Optimal width of quantum well for reversed polarization blue InGaN light-emitting diodes

GaN-based LEDs have been commercialized for lighting and displays due to their higher efficiency and longer lifetimes compared with conventional lighting and display sources.^1–4 The quantum confined stark effect (QCSE) and electron leakage current originated from piezoelectric effect are severe and limit the further development of the device performance.^5–7 A significant bottleneck is a reducing in emission efficiency at high injection current densities, which has been called efficiency droop. In order to improve the optical performance of GaN-based LEDs, various methods are applied to the device design and material growth, such as graded AlGaN electron blocking layer (EBL) structure LED,⁸ a-plane GaN on r-plane sapphire,⁹ complex quantum well and lattice-matched barrier.^10,11 These methods have been proposed to release the strain-induced polarization in heterojunction interface. Recently, RP concept has been proposed, which indicates both the applied forward bias and the piezoelectric fields enhance the electric field in the quantum well region.^12–14 RP LEDs can be achieved using a p-down structure on a Ga-polar substrate or grow N-polar GaN material on N-polar substrate. Simulations find that RP LEDs have several advantages over conventional LEDs, e.g. electron overflow, injection efficiency, and turn on voltage.¹⁵ The effect of RP blue LEDs with different number of QWs were also investigated by Yen-Kuang Kuo.¹⁶ The optimal number of QWs for blue InGaN/GaN light-emitting diodes is also shown in detail by Chang Sheng Xia.¹⁷ However, there have been very few reports of optimal width of QWs on RP blue InGaN LEDs. The influence of QWs width on efficiency droop, LOP and turn on voltage are still unknown to researchers.

In this letter, the optical performance of RP blue InGaN LEDs under different quantum wells (QWs) width is numerically studied using the APSYS simulation software with a non-equilibrium quantum transport model, polarization surface charge and self-consistent model. The optimal width of QWs and the mechanism of efficiency droop improvement in RP blue InGaN LEDs are defined and analyzed systematically.

The RP blue InGaN LEDs used in our simulation consist of a 2-um-thick n-type GaN:Si (5 × 10¹⁸ cm⁻³), a five periods of In_0.16Ga_0.84N(3 nm)/GaN(12 nm) MQW active regions, followed by a 20-nm-thick p-type Al_0.2Ga_0.8N(3 × 10¹⁷ cm⁻³) electron blocking layer (EBL) and a 0.2-um-thick p-type GaN:Mg (6 × 10¹⁷ cm⁻³) cap layer. As a comparison, QW width of 1 nm, 2 nm, 4 nm were also investigated. In the simulation, the Shockley-Read-Hall (SRH) lifetime within QWs is estimated to be 100 ns. The Auger recombination coefficient is set to be 1.0 × 10⁻³⁰ m⁶/s which is the same to the reported values. The built-in interface charges due to spontaneous and piezoelectric polarization are calculated by methods developed by Fiorentini et al.¹⁸ 50% of the theoretical value is used to account for the compensation by fixed defects and other interface charges. The AlGaN band offset ratio is assumed to be 50:50, according to the result of Piprek et al.¹⁹ We find that the simulation well number dependence in Ref. 20 can be reproduced only with a capture time constant of 1.0 × 10⁻⁶ s, meaning that carriers can directly flow over the QWs with large probability.

Figure 1 presents the simulated (a) I-V, (b) LOP and (c) IQE curves of the RP blue InGaN LEDs with different QW width. As shown in Fig. 1(a), the forward voltage decrease with the increasing of QWs, and reach the minimal for the QWs with 4 nm width. It indicates that wider QWs can improve the horizontal carrier mobility and reduce the series resistances. As shown in the Figure 1(b), the LOP increases significantly with the increasing of QW width. We also observe the different efficiency droop behaviors of these structures in Fig. 1(c). Here the droop ratio is defined as (Max_IQE-IQE at 60 A/cm²)/Max_IQE. It can be seen that the droop ratios are 14.8%, 12.3%, 9.1% and 4.4% for QW width of 1 nm, 2 nm, 3 nm and 4 nm, respectively. The efficiency droop consistently decrease with the increase of QW width.

Figure 2 shows the band diagrams of RP blue InGaN LED with different QW width at the current injection density of 15 A/cm². It is worth to note that the polarization filed is reversed and the effective potential height of conduction band (Δφ_e) increase remarkably from 250 meV to 546 meV with the increase of QW width. While effective potential height of valence band (Δφ_h) just increase slightly from 136 meV to 213 meV. Potential barrier of EBL and quantum barriers (QBs), which block the injection of carriers into the QW for the normal polarization blue InGaN LEDs are absent in the RP blue InGaN LEDs. It must be noticed that the wider of QW width, the higher of potential barrier of EBL and QBs. Therefore, the electron and hole injection efficiency and confinement can be improved. However, the overlap ratio of electron and hole wave function decrease with QW width increasing to 4 nm.

The calculated electron and hole concentration distribution of RP blue InGaN LEDs with different QW width at the current injection density of 15 A/cm² are plotted in Fig. 3. It can be seen that the electron and hole concentration near the last QW increased with the increase of QW width, and more electron and hole are confined in the QWs region. This indicates that the effective potential height can enhance the confinement of carrier and the reversed polarization accelerates the carrier injection. As the QW width increases, the carrier leakage decreases markedly. So the QW width should be wide enough when the LEDs work in large current density. Even though the QW width increases four-fold from 1 nm 4 nm, the electron and hole concentration don't increase four-fold simultaneously. This indicates that the mean current density could decrease by enlarging the width of QWs. So the RP blue InGaN LEDs of 4 nm width QWs can work in higher current density. It is useful for efficiency droop and leakage carrier reduction. However, the overlap ratio of electron and hole wave function also should be considered.

In order to study the influence of QW width on the RP blue InGaN LEDs clearly, the calculated radiative recombination rates are shown in Fig. 4. The radiation recombination rate increases uniformly with the increase of QW width from 1 nm to 2 nm (Fig. 4(a) and Fig. 4(b)). When QW width is 3 nm (Fig. 4(c)), the whole intensity of radiative recombination rate reduce due to the decreasing of the overlap ratio of wave function. The reduction is more serious for QW with 4 nm width. What's more, the radiative recombination rate at the last QW is also decreased by 19.9% as the QW width change from 3 nm to 4 nm. Therefore, the radiative recombination rate turns to be more uniform in Fig. 4(d). And the efficiency droop is decreased in Fig. 1(3). We believe that both the current injection efficiency and radiation recombination rate play an important role in the efficiency droop. Low current injection efficiency at QW width of 1 nm leads to a low maximum of IQE, while high current injection efficiency at QW width of 4 nm leads to a low overlap ratio of wave function. As a result, the optimal QW width of RP blue InGaN LEDs is about 3 nm in these four structures by considering the analysis above.

Figure 5 shows the total spontaneous rate of RP blue InGaN LEDs with different QWs width at current injection density of 15 A/cm². It finds that the emission wavelength (red line) increases from 385 nm to 428 nm with increasing the QWs width. Total spontaneous rate of RP blue InGaN LEDs (black line) decreases at the same time. But it reaches a lowest point when QWs width is 2 nm. It indicates that both the QWs width and reversed polarization affect the properties of RP blue InGaN LEDs together.

In conclusion, RP blue InGaN LEDs with different width of QWs have been investigated numerically. The simulation results show that the turn on voltage decreases with increasing the width of QWs and saturates gradually. Wider QWs improve the current spreading and the carrier distribution properties in the MWQ region. As a result, the output power and efficiency droop are improved with increasing the width of QWs. Moreover, the effective potential height of electron and hole and spontaneous emission wavelength enhance constantly. For the current injection density of 15 A/cm² in the simulation, 3 nm is the optimal width for the optical and electrical characteristic of the RP blue InGaN LEDs

This work was supported by the National High Technology Program of China under Grant No. 2011AA03A105.