Design and Analysis of Gallium Nitride-Based p-i-n Diode Structure for Betavoltaic Cell with Enhanced Output Power Density

Abstract

In this work, Gallium Nitride (GaN)-based p-i-n diodes were designed using a computer aided design (TCAD) simulator for realizing a betavoltaic (BV) cell with a high output power density (P_out). The short-circuit current density (J_SC) and open-circuit voltage (V_OC) of the 17 keV electron-beam (e-beam)-irradiated diode were evaluated with the variations of design parameters, such as the height and doping concentration of the intrinsic GaN region (H_i-GaN and D_i-GaN), which influenced the depletion width in the i-GaN region. A high H_i-GaN and a low D_i-GaN improved the P_out because of the enhancement of absorption and conversion efficiency. The device with the H_i-GaN of 700 nm and D_i-GaN of 1 × 10¹⁶ cm⁻³ exhibited the highest P_out. In addition, the effects of native defects in the GaN material on the performances were investigated. While the reverse current characteristics were mainly unaffected by donor-like trap states like N vacancies, the Ga vacancies-induced acceptor-like traps significantly decreased the J_SC and V_OC due to an increase in recombination rate. As a result, the device with a high acceptor-like trap density dramatically degenerated the P_out. Therefore, growth of the high quality i-GaN with low acceptor-like traps is important for an enhanced P_out in BV cell.

1. Introduction

Betavoltaic (BV) cells using a radioisotope have been developed for micro-battery applications, such as a power source of bio-medical implants and extreme environmental sensors [1,2,3], because of their long lifetime and micro-size. ⁶³Ni radioisotope–based BV cells can be used for a long period due to a half-life of about 100 years. The BV cells based on various semiconductors such as Si [4,5], GaAs [6], SiC [7,8,9], GaN [10,11,12,13,14], and GaP [15] have been studied for high power conversion efficiency. Among the semiconductors, it is known that GaN-based BV cells can theoretically obtain superior conversion efficiency because of a wider energy bandgap. Moreover, GaN-based BV cells are more suitable for BV applications with long-term stability because GaN material has exhibited a strong radiation hardness [16,17], which can reduce the effects of radiation damage on device performances [18]. The p-i-n junction [10,11,12] and Schottky barrier diode [13,14] have been used to realize GaN-based BV cells. The p-i-n junction diode can obtain a wider depletion width, which improves the collection efficiency. However, the efficiency of the fabricated device exhibited a lower power conversion efficiency than the theoretical efficiency. Recent studies on BV cells aimed at enhancing the conversion efficiency. Many researchers have made progress in the optimization design of diode structures using a theoretical calculation model [19,20]. However, the design considerations of the GaN-based BV cells still have to be addressed due to the inherent properties of GaN material, including the various native trap states that occur during growth. The short-circuit current density (J_SC) and open-circuit voltage (V_OC) associated with the output power density of the diode are significantly affected by the native defects that influence recombination.

In this work, we optimized the GaN-based p-i-n diode to achieve a BV cell with high output power density using the following design parameters: heights of p-type GaN and intrinsic GaN (H_p-GaN and H_i-GaN) and a doping concentration of i-GaN (D_i-GaN). The physical phenomenon and performance were analyzed using a three-dimensional (3-D) technology computer-aided design (TCAD) simulator with physical models including e-beam irradiation and trap-assisted recombination models. The effects of native defects on J_SC, V_OC, and P_out of the e-beam-irradiated devices were also investigated.

2. Device Structure and Simulation Method

Figure 1 shows the 3-D schematic of the GaN-based p-i-n diode for BV cells. The p-i-n diode structure is the conventional diode structure, which consisted of an intrinsic GaN (i-GaN) region between p-type GaN (p-GaN) and n-type GaN (n-GaN) regions to obtain a wide width in the depletion region. The D_i-GaN determines the depletion width, which affects the conversion efficiency for BV cells. Here, i-GaN denotes undoped GaN, which is almost an n-type due to the residual donor [21]. The background impurity concentration in undoped GaN grown by metal-organic chemical-vapor deposition (MOCVD) is typically in the range of 10¹⁵ to 10¹⁷ cm⁻³, depending on the condition of the reactor [22]. Furthermore, it is difficult to grow undoped GaN with simultaneous low doping concentration and high quality [23]. Thus, the D_i-GaN was varied in the range of 5 × 10¹⁵ cm⁻³ to 5 × 10¹⁶ cm⁻³ for optimizing the D_i-GaN. In order to reduce the resistance of the n-GaN and p-GaN layers, doping concentrations of the n-GaN and p-GaN (D_n-GaN and D_p-GaN) were designed as 5 × 10¹⁸ cm⁻³ and 5 × 10¹⁷ cm⁻³, respectively. We also changed the H_p-GaN and H_i-GaN to achieve high performance. The variation ranges of H_p-GaN and H_i-GaN were 60–200 nm and 500–900 nm, respectively. The ranges of H_p-GaN and H_i-GaN values were determined by considering the penetration depth of 17 keV electrons at about 1 μm [24]. The energy of the e-beam is the average energy of ⁶³Ni [25,26]. The contact resistance for p-GaN and n-GaN in the devices was 1 × 10⁻⁴ Ω·cm² [27,28].

The effects of e-beam irradiation on current characteristics were analyzed using a TCAD simulator [29]. Physical models were applied in the simulation, including Schockley–Read–Hall (SRH) and trap-assisted tunneling (TAT), and a low-field mobility model. The SRH and TAT models were used to reflect the carrier recombination phenomenon [30], which significantly affects the J_SC and V_OC of the diode. For the effects of native defects in the GaN material [31,32], acceptor and donor-like trap states were added to the simulation. The acceptor-like trap state is formed by Ga vacancies. The donor-like trap states are mainly associated with the N vacancies and nitrogen antisite point defect. When we optimized the structure, we analyzed the performances of the diodes applied by native traps. In addition, the individual impact of trap states on P_out were studied to investigate the dominant traps that degrade the performances.

3. Results and Discussion

Figure 2a shows the effects of e-beam irradiation on the reverse current characteristics of the GaN p-i-n diode. When the diode was irradiated by a 17 keV e-beam, the reverse current density significantly increased. This was because electron-hole pairs (EHPs) were generated by the injected high-energy electrons. The electrons and holes in the depletion region were respectively moved by internal electric field through n-GaN and p-GaN regions and the carriers converted to the electric current. The J_SC and a V_OC of the irradiated diode were 14.92 μA/cm² and 2.391 V, respectively. The J_SC and V_OC were defined as the current density at a voltage of 0 V and the voltage when the current density was 0 A/cm², respectively.

As shown in Figure 2b, the 17 keV electrons penetrated up to a depth of about 1 μm and the peak absorption rate was exhibited at a depth of about 300 nm. Because many EHPs generated in the i-GaN region contributed to the conversion efficiency, the H_i-GaN and D_i-GaN are important design parameters. A high conversion efficiency increases J_SC and V_OC, which influences the output power density (P_out). The diode exhibited the maximum P_out (P_{out_max}) at a voltage of 2.18 V, as shown in Figure 2c.

Figure 3a shows the variations of the reverse current characteristics of the irradiation diodes as a function of H_i-GaN. As the H_i-GaN increased, the reverse current density became higher due to extension of the absorption region. Many EHPs were generated in the extended absorption region, which converted the electric current. However, the current density of the diodes with a H_i-GaN above 900 nm was lower than that of the device with a H_i-GaN of 700 nm at a forward voltage above 0 V. This result indicated that excess carriers generated by the e-beam were reduced by the recombination mechanism as they moved through the n-GaN or p-GaN regions. This result affected the V_OC and J_SC of the diodes. As shown in Figure 3b, the device with a H_i-GaN of 700 nm had the highest V_OC. In terms of P_{out_max}, the device with a H_i-GaN of 700 nm exhibited the highest P_{out_max} because the device was less affected by the recombination phenomenon, as shown in Figure 3c.

The variations of J_SC, V_OC, and P_{out_max} depending on the H_i-GaN and H_p-GaN are shown in Figure 4. The J_SC of the devices increased with a rise in the H_i-GaN regardless of the H_p-GaN because a high H_i-GaN extended the absorption region. When the H_i-GaN above 800 nm increased, the J_SC slightly decreased due to the recombination phenomenon. As the H_p-GaN became shorter, the variation of J_SC according to the H_i-GaN increased. This result indicated that the absorption rate vs. depth was more affected in the irradiated device with a short H_p-GaN. The device with a H_p-GaN of 60 nm and H_i-GaN of 800 nm was the highest J_SC because the J_SC was enhanced by an additional absorption near the p-GaN region. In case of the V_OC, the device with a H_p-GaN of 100 nm and a H_i-GaN of 700 nm exhibited the highest V_OC, as shown in Figure 4b. Because a short H_p-GaN degenerated the carrier transport, the V_OC of the devices with a H_p-GaN of 60 nm was a smaller than that of the devices with a H_p-GaN of 100 nm. The device also obtained the highest P_{out_max}. The P_{out_max} value was affected by a change of the V_OC.

Figure 5 shows energy band diagrams of the diodes with different values of D_i-GaN. As the D_i-GaN decreased, the depletion region was extended in the i-GaN region. Because the depletion region was influenced by the D_i-GaN, we examined the variations of J_SC, V_OC and P_{out_max} depending on the D_i-GaN and H_i-GaN. As shown in Figure 6, the diode with a low D_i-GaN exhibited an improved J_SC because of a wider depletion region in the i-GaN region. The excess carriers could be moved by the built-in electric field. Although the device with a D_i-GaN of 1 × 10¹⁶ cm⁻³ exhibited a higher V_OC, the diode with a D_i-GaN of 5 × 10¹⁵ cm⁻³ obtained a higher P_{out_max}. This result indicated that reducing the D_i-GaN is important to improving transport efficiency. However, in terms of GaN epitaxial technology based on MOCVD method, it was difficult to reduce the D_i-GaN below 1 × 10¹⁶ cm⁻³ because residual impurities remained during the growth process. Therefore, we determined that the optimum point for the D_i-GaN was 1 × 10¹⁶ cm⁻³. As a result, the diode structure with a H_p-GaN of 100 nm, H_i-GaN of 700 nm, and D_i-GaN of 1 × 10¹⁶ cm⁻³ was optimized, and the effects of native trap states on performances of the optimized diode were investigated with variations of trap level and density.

The energy spectrum of the ⁶³Ni source exhibited a wide range to a 66 keV peak energy [19]. We additionally confirmed the performances of the optimized diode depending on the injected electron energy. The current characteristics of the diodes irradiated by different e-beam energies is shown in Figure 7a. As the energy increased up to 30 keV, the current became higher. This was because many EHPs were generated by a wide distribution of absorption rate as shown in Figure 7b. However, when the electrons with an energy above 40 keV were injected, the current of the irradiated device was lower than that of the device irradiated by the 17 keV e-beam. These results revealed that the variations of the current of the irradiated diodes depending on the energy of the e-beam were large. The probability of beta particles generated from the ⁶³Ni source showed a high distribution below 20 keV [19]. Also, the depletion width formed in the i-GaN region was small at about 600 nm (in case of D_i-GaN = 1 × 10¹⁶ cm⁻³), and the diffusion length of GaN can be shortened by native defects. Therefore, in order to achieve a high efficiency BV cell using the ⁶³Ni source, it is necessary to analyze the performances of GaN-based diodes considering the spectrum of the ⁶³Ni source.

Figure 8 shows reverse current density and P_out of the irradiated diodes with and without the native trap states including donor and acceptor-like traps. The reverse current density was significantly degenerated by the trap states. This result means that the trap-assisted recombination was caused by the native defects in the GaN material. As a result, the P_out of the device with the trap states was lower than that of the device without the trap states. We confirmed the effects of individual traps on current characteristics of the irradiated devices. As a shown in Figure 9, the impact of acceptor-like trap states was stronger than that of donor-like trap states. This result proved that the acceptor-like trap states represented the dominant factor for the recombination.

In addition, we investigated the effects of trap density on J_SC, V_OC, and P_{out_max}. As the trap density increased, the performances were totally degenerated by the acceptor-like trap state, as shown in Figure 10. The donor-like trap states reduced the J_SC less than the acceptor-like trap state. While the donor-like trap states (E_C-0.6 eV) slightly decreased the V_OC, the shallow donor-like trap states (E_C-0.23 eV) increased V_OC. As a result, the P_{out_max} was unaffected by the shallow donor-like trap states (E_C-0.23 eV). It is important to reduce the acceptor-like traps to improve the conversion efficiency of the betavoltaic cell.

4. Conclusions

In this work, we designed a p-i-n diode with a variation of geometric parameters, namely, H_i-GaN, D_i-GaN, and H_p-GaN, and analyzed P_out using 17 keV e-beam irradiation. The H_i-GaN and H_p-GaN affected the absorption rate vs. depth. A low D_i-GaN produced an increase in depletion width. The optimized structure with a H_i-GaN of 700 nm, D_i-GaN of 1 × 10¹⁶ cm⁻³, and H_p-GaN of 100 nm obtained an improved P_out. In addition, the effects of native trap states on reverse current characteristics were investigated with various trap levels and densities. When the acceptor-like trap density increased from 10¹⁴ cm⁻³ to 10¹⁶ cm⁻³, the trap significantly decreased the P_{out_max} by about 15%. GaN with low acceptor-like traps was needed to enhance the P_out of a BV cell. These results provide design considerations for achieving a high efficiency BV cell.