Calculating the Effect of AlGaN Dielectric Layers in a Polarization Tunnel Junction on the Performance of AlGaN-Based Deep-Ultraviolet Light-Emitting Diodes

In this work, AlGaN-based deep-ultraviolet (DUV) light-emitting diodes (LEDs) with AlGaN as the dielectric layers in p+-Al0.55Ga0.45N/AlGaN/n+-Al0.55Ga0.45N polarization tunnel junctions (PTJs) were modeled to promote carrier tunneling, suppress current crowding, avoid optical absorption, and further enhance the performance of LEDs. AlGaN with different Al contents in PTJs were optimized by APSYS software to investigate the effect of a polarization-induced electric field (Ep) on hole tunneling in the PTJ. The results indicated that Al0.7Ga0.3N as a dielectric layer can realize a higher hole concentration and a higher radiative recombination rate in Multiple Quantum Wells (MQWs) than Al0.4Ga0.6N as the dielectric layer. In addition, Al0.7Ga0.3N as the dielectric layer has relatively high resistance, which can increase lateral current spreading and enhance the uniformity of the top emitting light of LEDs. However, the relatively high resistance of Al0.7Ga0.3N as the dielectric layer resulted in an increase in the forward voltage, so much higher biased voltage was required to enhance the hole tunneling efficiency of PTJ. Through the adoption of PTJs with Al0.7Ga0.3N as the dielectric layers, enhanced internal quantum efficiency (IQE) and optical output power will be possible.


Introduction
AlGaN-based deep-ultraviolet (DUV) light-emitting diodes (LEDs) have many advantages, including environmental protection, low power consumption, Hg-free material, compact size, controllable wavelength, and a long lifetime, and they can be applied in the fields of disinfection, sterilization, purification, biomedicine, gas sensing, optical data storage, non-line-of-sight communication, identification of hazardous biological agents and so on [1]. AlGaN-based DUV LEDs with a short wavelength of 210 nm [2] and an improved external quantum efficiency (EQE) of 20.3% (for 275 nm) [3] have been achieved. However, the EQE is still lower than that of GaN-based blue and green LEDs, and the EQE drops dramatically with decreasing wavelength [1]. As is well-known, the EQE is determined by the internal quantum efficiency (IQE) and the light extraction efficiency (LEE), which can be enhanced by optimizing E p in the PTJ to improve the tunneling efficiency. The intensity of E c in a PTJ can be formulated as follows: where E is the intensity of E c in PTJ, e is the value of a unit of electronic charge, ε 0 is the absolute dielectric constant, ε r is the average relative dielectric constant for the PTJ, N dopant is the ionized dopant concentration in the space charge region, L depletion is the depletion region's width, and σ p is the polarization-induced sheet charge density. The symbol "±" represents the direction of E p . The symbol "+" represents the same direction as E b , and the symbol "-" represents the reverse direction to E b . According to the expression in Equation (1), E can be determined by the factors N dopant , L depletion , σ p , and ε r . It is necessary to point out that ε r is the inherent constant of a material. For InGaN, there is a linear relationship between ε r and the In content of InGaN, and ε r will become larger with an increase in the In content of InGaN. In addition, there is strong optical absorption in the PTJ when the In content of InGaN in the PTJ is higher than that in the active region, as it is quite disadvantageous to the LEE of an LED. AlGaN has a lower ε r than InGaN, and the ε r becomes small with an increase in the Al content of AlGaN. This means that AlGaN as the dielectric layer of a PTJ is superior to InGaN as the dielectric layer of a PTJ for enhancing the intensity of E c , promoting hole tunneling and avoiding optical absorption, as is very advantageous to the IQE and LEE of an AlGaN-based DUV LED.
However, there is still an inadequate view that AlGaN as the dielectric layer of PTJ cannot enhance the intensity of E c , due to the reverse direction of E p compared with E b . As a result, there are few reports on AlGaN as the dielectric layer of PTJs in LEDs. In 2017, InGaN-based near-ultraviolet (NUV) LEDs with p + -GaN/AlGaN/n + -GaN PTJs were optimized, and enhanced LED performance was achieved. This was the first report on the use of AlGaN as a dielectric material of a PTJ [36,37].
Additionally, the difficulty of heavy doping (a carrier concentration of over 1 × 10 20 cm −3 ) in a PTJ has slowed down the progress of research into AlGaN-based DUV LEDs with PTJ. However, the research into AlGaN-based DUV LEDs with PTJs never stopped. In 2018, an AlGaN-based DUV LED with a p + -Al 0.65 Ga 0.35 N/In 0.2 Ga 0.8 N/graded n + -AlGaN PTJ (p + = 5 × 10 19 cm −3 and n + = 1 × 10 20 cm −3 ) was grown and fabricated, with a wavelength of 287 nm, a forward voltage of 10.5 V, and an optical output power of 54.4 W/cm 2 at a current density of 1 kA/cm 2 [34][35][36]. In 2021, an AlGaN-based DUV LED with a p + -GaN/n + -AlGaN PTJ was grown and fabricated, with a wavelength of 245 nm, a maximum EQE of 0.35% and a wall-plug efficiencies (WPE) of 0.21% [36]. It was proven that high-performance AlGaN-based DUV LEDs with PTJs can be achieved. However, InGaN or GaN as the dielectric layer of a PTJ is quite unsuitable for AlGaN-based DUV LED due to strong optical absorption in PTJ. AlGaN has a lower ε r and a lower optical absorption than InGaN. This means that AlGaN is superior to InGaN as the dielectric layer of PTJ for promoting hole tunneling, suppressing current crowding, increasing current spreading, and avoiding optical absorption of the PTJ in AlGaN-based DUV LEDs.
In this work, AlGaN-based DUV LEDs with AlGaN as the dielectric layers in p + -Al 0.55 Ga 0.45 N/AlGaN/n + -Al 0.55 Ga 0.45 N PTJs were proposed. AlGaN with different Al content in PTJs was optimized to investigate the effect of p + -Al 0.55 Ga 0.45 N/Al x GaN/n + -Al 0.55 Ga 0.45 N PTJs on the performance of AlGaN-based DUV LEDs, where x = 0.4, 0.55, and 0.7. The output characteristics of the AlGaN-based DUV LEDs including the forward voltage, optical output power, IQE and WPE were characterized. APSYS software was used to conduct a finite element analysis of the electrical, optical, and thermal properties of the LEDs.

Results and Analysis
For Structure B, the PTJ is a p + -i-n + heterojunction, and Ec comes fro contributions of Eb and Ep, as shown in Figure 2b. Eb has a direction along the orientation, beginning with N21 in the n + -Al0.55Ga0.45N layer and ending with N22 in Al0.55Ga0.45N layer, and it can be calculated as N21 = 1.0 × 10 20 cm −3 and N22 = −1.0 × 10 as shown in Figure 2d. Ep is built up from the differences between N3 at the Al0.4Ga Al0.55Ga0.45N interface and N4 at the p + -Al0.55Ga0.45N/Al0.4Ga0.6N interface, where N3 > N4 < 0 under compressive strain of Al0.4Ga0.6N, and can be calculated as N3 = 2.9 × 1 and N4 = −3.1 × 10 20 cm −3 , as shown in Figure 2e. Ep has a direction along the orientation in the Al0.4Ga0.6N layer, in the same direction as Eb, and a direction alo [0001] orientation at both sides of the Al0.4Ga0.6N layer, in the reverse direction to shown in Figure 2b.
For Structure C, the PTJ is also a p + -i-n + heterojunction, and E c also comes from the contributions of E b and E p , as shown in Figure 2c.    Figure 2a. For Structure B, Ec comes from the contributions of Eb an has a direction along the [000-1] orientation. Ep has a direction along the [000-1] orie in the Al0.4Ga0.6N layer, in the same direction as Eb, and a direction along the orientation in the p + -Al0.55Ga0.45N and n + -Al0.55Ga0.45N layers, in the reverse directio as shown in Figure 2b. As a result, the intensity of Ec is enhanced by Ep in the Al0 layer, and degraded by Ep in the p + -Al0.55Ga0.45N and n + -Al0.55Ga0.45N layers compar Structure A, as shown in Figure 3. For Structure C, Ec comes from the contributio and Ep. Eb has a direction along the [000-1] orientation. Ep has a direction along th orientation in the Al0.7Ga0.3N layer, in the reverse direction to Eb, and a direction al [000-1] orientation in the p + -Al0.55Ga0.45N and n + -Al0.55Ga0.45N layers, in the same d as Eb, as shown in Figure 2c. As a result, the intensity of Ec is degraded by E Al0.7Ga0.3N layer, and enhanced by Ep in the p + -Al0.55Ga0.45N and n + -Al0.55Ga0.45N la compared with Structure A, as shown in Figure 3. Moreover, εr has a role in controlling the intensity of Ec, according to the exp in Equation (1). For AlGaN, εr becomes small with an increase in the Al content of For Structure B, Al0.4Ga0.6N as the dielectric layer has a higher εr than Structure Al0.55Ga0.45N, which should have decreased the intensity of Ec. Nevertheless, an in electric field is still obtained because of the contribution of a polarization-induced field in the center. For Structure C, Al0.7Ga0.3N as the dielectric layer has a lower Structure A with Al0.55Ga0.45N, which enhances the intensity of Ec because contribution of εr in the center. Thus, according to the final results regard contributions of Eb, Ep, and εr, the intensities of Ec are in the following order: Struc Structure C > Structure A in the center peak, and Structure C > Structure A > Stru at both sides of the center, as shown in Figure 3.
According to Figure 3, the calculated peak intensities of Ec are as follows: EA 10 6 V/cm, EB = 9.07 × 10 6 V/cm, and EC = 8.24 × 10 6 V/cm for Structures A, B, and C center peak, respectively. This means that very strong electric field intensi generated in the TJ regions of the LEDs in Structures A, B, and C. Driven by electrons in the valence band of the p + -Al0.55Ga0.45N layer can tunnel through the Moreover, ε r has a role in controlling the intensity of E c , according to the expression in Equation (1). For AlGaN, ε r becomes small with an increase in the Al content of AlGaN. For Structure B, Al 0.4 Ga 0.6 N as the dielectric layer has a higher ε r than Structure A with Al 0.55 Ga 0.45 N, which should have decreased the intensity of E c . Nevertheless, an increased electric field is still obtained because of the contribution of a polarization-induced electric field in the center. For Structure C, Al 0.7 Ga 0.3 N as the dielectric layer has a lower ε r than Structure A with Al 0.55 Ga 0.45 N, which enhances the intensity of E c because of the contribution of ε r in the center. Thus, according to the final results regarding the contributions of E b , E p , and ε r , the intensities of E c are in the following order: Structure B > Structure C > Structure A in the center peak, and Structure C > Structure A > Structure B at both sides of the center, as shown in Figure 3.
According to Figure 3, the calculated peak intensities of E c are as follows: E A = 7.40 × 10 6 V/cm, E B = 9.07 × 10 6 V/cm, and E C = 8.24 × 10 6 V/cm for Structures A, B, and C in the center peak, respectively. This means that very strong electric field intensities are generated in the TJ regions of the LEDs in Structures A, B, and C. Driven by E c , the electrons in the valence band of the p + -Al 0. 55 Figure 5b shows a comparison of the radiative recombination rates along the vertical direction at a relative horizontal position of 100 μm in the MQWs of the LEDs for Structures A, B, and C at a current of 180 mA. The radiative recombination rates along the vertical direction in the MQWs are in the following order: Structure C > Structure A > Structure B. The radiative recombination rates come from the contributions of the high electron and hole concentrations in the MQWs, as is consistent with the hole-concentration distributions in the MQWs, as shown in Figure 5a.
In order to investigate the effects of the TJs on the current spreading in LEDs, the lateral distributions of the hole concentrations and the radiative recombination rates along the horizontal direction (x-axis) in the LEDs were characterized. Figure 5c   In order to investigate the effects of the TJs on the current spreading in LEDs, the lateral distributions of the hole concentrations and the radiative recombination rates along the horizontal direction (x-axis) in the LEDs were characterized. Figure 5c shows a comparison of the lateral distributions of the hole concentrations and the radiative recombination rates along the horizontal direction (x-axis) and at a relative vertical position of the fifth QW (c-axis) in LEDs for Structures A, B, and C. For Structure B, the lateral distributions of the hole concentrations and the radiative recombination rates along the horizontal direction in the LEDs are very non-uniform: high at the horizontal positions of 0~50 µm, which is just below the anode, and low at the positions of 50~200 µm. This means that the positions under the anode are the main current flow paths going through the MQWs, which will cause current crowding and Joule heat. For Structures A, B, and C, the lateral distribution uniformities of the hole concentrations and the radiative recombination rates along the horizontal direction (x-axis) in the LEDs are in the following order: Structure C > Structure A > Structure B. The uniformities come from the contributions of high resistance in the TJs. If we compare Structures A, B, and C, the tunneling probability of electrons and the Al content of AlGaN in the TJs determine the resistance. Structure C has a lower electron tunneling probability and a higher Al content of AlGaN in the PTJ than Structure B, thus resulting in the higher resistance of the PTJ in Structure C. Therefore, Structure C with Al 0.7 Ga 0.3 N as the dielectric layer has higher uniformity than Structure B with Al 0.4 Ga 0.6 N as the dielectric layer, which means that relatively higher resistance of the TJ has a meaningful impact on the current spreading of an LED.
In order to quantitatively compare the lateral distribution uniformities of the hole concentrations and radiative recombination rates on the output characteristics of the LEDs for Structures A, B, and C, the integrated intensities of the lateral distributions of the hole concentrations and radiative recombination rates at the relative horizontal positions between 0 and 200 µm were characterized. Figure 5d shows a comparison of the integrated intensities of the lateral distributions of the hole concentrations and radiative recombination rates along the horizontal direction (x-axis) and at a relative vertical position of the fifth QW (c-axis) in LEDs for Structures A, B, and C. The integrated intensities for both the hole concentrations and radiative recombination rates are in the following order: Structure C > Structure A > Structure B. Compared with the lateral distributions of the hole concentrations and radiative recombination rates along the horizontal direction (x-axis), the integrated intensities more accurately reflected the output characteristics of LEDs with the different structures. Figure 6 shows a comparison of the output current-voltage (I-V) characteristics of the LEDs (300 × 300 µm 2 ) for Structures A, B, and C. The forward voltages of the LEDs are in the following order: Structure C > Structure A > Structure B. When an LED is operated at a forward biased voltage, the top TJ is operated at a reverse biased voltage. A TJ operating at a reverse biased voltage can be treated as a resistor, and its resistance determines the forward voltage of the LED, so that the forward voltage of an LED increases with an increase in the resistance of the JT. If we compare Structures A, B, and C, the tunneling probability of electrons and the Al content of AlGaN in the TJs determine the resistance, and the resistance determines the forward voltage of the LED. The resistances of the TJs are in the following order: Structure C > Structure A > Structure B, so the forward voltages of the LEDs are in the following order: Structure C > Structure A > Structure B. This indicates that the TJ has a nonnegligible impact on the forward voltage of DUV LEDs, and much higher biased voltage is required to realize higher tunneling efficiency for Structure C with a higher Al content of AlGaN.
intensities of the lateral distributions of the hole concentrations and recombination rates along the horizontal direction (x-axis) and at a relat position of the fifth QW (c-axis) in LEDs for Structures A, B, and C. The intensities for both the hole concentrations and radiative recombination rate following order: Structure C > Structure A > Structure B. Compared with distributions of the hole concentrations and radiative recombination rates horizontal direction (x-axis), the integrated intensities more accurately re output characteristics of LEDs with the different structures. Figure 6 shows a comparison of the output current-voltage (I-V) chara the LEDs (300 × 300 μm 2 ) for Structures A, B, and C. The forward voltages of th in the following order: Structure C > Structure A > Structure B. When an LED at a forward biased voltage, the top TJ is operated at a reverse biased vo operating at a reverse biased voltage can be treated as a resistor, and its determines the forward voltage of the LED, so that the forward voltage increases with an increase in the resistance of the JT. If we compare Structure C, the tunneling probability of electrons and the Al content of AlGaN in the TJs the resistance, and the resistance determines the forward voltage of the resistances of the TJs are in the following order: Structure C > Structure A > S so the forward voltages of the LEDs are in the following order: Structure C > St Structure B. This indicates that the TJ has a nonnegligible impact on the forw of DUV LEDs, and much higher biased voltage is required to realize highe efficiency for Structure C with a higher Al content of AlGaN.   Figure 5d, and inditcating that the enhanced IQE and op power of the LED for Structure C were achieved. Figure 7b shows a compar WPE of LEDs for Structures A, B, and C. The WPE of the LEDs is in the follow Structure B > Structure A > Structure C. The WPE is inversely proportional to t voltage, so the LED for Structure C had the lowest WPE due to the highest forw   Figure 5d, and inditcating that the enhanced IQE and optical output power of the LED for Structure C were achieved. Figure 7b shows a comparison of the WPE of LEDs for Structures A, B, and C. The WPE of the LEDs is in the following order: Structure B > Structure A > Structure C. The WPE is inversely proportional to the forward voltage, so the LED for Structure C had the lowest WPE due to the highest forward voltage.

Conclusions
AlGaN-based DUV LEDs with AlGaN as the dielectric layers in Al0.55Ga0.45N/AlGaN/n + -Al0.55Ga0.45N PTJs were proposed for promoting carrier tunn suppressing current crowding, avoiding optical absorption, and further enhancin performance of LEDs. Al0.7Ga0.3N with a lower dielectric constant can realize a highe concentration and a higher radiative recombination rate in MQWs than Al0.4Ga0.6N higher dielectric constant. The high hole concentration and high radiative recombin rate in MQWs come from enhanced lateral current spreading in the LED. Mor besides the high electrically conductive n + -Al0.55Ga0.45N layer in the PTJ, Al0.7Ga0.3N dielectric layer has relatively high resistance, which can increase the lateral c spreading and enhance the uniformity of the top emitting light of AlGaN-based LEDs. As a result, the IQE and optical output power can be enhanced. Howev relatively high resistance results in an increase in the forward voltage, wh disadvantageous to the WPE. Through the adoption of PTJ with Al0.7Ga0.3N a dielectric layers, enhanced IQE and optical output power can be achieved. It is str believed that the proposed structure is promising for further improving the IQEs of LEDs, and the physics of the reported device is also useful for better understandin carrier tunnel, transport and recombination mechanisms of DUV LEDs.

Conclusions
AlGaN-based DUV LEDs with AlGaN as the dielectric layers in p + -Al 0.55 Ga 0.45 N/AlGaN/ n + -Al 0.55 Ga 0.45 N PTJs were proposed for promoting carrier tunneling, suppressing current crowding, avoiding optical absorption, and further enhancing the performance of LEDs. Al 0.7 Ga 0.3 N with a lower dielectric constant can realize a higher hole concentration and a higher radiative recombination rate in MQWs than Al 0.4 Ga 0.6 N with a higher dielectric constant. The high hole concentration and high radiative recombination rate in MQWs come from enhanced lateral current spreading in the LED. Moreover, besides the high electrically conductive n + -Al 0.55 Ga 0.45 N layer in the PTJ, Al 0.7 Ga 0.3 N as the dielectric layer has relatively high resistance, which can increase the lateral current spreading and enhance the uniformity of the top emitting light of AlGaN-based DUV LEDs. As a result, the IQE and optical output power can be enhanced. However, its relatively high resistance results in an increase in the forward voltage, which is disadvantageous to the WPE. Through the adoption of PTJ with Al 0.7 Ga 0.3 N as the dielectric layers, enhanced IQE and optical output power can be achieved. It is strongly believed that the proposed structure is promising for further improving the IQEs of DUV LEDs, and the physics of the reported device is also useful for better understanding the carrier tunnel, transport and recombination mechanisms of DUV LEDs.