The drift velocity for holes is strongly influenced by the electric field in the p-type hole injection layer for III-nitride based deep ultraviolet light-emitting diodes (DUV LEDs). In this work, we propose an electric-field reservoir (EFR) consisting of a p-AlxGa1-xN/p-GaN architecture to facilitate the hole injection and improve the internal quantum efficiency (IQE). The p-AlxGa1-xN layer in the EFR can well reserve the electric field that can moderately adjust the drift velocity and the kinetic energy for holes. As a result, we are able to enhance the thermionic emission for holes to cross over the p-EBL with a high Al composition provided that the composition in the p-AlxGa1-xN layer is properly optimized to avoid a complete hole depletion therein.
© 2017 Optical Society of America
III-nitride compound semiconductor can theoretically cover a large color regime from deep ultraviolet to infrared emission . Thus far, tremendous maturity has been reached especially for III-nitride based blue LEDs which have been widely applied to indoor/outdoor lighting, head-lighting for automobiles, etc [2, 3]. However, besides visible lighting, the interest of our globe also includes the deep ultraviolet (DUV) light source that can be used in water sterilization, air purification, skin curing, cancer cell elimination, etc . Therefore, III-nitride based DUV LEDs have been proposed and developed. Compared to the bulky mercury based DUV light lamps, portable DUV LEDs feature no pollution to the environment, a low DC drive voltage, a good compatibility with driving circuits, a long lifetime, etc .
Nevertheless, the internal quantum efficiency (IQE) for DUV LEDs is low at the current stage. On one hand, because of the huge lattice mismatch and the significant difference in the thermal expansion coefficient between the epi-layer and the sapphire substrate , growing high-quality Al-rich AlGaN compound material is still rather challenging at the moment. On the other hand, the low IQE also partly originates from a low hole injection efficiency which arises from the even lower Mg doping efficiency for the Al-rich AlGaN layer . It is advisable to enhance the hole concentration in the Al-rich AlGaN layer by adopting the polarization induced three-dimensional hole gas (3DHG), which is realized by gradually varying the Al composition in the AlGaN layer along the polar growth orientation [7–10]. Alternatively, superlattice structure has been adopted by DUV LEDs to further increase the hole injection capability, e.g., inserting AlGaN/AlGaN superlattice layer before growing the p-AlGaN electron blocking layer (p-EBL)  or employing the AlGaN/AlGaN superlattice p-EBL [12, 13]. The superlattice architecture enables the p-EBL to possess a reduced valence band barrier height which in turn further facilitates the hole transport. Another proposal to enhance the hole injection is to energize holes by increasing the drift velocity for holes, and by doing so, the energy difference () between the kinetic energy for holes () and the valence band barrier height in the p-EBL () can be minimized, which promotes the thermionic emission of holes to cross over the p-EBL. The kinetic energy for holes can be increased when the hole mobility is improved by reducing the Mg doping concentration . However, considering the low Mg doping efficiency in p-type III-nitride layers, there is hardly any free space to further decrease the hole concentration. Fortunately, Zhang and associates have proposed increasing the drift velocity for holes by taking the advantage of the polarization induced electric field within a hole accelerator [15, 16].
In this work, we propose an electric-field reservoir (EFR) to increase the drift velocity of the holes for DUV LEDs. The EFR structure is depicted in Fig. 1(a), which comprises a p-AlxGa1-xN/p-GaN heterojunction. The p-AlxGa1-xN/p-GaN heterojunction is along the  orientation and therefore negative polarization induced interface charges are generated at the interface, which can then attract holes. It is also very import to keep the hole concentration for the p-AlxGa1-xN layer not lower than that for the p-GaN layer. Then, the p-AlxGa1-xN/p-GaN heterojunction can feature a hole accumulation at the p-GaN part and a slight hole depletion at the p-AlxGa1-xN part [see Fig. 1(a)]. The existence of the interface depletion region at the p-AlxGa1-xN part will simultaneously yield a local electric field as shown in Fig. 1(b), and the direction of the electric field opposes to the  orientation which can well increase the kinetic energy for the incoming nonequilibrium holes. Unlike the case in which the entire hole injection region is p-GaN layer, the advantage of the p-AlxGa1-xN/p-GaN heterojunction is that the electric field at the interface will not be screened by the free carriers, and thus the p-AlxGa1-xN/p-GaN heterojunction is called an “electric-field reservoir (EFR)”. If we assume that the holes in the hole supplier follow the Fermi-Dirac [F(E)] distribution and P(E) means the valence band density of states in the hole supplier, then the probability of finding the holes in the last quantum barrier can be expressed by . The concentration (p) for those holes that travel across the p-EBL can be formulated by , where P represents the nonequilibrium hole concentration in the hole supplier . As a result, p can be affected by both P and Ph.
2. Device architectures and physical parameters
To investigate the effectiveness of the EFR on the IQE for DUV LEDs, we design the device structures as shown in Figs. 2(a) and 2(b), respectively. Both device structures employ the AlN/Al0.55Ga0.45N superlattices (SLs) as the growth template, and then we use 2 µm thick n-Al0.55Ga0.45N layer with the Si doping concentration of 4 × 1018 cm−3 as the electron supplier. After that, 5-pair 2.3 nm-Al0.37Ga0.63N/10 nm-Al0.50Ga0.50N multiple quantum wells (MQWs) are included for the DUV emission centered at ~290 nm. Here, in order to suppress the electron escape from the MQW region, we purposely thicken the last quantum barrier to 20 nm . Both devices use Al-rich Mg doped AlyGa1-yN as the p-EBL with the thickness of 10 nm to further avoid the electron leakage. However, the device in Fig. 2(a) directly adopts a 230 nm thick p-GaN layer as the hole supplier while the device in Fig. 2(b) has a 50 nm thick p-AlxGa1-xN insertion layer before growing the rest 170 nm thick p-GaN layer to form the EFR. The effective hole concentration for all the p-type layers here is set to 3 × 1017 cm−3. Detailed values for the AlN composition in the p-EBL and the p-AlxGa1-xN insertion layer can be found in Table 1. The chip size is set to 350 × 350 µm2.
We conduct numerical calculations and comparatively study the devices by using APSYS [7, 15, 16], which can well manage Poisson’s equation, Schrödinger equation, current continuity equation, and drift-diffusion equation. Specifically, the carrier transport across the MQW region is modeled by the mean-free-path model which has been discussed in our previously published works [18, 19]. We set Shockley-Read-Hall (SRH) recombination lifetime and Auger recombination coefficient to 10 ns, 1 × 10−30 cm6/s accounting for the nonradiative recombination in MQWs , respectively. The energy band offset ratios between the conduction band offset and the valence band offset for the AlGaN/AlGaN and the GaN/AlGaN heterojunctions are both set to 50:50 . It is worth noting that DUV LEDs yield very strong polarized photons . However, the calculated light source by APSYS includes both TM and TE polarized DUV photons, and therefore we empirically set the light extraction to 9% to calculate the optical power density for DUV LEDs without any surface treatment [20, 23]. Since our devices are along the  orientation, thus the polarization effect at all the lattice-mismatch junctions are reflected by setting polarization induced charges , and we set 40% as the polarization level such that 60% of the theoretical polarization induced charges are released by generating dislocations . We also consider the self-absorption to the DUV photons by the absorptive material with a lower energy band gap, such that we set the absorption coefficient of the p-GaN to 1.45 × 107 m−1 while we neglect the DUV absorption by the p-AlGaN layer with high AlN compositions [26, 27]. Meanwhile, when modeling the impact of the EFR structure on the drift velocity for holes, we set a constant hole mobility of ~5 cm2/V-s for all the p-type layers, since neglecting the field dependence of hole mobility will not influence the conclusions for this work .
3. Results and discussions
We firstly calculate the electric field profiles in the EFR regions for all the devices, which are shown in Fig. 3. Clearly we can see that the electric field intensity in the EFR regions for the Original device is the smallest among the investigated devices, and thus the holes are not able to obtain sufficient kinetic energy, which turns out to be less effective in promoting the hole injection across the p-EBL. However, the electric field intensity within the EFR regions for the Reference device and Device 1 (D1) is stronger than that for the others. The stronger electric field in the EFR regions is well attributed to the p-Al0.49Ga0.51N layer, in which a higher AlN composition causes a larger effective valence barrier height Фh of 583.00 meV and 460.00meV [see Table 2], respectively. The higher value of Фh hinders the hole injection into the p-Al0.49Ga0.51N layer, thus leading to the hole depletion in the p-Al0.49Ga0.51N layer and suppressing field screening effect by the free holes. Furthermore, the Reference device shows the even stronger electric field magnitude in the EFR region than Device 1 (D1), and this is further caused by the higher AlN composition in the p-EBL that increases the polarization induced charges at the p-EBL/p-Al0.49Ga0.51N interface and enhances the electric field intensity. In addition, we can obtain that the values of Фh are reduced to 322.00 meV and 238.00 meV [see Table 2] for Device 2 (D2) and Device 3 (D3), respectively, while a reduced Фh can have more holes injected into the p-Al0.40Ga0.60N and p-Al0.30Ga0.70N layers, respectively. As a result, in the range between ~0.200 µm and ~0.225 µm in Fig. 3, the electric field in the EFR regions for Device 2 (D2) and Device 3 (D3) are partially screened by the free holes and only the p-AlxGa1-xN/p-GaN interface retains the depletion mode and therefore the stronger electric field at the interface, which have also been schematically discussed and shown in Fig. 1 previously.
To precisely prove the impact of the electric field in the EFRs on the kinetic energy for holes, we further calculate the net work (W) done to holes by using , in which Efield stands for the electric field in Fig. 3. The integration step (dx) has been properly adjusted through optimizing the mesh distribution in the simulated devices. The calculated values for W have been summarized in Table 2 which illustrates that, in general, the EFR structure can significantly increase the hole energy when compared to the Original device without the EFR structure. Nevertheless, the influence of different values of W on the hole injection and the IQE will be discussed subsequently.
Besides showing the electric field profiles, it is also necessary to demonstrate the energy band alignment for the discussed devices. The energy band alignment in the p-type layers for the Original device, the Reference device, Device 1(D1) and Device 3 (D3) are presented in Fig. 4. Note, the energy band alignment of the p-type layers for Device 3 is similar to that for Device 2, and therefore it is not show here. The energy band alignment in Fig. 4 agrees very well with the electric field profile in Fig. 3. The energy band for the p-GaN layer for the Original device is flat meaning that the holes are not able to be accelerated. The energy band of the p-AlxGa1-xN layer for the Reference device and Device 1 is aligned in the way favoring the increase of the hole kinetic energy. However, compared to that for the Original device, the quasi-Fermi level for holes in the p-AlxGa1-xN layer for the Reference device and Device 1is much smaller than the valence band edge of the p-AlxGa1-xN layer, which denotes a lower hole concentration, i.e, hole depletion in the p-AlxGa1-xN layer. Interestingly, as is shown in Fig. 4(d), the holes in the p-AlxGa1-xN layer for Device 2 is depleted in the range between ~0.225 µm and ~0.242 µm within which a stronger electric field is generated [also see Fig. 3].
Till now, we have realized that the hole concentration in the MQW region and IQE are simultaneously determined by the hole concentration and the electric field intensity in the EFR region, i.e, as has been mentioned previously. We then investigate how the device performance is subject to different EFR designs.
Figure 5(a) depicts the optical power density and the IQE in terms of the injection current density for the Original device and the Reference device. We can see that the Reference device can improve the IQE for DUV LEDs, and the enhanced IQE is further supported by Fig. 5(b) which illustrates a higher hole concentration in the MQW region for the Reference device. In the meanwhile, Fig. 5(b) also shows that the hole concentration in the p-Al0.49Ga0.51N layer is significantly reduced, thus representing the hole depletion in the whole p-Al0.49Ga0.51N layer. Fortunately, the better hole injection efficiency for the Reference device can still be obtained if the p-Al0.49Ga0.51N/p-GaN EFR substantially increases the kinetic energy for holes according to Table 2. The comparison between the Original device and the Reference device conceptually reveals that the hole blocking effect by the p-EBL can be remarkably suppressed by adopting the EFR structure though it is not fully optimized yet. Note, the discussions for the current-voltage characteristics of the Original device and the Reference device will be conducted in the supplementary material.
Figure 6 compares the Reference device and Device 1 (D1), which differ only in the AlN composition for the p-EBL as has been illustrated in Table 1. Figure 6(a) presents the optical power density and the IQE in terms of the injection current density, from which we can conclude that the reduced AlN composition in the p-EBL does not contribute to improve the IQE for Device 1 (D1). Not that a reduced AlN composition in the p-EBL reduces the polarization induced electric field intensity in the p-Al0.49Ga0.51N layer, and compared to the EFR of the Reference device, the EFR of Device 1 (D1) therefore supplies less energy for holes, which results in a worse hole injection across the p-EBL and the smaller hole concentration in the MQW region for Device 1 (D1) [see Fig. 6(b)]. Despite that the comparison between the Reference device and Device 1 (D1) further supports that the hole transport across the p-EBL can be enhanced if the holes can obtain more energy from the EFR, Fig. 6(a) however also demonstrates a very low hole concentration in the p-Al0.49Ga0.51N layer, which is not helpful to maximize the function of the EFR in significantly boosting the IQE for DUV LEDs. We also discuss the current-voltage characteristics for the Reference device and Device 1 (D1) in the supplementary material.
Lastly, we decrease the AlN composition in the p-AlxGa1-xN layer and probe the impact of the EFR on the hole injection. We fix the AlN composition of the p-EBL to 0.68 for the Reference device, Device 2 (D2) and Device 3 (D3). We calculate and present the optical output power density and the IQE at different injection current density levels in Fig. 7(a). We can see that the Reference device and Device 2 (D2) produce a higher IQE than Device 3 (D3) with the IQE for Device 2 (D2) being the strongest. To better interpret the obtained IQE characteristics, we demonstrate the vertical hole concentration profiles that are collected at the position of 100 µm from the left mesa edge [see Fig. 7(b)]. Interestingly, we can see that the hole concentration in the p-AlxGa1-xN layer for Device 2 (D2) and Device 3 (D3) is much higher than that for the Reference device thanks to the reduced valence band barrier for the p-AlxGa1-xN layer [here, x is equal to 0.40 and 0.30 for Device 2 (D2) and Device 3 (D3), respectively]. As a result, it is more fair to compare the hole concentration in Fig. 7(b) within the MQWs for Device 2 (D2) and Device 3 (D3). If we recall the kinetic energy for holes, we can get that the holes receive an even higher energy from the EFR for Device 2 (D2) (see Table 2), and this in turns enables a higher hole concentration in the MQW region for Device 2 (D2) than that for Device 3 (D3), which correspondingly contributes to the improved IQE. Note that in our physical models we have assumed the same optical absorption of the p-Al0.40Ga0.60N and the p-Al0.30Ga0.70N layers for Device 2 (D2) and Device 3 (D3), respectively, and hence the lower IQE given by Device 3 (D3) cannot be blamed to the self-absorption by the p-Al0.30Ga0.70N layer. Moreover, the higher hole concentration in the p-Al0.40Ga0.60N layer and the p-Al0.30Ga0.70N layer for Device 2 (D2) and Device 3 (D3) improves the electrical conductivity for the p-AlxGa1-xN layer which then enhances the current spreading effect. Thus more holes prefer to travel to the right side of the device and are then injected into the MQW region [see Fig. 7(c)] [29, 30]. Moreover, according to Fig. 7(c), the overall hole concentration in the MQW region for Device 2 (D2) is the highest among the three devices (here, we only show the lateral hole concentration profiles in the quantum well closest to the p-EBL for the three devices, since the lateral hole concentration profiles in other quantum wells follow the same trend for the three devices), and this gives rise to the strongest IQE in Fig. 7(a). Note, the EFR for the Reference device generates much more energy for holes than that for Device 3 (D3), and this may lead to a smaller overall hole concentration in the MQW region [see Figs. 7(b) and 7(c)], thus resulting in an even lower IQE for Device 3 (D3) when compared to the Reference device. Moreover, the current-voltage characteristics for the Reference device, Device 2 (D2) and Device 3 (D3) are demonstrated and compared in the supplementary material.
To summarize, we have proposed and theoretically investigated the EFR structure for  oriented DUV LEDs in this work, which utilizes the interface depletion mode in the p-AlxGa1-xN region for a p-AlxGa1-xN/p-GaN heterojunction. Then the local electric field can be simultaneously produced in the depletion region. More importantly, such electric field cannot be screened by the free holes, and thus the holes can continuously gain the energy from the EFR. Because the hole concentration in the MQW region is the coupled effect of both the hole concentration and the electric field intensity in the p-AlxGa1-xN layer, plenty of attention has to be paid when designing the EFR structure, such that the AlN composition in the p-AlxGa1-xN layer has to be properly optimized so that both the hole concentration and the electric field intensity in the p-AlxGa1-xN layer is high. We strongly believe the proposed EFR structure is promising to facilitate the hole injection and can further promote the IQE for DUV LEDs. Hence the EFR structure is very useful and the developed EFR model provides additional physical understanding for the III-nitride DUV LEDs which also adopt the p-AlxGa1-xN/p-GaN design as the hole injection layer [10–13].
5 Supplementary material
We also study and compare the current-voltage (IV) characteristics numerically which are shown in Fig. 8. All the investigated devices are turned on at ~4 V though the Reference device and Device (D1) show the quick current increase at ~12 V and ~10 V, respectively. We believe that the extremely large voltage consumption for the Reference device and Device (D1) is well attributed to the fully depleted p-AlxGa1-xN layer within which the very strong electric field is generated (see Fig. 3), and as a result, according to Fig. 8(a), the Reference device requires the even higher forward voltage than the Original device. Moreover, the electric field intensity in the depleted p-AlxGa1-xN layer for the Reference device is also stronger than that for Device 1 (D1), and this leads to the even larger forward voltage for the Reference device [see Fig. 8(b)]. In the meanwhile, the electric field intensity within the p-AlxGa1-xN layer for Device 2 (D2) is larger than that for Device 3 (D3), which interprets the higher forward voltage for Device 2 (D2) in Fig. 8(c). Nevertheless, Device 2 (D2) has remarkably improved the IV characteristics when compared with the Reference device.
In the meanwhile, we also demonstrate the wall plug efficiency [wall plug efficiency (WPE) is defined as the ratio between the optical power density and the electrical power density] for the investigated DUV LEDs in Fig. 9. Clearly we can see that Device 2 (D2) shows the largest WPE due to the fact that the proposed EFR for Device 2 (D2) can increase the hole drift velocity and keep the high hole concentration in the p-AlxGa1-xN layer. However, we believe that an even higher WPE can be obtained if the forward voltage can further reduced by optimizing the device architecture in the future perspective.
The National Key Research and Development Program of China (Program No. 2016YFB0400800, Project No. 2016YFB0400801); National Natural Science Foundation of China (Project Nos. 51502074, 61604051); Natural Science Foundation of Tianjin City (Project No. 16JCYBJC16200, 16JCQNJC01000); Technology Foundation for Selected Overseas Chinese Scholar by Ministry of Human Resources and Social Security of the People's Republic of China (Project No. CG2016008001); Research Grant for Top Young Scientist of Excellence of Hebei Province (Project No. 210013).
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