In this work, we simply take advantage of the polarization effect to efficiently improve the hole injection from the p-type electron blocking layer (p-EBL) to the end of the active region for AlGaN based deep ultraviolet light emitting diodes (DUV LEDs). By properly increasing the AlN composition of AlGaN quantum barriers, a smaller positive polarized charge density at the last quantum barrier/p-EBL interface can be obtained, which correspondingly leads to the suppressed hole depletion and the reduced hole blocking effect in the p-EBL. Meanwhile, we properly increase the quantum well thickness so that the polarized electric field can even more accelerate the holes, and this will homogenize the hole distribution more across the MQWs. Therefore, the external quantum efficiency for DUV LEDs can be enhanced.
I. INTRODUCTION
Featured with very small size, low-power consumption, DC driving, and environmental friendliness, AlGaN based deep-ultraviolet light-emitting diodes (DUV LEDs) can be widely used in medical therapy, air purification, water sterilization, and biological analysis, and traditional solid-state light sources are expected to be replaced by the year 2020, according to the Minamata Convention on Mercury.1–5 Therefore, AlGaN-based DUV LEDs have drawn significant attention. However, the external quantum efficiency (EQE) for AlGaN-based DUV LEDs is still lower than 10%, which severely restricts the further popularization and application of DUV LEDs.5–8 The low EQE partly originates from the poor internal quantum efficiency (IQE), which is strongly limited by the poor hole injection capability. The poor hole injection efficiency for DUV LEDs arises from the very big activation energy of Mg acceptors for Al-rich p-AlGaN layers, which, therefore, causes a low hole concentration. Simon et al. have pointed out that increasing the AlN composition linearly along the [0001] direction can improve the ionization rate of Mg acceptors by taking advantage of the polarization induced electric field.9 By using the strong polarization effect and the minbands, the p-AlxGa1−xN/p-AlyGa1−yN superlattice can also effectively enhance the ionization rate of Mg dopants.10,11 Reference 12 proposes tunnel junctions to increase the hole concentration. On the other hand, the poor hole injection is also partly caused by the blocking effect of the p-type electron blocking layer (p-EBL).13 There have been substantial efforts to design alternative p-EBLs for reducing the blocking effect and simultaneously reducing the electron leakage, e.g., the superlattice AlGaN p-EBL,14,15 the p-EBL with stair-cased AlN composition,16 the p-EBL with graded AlN composition,17 and the AlxGa1−xN/AlyGa1−yN/AlxGa1−xN (y < x) p-EBL.18 However, care should also be given to the positive polarization interface charges at the last quantum barrier (LQB)/p-EBL interface for [0001] oriented DUV LEDs, as shown in Fig. 1.19 These positive interface charges result in hole depletion at the interface of the LQB/p-EBL, giving rise to a low hole concentration in the p-EBL. The positive polarization charge density at the LQB/p-EBL interface can be reduced by lowering the polarization level between the LQB and the p-EBL, which is doable by increasing the AlN composition for AlGaN quantum barriers. Nevertheless, the increased AlN composition for AlGaN quantum barriers leads to increased valence band barrier height for MQWs, which will block the hole transport in the active region. On the other hand, according to the Fermi–Dirac distribution, the hole transport can be improved by increasing the hole energy.20 Then, we take advantage of the polarization induced electric field to accelerate holes, which promotes more efficient transportation of the holes in the MQWs, and this can be achieved by properly increasing the quantum well thickness. It is worth noting that the reported hole injection for this work is linked with hole energy rather than the barrier heights for the quantum barriers as has been reported by other groups.21,22
Schematic energy band diagram for investigated DUV LED structures which are grown along the [0001] orientation. Polarization induced positive charges are generated at the LQB/p-EBL interface.
Schematic energy band diagram for investigated DUV LED structures which are grown along the [0001] orientation. Polarization induced positive charges are generated at the LQB/p-EBL interface.
II. DEVICE STRUCTURES AND NUMERICAL PARAMETERS
The investigated DUV LEDs consist of a 4-μm-thick n-type Al0.60Ga0.40N layer as the electron supplier for which the Si doping concentration is 8 × 1018 cm−3. After that, five periods of Al0.45Ga0.55N (Lw nm)/AlyGa1−yN (y > 0.45, 10 nm) MQWs serve as the active region. We then cap the MQWs with a 10-nm-thick p-type Al0.60Ga0.40N EBL with a Mg doping concentration of 2 × 1017 cm−3 to suppress the electron escape from the MQW region. Next, a heterojunction consisting of a 50-nm-thick Al0.40Ga0.60N layer and a 50-nm-thick GaN layer is designed and used as the p-type hole supplier. The hole concentration for all the p-type layers here is set to 2 × 1017 cm−3, whose number is much lower than the Mg doping concentration, considering the very low ionization efficiency for Mg dopants. The mesa size is set to 350 × 350 µm2.
We utilize APSYS to investigate the underlying device physics for the DUV LEDs in this work. Important equations include Poisson’s equation, the Schrödinger equation, the current continuity equation, and the drift-diffusion equation. Specially, we adopt the very well-developed mean-free-path model when calculating the carrier transport in the active region for DUV LEDs.23,24 When calculating the polarization induced electric field, we shall take the polarization induced charges at the polarization-mismatched interfaces into consideration. The polarization level is set to 40%.18–20 The Shockley–Read–Hall (SRH) recombination lifetime is set to 10 ns, and the Auger recombination coefficient is 1.0 × 10−30 cm6/s in our model,18 which account for the nonradiative recombination processes. 50:50 is set as the energy band offset ratio between the conduction band offset and the valence band offset for the AlGaN/AlGaN and the GaN/AlGaN heterojunctions.18,25 The light extraction efficiency is set to 6% in this work when calculating the optical power density and the EQE.26
III. RESULTS AND DISCUSSIONS
A. Effect of AlN composition for AlyGa1−yN quantum barriers on hole injection
We change the AlN composition for AlyGa1−yN quantum barriers, ranging from 55% to 65%. The thicknesses of the quantum barriers and quantum wells are set to 10 nm and 3 nm, respectively. Figure 2(a) shows the external quantum efficiency (EQE), the optical power, and the peak emission wavelength in terms of the quantum barrier AlN composition for different DUV LEDs at a current density of 110 A/cm2. We can see from Fig. 2(a) that the EQE and the optical power density monotonically increase and then slightly decrease with the AlN composition for AlyGa1−yN quantum barrier increases. By observing the inset for Fig. 2(a), we can also get that the peak emission wavelength shows a slight blue shift once when more AlN is included in AlyGa1−yN quantum barriers. We then selectively choose three devices (i.e., devices A1, B1, and C1) with AlN compositions of 57%, 61% and 65%, respectively, for quantum barriers for insightful demonstrations. Figure 2(b) presents the EQE and the optical power for devices A1, B1, and C1 in terms of the injection current density. Besides the enhancement in the EQE, the efficiency droop for devices B1 and C1 has been tremendously reduced when compared with device A1. Note that the experimentally measured EQE and optical power for device A1 are also shown, which are consistent with the calculated results at different current densities, which confirms the effectiveness of our physical parameters and models.
(a) EQE and optical power in terms of the AlN composition for the AlyGa1−yN quantum barrier at a current density of 110 A/cm2. The inset shows the wavelength as the function of various AlN compositions for quantum barriers and (b) the numerically calculated EQE and optical power for devices A1, B1, and C1 in terms of current densities. The experimentally measured EQE and optical power for device A1 are also shown in (b).
(a) EQE and optical power in terms of the AlN composition for the AlyGa1−yN quantum barrier at a current density of 110 A/cm2. The inset shows the wavelength as the function of various AlN compositions for quantum barriers and (b) the numerically calculated EQE and optical power for devices A1, B1, and C1 in terms of current densities. The experimentally measured EQE and optical power for device A1 are also shown in (b).
To explain the above phenomenon, we then calculate the energy band diagrams for devices A1, B1, and C1 and show them in Figs. 3(a)–3(c). Note that because of the unique properties of Al-rich AlGaN quantum wells, we can see that the energy level for the crystal-field split-off hole (CH) band is lower than that for the heavy hole (HH) band,27 and hence, the conduction band to the CH (C–CH) transition dominates the optical emission for the devices in this work. For that reason, the hole injection is mainly affected by the CH band. The detailed values of the effective valence band barrier heights (Ψ) for the p-EBLs can be found in Table II. We find that the values of Ψ are 478.4 meV, 348.3 meV, and 259.4 meV for devices A1, B1, and C1, respectively. The hole blocking effect by the p-EBL decreases with the increase of the AlN composition for AlyGa1−yN quantum barriers. The reduced barrier height for the p-EBL is well attributed to the suppressed hole depletion effect and the enhanced hole concentration in the p-EBL [see Fig. 3(d)]. The observations here agree well with another report.20 The decreased hole depletion in the p-EBL arises from the decreased density of the positive polarization interface charges at the LQB/p-EBL interface. Further observations of Tables I and II also illustrate that the effective conduction band barrier heights (Φ1, Φ2, Φ3, and Φ4) and the effective valence band barrier heights for the CH band (ϕ1, ϕ2, ϕ3, and ϕ4) get increased when the AlN composition for the quantum barriers becomes high.
Energy band diagrams in the vicinity of the active region, the p-EBL, and the partial p-AlGaN layer for (a) device A1, (b) device B1, and (c) device C1 at an injection current density of 110 A/cm2 and (d) hole concentration profiles in the p-EBLs for the three DUV LEDs at an injection current density of 110 A/cm2. Note that the CH band and the HH band for devices B1 and C1 are shown.
Energy band diagrams in the vicinity of the active region, the p-EBL, and the partial p-AlGaN layer for (a) device A1, (b) device B1, and (c) device C1 at an injection current density of 110 A/cm2 and (d) hole concentration profiles in the p-EBLs for the three DUV LEDs at an injection current density of 110 A/cm2. Note that the CH band and the HH band for devices B1 and C1 are shown.
Values of Φi for the quantum barriers 2, 3, 4, and 5 at an injection current level of 110 A/cm2.
. | Φ1 (meV) . | Φ2 (meV) . | Φ3 (meV) . | Φ4 (meV) . |
---|---|---|---|---|
Device A1 | 228.9 | 230.5 | 229.9 | 221.7 |
Device B1 | 277.4 | 277.8 | 277.5 | 276.2 |
Device C1 | 356.7 | 356.5 | 355.2 | 354.5 |
. | Φ1 (meV) . | Φ2 (meV) . | Φ3 (meV) . | Φ4 (meV) . |
---|---|---|---|---|
Device A1 | 228.9 | 230.5 | 229.9 | 221.7 |
Device B1 | 277.4 | 277.8 | 277.5 | 276.2 |
Device C1 | 356.7 | 356.5 | 355.2 | 354.5 |
Values of ϕi for the quantum barriers 2, 3, 4, and 5; Ψ for the p-EBL at the injection current level of 110 A/cm2.
. | ϕ1 (meV) . | ϕ2 (meV) . | ϕ3 (meV) . | ϕ4 (meV) . | Ψ (meV) . |
---|---|---|---|---|---|
Device A1 | 256.6 | 255.5 | 254.9 | 255.2 | 478.4 |
Device B1 | 299.2 | 295.2 | 294.9 | 294.8 | 348.3 |
Device C1 | 372.1 | 367.4 | 366.6 | 365.4 | 259.4 |
. | ϕ1 (meV) . | ϕ2 (meV) . | ϕ3 (meV) . | ϕ4 (meV) . | Ψ (meV) . |
---|---|---|---|---|---|
Device A1 | 256.6 | 255.5 | 254.9 | 255.2 | 478.4 |
Device B1 | 299.2 | 295.2 | 294.9 | 294.8 | 348.3 |
Device C1 | 372.1 | 367.4 | 366.6 | 365.4 | 259.4 |
Then, we present the electron concentration profiles and hole concentration profiles in the MQWs for devices A1, B1, and C1. For better resolution, the carrier concentration profiles for devices B1 and C1 are artificially shifted by 2 nm and 4 nm, respectively, with reference to device A1. When compared with device A1, the increased electron concentrations for devices B1 and C1 shown in Fig. 4(a) are attributed to the increased conduction band barrier heights, as presented in Table I. Interestingly, Fig. 4(b) also shows the enhanced hole concentration in the MQWs despite the increased AlN composition for the quantum barriers, which is exactly attributed to the reduced hole blocking effect of the p-EBL.20 However, Fig. 4(b) also indicates that the hole concentration gets decreased as the quantum well is apart from the p-EBL for device C1 such that the hole injection across the MQW region needs further improvement when the AlN composition in the quantum barriers increases.
(a) Electron concentration profiles and (b) hole concentration profiles of the active region for devices A1, B1, and C1 at an injection current density level of 110 A/cm2.
(a) Electron concentration profiles and (b) hole concentration profiles of the active region for devices A1, B1, and C1 at an injection current density level of 110 A/cm2.
Figure 5 shows the total radiative recombination rate and the total Auger recombination rate within the MQWs as a function of AlN composition for the AlyGa1−yN quantum barrier at an injection current density of 110 A/cm2 for devices A1, B1, and C1. The total recombination rates are calculated by integrating the radiative or Auger recombination rates of the active region [see the insets of Figs. 5(a) and 5(b)]. For better resolution, the recombination rates for devices B1 and C1 are artificially shifted by 2 nm and 4 nm, respectively, with reference to device A1. Figure 5(a) shows that the radiative recombination rates are enhanced as the AlN composition for AlyGa1−yN quantum barriers increases and trend to saturate when the AlN composition exceeds 61%, which is consistent with the EQE and the optical power shown in Fig. 2(a). The saturation for the radiative recombination rate is tentatively ascribed to the stronger Auger recombination. We then show the Auger recombination rates in terms of the AlN composition for the AlyGa1−yN quantum barriers in Fig. 5(b), which shows that the Auger recombination rate is continuously increasing with the increasing AlN composition for the AlyGa1−yN quantum barriers. It is known that the Auger recombination scales with the cubic power of the carrier density, and hence, the enhanced carrier concentrations in the MQWs also contribute to a larger Auger recombination rate; this process may consume plenty of carriers, which will sacrifice the radiative recombination,28 i.e., the saturated radiative recombination rate is observed when the AlN composition for the quantum barriers is beyond 61% in this work.
(a) Total radiative (rad. for short) recombination rates and (b) total Auger recombination rates in the MQWs for devices A1, B1, and C1 at a current level of 110 A/cm2. The insets selectively show the radiative recombination rates and Auger recombination rates in the active region at an injection current density of 110 A/cm2.
(a) Total radiative (rad. for short) recombination rates and (b) total Auger recombination rates in the MQWs for devices A1, B1, and C1 at a current level of 110 A/cm2. The insets selectively show the radiative recombination rates and Auger recombination rates in the active region at an injection current density of 110 A/cm2.
B. Effect of quantum well thickness on hole injection capability
As has been stated previously, we encounter the fact that the hole concentration for Al-rich quantum barriers is less homogenized in the MQWs. This is because of the increased valence band barrier height as the AlN composition for the quantum barriers increases, as shown in Table II. Therefore, we have to maintain both the enhanced hole concentration and the homogenized hole distribution in the MQWs for DUV LEDs. Here, we propose to properly increase the quantum well thickness so that the polarization induced electric field in the quantum wells can accelerate holes.
To address that point, we further design DUV LEDs with various quantum well thicknesses, which are 3 nm, 4 nm, 5 nm, and 6 nm. The AlN composition for the quantum barriers and the p-EBL are kept at 61% and 60%, respectively for all the investigated devices. The EQE and the optical power as a function of quantum well thickness are shown in Fig. 6(a) (data are calculated at a current density of 110 A/cm2). We also selectively show the EQE and the optical power for devices B1, B2, and B3 with quantum well thicknesses of 3 nm, 4 nm, and 6 nm, respectively, in Fig. 6(b). Both Figs. 6(a) and 6(b) present that the EQE and the optical power further increase as the quantum wells become thick. It is worth noting that the program has the issue of numerical nonconvergence when we further increase the quantum well thickness. The numerical nonconvergence is attributed to the very strong quantum confined Stark effect (QCSE) that separates the electron and hole wave functions when quantum wells become too thick. The inset of Fig. 6(a) shows a redshift for the peak emission wavelength when the quantum well thickness increases, which further indicates the increasing QCSE as the quantum well becomes thick.
(a) EQE and optical power in terms of quantum well thicknesses at a current density of 110 A/cm2. The inset shows the wavelength as a function of various thicknesses of quantum wells and (b) the EQE and the optical power for devices B1, B2, and B3 at different current densities.
(a) EQE and optical power in terms of quantum well thicknesses at a current density of 110 A/cm2. The inset shows the wavelength as a function of various thicknesses of quantum wells and (b) the EQE and the optical power for devices B1, B2, and B3 at different current densities.
It is known that the confinement factor for each quantum well can be increased because of the increased quantum well thickness if we use the mean-free-path model to analyze electron transportation.24 For holes, the mean-free-path model can be revised and modeled to Eqs. (1) and (2). Pi, Pi+1, tQW, and lMFP represent the captured hole density in the ith (ith > 1, note the first quantum wells is the one closest to the n-AlGaN region, according to Fig. 1) quantum well, the incoming hole density which fails to be captured by the ith + 1 quantum well, the quantum well thickness, and the mean free path, respectively. The mean free path is a product of the scattering time (τsc) and the hole velocity (vth), as shown in Eq. (2). The scattering time is set to 0.0091 ps.24,29 The holes have a heavier effective mass and lower mobility, and hence, according to the common belief, the quantum well shall be properly thinned for promoting hole injection,30 which can also be reflected by Eq. (1), i.e., the next quantum well can capture more holes if the quantum well thickness decreases. The energy band offset of Al0.45Ga0.55N/Al0.61Ga0.39N as MQWs of the DUV LEDs is only 467.2 meV, compared with 703.5 meV when In0.15Ga0.85N/GaN is the active region of blue LEDs.31 Hence, considering the smaller energy band offset for DUV LED MQWs, thin quantum wells may sacrifice electron injection. Thus, this work suggests increasing the AlN composition for quantum barriers. As has been shown in Fig. 4(b), the increased AlN composition for quantum barriers will make hole distribution less uniform. Therefore, we shall increase the mean free path for holes, and this can be doable by using polarization induced electric field in quantum wells. Note that the electric field in the quantum wells for [0001] oriented DUV LEDs is along the same direction of the external-bias-generated electric field when the DUV LED is forward biased. We can make “hot” holes by increasing vth,
Figure 7 presents the energy, which is received by holes during transport through each quantum well/quantum barrier pair. The calculation is conducted by Eq. (3), where E denotes the electric field in the ith + 1 (ith > 1) quantum barrier and the ith + 1 quantum well and ti means the total thickness for the ith + 1 quantum barrier and the ith + 1 quantum well. The negative value means that the holes obtain the energy from the ith + 1 quantum well/quantum barrier pair. Figures 7(a)–7(d) all indicate that the holes are able to receive more energy when the quantum wells become properly thick,
Quantum-well-thickness-dependent energy that the holes receive after traveling through (a) the second quantum well and quantum barrier, (b) the third quantum well and quantum barrier, (c) the fourth quantum well and quantum barrier, and (d) the fifth quantum well and quantum barrier. The data are calculated at an injection current density of 110 A/cm2.
Quantum-well-thickness-dependent energy that the holes receive after traveling through (a) the second quantum well and quantum barrier, (b) the third quantum well and quantum barrier, (c) the fourth quantum well and quantum barrier, and (d) the fifth quantum well and quantum barrier. The data are calculated at an injection current density of 110 A/cm2.
To further prove our point, we then selectively show the electron and hole concentration profiles in the MQWs in Figs. 8(a) and 8(b), respectively. The electron concentration in the MQWs is improved, which can be well explained by the mean-free-path model, where the thick quantum wells can capture electrons better. Figure 8(b) shows that the hole concentration is also enhanced when the quantum wells are further thickened, which agrees well with our previous analysis, as shown in Fig. 7. Figure 8(c) further shows the hole concentration for devices B1, B2 and B3 without considering the polarization field in the MQWs (wo/P), and it clearly shows that the hole concentration is remarkably decreased as we increase the quantum well thicknesses, which strongly confirms our conclusion that the polarization induced electric field in the quantum wells for [0001] oriented DUV LEDs can make “hot” holes by increasing the drift velocity.
(a) Electron concentration profile and (b) the hole concentration profile (considering the polarization effect in the MQWs) of the active region for devices B1, B2, and B3 and (c) the hole concentration profile without considering the polarization effect in the MQWs for devices B1, B2, and B3. The data are calculated at an injection current density level of 110 A/cm2.
(a) Electron concentration profile and (b) the hole concentration profile (considering the polarization effect in the MQWs) of the active region for devices B1, B2, and B3 and (c) the hole concentration profile without considering the polarization effect in the MQWs for devices B1, B2, and B3. The data are calculated at an injection current density level of 110 A/cm2.
Finally, we calculate the total radiative recombination rate in the MQWs in terms of quantum well thickness at an injection current density of 110 A/cm2. The results are presented in Fig. 9. The inset in Fig. 9 selectively shows the radiative recombination rates in the active region for devices B1, B2, and B3. We can observe from Fig. 9 that the total radiative recombination rates improve as the quantum well thickness increases, which is consistent with that shown in Figs. 6(a) and 6(b). However, because of the QCSE in the [0001] oriented DUV LED MQWs, care should be taken when using thick quantum wells.
Numerically calculated total radiative (rad. for short) recombination rates in the MQWs at a current density level of 110 A/cm2. The inset shows the radiative recombination rates in the active region for devices B1, B2, and B3 at an injection current density of 110 A/cm2.
Numerically calculated total radiative (rad. for short) recombination rates in the MQWs at a current density level of 110 A/cm2. The inset shows the radiative recombination rates in the active region for devices B1, B2, and B3 at an injection current density of 110 A/cm2.
IV. CONCLUSIONS
To summarize, in this work, we find that an appropriately high AlN composition for the AlGaN quantum barrier can reduce the polarization induced positive interface charges at the LQB/p-EBL interface, which can suppress the hole depletion effect and reduce the effective valence band barrier height for the p-EBL. Hence, the hole blocking effect that is caused by the p-EBL is decreased. Nevertheless, the high AlN composition for the quantum barriers can increase the valence band barrier height for the MQWs, thus sacrificing the hole transport therein. We then increase the hole energy by properly increasing the thickness of the quantum wells such that the polarization induced electric field in the quantum wells is able to generate “hot” holes, thus facilitating hole transport across the MQWs. We also point out that, considering the QCSE for [0001] DUV LEDs, care should be taken when using thick quantum wells. Therefore, the external quantum efficiency for DUV LEDs can be improved by simply designing MQWs with proper quantum well thickness and AlN composition for quantum barriers. We strongly believe that the findings in this article provide another alternative easy way to make high-efficiency DUV LEDs and the device physics reported in this work offers more understanding to the DUV LED community.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.
ACKNOWLEDGMENTS
This work was supported by the Natural Science Foundation of Hebei Province (Project No. F2018202080), the Program for Top 100 Innovative Talents in Colleges and Universities of Hebei Province (Project No. SLRC2017032), the Program for 100-Talent-Plan of Hebei Province (Project No. E2016100010), the Suzhou Institute of Nano-Tech and Nano-Bionics (SINANO) Research Fund of the Chinese Academy of Science (Project No. 19ZS02), and the Graduate Innovation Foundation of Hebei Province (No. CXZZBS2020027).