Polarization Modulation at Last Quantum Barrier for High Efﬁciency AlGaN-Based UV LED

—The performance of AlGaN-based light-emitting diodes (LEDs) emitting at UVA–UVC regions can be severely compromised due to the polarization difference ( Δ P) between the last quantum barrier (LQB) and the electron blocking layer (EBL). In this work, the different situations of the bandgap difference ( Δ E g ) and Δ P of InAlN/AlGaN and AlGaN/AlGaN heterojunctions fully strainedonGaNandAlNsubstratesarediscussed.ItshowsthattheInAlN/AlGaNheterojunctionscouldproducepositiveornegative sheetchargesattheheterointerfaceunder Δ E g > 0, which could not be realized by the conventional AlGaN/AlGaN heterojunctions. To demonstrate and utilize the feature, the polarization-modulated InAlN LQBs with 0.14–0.16 indium compositions of 320 nm UVB LEDs are designed and investigated. It is observed that the InAlN LQBs could replace the conventional AlGaN LQB to improve elec- tron conﬁnement and hole injection by affecting effective barrier heights. By modulating the LQB/EBL polarization using InAlN, the proposed UV LED has a 32% enhancement in internal quantum efﬁciency and lower efﬁciency droop (from 16.9% to 0.7%) compared with the conventional one without modulation. The operation voltage at the same current also signiﬁcantly decreases. The improvement of optical output power and wall plug efﬁciency at 60 mA in proposed structures are near 90% and 100%, respectively. This study provides a novel and highly effective methodology for development of high efﬁciency UV LEDs.

Besides, the unique polarization characteristics of the IIInitrides could compromise UV LED performance. On one hand, the polarization-induced quantum-confined Stark effect (QCSE) in multiple quantum wells (MQWs) brings about wavelength redshift and reduces electron-hole wavefunction overlap [8], [9]. To address this issue, researchers have utilized various approaches, including nonpolar and semi-polar orientations [10]; and introduced Si doping in quantum barriers (QBs) to screen the internal polarization induced by the electric field [11]; and polarization-matched and lattice-matched MQWs have been designed [12], [13]. Besides, Shervin et al. modified the piezoelectric polarization and significantly improved the LED efficiency by external bending [14].
On the other hand, the positive polarization charge could exist at the interface between the last quantum barrier (LQB) and the wider-bandgap electron blocking layer (EBL), hereafter the 'LQB/EBL polarization', because of the negative heterointerface polarization difference (ΔP) [15]. The positive charge can bend the LQB bands, resulting in a lower effective electron barrier and higher effective hole barrier. Therefore, the electron blocking and hole injection could be seriously compromised, ultimately contributing to poorer optical power and efficiency [16].
To mitigate the issue, two methods have been proposed. One is to adopt a more complex LQB or EBL structure to mitigate the LQB band bending. Qian et al. proposed the superlattice LQB and Zhang et al. designed the composition graded EBL [17], [18]. The other is to design different heterojunctions utilizing polarization engineering. For instance, lattice-matched InAlN and polarization-matched AlInGaN were used as EBLs in InGaN-based visible LEDs [19], [20]. However, the improvement by the lattice-matched InAlN EBL (i.e., without piezoelectric polarization) is limited because the positive charges still exist at the LQB/EBL interface due to the spontaneous polarization difference; and it is challenging to control the composition precisely for the polarization-matched EBL. Besides, Ji and Lin et al. showed that the polarization-reversed AlInGaN EBL with the negative polarization charges at the LQB/EBL interface could enhance the effective electron barrier. But it still needs to overcome the complex growth technique for the quaternary alloy [21], [22]. For UV LEDs, however, the polarization-matched or -reversed structures addressing the LQB/EBL polarization are rarely reported [23]. Besides, the N-polar and p-down design DUV LEDs were demonstrated to have better electron blocking due to the enhanced electron barrier in the EBL [24], [25].
In relationships between the bandgap difference (ΔE g ) and the polarization difference (ΔP) of InAlN/AlGaN heterojunctions are revealed, which is hopefully applied in various devices. To further demonstrate it, the InAlN alloys are proposed as the LQBs to modulate the LQB/EBL polarization for UV LEDs. As a result, the effective electron and hole barrier are enlarged and decreased, respectively, promoting electron confinement and hole injection.

II. POLARIZATION ENGINEERING OF INALN/ALGAN HETEROJUNCTIONS
To realize enhanced electron blocking and hole injection, the ΔE g and the ΔP of the LQB/EBL heterojunctions need to be considered simultaneously. For instance, one could modulate the LQB/EBL polarization through changing the composition of the two layers; however, this should be conducted under the condition that the EBL bandgap is wider than the LQB (for the type I heterojunction) to block electrons effectively. Moreover, if we design polarization-matched MQWs by employing different materials as QBs, it is essential that the bandgap of QBs are larger than QWs. Consequently, the InAlN/AlGaN heterojunction is a hopeful candidate because InAlN possesses a large range of bandgap and different polarization from AlGaN. In this section, we have systematically studied the bandgap and polarization properties of the InAlN/AlGaN heterojunctions and make comparison with the conventional AlGaN/AlGaN heterojunctions.
The investigated structures are shown in Fig. 1(a)-(d). In Fig. 1(a) and (b), Al y Ga 1-y N (layer 1) is firstly deposited on GaN or AlN substrates followed by another Al x Ga 1-x N layer (layer 2). Both layers are fully strained on the substrates. The In y Al 1-y N/Al x Ga 1-x N heterojunctions are used for comparison in Fig. 1(c) and (d). In general, the n-type AlGaN layer of UV LEDs is thick enough (about few micrometers) such that the active region and the EBL grown on it could be partially or fully strained on the n-AlGaN layer. That means they have a similar lattice constant as that of the n-AlGaN layer, which would be used to calculate the piezoelectric polarization. Besides, the Al composition of the n-AlGaN layer varies according to the operation wavelength of the UV LED, which could be within 5% for the UVA LED, about 30% for UVB LED, and more than 50% for the UVC LED. Hence in this study, GaN and AlN substrates corresponding to the largest and smallest lattice constant in the AlGaN material system are chosen as two extreme cases to calculate the piezoelectric polarization and total polarization. It could reveal the general properties and trends of In y Al 1-y N/Al x Ga 1-x N heterojunctions on n-AlGaN substrates instead of focusing on one specific operation wavelength. For the specific n-AlGaN substrate, one could modify the corresponding lattice constant to calculate the polarization.
The spontaneous and piezoelectric polarization (P sp and P pz ) parameters as well as the in-plane lattice constants (a) of AlGaN and InAlN are obtained from [26] shown in Table I. The e 31 and e 33 are the piezoelectric constants and the C 13 and C 33 are the elastic constants of the epitaxial layers. The total polarization P total is defined as the sum of the spontaneous and piezoelectric polarization, which could be calculated using (1). Based on the total polarization of layers 1 and 2, the ΔP is defined in (2). The positive ΔP corresponds to negative sheet interface charges and the negative ΔP corresponds to positive polarization charges. The bandgap bowing parameter (b) of the In y Al 1-y N alloys (0≤y≤1) is extracted from the studies by Schultz et al. [27] shown in the (3); and the bandgaps of AlN, GaN, and InN are also from [27]. The bowing parameter of the AlGaN bandgap is from [28].The heterojunction ΔE g is defined in (4). According to the sign of the ΔP and the ΔE g in Eqs. (2) and (4), there are nine types of situations shown in Table II with the labels from A to I.   Fig. 3(a) to (e). For Types C and G, the In y Al 1-y N/Al x Ga 1-x N are similar to Al y Ga 1-y N/Al x Ga 1-x N.
In particular, Type D means no polarization sheet charges but with band discontinuity at the heterointerface, which is on the dash line with ΔP = 0 in the situation diagram. It could be used to design polarization-matched structures such as MQWs to eliminate the QCSE. The two layers of Type B have the same bandgap, but with polarization sheet charges at the heterointerface, which is expected to be used in some specially designed structures. For Type A (shaded region in Fig. 2), the Al x Ga 1-x N layer has a wider bandgap compared with the In y Al 1-y N layer and the sheet charges at the heterointerface are negative, which is the polarization-reversed structure mentioned above and could be applied to the LQB/EBL heterojunction. In this study, we utilize this unique property to design InAlN LQBs to replace the conventional AlGaN LQB to modulate the LQB/EBL polarization in the 320 nm UVB LED as a special case. Additionally, it is observed that the Type A situation covers all Al content of the AlGaN layer. Thus, this method could be easily extended to LEDs and LDs in other UV regions.

III. LED STRUCTURE AND PARAMETERS
The cross-sectional schematic structure of the 320 nm UVB LEDs, including the conventional AlGaN LQB and proposed InAlN LQBs used in the simulation are shown in Fig. 4. For the conventional structure (Device 1), a 3 µm n-type Al 0.3 Ga 0.7 N layer doped with Si of 5×10 18 /cm 3 is grown on the AlN template. It is followed by six pairs of AlGaN/AlGaN MQWs comprising 12 nm Al 0.3 Ga 0.7 N QBs and 3 nm Al 0.2 Ga 0.8 N QWs. 5×10 17 /cm 3 silicon doping in QBs except the LQB is included to screen the QCSE [29]. The LQB is not doped in that it could reduce the effective electron barrier and increase the electron leakage [30]. Above the LQB is the 20 nm p-type Al 0.5 Ga 0.5 N layer EBL and the 100 nm p-type Al 0.3 Ga 0.7 N hole injection layer. The Mg doping concentrations are 5×10 18 /cm 3 and 3×10 19 /cm 3 , respectively. Finally, a 50 nm p-type GaN contact layer with the Mg doping concentration of 1×10 20 /cm 3 caps the structure. The mesa size of the devices in the simulation is 300 µm × 300 µm. For the proposed structures, they are the same as Device 1 except for the use of In 0.16 Al 0.84 N (Device 2), In 0.15 Al 0.85 N (Device 3), and In 0.14 Al 0.86 N (Device 4) as the LQB to examine and modulate the LQB/EBL ΔP for various electron blocking and hole injection capabilities.
The APSYS software by Crosslight is employed in this study to self-consistently solve various physical equations including drift-diffusion equations, Schrodinger and Poisson's equations, current continuity equations, etc. with proper boundary conditions [31].
The AlGaN band offset ratio is set to be 0.65/0.35 [32]. The electron affinity of the InAlN alloys is from [27]. The Shockley-Read-Hall (SRH) recombination lifetime and the Auger recombination coefficient are 50 ns and 1.0×10 -30 /cm 3 [33]. A 0.6 polarization screening factor is set because the interface charge density obtained from the experiment is usually smaller than the theoretical value due to the screening of defects and injected carriers [34], [35]. The operating temperature and background loss are separately estimated to be 300 K [36] and 2000 m -1 [37]. The activation energy of GaN and AlGaN are set to be 170 and 270 meV [38], [39]. Besides, we assume that the 3 µm n-Al 0.3 Ga 0.7 N layer is fully relaxed on the AlN template and other layers are fully strained on the n-layer. The LQB/EBL ΔP without the effect of the polarization screening factor and the bandgaps of Devices 1 to 4 are shown in Table III. Although from   TABLE III  THE LQB/EBL ΔP WITHOUT THE EFFECT OF THE POLARIZATION SCREENING  FACTOR

IV. RESULT AND DISCUSSION
The band diagrams of Devices 1 and 2 are plotted in Fig. 5(a) and (b). Fig. 5(a) shows that due to the negative LQB/EBL ΔP (−0.0207 C/m 2 ), the positive sheet charges accumulate at the heterointerface. The conduction and valence bands of the LQB near the EBL of Device 1 bend down and up significantly, resulting in 290.2 and 357.1 meV effective barrier heights for electrons and holes, respectively. The limited effective electron barrier indicates that electrons could move over the barrier leading to considerable electron overflow; and the large effective hole barrier could pose major challenges for holes to inject into the active region. For Device 2 in Fig. 5(b), the In 0.16 Al 0.84 N/Al 0.5 Ga 0.5 N ΔP is positive and lower (0.0061 C/m 2 ) compared with Device 1 and only a small amount of negative polarization charges localize at the heterointerface. Thus, the band bending direction To reveal the electron and hole distribution of Device 1 and Device 2, we calculate the carrier concentration across the active region shown in Fig. 6(a) and (b). It indicates that an electron peak is observed in the LQB of Device 1, which is consistent with the electrostatic field profile and band bending effects at the LQB/EBL interface. For Device 2, it is observed that a hole peak exists in the LQB due to the downward bending; and the electron concentration in the last quantum well (LQW) is quite high because of the downward bending of the conduction band as a result of the larger LQW/LQB ΔP. Although Device 2 has the higher barrier for electrons and the lower barrier for holes thanks to the polarization modulation, the carrier concentration in the first five QWs is similar with Device 1 because of the accumulation of electrons and holes in the LQW and the LQB, respectively. As mentioned above, the bands are flat enough in the LQB of Device 2 thus the energy variety is diminutive. Therefore, the high-level electron concentration in the LQW could be extended to the LQB to a certain extent. Similar concentration extension could be also observed for holes. The overlapping of electrons and holes could generate the extra recombination in the LQB and could be proven by the radiative recombination distribution shown later.
The situations are different for Devices 3 and 4 as Fig. 7 and Fig. 8 show. It is observed there are still an electron and a hole peak in the LQW and the LQB respectively. But owing to the bigger positive LQB/EBL ΔP (0.0090 and 0.0119 C/m 2 ) as well as the larger LQW/LQB ΔP compared with Device 2, the conduction and valence band in the LQB sharply bends upward and downward, respectively, causing the quicker energy change in the LQB and less carrier concentration between the electron and hole concentration peaks. Therefore, there would be less or no recombination in the In 0.15 Al 0.85 N and In 0.14 Al 0.86 N LQBs. The carrier concentration in MQWs of Devices 3 and 4 also improves. The electron barrier heights for Device 3 (568.7 meV) and Device 4 (547.0 meV) are lower than that of Device 2 (575 meV), but the hole barrier (244.4 and 214.0 meV) in EBL is lower. Besides, as shown in Fig. 7 and Table IV,     the width of the LQB is narrower than the EBL. And numerically, they are still competitive compared with the hole barrier height in Device 1.
The radiative recombination rate in the fifth QW, sixth QW (LQW), and LQB of Devices 1 to 4 are shown in Fig. 9(a). The radiative recombination rate in the previous four QWs are similar with the fifth one thus not shown in the figure. In the first five QWs, Device 1 has the lowest radiative recombination rates and the average is about 1.9×10 26 cm -3 /s. Inversely, the average rate of Device 4 is the highest (3.9×10 26 cm -3 /s) because of more carriers in MQWs, which are over two times than those of Device 1. As for Devices 2 and 3, the high-level carrier concentration in the LQW and the LQB only produce little recombination because the distance between the peaks of electron and hole is about 12 nm (the QB width) and only a part of carriers between the two peaks can generate recombination effectively. It also causes a worse average radiative recombination rate in the first five QWs (2.0×10 26 and 3.7×10 26 cm -3 /s) compared to Device 4. Thus, although the radiative recombination in the LQB of Device 2 is a part of improvement origin relative to Device 1, Devices 3 and 4 distribute more carriers to MQWs instead of accumulating in the LQB. And this improves the overall radiative recombination intensity and efficiency compared with Device 2. It is noted that the recombination rates in the LQW of the proposed structures are suppressed due to the low hole concentration. However, the overall performance of the proposed structures is better compared with the conventional one, which could be proven by the total spontaneous emission rate shown in Fig. 9(b). Besides, no obvious wavelength shift is observed in the proposed devices. These results are consistent with our analysis on the band diagram and carrier concentration above. We believe that In 0.15 Al 0.85 N and In 0.14 Al 0.86 N LQB LEDs could have better performance due to the better electron blocking and hole injection and less carrier accumulation and recombination in the LQB. Fig. 10 (a) shows the I-V characteristic of four different structures. It indicates that better electron confinement and hole injection contribute to lower operation voltage at the same current in proposed structures, which means lower power consumption in LED. It is worth noting that in comparison with Device 2, the operation voltage is larger in Devices 3 and 4 because of the lower effective electron barrier in EBLs and higher hole injection barrier in LQBs.
At last, we calculate the internal quantum efficiency (IQE), efficiency droop, optical output power, and wall plug efficiency (WPE) of Devices 1-4 shown in Fig. 10(b) and Table V, respectively.
The proposed structures have a higher IQE and less efficiency droop compared with the conventional one. Device 4 shows the best performance among all the structures owing to better carrier transportation and more effective recombination in MQWs. Its   [40]. Moreover, the InAlN alloys could be applied to UV LEDs with lower indium compositions and thus larger bandgap [41]. On the other hand, it is not straightforward to grow high quality InAlN because of phase separation and composition inhomogeneity [42], [43]. Nevertheless, high quality InAlN LEDs and power devices with lower indium compositions have been achieved. Anna et al. reported the In 0.14 Al 0.86 N /AlN/GaN high electron mobility transistor (HEMT) [44] and Pietro et al. fabricated the UVA LED with In 0.14 Al 0.86 N polarization matched quantum well [45]. Thus, we believe our design could effectively improve the polarization issue in AlGaN-based UV LED without introducing complex structures and growth techniques.

V. CONCLUSION
Polarization modulation and band engineering are powerful methods for achieving high efficiency III-nitride devices. In this work, the different situations of the InAlN/AlGaN heterojunction ΔP-ΔE g fully strained on AlN and GaN substrates are investigated. The InAlN/AlGaN heterojunctions exhibit three unique ΔP-ΔE g situations: ΔP>0, ΔE g >0 (A); ΔP>0, ΔE g = 0 (B); and ΔP = 0, ΔE g >0 (D), which could not be realized by the common AlGaN/AlGaN heterojunctions. This special property is expected to apply to the design of distinctive devices such as LED and LD. As a specific example of Type A, the InAlN last quantum barrier with 0.14-0.16 indium composition substituting for the conventional AlGaN LQB in the 320 nm UVB LED have been numerically studied. The simulation results indicate that by the polarization modulation, the effective electron barrier is enlarged drastically from 290.2 to more than 547.0 meV and the effective hole barrier is also significantly decreased. Thus, the proposed structures have better optical performance attributed to the improvement of electron confinement and hole injection. By properly decreasing indium composition from 0.16, much higher IQE and WPE could be achieved. The method could be extended to other UV regions through appropriately choosing the composition of the InAlN LQB and AlGaN EBL based on the ΔP-ΔE g diagram. This theoretical work provides a new horizon and perspective for development of high efficiency UV LEDs.