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

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 (Pout). The short-circuit current density (JSC) and open-circuit voltage (VOC) 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 (Hi-GaN and Di-GaN), which influenced the depletion width in the i-GaN region. A high Hi-GaN and a low Di-GaN improved the Pout because of the enhancement of absorption and conversion efficiency. The device with the Hi-GaN of 700 nm and Di-GaN of 1 × 1016 cm−3 exhibited the highest Pout. 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 JSC and VOC due to an increase in recombination rate. As a result, the device with a high acceptor-like trap density dramatically degenerated the Pout. Therefore, growth of the high quality i-GaN with low acceptor-like traps is important for an enhanced Pout in BV cell.


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. 63 Ni 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. 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 10 15 to 10 17 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 × 10 15 cm −3 to 5 × 10 16 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 × 10 18 cm −3 and 5 × 10 17 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 63 Ni [25,26]. The contact resistance for p-GaN and n-GaN in the devices was 1 × 10 −4 Ω·cm 2 [27,28].

Device Structure and Simulation Method
Micromachines 2020, 11, x FOR PEER REVIEW 2 of 13 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 (JSC) and open-circuit voltage (VOC) 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 (Hp-GaN and Hi-GaN) and a doping concentration of i-GaN (Di-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 JSC, VOC, and Pout of the e-beam-irradiated devices were also investigated. 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 Di-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 10 15 to 10 17 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 Di-GaN was varied in the range of 5 × 10 15 cm −3 to 5 × 10 16 cm −3 for optimizing the Di-GaN. In order to reduce the resistance of the n-GaN and p-GaN layers, doping concentrations of the n-GaN and p-GaN (Dn-GaN and Dp-GaN) were designed as 5 × 10 18 cm −3 and 5 × 10 17 cm −3 , respectively. We also changed the Hp-GaN and Hi-GaN to achieve high performance. The variation ranges of Hp-GaN and Hi-GaN were 60-200 nm and 500-900nm, respectively. The ranges of Hp-GaN and Hi-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 63 Ni [25,26]. The contact resistance for p-GaN and n-GaN in the devices was 1 × 10 −4 Ω·cm 2 [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. 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/cm 2 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/cm 2 , respectively.

Results and Discussion
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.
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 Hi-GaN and Di-GaN are important design parameters. A high conversion efficiency increases JSC and VOC, which influences the output power density (Pout). The diode exhibited the maximum Pout (Pout_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 Hi-GaN. As the Hi-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 Hi-GaN above 900 nm was lower than that of the device with a Hi-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 VOC and JSC of the diodes. As shown in Figure 3b, the device with a Hi-GaN of 700 nm had the  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 .
Micromachines 2020, 11, x FOR PEER REVIEW 6 of 13 to the Hi-GaN increased. This result indicated that the absorption rate vs. depth was more affected in the irradiated device with a short Hp-GaN. The device with a Hp-GaN of 60 nm and Hi-GaN of 800 nm was the highest JSC because the JSC was enhanced by an additional absorption near the p-GaN region. In case of the VOC, the device with a Hp-GaN of 100 nm and a Hi-GaN of 700 nm exhibited the highest VOC, as shown in Figure 4b. Because a short Hp-GaN degenerated the carrier transport, the VOC of the devices with a Hp-GaN of 60 nm was a smaller than that of the devices with a Hp-GaN of 100 nm. The device also obtained the highest Pout_max. The Pout_max value was affected by a change of the VOC.   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 × 10 16 cm −3 exhibited a higher V OC , the diode with a D i-GaN of 5 × 10 15 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 × 10 16 cm −3 because residual impurities remained during the growth process. Therefore, we determined that the optimum point for the D i-GaN was 1 × 10 16 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 × 10 16 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.    Figure 6, the diode with a low Di-GaN exhibited an improved JSC 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 Di-GaN of 1 × 10 16 cm −3 exhibited a higher VOC, the diode with a Di-GaN of 5 × 10 15 cm −3 obtained a higher Pout_max. This result indicated that reducing the Di-GaN is important to improving transport efficiency. However, in terms of GaN epitaxial technology based on MOCVD method, it was difficult to reduce the Di-GaN below 1 × 10 16 cm −3 because residual impurities remained during the growth process. Therefore, we determined that the optimum point for the Di-GaN was 1 × 10 16 cm −3 . As a result, the diode structure with a Hp-GaN of 100 nm, Hi-GaN of 700 nm, and Di-GaN of 1 × 10 16 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 63 Ni 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 63 Ni 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 × 10 16 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 63 Ni source, it is necessary to analyze the performances of GaN-based diodes considering the spectrum of the 63 Ni source. The energy spectrum of the 63 Ni 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 63 Ni 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 Di-GaN = 1 × 10 16 cm −3 ), and the diffusion length of GaN can be shortened by Figure 8 shows reverse current density and Pout 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 Pout 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.  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 JSC, VOC, and Pout_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 JSC less than the acceptor-like trap state. While the donor-like trap states (EC-0.6 eV) slightly decreased the VOC, the shallow donor-like trap states (EC-0.23 eV) increased VOC. As a result, the Pout_max was unaffected by the shallow donor-like trap states (EC-0.23 eV). It is important to reduce the acceptor-like traps to improve the conversion efficiency of the betavoltaic cell.  In addition, we investigated the effects of trap density on JSC, VOC, and Pout_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 JSC less than the acceptor-like trap state. While the donor-like trap states (EC-0.6 eV) slightly decreased the VOC, the shallow donor-like trap states (EC-0.23 eV) increased VOC. As a result, the Pout_max was unaffected by the shallow donor-like trap states (EC-0.23 eV). It is important to reduce the acceptor-like traps to improve the conversion efficiency of the betavoltaic cell. 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.

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 × 10 16 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 10 14 cm −3 to 10 16 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.