 32 Si (shown as a green dash line).

Fig. 5 .
Fig. 5. Prototype of 32 SiC-SiC integrated betavoltaic battery.The radioactive 4H-32 SiC is worked both as energy converting material and beta source.

Table I .
Lattice parameters of different configurations of Si 63 PC 64 .

Table II .
Total and formation energy of Si 63 PC 64 configurations.

Table III .
Lattice parameters of different configurations of Si 62 PSC 64 .

Table IV .
Total energy, formation energy and magnetic moments of Si 62 PSC 64 configurations.