Design and simulation of high conversion efficiency betavoltaic battery based on a stacked multilayer structure

In recent years, betavoltaic batteries have received attention for potential applications in powering wireless sensor networks because of their ultra-miniature sizes, long operating lives, and anti-interference properties. Using semiconductor converters that absorb β particles from an isotope source, betavoltaic batteries can convert radioisotope energy into electrical energy. The partial kinetic energies of the β particles that enter the converters produce numerous electron-hole pairs (EHPs). Those nonequilibrium electron-hole pairs are separated by the built-in electric field of the junction, with holes drifting to the positive pole while electrons drift to the negative pole. The electrodes collect the separated holes and electrons to produce voltage and current to power loads.

Silicon p-n junction-based converters are more commonly used in betavoltaic batteries than converters based on other semiconductors such as SiC, Ge, and GaAs. This is due to the abundance of mature silicon micro-fabrication processes and their relatively low cost.^1–3 Among isotope sources, ⁶³Ni is more convenient and safer to handle than other sources such as ¹⁴⁷Pm, ⁹⁰Sr, and ³H because of its solid-metal form and low energy spectrum.^4–6 The energy spectrum of β particles emitted from ⁶³Ni is shown in Fig. 1. The average energy is 17.6 keV and the maximum energy is 65.9 keV. These are both below the damage threshold for silicon.^7–9 Thus, betavoltaic batteries based on ⁶³Ni and silicon can supply energy for decades without a significant performance decline.

Conventional betavoltaic batteries are composed of a simple two-layer structure with the isotope source attached to one side of a semiconductor converter. Typically, various techniques are used to increase the source thickness and optimize converter doping to increase the maximum output power of a conventional battery.^10,11 However, it is difficult to improve battery performance significantly within this conventional two-layer structure because only one side of the isotope source is used.¹² Moreover, increasing the source thickness decreases the battery conversion efficiency due to self-absorption.¹³ 

In this paper, we introduce a new design for betavoltaic batteries based on ⁶³Ni and a silicon p-n junction. This type of betavoltaic battery uses a stacked multilayer structure to improve its maximum power and conversion efficiency significantly through full consideration of reasonable source utilization and converter design.

A reasonable isotope source film thickness is crucial to the betavoltaic battery design. An excessively thin source film cannot offer enough isotopic energy for betavoltaic batteries, resulting in low battery output. When the film thickness exceeds the saturation value, the isotopic energy of the excess source material is wasted due to self-absorption and cannot be absorbed by the converter. The apparent radiation spectrums of ⁶³Ni films with various thicknesses were investigated via Monte Carlo simulation with the Geant4 radiation transport toolkit as shown in Fig. 2. The activity of radioisotope can be calculated as the following equation,

where A is the activity of radioisotope, N_A is Avogadro’s number, T_1/2 is the half-life, M is the molar mass, ρ is the density of the film, a is the side length of the square film, and d is the thickness of the film. The size of the source remains the same except for the thickness during the simulation, so the activity equation can be simplified as the following equation,

where C is the constant, and d is the thickness of the film. Activity A is proportional to thickness d. We use relative activity to reduce the amount of calculation by eliminating C. The relative number of particle is the result of the average spectrum per particle times the relative activity which is a dimensionless proportion number and in proportion to the thickness. The peak of the β particle energy distribution moves towards the high-energy section as the thickness increases. This is consistent with similar phenomena observed in previous studies.^12,14 The relative number of β particles emitted from the ⁶³Ni film increases with the film thickness, and this can improve the maximum achievable battery power accordingly. However, this relative number is not proportional to the source thickness and begins to saturate at a thickness of 5 μm due to self-absorption. Self-absorption within the source becomes more substantial as the film thickness increases. In extreme cases, the apparent energy spectrum of the 9 μm ⁶³Ni film almost overlaps with that of the 5 μm film, which means that the portion of the film that exceeds 5 μm contributes little to improving the output radiation power.

In conventional battery design, a saturated thickness source is typically chosen to increase the maximum possible output power and reasonable converter parameters are selected to increase the energy conversion efficiency. As shown in Fig. 3(a), the conventional battery is a two-layer structure consisting of a 5 μm thick ⁶³Ni source and a 30 μm thick converter. The latter can completely absorb the energy from of β particles with maximum energies of 65.9 keV from the source.¹⁵ 

During the manufacturing process, increasing the number of layers in the stacked structure increases the technical difficulty and cost of production. It is crucial to design the battery with a suitable number of layers in order to improve its performance. The thicknesses of the radioisotope source and the semiconductor converter are the two key parameters that determine the number of layers that the battery should be designed to have. First, the source thickness should be small enough to increase source utilization by reducing the self-absorption. Second, the semiconductor converter should be thick enough to reduce waste due to energy that penetrates the top and bottom converter layers. However, if the total battery volume is to be kept constant, decreasing the thickness of the source should reduce that of the converter in the alternately stacked structure, which results in wasted radiation energy at both ends of the stacked battery. The thicknesses of the source and converter should be traded off to improve the stacked battery performance. Because the energy availability rate of a 1 μm thick ⁶³Ni source is more than 3.5 times that of a saturated source and less than 15 percent of the energy of the ⁶³Ni source would penetrate a 5 μm-thick. silicon converter, we combine a 1 μm-thick source and a 5μm-thick converter to improve the performance of the modeled stacked structure battery. The process used to transition from conventional battery to stacked battery design is shown in Fig. 3. In our model, the total and source volumes of the proposed battery remain the same as that of the conventional battery. First, the source of the conventional battery is divided into 5 layers, each 1 μm-thick. This improves the total output radiation power by reducing self-absorption. Then, the 30 μm-thick converter is divided into 6 units that are each 5μm-thick. Finally, the source and converter layers are stacked alternately to ensure that radiation energy can be absorbed from both sides of the source films. Such a stacked multilayer battery can improve source utilization.

In order to quantitatively compare the amounts of energy absorbed by the converters in the two differently structured batteries, the Monte Carlo method is used to simulate the motion of the β particles emitted from ⁶³Ni films and calculate energy absorption in the silicon converters. In this simulation, the ⁶³Ni films and silicon converters are taken to be 1 mm×1 mm in size, and all thicknesses are as shown in Fig. 3. For accuracy, the Monte Carlo simulation was performed using beta particle energies that were based on the ⁶³Ni energy spectrum rather than the average energy.

Fig. 4 shows the β particle energy deposition (E_dep) distributions and accumulation energy deposition distributions in the converters of the two differently structured batteries. In the conventional battery, the deposited energy decreases exponentially with depth due to the simple, two-layer structure. The energy deposition distribution in the silicon converters of the proposed battery has the same symmetry as the stacked multilayer structure. It is clear that the accumulation energy deposition of the proposed battery is much larger than that of the conventional battery. This indicates that the total energy absorption is larger in the proposed battery than in the conventional battery. The estimated calculation error of the Monte Carlo simulation is about 1.03%. The simulation results are consistent with the previous analysis and indicate improvement in source utilization via reduced self-absorption and utilization of both sides of the source film.^1,2,4

Theoretically, the average energy required for the generation of an electron-hole pair (EHP) can be calculated using the following equation:¹⁶ 

where E_g is the band-gap of silicon. Thus, the EHP generation rate distribution in the silicon can be calculated from the energy deposition distribution using the following equation:¹² 

where x is the position along the thickness direction in the silicon. The probability of collecting an EHP generated in the depletion region is 100%. Thus, it is necessary to design a shallow junction. This aids in EHP collection. A junction depth of 300 nm was adopted based on our ability to process shallow junctions within our facility. A rational depletion region width is also vital for converter design. This width can be calculated using the following equations:

where k is the Boltzmann constant, V_D is the built-in potential difference, T is the absolute temperature, q is the electron charge, ε_r is the dielectric constant, ε₀ is the vacuum dielectric constant, n_i is the intrinsic carrier concentration, and N_a and N_d are the doping concentrations in the P region and N regions, respectively. The relationship between the depletion region width and the P and N region doping concentrations is shown in Fig. 5. The width of the depletion region varies from 40 nm to 25 um according to the doping concentrations. The minority carrier diffusion length can be obtained using the following equation:

where D is the diffusion coefficient, τ is the minority carrier life, and μ is the minority carrier mobility. The minority carrier diffusion length in P region and N region for silicon semiconductor can be calculated as the following equations,¹⁷ 

EHPs generated outside the depletion region are collected with the following probability:^17–19 

where L is the minority carrier diffusion length and d(x) is the distance between position x and the depletion region. The EHPs are collected to form the short current calculated in the following equation:¹⁷ 

The open-circuit voltage of the battery is obtained using the following equation:

where I₀ is the p-n junction leakage current and is determined by the doping concentrations N_a and N_d in the P and N regions, respectively, via the following equation:²⁰ 

where S is the junction area, n_i is the intrinsic carrier concentration, q is the electron charge, D_p and L_p are the hole diffusion efficiency and diffusion length respectively, and D_n and L_n are the electron diffusion efficiency and diffusion length, respectively. The leakage current of the 1 mm × 1 mm junction and the doping concentrations in the P and N regions are given in Fig. 6. The leakage current decreases as the doping concentration increases.

The maximum output power P_m and overall conversion efficiency η determine the battery performance, and are calculated via the following equations:²¹ 

where FF is the fill factor, P_in is the radiant power of the source, and $E¯$ is the average energy (17.6 keV) of β particles emitted from the source. The calculated V_oc and I_sc are both related to the silicon PN junction converter parameters N_a and N_d. When energy deposition in the converter is constant, the value of P_m is ultimately determined by the converter doping concentrations. In order to verify this model, simulation results for a battery with an area of 1 mm × 1 mm are compared with both the experimental and the theoretical results in the previous literature, as shown in Table I. After adjusting for area, our results are consistent with the theoretical results in the literature.²² This serves to verify our model. Due to converter defects that are caused by heavy doping and described in the literature,²¹ there are some differences between the experimental results and our theoretical results.

The power output and the overall efficiency of the proposed battery can be expressed using the following equations:

Using the above formulas, the relationship between the output power of the proposed battery and the converter doping concentrations was calculated and is shown in Fig. 7. The parameters used in the simulation are shown in Table II. For the proposed battery, the maximum output power of 17.48 nW/mm² is achieved by combining the doping concentrations Na=1.91×10¹⁹cm^-3 and Nd=5.13×10¹⁷cm^-3. The overall conversion efficiency of the proposed battery is 3.3%. Table III shows the output power P_i of each unit in the proposed battery, presuming that it works at its maximum output power.

When each individual converter unit receives β particles from a different source, the quantity of layers penetrated by the particle is shown in Table IV. The total quantity of layers penetrated is lowest for units 3 and 4, so they can provide the highest power output by absorbing more energy from β particle. The collection probability of EHPs for the multilayer structure is shown in Figure 8, which is almost above 90%.

The same calculation method indicates that the maximum output power and overall conversion efficiency of the conventional battery are 2.7nW/mm² and 0.51%, respectively. The structural parameters and output performance of the conventional and layered batteries are compared in Table V.

A betavoltaic battery with multiple alternating, stacked layers of silicon converters and ⁶³Ni films effectively increased isotope source utilization. By optimizing the doping concentration in the p-n junction converter based on the energy distribution, we were able to propose an optimized betavoltaic battery with a stacked multilayer structure and a maximum output power of 17.48 nW/mm² with N_a=1.91×10¹⁹cm^-3 and N_d=5.13×10¹⁷cm^-3. The overall conversion efficiency of the proposed battery is 3.3%, which is almost 6.5 times that of the conventional battery.

This work is supported by a grant from the National Basic Research Program of China (973 Program) (No. 2015CB352100).