Optimization and experimental demonstration of mesh-patterned 4H-SiC betavoltaic cells for enhanced power density

Abstract

Betavoltaic (BV) cells based on wide-bandgap semiconductors are promising power sources for long-term operation in harsh environments, yet their energy-conversion efficiency remains below the theoretical limit because only a fraction of β-generated carriers are collected in the depletion region. Here, we propose a mesh-patterned 4H silicon carbide (4H-SiC) BV cell in which the top p-SiC layer is patterned into a two-dimensional mesh, and evaluate its performance using three-dimensional technology computer-aided design (3D TCAD) simulations and measurements of fabricated devices. Generation profiles for 5, 17, and 25 keV electron-beam irradiation, representing the Ni-63 β spectrum, are obtained from CASINO simulations and implemented in Silvaco ATLAS. By sweeping the mesh opening width and the i- and p-layer thicknesses, we identify an optimized geometry yielding a maximum output power density P_{out_max} ≈ 2.60 µW/cm² at 17 keV. Relative to a conventional planar p–i–n cell, the mesh-type cell shows simulated P_{out_max} enhancements of 32.5%, 2.49%, and 0.35% at 5, 17, and 25 keV, and measured enhancements of 65.1%, 4.57%, and 4.32%, respectively. These results demonstrate that a p-layer mesh pattern is an effective structural route to enhance the efficiency of Ni-63-based 4H-SiC betavoltaic cells.

Introduction

Betavoltaic (BV) cells are micro power sources that convert the kinetic energy of β-particles emitted from radioisotopes into electrical energy. Because they can operate for decades without an external light source or periodic recharging, they are considered promising power supplies for applications that demand long-term reliability, such as implantable medical devices, remote sensor networks, and space or extreme-environment instrumentation systems^1–7. In such applications, the power source must remain stable under high temperature and intense radiation, and BV cells can satisfy this requirement by combining semiconductor device technology with radioisotopes⁸.

The performance of a BV cell is strongly correlated with the physical properties of the semiconductor material. BV cells based on various semiconductors, including Si⁹, GaAs¹⁰, 4H-SiC¹¹, and GaN¹², have been reported, and each material exhibits distinct advantages and disadvantages determined by its bandgap, thermal conductivity, breakdown electric field, electron mobility, threshold displacement energy, and other parameters. The bandgaps, thermal and electrical properties, and radiation hardness of representative candidate materials for BV cells have been systematically compared in the literature^13–19. According to these studies, 4H-SiC is regarded as a particularly promising semiconductor for BV cells that must maintain long-term reliability under high-energy particle irradiation, because it simultaneously offers a wide bandgap of ~ 3.26 eV, high thermal conductivity, excellent radiation resistance, and partial defect-recovery capability.

Nevertheless, the conversion efficiency of practical BV cells is still often reported to be well below the theoretical limit^20–22. This is mainly because the electron–hole pairs generated by β-particles do not sufficiently overlap with the depletion region, or because the generated carriers recombine before they can be collected at the electrodes. Therefore, a key design challenge for BV cells is to develop device structures that simultaneously increase the carrier generation yield of β-particles and improve the efficiency with which the generated carriers are separated and collected.

For this reason, numerous studies have attempted to improve the output characteristics of BV cells by introducing various geometric modifications^23,24. However, for SiC-based BV cells, there is still a lack of systematic studies that correlate structural variations with changes in the incident particle energy, while consistently comparing TCAD simulation results with experimental measurements within a unified framework.

In a conventional planar p–i–n structure, the top p-SiC layer completely covers the underlying i-SiC layer, which confines the depletion region near the top surface and increases the likelihood that carriers generated near the surface will recombine before being collected, as schematically illustrated in Fig. 1a,b. In contrast, patterning the top p-SiC layer into a mesh and thereby forming openings on the i-SiC surface can extend the depletion region closer to the surface and improve the overlap between the carrier generation region and the collection region under β-particle irradiation. In contrast, patterning the top p-SiC layer into a mesh and thereby forming openings on the i-SiC surface can extend the depletion region closer to the surface and improve the overlap between the carrier generation region and the collection region under β-particle irradiation. When the side length of each opening, W_i-SiC, and the mesh-line width, W_p-SiC, are properly designed, carriers generated near the surface can be separated and transported along short paths, while the p-SiC mesh lines maintain an electrical connection to the anode electrode and prevent an excessive increase in series resistance. In other words, the mesh structure provides additional structural degrees of freedom that simultaneously enlarge the near-surface carrier-generation region and enhance charge-collection efficiency x–z.

Fig. 1.

(a) Three-dimensional schematic of the simulated conventional vertical 4H-SiC p–i–n BV cell (4 µm × 4 µm × 4 µm). (b) x–y cross-sectional view at z = 2 µm, showing the stacked p-SiC/i-SiC/n-SiC layers and the definitions of the p-layer and i-layer thicknesses, H_p-SiC and H_i-SiC. (c) Three-dimensional schematic of the proposed mesh-type 4H-SiC BV cell in which the top p-SiC layer is patterned into a two-dimensional mesh. (d) x–y cross-sectional view at z = 2 µm and (e) x–z cross-sectional view at y = 0.1 µm, indicating the p-SiC mesh-line width W_p-SiC, the opening width W_i-SiC, and the i- and p-layer thicknesses H_i-SiC and H_p-SiC.

In this work, we propose a 4H-SiC BV cell structure in which the top p-SiC layer is patterned into a two-dimensional mesh in the x–z plane, as shown in Fig. 1c–e, and quantitatively evaluate its output power characteristics through both simulations and experiments. First, using three-dimensional TCAD simulations, we calculate the J–V characteristics and output power density of the proposed mesh structure under 17 keV electron-beam (e-beam) irradiation. By sweeping the mesh opening width W_i-SiC, the mesh-line width W_p-SiC, and the i- and p-layer thicknesses H_i-SiC and H_p-SiC, we analyze the variations in short-circuit current density J_sc, open-circuit voltage V_oc, and maximum output power density P_{out_max}, and thereby determine the optimal design window for the mesh-type BV cell. Based on these results, we compare the simulated output power curves of the planar (conventional) and mesh-type (proposed) structures under 5, 17, and 25 keV e-beam. We then fabricate 4H-SiC BV devices with both structures and compare the measured output power densities under identical irradiation conditions, experimentally confirming that the proposed mesh structure improves P_{out_max} over the conventional planar structure at all beam energies. By combining the simulation and experimental results, we aim to provide guidelines for the effective use of mesh patterns in the structural design of SiC-based BV cells.

Device structure, simulation, and experimental methods

Simulated device structure and e-beam generation model

Figure 1a shows the three-dimensional geometry of the conventional p-i-n 4H-SiC BV cell used in the simulations. In all simulations, the outer dimensions of the device were fixed at 4 µm × 4 µm × 4 µm. The top and bottom electrodes were assigned as the anode and cathode, respectively, and the p-SiC, i-SiC, and n-SiC layers were stacked from top to bottom to form a conventional vertical p-i-n structure. Figure 1b presents an x–y cross-sectional view at z = 2 µm, where the i-layer and p-layer thicknesses are defined as H_i-SiC and H_p-SiC, respectively.

Figure 1c illustrates the three-dimensional geometry of the proposed structure, in which the top p-SiC layer is patterned into a mesh. The overall device size and electrode configuration are identical to those of the conventional cell, but the p-layer is patterned into a grid-like mesh so that multiple openings are distributed over the i-SiC surface. Figure 1d shows an x–y cross section at z = 2 µm, where the p-SiC, i-SiC, and n-SiC layers are stacked in the vertical direction and the p-layer and i-layer thicknesses are again defined as H_p-SiC and H_i-SiC. Figure 1e shows an x–z cross-sectional view at y = 0.1 µm, representing the in-plane layout of the mesh pattern and clearly defining the p-SiC mesh-line width W_p-SiC and the side length W_i-SiC of each i-SiC opening.

Three-dimensional TCAD simulations were performed using Silvaco ATLAS²⁵. Carrier transport was analyzed by solving the drift–diffusion equations, and recombination and tunneling were modeled by including Shockley–Read–Hall (SRH) recombination, Auger recombination, and trap-assisted tunneling (TAT). Material parameters such as mobility and saturation velocity were set based on reported values for 4H-SiC²⁶, and the simulation temperature was fixed at 300 K for all cases.

In both the planar and mesh structures, the doping concentrations of the p-i-n layers were kept identical. The top p-SiC layer was defined with a uniform p-type doping concentration of 1 × 10²⁰ cm⁻³, the middle i-SiC layer with a lightly doped n-type (drift-layer) concentration of 1 × 10¹⁵ cm⁻³, and the bottom n-SiC layer with a uniform n-type concentration of 1 × 10²⁰ cm⁻³. These doping profiles were held constant in all simulations, even when W_i-SiC, W_p-SiC, H_i-SiC, and H_p-SiC were varied.

Because it is practically impossible to completely eliminate defects (traps) generated during fabrication and irradiation in real BV cells, we assumed an identical bulk trap distribution for all device structures. Following DLTS-based defect studies on 4H-SiC epilayers and power devices, an acceptor-like trap level was placed at E_c − 0.63 eV below the conduction-band edge, and a donor-like trap level was placed at E_v + 1.6 eV above the valence-band edge²⁷. The densities of both traps were set to 1 × 10¹⁴ cm⁻³. For the acceptor-like trap, the electron and hole capture cross sections were set to σn = 2 × 10⁻¹⁴ cm² and σp = 3.5 × 10⁻¹⁴ cm², respectively, whereas for the donor-like trap both capture cross sections were set to σ_n = σ_p = 1 × 10⁻¹⁵ cm². These trap parameters represent typical deep-level characteristics reported in previous device studies^27,28, and an ideal trap-free structure was not considered separately.

Electron–hole pair generation under e-beam irradiation was implemented using the depth-dependent generation rate obtained from CASINO Monte Carlo simulations^29,30. For beam energies of 5, 17, and 25 keV, the depth-dependent energy-deposition profiles calculated by CASINO were used as references, and the peak positions and shapes of the absorption-rate curves used in ATLAS were adjusted to match these profiles, thereby defining the generation-rate distributions. In this context, the “CL intensity” reported by CASINO denotes the relative cathodoluminescence intensity as a function of depth, which is proportional to the local electron–hole pair generation rate under e-beam irradiation. In this study, we normalize these CL-intensity profiles and use them as a proxy for the spatial dependence of the generation rate; the ATLAS absorption-rate curves are fitted to follow the same depth dependence. Figure 2a–c compare the depth-dependent CASINO CL intensity with the corresponding ATLAS absorption-rate profiles for each energy, confirming that the two results are well matched in terms of the depth dependence. These generation-rate profiles for 5, 17, and 25 keV were then used in all subsequent J–V and power-density simulations.

Fig. 2.

Depth-dependent CL intensity profiles obtained from CASINO Monte Carlo simulations (green bars) and the corresponding absorption-rate curves implemented in ATLAS (red lines) for (a) 5 keV, (b) 17 keV, and (c) 25 keV e-beam irradiation. The ATLAS absorption-rate profiles are fitted to the CASINO results and used as the generation-rate input for the 4H-SiC BV-cell simulations. (d) Top-view SEM image of the fabricated mesh-type 4H-SiC BV cell. The green square indicates the active device area of approximately 816 µm × 816 µm, while the lateral size of the cell is 900 µm × 900 µm.

The electron-beam energy conditions were chosen to emulate the β spectrum of Ni-63, a representative low-energy β-emitting source. The mean and maximum β-particle energies of Ni-63 have been reported to be approximately 17 keV and 67 keV, respectively, and Ni-63 is widely used as a radioisotope for long-lifetime betavoltaic cells^31,32. Accordingly, 17 keV was selected as the reference condition representing the average operating environment of a practical Ni-63-based BV cell, while 5 keV and 25 keV were employed as auxiliary conditions to examine the behavior at lower and relatively higher energies.

As shown by the CASINO depth profiles in Fig. 2, the 25 keV case already corresponds to an electron–hole pair generation region extending nearly across the 4 µm device thickness considered in the simulations, so using higher electron-beam energies would mainly shift the generation deeper into the bulk where the planar and mesh structures behave similarly.

Structural parameter optimization and the definition of the basic metrics (J_sc, V_oc, and P_{out_max}) were carried out under 17 keV e-beam irradiation. Specifically, the J–V characteristics and power-density curves were calculated while varying W_i-SiC, W_p-SiC, H_i-SiC, and H_p-SiC at 17 keV, and the resulting changes in J_sc, V_oc, and P_{out_max} were summarized to determine the optimal design window of the mesh-type BV cell. For further analysis, the optimized structure was then used as a reference, and J–V and power-density curves were simulated for beam energies of 5, 17, and 25 keV; these curves are presented in the next section together with the experimental results.

Experimental device and measurement methods

The 4H-SiC BV cells were fabricated on n-type 4H-SiC epitaxial wafers. The wafers consisted of a thick n⁺ substrate and an n-type drift layer with a thickness of approximately 10.87 µm and a donor concentration of about 2.08 × 10¹⁶ cm⁻³. In the notation used for the TCAD analysis, this drift layer corresponds to an effective i-SiC thickness of H_i-SiC ≈ 10.47 µm, obtained by subtracting the p⁺ junction depth from the epitaxial thickness. The top p⁺ region was formed by Al ion implantation, with a target junction depth of ~ 0.4 µm (H_p-SiC ≈ 0.4 µm) and a box concentration of 1 × 10²⁰ cm⁻³. High-temperature activation annealing and sacrificial oxidation/etching were subsequently performed to mitigate surface defects induced by ion implantation. Ni-based metal with Al pads was deposited on the front side, and a Ti/Ni/Ag metal stack was deposited on the backside to form ohmic anode and cathode electrodes, respectively. The quality of the p⁺ Al-implanted anode region was verified using transmission-line-method (TLM) structures fabricated on the same wafer, from which a contact resistance of R_c ≈ 2.7 × 10⁻³ Ω⋅cm² Ω per contact was extracted, confirming good ohmic behavior. The lateral size of each device (width  ×  length) was approximately 900 µm  ×  900 µm.

The planar (conventional) BV cells and mesh-type (proposed) BV cells shared an identical overall process flow, except for the p⁺ ion-implantation mask pattern. In the planar cells, the entire active region was formed as a continuous p⁺ region. In the mesh-type cells, the pattern was designed such that square i-layer openings with a side length of 50 µm (W_i-SiC ≈ 50 µm) were surrounded by p-layer mesh lines with a width of 10 µm (W_p-SiC ≈ 10 µm) in a repeated array. The active device area defined inside the anode electrode is approximately 816 µm  ×  816 µm, corresponding to the region highlighted in the SEM image of Figure 2d.

Electrical characterization was carried out in a high-vacuum environment using a scanning electron microscope (SEM, Carl Zeiss SUPRA-55VP) equipped with nanoprobe contacts. The electron-beam energy was set to 5, 17, and 25 keV, identical to the simulation conditions, and I–V sweeps were measured while a stationary beam was focused on the device surface at each energy. For all measurements, the e-beam was aligned with the open i-SiC region where the radioisotope source would be located in a practical BV cell, so that each device was irradiated consistently with the intended Ni-63 position. The beam position was kept fixed during each J–V sweep. In this work, a focused stationary SEM beam was intentionally used to mimic a localized Ni-63 source placed above the open i-SiC region and to ensure that the planar and mesh-type cells experienced identical generation profiles; under this configuration, any additional recombination associated with the focused spot is expected to affect both structures in a similar way, so the measured difference in output power mainly reflects the structural effect of the p-SiC mesh. The resulting J–V and P–V characteristics of the planar and mesh-type BV cells are analyzed in the following section together with the simulation results, and are used to verify whether the proposed mesh structure provides enhanced output power density compared with the conventional structure in actual devices.

Results and discussion

Figure 3a compares the J–V characteristics of the mesh-type 4H-SiC BV cell with and without 17 keV e-beam irradiation. In this case, the geometric parameters of the mesh structure are set to W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, and H_p-SiC = 0.2 µm. Without e-beam irradiation, the current density remains nearly zero over the entire forward and reverse bias range, confirming the low dark-current characteristics of the wide-bandgap 4H-SiC p–i–n diode. In contrast, when a 17 keV e-beam is incident, a finite current appears in the reverse-bias region, and in the range from 0 V to V_oc, negative current flows at positive voltage so that power is delivered to the external circuit. Here, J_sc is defined as the current density at 0 V, and V_oc is defined as the voltage at which the current becomes zero. The current density J is obtained by dividing the total current from the ATLAS simulations by the active area of 4 µm  ×  4 µm (1.6  ×  10⁻⁷ cm²), and this definition is used throughout the remainder of this work. From the results shown in Figure 3a, J_sc and V_oc are approximately − 1.34 µA/cm² and 2.21 V, respectively.

Fig. 3.

(a) Simulated J–V characteristics of the proposed mesh-type 4H-SiC BV cell under17 keV e-beam irradiation (W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, H_p-SiC = 0.2 µm; I_beam = 10 pA, electron flux ≈ 5.0 × 10¹⁴ e⁻·cm⁻²·s⁻¹), together with the case without irradiation for comparison. (b) Corresponding P–V curve under 17 keV e-beam irradiation, highlighting the extracted short-circuit current density J_sc, open-circuit voltage V_oc, and maximum output power density P_{out_max}.

Figure 3b shows the corresponding P–V characteristics calculated under the same conditions. The output power density P_out is evaluated from the J–V curve using P_out = |J|  ×  V; the absolute value of J is used so that the generated power is expressed as a positive quantity because the reverse current is negative. The maximum value of the P–V curve is defined as P_{out_max}. For the mesh-type BV cell, P_{out_max} is about 2.55 µW/cm². In the following analysis, J_sc, V_oc, and P_{out_max} defined from Figure 3 are used as key figures of merit to discuss how the output characteristics change with the mesh opening width and mesh-line width (W_i-SiC and W_p-SiC) and with the i-layer and p-layer thicknesses (H_i-SiC and H_p-SiC).

The dependence of J_sc and V_oc on W_p-SiC is summarized in Figure 4a. When W_p-SiC is increased from 0.4 to 1.2 µm while keeping H_i-SiC = 1.7 µm, H_p-SiC = 0.2 µm, and a bulk trap density of 1 × 10¹⁴ cm⁻³, the magnitude of J_sc slightly decreases from about − 1.343 µA/cm² at W_p-SiC = 0.4 µm to − 1.336 µA/cm² at W_p-SiC = 1.2 µm. This behavior can be attributed to the reduction of the i-SiC opening area exposed to the top surface as the p-SiC mesh-line width increases, which gradually diminishes the additional carrier-generation region near the surface that is gained by introducing the mesh structure. In contrast, V_oc increases slightly from about 2.214 V to around 2.22 V as W_p-SiC increases from 0.4 µm to the range of 0.8–1.0 µm, and then remains almost constant with no further noticeable increase. This is because widening the p-SiC mesh lines up to a certain point enhances the three-dimensional electric-field distribution around each p–i junction, allowing the generated carriers to be separated and collected more efficiently, whereas once W_p-SiC exceeds a certain range, additional widening provides little extra benefit to the electric-field distribution.

Fig. 4.

(a) Variations of the short-circuit current density J_sc and open-circuit voltage V_oc of the mesh-type 4H-SiC BV cell as a function of the p-SiC mesh-line width W_p-SiC under 17 keV e-beam irradiation (H_i-SiC = 1.7 µm, H_p-SiC = 0.2 µm, I_beam = 10 pA, electron flux ≈ 5.0 × 10¹⁴ e⁻·cm⁻²·s⁻¹). (b) Corresponding maximum output power density P_{out_max} as a function of W_p-SiC.

The corresponding variations in the maximum output power density P_{out_max} are shown in Fig. 4b. When W_p-SiC is increased from 0.4 µm to 1.0 µm, P_{out_max} increases gradually from approximately 2.55 µW/cm² to about 2.577 µW/cm², and then slightly decreases to ~ 2.5767 µW/cm² at W_p-SiC = 1.2 µm. For comparison, Fig. 4b also plots the P_{out_max} of the planar BV cell (solid line). These results indicate that, in the range W_p-SiC ≈ 0.8–1.2 µm, the mesh-type BV cell provides a slightly higher P_{out_max} than the planar BV cell. In this region, compared with the planar structure, the openings between the p-layer mesh lines secure additional i-SiC depletion and generation volume extending toward the surface, while the three-dimensional electric field around the p-SiC mesh lines and the relatively short charge-collection paths together lead to modestly improved carrier generation, separation, and collection efficiencies. Conversely, if W_p-SiC is increased excessively so that the openings nearly vanish, the structure increasingly resembles the planar BV cell, the advantages of the mesh configuration are lost, and P_{out_max} converges to that of the planar cell. Therefore, from a design perspective for the mesh-type 4H-SiC BV cell under the present conditions (H_i-SiC = 1.7 µm and H_p-SiC = 0.2 µm), choosing W_p-SiC around 0.8–1.0 µm is a reasonable compromise that provides a slightly higher P_{out_max} than the planar (conventional) BV cell while maintaining sufficient design margin.

Figure 5a summarizes the variations in J_sc and V_oc as a function of the i-SiC layer thickness H_i-SiC. Under the conditions H_p-SiC = 0.2 µm, W_p-SiC = 0.4 µm, and a bulk trap density of 1 × 10¹⁴ cm⁻³, increasing H_i-SiC from 0.9 to 2.5 µm causes the magnitude of J_sc to rise rapidly from about 0.95 µA/cm² at H_i-SiC = 0.9 µm to approximately 1.36 µA/cm² for H_i-SiC ≈ 1.9–2.5 µm, after which it saturates with little further change. As the i-layer becomes thicker, the effective volume in which electron–hole pairs are generated by the 17 keV electron beam increases, leading to an increase in J_sc. However, beyond the penetration depth of ≈2.3 µm estimated from CASINO, there are almost no additional generated carriers, and the generation region shifts farther away from the electrodes, where recombination becomes dominant; as a result, J_sc no longer increases significantly. V_oc increases gradually from about 2.20 V to ~ 2.214 V as H_i-SiC is increased from 0.9 µm to 1.5–1.7 µm, and then shows a slight decrease at larger thicknesses. This behavior can be explained by the fact that, up to an appropriate i-layer thickness, the increase in J_sc is accompanied by a larger net number of carriers that are separated and collected under the internal electric field, leading to a higher V_oc, whereas an excessively thick i-layer weakens the average electric field and increases recombination losses in the regions with longer transport paths, thereby offsetting the V_oc enhancement.

Fig. 5.

(a) Variations of the short-circuit current density J_sc and open-circuit voltage V_oc of the mesh-type 4H-SiC BV cell as a function of the i-layer thickness H_i-SiC under 17 keV e-beam irradiation (W_p-SiC = 0.4 µm, H_p-SiC = 0.2 µm, I_beam = 10 pA, electron flux ≈ 5.0 × 10¹⁴ e⁻·cm⁻²·s⁻¹). (b) Corresponding maximum output power density P_{out_max} as a function of H_i-SiC.

The corresponding variations in the maximum output power density P_{out_max} are shown in Fig. 5b. When H_i-SiC is increased from 0.9 µm to about 1.7–1.9 µm, P_{out_max} increases markedly from ~ 1.85 µW/cm² to ~ 2.55 µW/cm² owing to the simultaneous increase in J_sc and V_oc, but at larger thicknesses it becomes nearly saturated or slightly decreases. If the i-layer is too thin, the total number of electron–hole pairs generated by β-particles is insufficient and the output is limited, whereas when the thickness exceeds ~ 2 µm, the reduction in V_oc caused by the weakened electric field and increased recombination outweighs the gain in carrier generation obtained from the additional thickness. Therefore, for the mesh-type BV cell under the present conditions (H_p-SiC = 0.2 µm and W_p-SiC = 0.4 µm), designing H_i-SiC in the range of approximately 1.7–1.9 µm is found to be most favorable for maximizing P_{out_max} by balancing the carrier-generation yield and the charge-collection efficiency.

Figure 6a shows the variations in J_sc and V_oc as a function of the p-SiC thickness H_p-SiC. When H_p-SiC is varied from 0.2 to 0.8 µm under the conditions W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, and a bulk trap density of 1 × 10¹⁴ cm⁻³, J_sc is approximately − 1.342 × 10⁻⁶ A/cm² (≈ − 1.34 µA/cm²) at H_p-SiC = 0.2 µm, reaches its largest magnitude at H_p-SiC = 0.4 µm, and then decreases as H_p-SiC is further increased to 0.6 and 0.8 µm. This behavior arises because, when H_p-SiC is too small, the p-SiC mesh does not have sufficient thickness, and thus the paths and electric field required for carriers generated in the upper i-SiC opening region (shown in Fig. 1d) to drift laterally toward the p-mesh are not fully developed. As H_p-SiC is increased to 0.4 µm, the p region beneath the mesh attains an appropriate thickness, so that carriers generated in the upper opening (i-layer) are more effectively separated and transported toward the p-SiC sidewalls, maximizing |J_sc|. However, when H_p-SiC is further increased to 0.6 and 0.8 µm, the effective thickness and area of the upper i-SiC region, where most of the generation by the 17 keV electron beam occurs, are reduced, which decreases the total number of generated electron–hole pairs. This reduction in generation becomes more significant than the improvement in separation efficiency, leading to a noticeable decrease in |J_sc|. Meanwhile, V_oc is largest at H_p-SiC = 0.2 µm, with a value of about 2.214 V, and shows a decrease in the range Hp-SiC = 0.4–0.8 µm. As the p-layer becomes thicker, the potential distribution inside the p-SiC and around the mesh is spread out, increasing the equivalent series resistance encountered by carriers separated in the upper i-SiC region on their way to the anode, which in turn causes a slight reduction in the V_oc obtained under open-circuit conditions.

Fig. 6.

(a) Variations of the short-circuit current density J_sc and open-circuit voltage V_oc as a function of the p-SiC thickness H_p-SiC (W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, I_beam = 10 pA, electron flux ≈ 5.0 × 10¹⁴ e⁻·cm⁻²·s⁻¹). (b) Corresponding maximum output power density P_{out_max} versus H_p-SiC, showing an optimum around H_p-SiC ≈ 0.4 µm.

The corresponding variations in the maximum output power density P_{out_max} are summarized in Fig. 6b. At H_p-SiC = 0.2 µm, P_{out_max} is about 2.55 µW/cm², whereas at H_p-SiC = 0.4 µm it increases clearly to approximately 2.60 µW/cm² owing to the combined effects of enhanced carrier generation (increased J_sc) and improved separation/collection efficiency. When H_p-SiC is further increased to 0.6 µm, P_{out_max} decreases slightly to ~2.59 µW/cm², and at H_p-SiC = 0.8 µm it drops to ~ 2.55 µW/cm², which is already comparable to the value at 0.2 µm. In other words, if the p-layer is too thin, lateral separation and collection of carriers generated in the upper openings are insufficient, resulting in low J_sc and P_{out_max}; if the p-layer is excessively thick, the generation area in the upper i-layer is reduced, decreasing the total carrier generation and thereby degrading the output. The interplay of these two effects leads to an optimum around H_p-SiC ≈ 0.4 µm, at which P_{out_max} is maximized.

By combining the parameter-sweep results in Figures 4, 5, 6, we find that the combination W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, and H_p-SiC = 0.4 µm yields the highest P_{out_max} of approximately 2.60 µW/cm². Therefore, in this work, the condition indicated in Fig. 6b is selected as the optimized structure of the mesh-type 4H-SiC BV cell, and all subsequent comparisons between simulation and experiment are discussed with respect to this parameter set.

Figure 7 compares the power density–voltage (P–V) curves of the optimized mesh-type 4H-SiC BV cell and the conventional planar p-i-n structure obtained from three-dimensional TCAD simulations as a function of the electron-beam energy. In these simulations, the optimized structure derived in the previous subsection (W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, H_p-SiC = 0.4 µm, with W_i-SiC fixed to the value optimized in Figs. 4, 5, 6) is used commonly for all cases unless otherwise noted. Here, ΔP_{out_max} denotes the difference in the maximum output power density between the proposed mesh-type structure and the conventional planar structure.

Fig. 7.

Simulated power density–voltage (P–V) characteristics of the conventional planar BV cell and the proposed mesh-type BV cell under different e-beam energies. The optimized mesh structure (W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, H_p-SiC = 0.4 µm) is used for panels (a–c), and the same lateral mesh geometry is retained in panel (d). The blue markers and annotations indicate the difference in the maximum output power density P_{out_max} (ΔP_{out_max}) and the corresponding improvement ratio of the proposed BV cell over the conventional cell: (a) 5 keV, I_beam = 10 pA, electron flux ≈ 3.8 × 10¹⁶ e⁻·cm⁻²·s⁻¹; (b) 17 keV, I_beam = 10 pA, electron flux ≈ 5.0 × 10¹⁴ e⁻·cm⁻²·s⁻¹; and (c) 25 keV e-beam irradiation, I_beam = 10 pA, electron flux ≈ 1.3 × 10¹⁴ e⁻·cm⁻²·s⁻¹; (d) 17 keV with modified drift-layer parameters (H_i-SiC = 10.5 µm, H_p-SiC = 0.4 µm, i-layer doping 2.0 × 10¹⁶ cm⁻³), I_beam = 10 pA, electron flux ≈ 5.0 × 10¹⁴ e⁻·cm⁻²·s⁻¹, chosen to approximate the fabricated BV-cell structure.

Figure 7a shows the simulated P–V characteristics under 5 keV e-beam irradiation. Compared with the conventional BV cell, the mesh-type BV cell exhibits an increase in P_{out_max} of 1.82 × 10⁻² µW/cm² (approximately 32.5%), confirming that the proposed structure greatly enhances the output power density under low-energy e-beam conditions. This improvement arises because the mesh structure widens the depletion region formed above the i-SiC layer and shortens the path that the generated charge must travel to the anode, thereby allowing electron–hole pairs generated near the surface to be collected more efficiently.

Figure 7b and c show the simulated P–V characteristics under 17 keV and 25 keV e-beam irradiation, respectively. At 17 keV, the P_{out_max} of the proposed BV cell is larger than that of the conventional structure by 6.92 × 10⁻² µW/cm² (about 2.49%), and at 25 keV it is larger by 1.74 × 10⁻² µW/cm² (about 0.35%). Because 17 keV corresponds to the mean β-particle energy of a Ni-63 source, the mesh geometry was optimized at this energy to represent the average operating condition of a practical Ni-63-based BV cell. When the same optimized structure is evaluated at 5 keV, which represents the low-energy side of the Ni-63 β spectrum, the relative improvement in P_{out_max} becomes much larger (~ 32.5%), indicating that the proposed mesh pattern effectively recovers the contribution of low-energy carriers and is therefore expected to enhance the overall conversion efficiency under the full Ni-63 spectrum, even though the percentage gain at 17 keV itself is only a few percent. As the e-beam energy increases, the electron–hole pair generation region moves deeper into the bulk, making EHP collection more similar in the two structures, so the improvement in P_{out_max} becomes smaller than at 5 keV. Nevertheless, the mesh-type BV cell maintains a higher P_{out_max} than the planar p-i-n structure at all energies, demonstrating the superior power-conversion characteristics of the proposed design from a simulation standpoint.

To further examine the impact of using device parameters close to those of the fabricated BV cells, Fig. 7d presents an additional set of simulated P–V curves at 17 keV in which the drift-layer thickness and doping profile are adjusted to closely approximate the experimental wafer. Specifically, H_i-SiC is set to 10.5 µm to represent the effective drift thickness of about 10.47 µm, the middle i-SiC drift layer is defined with an n-type doping concentration of 2.0 × 10¹⁶ cm⁻³ while the top p-SiC and bottom n-SiC layers are kept at 1 × 10²⁰ cm⁻³ as in the previous simulations, and H_p-SiC is fixed at approximately 0.4 µm. The lateral mesh geometry is kept identical to that in panels (a)–(c). Under these conditions, the maximum output power density of the mesh-type BV cell is higher than that of the planar BV cell by about 1.47 × 10⁻² µW/cm² (approximately 1.44%), indicating that the structural benefit of the p-SiC mesh persists even when the drift-layer thickness and doping are set to values that closely reflect those of the fabricated BV cells and providing a direct link between the TCAD predictions and the experimental J–V and P–V characteristics summarized in Figure 8.

Fig. 8.

Measured current density–voltage (J–V) and power density–voltage (P–V) characteristics of the conventional planar BV cell and the proposed mesh-type BV cell under e-beam irradiation. Open symbols denote the conventional BV cell and solid symbols denote the proposed BV cell. The blue markers and annotations indicate the enhancement o f the maximum output power density P_{out_max} (ΔP_{out_max}) and the corresponding improvement ratio of the proposed cell compared with the conventional structure: (a) 5 keV (I_beam = 1 nA, electron flux ≈ 9.4 × 10¹¹ e⁻·cm⁻²·s⁻¹), (b) 17 keV (I_beam = 9.2 nA, electron flux ≈ 8.6 × 10¹² e⁻·cm⁻²·s⁻¹), and (c) 25 keV (I_beam = 9.2 nA, electron flux ≈ 8.6 × 10¹² e⁻·cm⁻²·s⁻¹) e-beam irradiation. All measurements were performed on devices with W_i-SiC ≈ 50 µm, W_p-SiC ≈ 10 µm, H_i-SiC ≈ 10.47 µm, H_p-SiC ≈ 0.4 µm.

Figure 8 summarizes the measured J–V and P–V characteristics of the conventional planar BV cell and the mesh-type BV cell under 5, 17, and 25 keV e-beam irradiation. Figure 8a–c present the measurement results for 5, 17, and 25 keV, respectively. Under the 5 keV condition, the measured current density remains relatively small over the entire voltage range because the penetration depth of the 5 keV e-beam is extremely shallow and most of its energy is dissipated in the top p-SiC and surface-defect regions, as shown in Fig. 8a. Nevertheless, a finite output power density can be extracted from the P–V curves: the maximum output power density of the mesh-type BV cell exceeds that of the planar BV cell by ΔP_{out_max} ≈ 3.56 × 10⁻³ mW/cm², corresponding to an enhancement of approximately 65.1% in P_{out_max}. This result indicates that even when the generation region is confined very close to the surface, the mesh structure enables a larger fraction of the generated electron–hole pairs to be collected.

At 17 keV and 25 keV, clear BV operation is observed for both structures, and the performance enhancement of the proposed BV cell becomes more evident in absolute power density, as shown in Fig. 8b and c. At 17 keV, the maximum output power density of the mesh-type BV cell is higher than that of the conventional p–i–n structure by ΔP_{out_max} ≈ 0.16 mW/cm², which corresponds to an improvement of about 4.57% in P_{out_max}. At 25 keV, ΔPout_max is approximately 0.19 mW/cm² and the enhancement ratio reaches roughly 4.32%. Although these percentage gains are more modest than in the 5 keV case, they follow the simulation trend that the mesh-type BV cell provides a higher output power density than the planar cell over the entire e-beam energy range.

The experimentally observed enhancement ratios are larger than the simulated values, particularly at 5 keV. This discrepancy can be attributed to the thicker and more heavily doped drift layer in the fabricated devices, which enhances the relative impact of the mesh-induced depletion expansion near the surface while simultaneously increasing recombination losses in the planar structure. As a result, the mesh pattern becomes more effective in suppressing recombination and improving charge collection in the experimental devices, especially under shallow-generation conditions.

In summary, both the TCAD analysis in Fig. 7 and the experimental results in Fig. 8 consistently show that, over the entire e-beam energy range of 5, 17, and 25 keV, the mesh-type 4H-SiC BV cell delivers a higher P_{out_max} than the conventional planar p–i–n structure. This agreement between simulation and experiment, despite the differences in layer thicknesses and doping profiles, confirms that introducing a p-layer mesh pattern is an effective structural approach for improving the energy conversion efficiency of 4H-SiC BV cells operating in a Ni-63-based β-particle environment.

Conclusion

In this work, we proposed and experimentally demonstrated a mesh-type 4H-SiC betavoltaic cell in which the top p-SiC layer is patterned into a two-dimensional mesh, and we compared its performance with that of a conventional planar p–i–n structure using three-dimensional TCAD simulations and measurements of fabricated devices. CASINO-based electron-beam generation rates were linked to ATLAS to emulate irradiation conditions at 5, 17, and 25 keV, and both structures were analyzed under identical doping and trap conditions.

Structural optimization performed at 17 keV by sweeping W_p-SiC, H_i-SiC, and H_p-SiC revealed that the maximum output power density, P_{out_max} ≈ 2.60 µW/cm², was obtained for W_p-SiC = 0.4 µm, H_i-SiC = 1.7 µm, and H_p-SiC = 0.4 µm. This behavior can be attributed to the fact that the mesh structure extends the i-SiC depletion region toward the surface and shortens the charge-collection paths, while the thickness and width of the p-SiC mesh lines are properly maintained so as to suppress increases in series resistance and internal recombination.

When the P–V characteristics were compared as a function of beam energy using this optimized structure, the simulations showed that P_{out_max} of the mesh-type BV cell was higher than that of the conventional BV cell by approximately 32.5%, 2.49%, and 0.35% at 5, 17, and 25 keV, respectively. Although the enhancement decreases at higher e-beam energies because the EHP generation region moves deeper into the bulk and the collection characteristics of the two structures become more similar, P_{out_max} of the mesh-type BV cell remains higher than that of the planar cell over the investigated e-beam energy range. Measurements of fabricated 4H-SiC BV cells designed with the same geometry as in the simulations further confirmed that the Pout_max enhancement ratios reach approximately 65.1%, 4.57%, and 4.32% at 5, 17, and 25 keV, respectively, demonstrating that the structural advantages predicted by the simulations are reproduced in real devices.

In summary, designing the top p-layer in a mesh pattern provides an effective structural approach for enhancing the energy conversion efficiency of 4H-SiC BV cells operating in a Ni-63-based β-particle environment. The proposed mesh-type BV cell simultaneously achieves depletion-region expansion and shortened collection paths, thereby consistently delivering higher P_{out_max} than the conventional planar BV cell over the investigated e-beam energy range of 5–25 keV. Future work will also address quantitative comparisons between the calculated electron–hole pair generation rates and the measured output currents in order to clarify the role of recombination in Ni-63-based 4H-SiC BV cells. Furthermore, future work will focus on further optimizing the period and shape of the mesh pattern and on long-term reliability assessments using actual radioisotope sources, which are expected to refine the design guidelines for SiC-based betavoltaic cells.

Author contributions

K. M. K. prepared figures and wrote the main manuscript text. Y. J. Y., and J. H. S. conceptualized the study, contributed to the investigation, supervision, review, and editing of the manuscript. J. H. M. corrected and improved the details of the manuscript. K. M. K., and K. H. K. conducted simulation study and data analysis. All authors reviewed the manuscript. Corresponding authors are Y. J. Y., and J. H. S.

Funding

J. H. M. (Jeong Hyun Moon), and J. H. S. (Jae Hwa Seo): This research was supported by Korea Electrotechnology Research Institute (KERI) Primary research program through the National Research Council of Science & Technology (NST) funded by the Ministry of Science and ICT (MSIT) (No. 25A01006, 25A03051, 25A02037, 26A01026). K. M. K. (Kyeong Min Kim), K. H. K. (Kyung Hee Kim), and Y. J. Y. (Young Jun Yoon): This work was also supported by a Research Grant of Gyeongkuk National University.

Data availability

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.