I. INTRODUCTION

Ultrawide bandgap (UWB) semiconductors exhibit great promise in maintaining higher voltages and better conversion efficiency for modern industrial and electronic products since they are able to sustain higher critical fields, allowing for higher blocking voltages at lower resistances ^[1]. Beta-gallium oxide (β-Ga₂O₃) has attracted significant interest as a highly promising ultrawide bandgap material with immense potential in the field of power semiconductors devices. Owing to its large bandgap of 4.8 eV, high critical electric field of 8 MV/cm, and high Baliga’s figure of merit of 3400, Ga₂O₃ became an excellent candidate for high-power applications, outperforming semiconductors like Si, GaN, and SiC ^{[2- 4]}. Despite the materials inherent capability, the current performance of the Ga₂O₃ based Schottky diodes, in particular the demonstrative device’s parameter power figure-of-merit (PFOM) remains significantly lower than the projected material’s limits. In β-Ga₂O₃ Schottky diodes, the high surface electric field at the Schottky contacts induce excessive leakage currents resulting in premature breakdown of the device. Further, the defects at the metal/β-Ga₂O₃ interface introduced during the fabrication processing steps may result in large reverse leakage currents under large reverse electrical fields. A suppression of the reverse leakage current and enhancement in the breakdown voltage can be attained employing a variety of field management techniques like field plates, trench type structures and injection termination structures ^{[5- 9]}. Additionally, the lack of an efficient p-type doping technique for Ga₂O₃ is severely limiting the development of advanced Ga₂O₃ bipolar power electronics and as well for potential optoelectronic device applications using p-n junction structures ^{[10- 13]}. This obstacle can be overcome by an alternative approach of constructing p-n junctions employing p-type oxide semiconductors and n-type Ga₂O₃. Li et al. ^[2] fabricated NiO/Ga₂O₃ vertical heterojunctions and achieved remarkable breakdown voltage of 13.5 kV signifying the importance of p-type NiO in forming Ga₂O₃-based p-n junctions. for high power device applications. This approach allows the formation of various heterojunction devices with enhanced electrical performance, including p-n heterojunction diodes (HJD) ^[14], heterojunction barrier Schottky diodes (HJBS) ^[15] heterojunction field-effect transistors (JFET) ^{[16- 18]} and super junction metal-oxide-semiconductor field-effect transistors (SJ-MOSFET) ^[19]. NiO is a superior p-type partner for Ga₂O₃ in high-power applications owing to its wide bandgap and superior breakdown voltage. While Cu₂O offers significant advantages in cost, ease of fabrication, and specific optoelectronic applications. Cu₂O is particularly advantageous for applications requiring high-efficiency visible light absorption and offers a more accessible, earth-abundant material set. To approach a 13.5 kV breakdown voltage in a Cu₂O/Ga₂O₃ structure as reported by Li et al. ^[2] for NiO/Ga₂O₃ based devices, the drift layer thickness must be increased to 17–18 μm and the doping concentration need to be approximately $8.8\times 10^{15}\text{ cm}^{-3}$. Practical limitations with Cu₂O include its narrower bandgap which increases leakage current, and the critical need for advanced edge termination to manage the massive electric fields at the device boundaries. Nevertheless, NiO possesses a much wider bandgap, superior thermal and chemical stability compared to Cu₂O, with the defect generation and migration under high electric fields are relatively suppressed in NiO making it advantageous for achieving a higher critical electric field and thus a higher breakdown voltage. In contrast, Cu₂O has a narrower bandgap and a higher sensitivity to defects limiting the attainabl e breakdown voltage under identical processing conditions. Approaching the performance level of NiO-based heterojunctions using Cu₂O would need advanced device engineering techniques like careful design of electric-field management schemes, multilayer band-step architectures and extension of the drift region. Based on recent research, Cu₂O/Ga₂O₃ heterojunction diodes, particularly in Junction Barrier Schottky or p-n heterojunction structures, exhibit superior reverse recovery times and switching losses compared to conventional Ga₂O₃ Schottky Barrier Diodes (SBDs) due to charge storage effects associated with interfacial and bulk trap states often leading to higher performances. They leverage a high-barrier p-type material to reduce leakage current while maintaining low on-state resistance. While, the NiO/Ga₂O₃ structure benefits from relatively lower trap activity and a wider bandgap, which leads to more favorable reverse recovery characteristics and reduced switching losses. The Cu₂O/Ga₂O₃ heterojunctions are more suitable for medium-voltage, cost-sensitive applications rather than ultra-high-frequency applications. However, owing to the intrinsic material property limitations of Cu₂O, there remains practical constraints on achieving full parity with NiO/β-Ga₂O₃-based devices and needs intensive research. Till now, the Ga₂O₃-based p-n heterojunction devices formed employing p-type NiO demonstrated high breakdown voltages and the formation of p-n heterojunction devices with p-type Cu₂O could be highly promising resulting in higher breakdown voltages.

Recently, various p-type oxide materials such like Cr₂O₃ ^{[20, 21]}, ZnCo₂O₄ ^[22], NiO ^{[23- 25]}, SnO ^{[26, 27]} and Cu₂O ^[28] have been successfully employed in the fabrication of the β-Ga₂O₃-based heterojunction diodes. So far, there have been several reports available on the fabrication of Ga₂O₃-based p-n heterojunction diodes with improved electrical performance ^{[20- 31]}. Among the several p-type oxide materials, Cu₂O with an energy bandgap of 2.1 eV is one of the most promising materials with an intrinsic p-type conductivity owing to the creation of an acceptor level above the valence band maximum associated with the negatively charged Cu vacancies ^{[28, 29]}. Watahiki et al. ^[28] fabricated p-Cu₂O/n-β-Ga₂O₃ diode and reported a reverse breakdown voltage of 1.49 kV with a specific on-resistance of 8.2 mΩ·cm². Wang et al. ^[32] reported a notable breakdown voltage of 2.86 kV for Cu₂O/β-Ga₂O₃ heterojunction diode employing a stepped double-layer (SDL) structure of Cu₂O. The diode exhibited a turn-on voltage of 1.2 V, a specific on-resistance of 8.1 mΩ·cm², a power figure-of-merit exceeding 1.0 GW/cm² and operates normally to temperatures up to 473 K implying its thermal stability. Jia et al. ^[33] fabricated the vertical Cu₂O/β-Ga₂O₃ heterojunction p–n diodes with Cu₂O films deposited employing magnetron sputtering at substrate temperature of 600 °C demonstrated superior performance compared to devices fabricated with polycrystalline Cu₂O thin films and exhibited a breakdown voltage of 1015 V. Takatsuka et al. ^[34] demonstrated Ga₂O₃ trench heterojunction barrier Schottky diodes using a p-type Cu₂O/n-type Ga₂O₃ heterojunction structure with a maximum current of 3.5 A and breakdown voltage of 986 V. Jiang et al. ^[35] fabricated Cu₂O/Zr-doped β-Ga₂O₃ heterojunction diode that exhibited a near-ideal electrical behavior with a low ideality factor of 1.6 and that Zr doping markedly enhanced the crystallinity of Ga₂O₃ at low substrate temperatures with a transformation of the amorphous structure of pristine Ga₂O₃ films into the crystallized β phase. Despite the availability of the reports on the Cu₂O/β-Ga₂O₃ p-n heterojunction diodes, it is of high importance to thoroughly understand the effect of the doping concentration and thickness of the p-type Cu₂O layer on the electrical characteristics of the Cu₂O/β-Ga₂O₃ p-n heterojunction diode, in particular towards enhancing the breakdown voltage and the on-resistance that determines the performance of the high-power device. Following the recent 2025 reports by pearton et al. ^[13] and, in particular, studies published near the timeframe of the Pearton et al. 2025 review on β-Ga₂O₃, the optimized Cu₂O/Ga₂O₃ heterojunction diode showed a Power Figure-of-Merit ($\text{PFOM}=V^2/R_{on}$) around 0.49–1.2 GW/cm² makes it competitive with other p-type oxides. Till now, the NiO/β-Ga₂O₃ p-n heterojunction diode currently hold the highest PFOM reported record for the material system often exceeding 5–9 GW/cm². The optimized Cu₂O/Ga₂O₃ HJDs with a careful device engineering could lead to a very favourable balance of high voltage and low resistance, placing them as a top alternative in the p-type oxide/Ga₂O₃ based p-n heterojunction systems.

In this work, we investigated the performance of the Cu₂O/β-Ga₂O₃ p-n heterojunction diode by varying the parameters such as bandgap, electron affinity, doping concentration and thickness of the p-type Cu₂O layer. We have performed an extensive and systematic investigation on the impact of these parameters on the electrical and breakdown voltage characteristics and the electric field distribution under the anode contact edge of the Cu₂O/β-Ga₂O₃ p-n heterojunction diode employing commercial technology computer-aided design (TCAD) software Silvaco Atlas. These simulations have been carried out towards achieving an enhancement in breakdown voltage of the Cu₂O/β-Ga₂O₃ p-n heterojunction diode and its optimization. It is shown that the breakdown voltage increased with increase in doping concentration of the p-type Cu₂O layer until $1\times 10^{18}\text{ cm}^{-3}$ and remained constant for $1\times 10^{19}\text{ cm}^{-3}$ implying that the depletion width of the drift layer determined by the doping concentration has reached its limit at $1\times 10^{18}\text{ cm}^{-3}$ thus limiting the voltage that the drift layer can withstand. Further, the breakdown voltage of the Cu₂O layer with doping concentration of $1\times 10^{18}\text{ cm}^{-3}$ increased with increase in the thickness until 200 nm after which the breakdown voltage is noted to be unchanged. A detailed discussion on the effect of doping concentration and thickness of the p-type Cu₂O layer on the Cu₂O/β-Ga₂O₃ p-n heterojunction diode performance has been provided.

II. SIMULATION DETAIL

Fig. 1 shows the schematic cross-section of the p-type Cu₂O/n-type Ga₂O₃ heterojunction p-n diode used in the simulation. A highly doped n⁺ Ga₂O₃ substrate with a doping concentration of $1\times 10^{19}\text{ cm}^{-3}$ is used to form an n⁻ β-Ga₂O₃ epitaxial layer having a doping concentration of $2\times 10^{16}\text{ cm}^{-3}$, upon which p-type Cu₂O thin films with various doping concentrations and thicknesses are deposited. For the convenience of the simulation, the thicknesses of the n⁺ Ga₂O₃ substrate and n⁻ Ga₂O₃ epitaxial layer were set to 1 μm and 10 μm, respectively. The simulation was conducted using a 2D device simulator and Atlas Technology computer aided design (TCAD) software. To simulate the electrical characteristics of the device, the thermionic current model, Shockley-Read-Hall (SRH) recombination model, and band-to-band tunneling model were employed. For simulating the breakdown voltage characteristics, the impact ionization model was employed. The physical parameters of Ga₂O₃, including bandgap, electron affinity, relative dielectric constant, and carrier mobility, are summarized in Table 1. In contrast, the physical parameters of Cu₂O were obtained from calibrated values extracted from previously reported experimental data.

Fig. 1. Schematic of p-type Cu2O/n-type β-Ga2O3 heterojunction PN diode used for simulation.

III. RESULTS AND DISCUSSION

Fig. 2 illustrates the simulated current density (J)–voltage (V) characteristics of the p-type Cu₂O/n-type Ga₂O₃ heterojunction in response to variations in the bandgap and electron affinity of Cu₂O. As the bandgap of Cu₂O increased from 1 eV to 3 eV, the turn-on voltage increased from 0.7 V to 2.7 V. This is because an increase in the bandgap of the semiconductor increases the energy barrier formed at the p-n junction leading to a requirement of high turn-on voltage to enable conduction in the diode allowing significant current flow ^{[36, 37]}. Additionally, as well known, a conduction band offset is generated when different semiconductors form a heterojunction given by the electron affinity difference between the semiconductors. A larger conduction band offset ($\Delta E_C$) is formed at the p-type Cu₂O/β-Ga₂O₃ interface that act as a barrier to electron injection from n-Ga₂O₃ to p-Cu₂O, reducing forward current and increasing turn-on voltage, reducing injection efficiency. To attain high injection efficiency, $\Delta E_C$ need to be relatively low to allow high forward currents, while still allowing the heterojunction to function. $\Delta E_C$ can be minimized by utilizing a junction barrier structure with a periodic Cu₂O pattern on β-Ga₂O₃ leading to a low turn-on voltage via the Schottky junctions while the p-type Cu₂O/β-Ga₂O₃ heterojunction blocks the reverse leakage current. $\Delta E_C$ can be reduced by inserting a thin buffer layer between Cu₂O and β-Ga₂O₃ and also, by tuning the oxygen concentration in the Cu₂O during deposition thus tuning the p-type carrier concentration and reduce oxygen vacancy-related defects, thereby improving the band alignment. The variation of electron affinity for Cu₂O between 3.0 eV and 4.0 eV in simulations accounts for the significant impact of surface states, stoichiometry, and intrinsic defects on the material's energy levels. Pure Cu₂O usually exhibits an electron affinity near 3.2 eV with the experimental values shifting as the material deviates toward CuO or Cu₄O₃ mixed phases. Higher oxygen flow during deposition can alter the conduction band minimum effectively shifting electron affinity across the simulated range. Cu₂O is intrinsically p-type due to copper vacancies ($V_{Cu}$), but oxygen vacancies ($V_O$) are also usual. $V_O$ acts as a shallow donor that can introduce localized states near the CBM, leading to band gap narrowing. This defect-driven shifting of the CBM directly justifies exploring a wider electron affinity range to capture realistic electronic environments. Form Fig. 2(b), it can be noted that as the electron affinity of Cu₂O was varied from 3.0 eV to 4.0 eV, the on-resistance of the p-type Cu₂O/n-type Ga₂O₃ heterojunction p-n diode is decreased from 41.2 MΩ·cm² to 0.815 mΩ·cm². In general, the on-resistance of a p-n junction diode decreases with increasing electron affinity of the p-type layer. This is associated with the fact that a higher electron affinity of the p-type material results in a lower potential barrier at the junction allowing increased current flow and lower resistance on forward biasing. This indicates that by altering the bandgap and electron affinity, it is possible to control the turn-on voltage and on-resistance. The crystallinity of Cu₂O exhibits a direct impact on carrier mobility and interfacial defect density that effects the forward on-voltage and leakage current characteristics. In usual, the polycrystalline Cu₂O exhibits lower mobility and higher leakage current due to grain-boundary scattering and a higher density of defects. While the epitaxial or highly crystalline Cu₂O alleviates these non-ideal effects. As the deposition temperature increases, the crystallinity of Cu₂O improves; however, excessive increase in deposition temperature results in the increase of the concentration of vacancies and interfacial degradation. The simulation results assume the ideal material properties and does not consider the process-induced defects. As a result, the practical devices exhibits higher on-resistance and leakage current than predicted by ideal devices as in the case of the simulation. The simulation results consider the ideal conditions of the substrate or the fabricated device like the absence of trap states, interface state density, structural defects, full depletion of the drift region and so on ^[38]. Also, the simulation results do not consider any interface inhomogeneity caused by the metal contact formation or edge leakage currents that may possibly present in the fabricated device. Owing to these above facts, the reverse leakage current increases leading to a premature breakdown occurrence in the experimentally fabricated device as against the simulated results. Further, the field-driven migration of intrinsic vacancies are the long-term reliability concerns and degradation mechanisms in high-field metal-oxide devices that alters junction properties and results in failure mechanisms like increase in leakage current, dielectric breakdown and resistive switching. Cu₂O is a p-type semiconductor where copper vacancies ($V_{Cu}$) are the dominant defects. Under high electric field stress, $V_{Cu}$ migrate towards the cathode causing a significant degradation. This migration leads an increase in trap-assisted leakage currents, and increased conductivity resulting in a premature breakdown of the p-Cu₂O/β-Ga₂O₃ junction. In β-Ga₂O₃, oxygen vacancies ($V_O$) act as deep donors. Under high field, positively charged $V_O$ migrate causing accumulation at the cathode generating a high concentration of traps leading to defect-mediated leakage currents. NiO is generally more chemically and thermally stable than Cu₂O, reducing the propensity for phase degradation at the interface that is better suited for forming stable, high voltage devices.

Fig. 2. Simulated J–V characteristics of p-type Cu2O/n-type β-Ga2O3 heterojunction PN diode in response to variations in (a) bandgap and (b) electron affinity of Cu2O.

Fig. 3(a) and (b) presents the simulated forward and reverse current density-voltage (J–V) characteristics for the p-type Cu₂O/n-type Ga₂O₃ heterojunction p-n diode with Cu₂O thickness of 200 nm having doping concentration of $1 \times 10^{18}\text{ cm}^{-3}$. The forward bias current in the linear region varied over 10 orders. The turn-on voltage and specific on-resistance of 1.7 V and 8.33 mΩ·cm² was obtained from the forward bias J–V characteristics. The simulated Cu₂O/Ga₂O₃ heterojunction p-n diode exhibited a reverse breakdown voltage of 1500 V. A validation of the simulation results was made using the experimental results from previous research studies. To align with the experimental results, the bandgap and electron affinity values of Cu₂O were adjusted to 2.0 eV and 3.6 eV, respectively. The simulation results obtained closely matched with those reported by Wang et al. ^[39]. Wang et al. ^[39] reported a turn-on voltage of 1.7 V, specific on-resistance of 8.2 mΩ·cm², and breakdown voltage of 1490 V for the CuO_x/Ga₂O₃ heterojunction diode. This clearly demonstrates that electrical characteristics are almost similar to the reported experimental data validating the simulation of the p-type Cu₂O/n-type Ga₂O₃ heterojunction PN diode. The edge termination techniques such as field plates, guard rings, and junction termination extensions can significantly enhance the breakdown voltage of Cu₂O/Ga₂O₃ heterojunctions beyond the 1.5 kV that was achieved by optimizing only the junction parameters for an un-terminated device. The employment of edge termination reduces the peak electric fields at the device periphery managing the electric field crowding at the anode edge can push these devices to higher kilovolt-class performance levels. The Cu₂O/Ga₂O₃ devices with edge termination can result in comparable, if not identical, high-voltage, low-leakage performance as compared with NiO/Ga₂O₃ devices. The reverse voltage at which the leakage current of 1 A/cm² occurs is defined as the breakdown voltage. The breakdown voltage obtained for the power devices using TCAD simulation methodologies is usually determined by the impact ionization onset, usually identified as the voltage where the multiplication factor approaches unity or the leakage current shows an abrupt and exponential increase indicating the onset of avalanche multiplication. Breakdown voltage ($V_{BR}$) predictions are highly sensitive to the impact ionization model, specifically the ionization coefficients, the critical electric field and to literature-based material parameters of both Cu₂O and Ga₂O₃. Since the impact ionization relies on high-energy carriers initiating further ionization, small changes in the material parameters like doping density, trap-limited conduction, or bandgap can lead to significant variations in the calculated $V_{BR}$. The simulation results must be validated against devices with known, measured doping concentrations and defect densities to confirm the modelled ionization behavior reflecting the realistic, rather than ideal properties. As considering the temperature dependence of the $V_{BR}$, the $V_{BR}$ of high-power devices usually decreases with increasing temperature, however the rate of decrease in $V_{BR}$ varies depending on device structure and termination. This decrease in $V_{BR}$ is associated with the increase in leakage current and impact ionization. A detailed study of the temperature-dependence of the $V_{BR}$ of the Cu₂O/β-Ga₂O₃ p-n heterojunction diode will be carried out through simulation and for the fabricated diodes as our future work the results which will be published elsewhere. The temperature reliability of the devices can be improved through careful device design such as implementing advanced trench structures.

Fig. 3. (a) Forward J–V and (b) reverse J–V characteristics of p-type Cu2O/n-type β-Ga2O3 heterojunction PN diode obtained through simulation.

The operational J–V characteristics of the p-type Cu₂O/n-type Ga₂O₃ heterojunction PN diode with the structure depicted in the inset in Fig. 4(a) were investigated as a variation of doping concentration of the p-type Cu₂O, with the results illustrated in Fig. 4. The doping concentration of Cu₂O was varied from $1\times 10^{15}\text{ cm}^{-3}$ to $1\times 10^{19}\text{ cm}^{-3}$ to study its effect on the electrical characteristics. As the doping concentration increased, the breakdown voltage rose from 390 V to 1500 V, with recorded values of 390 V, 400 V, 460 V, 1500 V, and 1500 V. However, the breakdown voltage remained unchanged for doping concentrations exceeding $1\times 10^{18}\text{ cm}^{-3}$. The increase in breakdown voltage with higher doping concentrations of p-type Cu₂O is attributed to the widening of the depletion width in the drift layer, specifically the Ga₂O₃ epitaxial layer, as illustrated in Fig. 5. This is because the n-region (β-Ga₂O₃) is lightly doped leading to low donor impurity causing a wider depletion region in β-Ga₂O₃. As the depletion width of the drift layer widens, the electric field can be distributed over a larger area ^{[40- 42]}. The depletion layer is a high-resistance region formed by the space charge created on recombination of holes from the p-type semiconductor with electrons from the n-type semiconductor at the junction with the space charge density in the depletion layer being same for both the p-type and n-type semiconductors. On assuming that the doping concentration of the p-type semiconductor is significantly higher than that of the n-type semiconductor, the depletion width of the p-type semiconductor can be neglected. In this case, the depletion width of the n-type semiconductor can be considered equal to the total depletion width. In fact, it can be noted from Fig. 5 that the depletion width of the drift layer converges to approximately 9 μm at the obtained breakdown voltage with p-type Cu₂O doping concentrations of $1\times 10^{18}\text{ cm}^{-3}$ and $1\times 10^{19}\text{ cm}^{-3}$. The unchange in the breakdown voltage with increase in doping concentration of the p-type Cu₂O above $1\times 10^{18}\text{ cm}^{-3}$ is associated with the fact that the depletion width of the drift layer determined by the doping concentration has reached its limit at $1\times 10^{18}\text{ cm}^{-3}$ thus limiting the voltage that the drift layer can withstand ^[43]. When the doping concentration of Cu₂O is low, the resistance of the Cu₂O thin film is high, resulting in the formation of a depletion layer that conforms to the shape of the anode electrode. However, as the doping concentration of Cu₂O increases, the resistance of the Cu₂O thin film decreases, causing the depletion layer, initially formed only beneath the anode electrode, to spread laterally across the Cu₂O thin film. Consequently, the electric field, initially concentrated beneath the electrode, becomes distributed as the depletion layer expands laterally. As shown in Fig. 6, the electric field, initially concentrated at the edges of the metal, becomes well dispersed with the increase in doping concentration from $1\times 10^{17}\text{ cm}^{-3}$ to $1\times 10^{18}\text{ cm}^{-3}$, resulting in a significant increase in breakdown voltage ^[40].

Fig. 4. (a) Forward J–V and (b) reverse J–V characteristics of p-type Cu2O/n-type Ga2O3 heterojunction PN diode with varying Cu2O doping concentrations obtained through simulation.

Fig. 5. Simulated depletion width in the p-type Cu2O/n-type β-Ga2O3 heterojunction PN diode at breakdown voltage with varying Cu2O doping concentrations.

Fig. 6. Simulated electric field distribution in the p-type Cu2O/n-type Ga2O3 heterojunction PN diode at breakdown voltage with varying Cu2O doping concentrations.

Figs. 7(a) and (b) shows the forward and reverse bias current-voltage characteristics of the p-type Cu₂O/n-type Ga₂O₃ heterojunction PN diode structure as a variation of the thickness of the Cu₂O film from 50 nm to 500 nm at a Cu₂O doping concentration of $1\times 10^{18}\text{ cm}^{-3}$. From Fig. 7(b) it can be noted that the breakdown voltage rose from 610 V to 1500 V, with recorded values being 610 V, 940 V, 1310 V, 1500 V, and 1500 V with increase in the thickness of the Cu₂O film from 50 nm to 500 nm. However, no change in breakdown voltage was observed for thicknesses greater than 200 nm. The increase in breakdown voltage with the increasing thickness of the p-type Cu₂O film is attributed to the change in the depletion width of the drift layer, similar to the effects of doping concentration in p-type Cu₂O ^{[40, 42]}. The increase in $V_{br}$ with increasing thickness is due to the fact that the thicker drift layer can accommodate a wider depletion region that allows the electric field distribution to occur over a wider area enough to accommodate the entire depletion region ^{[44- 47]}. At a doping concentration of $1\times 10^{18}\text{ cm}^{-3}$, the depletion width of the Cu₂O thin film at the maximum attained breakdown voltage is calculated to be approximately 180 nm. The lower breakdown voltages in the case of the diode with thickness of the Cu₂O layer less than 150 nm could be associated with the fact that the thickness of the drift layer is narrower than the depletion layer width and that the depletion layer spreads to the metal contact ^[48]. As the depletion width cannot exceed the thickness of the Cu₂O thin film, for thicknesses below 180 nm, the maximum depletion width in the Cu₂O thin film is determined by its thickness. Therefore, as shown in Fig. 8, the depletion width of the drift layer increases linearly with the thickness of the Cu₂O film up to 200 nm, but no further changes occur beyond that thickness. A simulation was also carried out to determine the dispersal of the electric field in the p-type Cu₂O/n-type Ga₂O₃ heterojunction PN diode structure as a variation of the thickness of the p-type Cu₂O layer in the range of 50 nm–500 nm, with the results shown in Fig. 9. As illustrated in Fig. 9, the electric field is concentrated initially at the edges of the anode metal for lower Cu₂O layer thickness. As the thickness of the Cu₂O layer increases towards 200 nm, the electric field gets well distributed laterally in the Cu₂O layer ^[40]. The increase in breakdown voltage with increasing thickness could be due to the increase in the depletion width leading to a lower electric field as the applied voltage will get distributed over a larger distance ^{[47, 49, 50]}. This imply that the PN diode structures fabricated with larger thickness has the ability in handling high electric field at high reverse bias.

Fig. 7. Simulated (a) forward J–V and (b) reverse J–V characteristics of the p-type Cu2O/n-type Ga2O3 heterojunction PN diode with varying thicknesses of the Cu2O film.

Fig. 8. Simulated depletion width in the p-type Cu2O/n-type Ga2O3 heterojunction PN diode with varying thicknesses of the Cu2O film at breakdown voltage.

Fig. 9. Simulated electric field distribution in the p-type Cu2O/n-type Ga2O3 heterojunction PN diode with varying thicknesses of the Cu2O film at breakdown voltage.

IV. CONCLUSIONS

In this study, the electrical characteristics of the p-type Cu₂O/n-type β-Ga₂O₃ heterojunction structure were systematically analyzed through simulations with a focus on the variation of depletion width as a function of doping concentration and thickness of the p-type Cu₂O thin film. The turn-on voltage of the p-type Cu₂O/n-type Ga₂O₃ heterojunction p-n diode increased from 0.7 to 2.7 V with an increase in the bandgap of Cu₂O from 1 to 3 eV since it is difficult for electrons to move from the valence band to the conduction band with increasing large bandgap. The on-resistance of the heterojunction p-n diode decreased from 41.2 MΩ·cm² to 0.815 mΩ·cm² with increasing electron affinity of the p-type Cu₂O layer due to increased current flow associated with a lower potential barrier at the junction. The breakdown voltage increased with increasing doping concentrations of p-type Cu₂O attributed to the widening of the depletion width in the drift layer. The breakdown voltage increased with increasing thickness of the Cu₂O layer due to the fact that the thicker layer could accommodate a wider depletion region allowing the electric field distribution occurrence over a wide area enough to accommodate the entire depletion region. From the simulation results, the optimized doping concentration and thickness values for the Cu₂O layer in the p-type Cu₂O/n-type β-Ga₂O₃ was determined to be $1 \times 10^{18}\text{ cm}^{-3}$ and 200 nm, respectively that resulted in a breakdown voltage of 1500 V with an on-voltage and on-resistance of 1.7 V and 8.33 mΩ·cm², respectively. This study demonstrates the potential for optimizing the performance of Ga₂O₃-based p-n heterojunction diode employing p-type Cu₂O thin films and paves the way for the design and performance enhancement of next-generation high-voltage devices.