Betavoltaic cell based on Ni/β-Ga₂O₃ and ⁶³Ni source

Betavoltaic power cells occupy an important niche among low-current power supplies for microelectronic devices. Their pronounced advantages are reliability, long service life, compactness, and autonomy, making betavoltaic cells very attractive for many practical applications, including devices for space, electronic implants in healthcare, sensors, and micromechanics.^1–6 The betavoltaic cell typically includes two major components: a β-particles emitter and a converter (or absorber) based on semiconductor materials, which absorbs radiation energy and converts it into electric power. Wide-bandgap semiconductors are the most promising materials for beta-particle energy converters because they can provide the larger open circuit voltage V_oc. Therefore, much work has been devoted to the prediction of parameters of betavoltaic cells based on 4H-SiC, GaN, and diamond and the formation of betavoltaic cells based on these materials. The β-polytype of Ga₂O₃ with a wide-bandgap close to 5 eV has excellent potential for applications in power electronics^7,8 and solar-blind photodetectors;^8–10 however, up to now, its possible application as a converter in betavoltaic cells has not been considered. Only a brief analysis in comparison with other wide-bandgap semiconductors has appeared.⁴ A discussion of the impact of bandgap on the efficiency of betavoltaic batteries has also been reported.¹¹ 

It is also fortuitous that Ni, one of the more suitable beta-radiation sources, can be used to form the Schottky barrier on Ga₂O₃; thus, the layer containing radioactive ⁶³Ni can be used as a metal contact. Therefore, it seems interesting to evaluate the potential of Ga₂O₃ for betavoltaic cells. Since the fabrication of a highly isotope-enriched material is expensive, e-beam in a scanning electron microscope (SEM) can be used to estimate the efficiency of the semiconductor converter.^12–15 However, the depth-dependent energy deposition for beta-irradiation essentially differs from that for monoenergetic e-beam.^16–18 Therefore, the approach proposed in Ref. 15 should be used, in which the depth-dependent generation rate is calculated by the Monte Carlo program specially adapted for beta-irradiation simulation and the output parameters are obtained using the SEM measurements.

In this letter, the parameters of betavoltaic cells based on the Ni/β-Ga₂O₃ Schottky barrier are evaluated. The depth-dependent generation rate of excess carriers produced by beta-radiation from ⁶³Ni source is calculated for a few Ni film thicknesses by the Monte Carlo method. The short circuit current I_sc is calculated for the Schottky barrier with parameters obtained from the electron beam induced current (EBIC) studies of Ni Schottky barriers formed on n-type β-Ga₂O₃. The open circuit voltage V_oc and maximum power P_max are measured using the e-beam of SEM to imitate the beta-particle source containing ⁶³Ni.

The samples used in this work were β-polytype Si-doped n-Ga₂O₃(Si) films grown by halide vapor phase epitaxy on Sn-doped n-Ga₂O₃(Sn) substrates cut from bulk single crystals grown by edge-defined film-fed growth. The structures were acquired from Tamura/Novel Crystal Technology (Japan). The net electron concentration of the films was ∼10¹⁶ cm⁻³ with an epi thickness of 7–10 μm. The net donor density of the substrates was 3 × 10¹⁸ cm⁻³. The orientation of the structures was (001). The back Ohmic contacts were prepared by Ti/Au (20 nm/80 nm) e-beam evaporation with subsequent rapid thermal annealing at 500 °C for 30 s in nitrogen. Schottky diodes on the front surface were made by e-beam evaporation of Ni (20 nm) through a shadow mask. The diameter of the circular diodes was 1 mm. A schematic of the experimental rectifier structure is shown in Fig. 1(a). It is convenient that the Ni contact layer imitates a β-particles emitter containing ⁶³Ni that seems reasonable because commonly available sources, which can purchased, contain about 20% of ⁶³Ni. The design is illustrated schematically in Fig. 1(b), showing the similarity of the projected design with existing rectifiers. The main factor is to use the optimal thickness of the radioactive layer to increase the flow of radioactive particles, but to minimize the impact of self-absorption. The thickness of the Au overlayer in that arrangement is of minor importance. The matter is discussed in more detail below.

The results of electrical measurements of the experimental Schottky barriers were described in detail elsewhere.^19–21 Since most Schottky barriers on β-Ga₂O₃ demonstrate photosensitivity gain,^22,23 which is associated with leakage current increase under e-beam excitation and prevents the correct measurements of converter parameters, we used only structures that did not demonstrate this effect.

To evaluate the parameters of betavoltaic cells based on β-Ga₂O₃ and ⁶³Ni radioactive source as the Schottky contact, the approach proposed in Refs. 15 and 24 is used. Briefly, this approach consists of the Monte Carlo simulation of the depth dependence of electron–hole pair generation rate due to the absorption of the beta-particles emitted by the ⁶³Ni source, the estimate of the current collection efficiency from the experimental EBIC dependence on the probing beam energy for the studied samples, and experimental measurements of the current–voltage characteristics of the studied sample obtained under the e-beam excitation in EBIC. From the latter measurements, the open circuit voltage and the maximum power were calculated in the standard fashion. The simulation of the depth-dependent deposited energy was carried out using the in-house algorithm specially adapted for the fast calculation of multilayer betavoltaic structures.²⁵ It is important to take into account in simulations that the beta-particles have a continuous beta-energy spectrum and they are emitted uniformly over the source and isotropically along the electron emission directions;^15–18 therefore, the electron trajectories were assumed to start uniformly over the radioisotope layer thickness and isotropically.

The real spectrum of beta-particles was used in the program. Such an approach self-consistently takes into account the self-absorption in the radioactive layer and the backscattering from the semiconductor converter. The layer specific activity was assumed as 100 Ci/cm³, which corresponds to about 20% of ⁶³Ni in the Ni film. The depth-dependent excess carrier generation rate was calculated by dividing the depth-dependent energy deposition by the electron–hole pair creation energy of 15.6 eV measured by us in Ref. 26. The short circuit current I_sc induced by beta-particles was calculated as a convolution of this depth-dependent generation rate with the collection efficiency of the current induced by beta-particles.^27–29 This collection efficiency was calculated using the diffusion length of nonequilibrium charge carriers L and the width of the space charge region at 0 V bias obtained experimentally for the studied Ni/β-Ga₂O₃ Schottky barriers from fitting the dependence of the collected current in the EBIC mode I_c on beam energy E_b.^28–30 

Then, the open circuit voltage V_oc, and the value of maximum power P_max were extracted from experimentally measured current–voltage characteristic under the e-beam excitation with the electron beam current I_b adjusted so that the EBIC current I_c at reverse bias was equal to the calculated value of I_sc. To obtain the power dependence on a load, the I_c values in the current–voltage curve corresponding to forward bias V_d were used to calculate the power I_c(V_d) × V_d and to find the value of forward bias V_d at which the power was at its maximum P_max. Thus, the values of V_oc and P_max of the studied structure corresponding to the ⁶³Ni beta-particles excitation could be determined without the actual deposition of the radioactive ⁶³Ni simply from modeling using the EBIC data collected under the e-beam excitation of the SEM with the values of the probing e-beam current appropriately chosen based on simulation. All measurements were carried out in the SEM JSM 840 at room temperature. We separately describe the approach used to calculate the parameters from the I_c(E_b) experiment and give the actual results of the I_c collection efficiency measurements and the parameters deduced from them by fitting—see supplementary material for a discussion on how these filling parameters were obtained.³⁵ 

The results of the Monte Carlo calculations of the depth-dependent carrier generation rate are shown in Fig. 2 for radioactive layer thicknesses of 0.2, 1, and 3 μm. For thicknesses larger than 3 μm, the energy absorbed in the semiconductor converter is saturated due to self-absorption in the Ni film.¹⁴ The dependences are close to exponential ones with a characteristic length of 1.3 μm. It is seen that the 6 μm thick Ga₂O₃ layer absorbs more than 99% of the irradiation energy and the generation rate at this depth drops by a few orders of magnitude; therefore, such a thickness is enough for the effective absorption of the radiation energy. Fitting the I_c(E_b) dependence measured on the Schottky diodes gives a depletion region width of 180 nm and a diffusion length L of 300 nm. Using these parameters, the short circuit current I_sc is calculated and for a 3 μm thick Ni layer it is 8.9 nA/cm². Measurements of V_oc and P_max give values of 380 mV and 1.78 nW/cm², respectively. The filling factor FF = 0.53. For a 1 μm thick Ni layer, the I_sc, V_oc, and P_max parameters are estimated as 6.53 nA/cm², 350 mV, and 1.15 nW/cm², respectively (Fig. 3). To simplify the betavoltaic cell formation procedure, the radioactive layer can be electrolytically deposited on the preprepared Ni/β-Ga₂O₃ Schottky barrier. If the thicknesses of the natural Ni layer and that of the radioactive layer are 10 nm and 3 μm, respectively, I_sc decreases to 8.76 nA/cm², V_oc does not practically change, and P_max decreases to 1.75 nW/cm².

The approach used allows to predict the beta battery parameters with the accuracy better than 30%.²⁴ Thus, it can be expected that the calculated parameters are close to those that would be observed for the same Schottky diodes with a radioactive source. Moreover, these parameters are obtained on the real structures; therefore, the optimization of material properties and the Schottky barrier formation procedure can essentially improve them, especially V_oc, which is mainly determined by the leakage current. For example, a diffusion length increase to 1 μm without changing the procedure of Schottky barrier formation will alone increase I_sc, V_oc, and P_max for 3 μm thick Ni layer up to 14.8 nA/cm², 410 mV, and 3.58 nW/cm², respectively.

The power dependences on cell voltage, from which the maximum power is obtained, are shown in Fig. 3 for the discussed Ni film thicknesses and L values. Beta-particles are emitted isotropically; therefore, only about a half of the energy is emitted to the converter but the other part is emitted in the opposite direction. To improve the element efficiency, two Ga₂O₃ converters can be located on both sides of radioactive source sandwiching it. Since the sources are then practically independent, the power of such an element would be two times higher than that of the element containing only one converter. Another way to utilize the energy emitted in the direction opposite to the converter could be to deposit a heavy metal layer, e.g., Au, on the Ni source to backscatter beta-particles, as schematically shown in Fig. 1(b). However, as the simulation shows, such a procedure increases the element efficiency for the thin Ni layers only. For a 1 μm thick Ni source and 100 nm Au layer, the energy deposited in the Ga₂O₃ converter will increase only by 6% and for 3 μm thick Ni source this increase is lower than 1%.

Thus, the parameters of betavoltaic cells based on Ni/β-Ga₂O₃ Schottky barrier and ⁶³Ni radioisotope are obtained. It should be stressed that these parameters are obtained for real structures formed on n-type β-Ga₂O₃. The parameters obtained are comparable with those obtained on GaN based and diamond based betavoltaic cells^24,31–33 and show the potential for Ga₂O₃ betavoltaic applications. Ga₂O₃ devices are very radiation tolerant and in this respect are on par with GaN or diamond and certainly better (by more than 2 orders of magnitude) than Si,^8,34 so that radiation damage produced in the material by beta-particles emitted by ⁶³Ni isotope can be safely disregarded during the entire desired lifetime of the autonomous battery. At the same time, compared to GaN the crystalline quality of Ga₂0₃ is radically better [the dislocation density typically on the order of 10⁴ cm⁻² (Ref. 8) versus 10⁶ cm⁻² even for the best bulk GaN], with the diffusion length typically also several times higher, while, compared to diamond, Ga₂O₃ has an advantage related to the ability to fabricate high-quality structures of big diameter (up to 100 versus ∼20 mm for good quality single crystalline films of diamond). It can be also mentioned that surface polishing of Ga₂O₃ substrates for epitaxy is also easier than for bulk diamond substrates. Both factors make Ga₂O₃ technologically and economically more attractive than diamond. It could be noted that, in a recent publication,¹¹ the authors question the commonly held belief that the efficiency of betavoltaic sources based on wide-bandgap semiconductors is higher than for Si, mostly because of the relatively low values of diffusion length in such materials compared to Si. However, the availability of very high crystalline quality Ga₂O₃ films sets them apart from, say, GaN. With proper surface passivation, the increase in the Schottky barrier heights by using oxidized metals, and the decrease in the density of deep traps responsible for the nonradiative recombination, the values of leakage currents and of diffusion lengths are expected to substantially increase, thus making the performance of the Ga₂O₃ betavoltaic batteries much more promising.

The work at IMTRAS was supported by the State Task No. 075-00355-21-00. The work at UF was performed as part of Interaction of Ionizing Radiation with Matter University Research Alliance (IIRM-URA), sponsored by the Department of the Defense, Defense Threat Reduction Agency under Award No. HDTRA1-20-2-0002. The content of the information does not necessarily reflect the position or the policy of the federal government, and no official endorsement should be inferred. The work at UF was also supported by NSF DMR under No. 1856662 (James Edgar). The authors have no conflicts to disclose.

The data that support the findings of this study are available within the article.