## Factors Influencing the Modulation Bandwidth  
### Quantum Confined Stark Effect and Carrier Localization Effect  
In order to reach data transmission speeds of the order of Gb/s, the modulation bandwidth of LEDs for VLC applications needs to be substantially increased. There are two major factors affecting the modulation bandwidth of GaN-based LEDs: RC time constant and carrier lifetime in the active region [29]. An efficient way of reducing the RC time constant is to diminish the active region [30; 31; 32; 33]. Several approaches have been suggested by decreasing the carrier lifetime, including reduction of active layer thickness [34], using a barrier-doped multiple quantum well (MQW) structure [29], using surface plasmon coupling [35], or using resonant cavity structures [36]. In addition, carrier lifetime can also be shortened by increasing the current density of the injection, thus increasing the bandwidth for the modulation [37]. However, increasing the current density may lead to reduction of the quantum efficiency and performance of LEDs [38]. The carrier lifetime is influenced by both the non-recombination lifetime \(\tau_{\text{nr}}\) and recombination lifetime \(\tau_{\text{r}}\), and without affecting the luminous efficiency, a reliable way to improve the modulation bandwidth is to decrease the recombination lifetime [39]. The recombination lifetime is given by \(\tau_{r}=1/B(n_{o}+p_{o}+\Delta n)\), so in order to decrease the recombination lifetime, it is important to increase B to acknowledge the high speed of LED at a lower current density. Several studies have revealed that the carrier recombination processes in GaN-based LEDs can be greatly affected by the effect of quantum confined Stark effect (QCSE) [40; 41] and carrier localization [42; 43; 44]. To address this issue, [PERSON] et al. investigated the influence of the QCSE and carrier localization effect on the carrier lifetime by regulating QWs thickness [19]. Three GaN-based LED epilayers were developed using metal organic chemical vapor deposition (MOCVD) on c-axial sapphire (0001) substrates. The three epitaxial structures comprise of a 2 \(\upmu\)m undoped GaN layer, a 2.3 \(\upmu\)m Si-doped n-GaN layer, two sets of InGaN/GaN pre-wells, and five pairs of multiple quantum wells active with a 10 nm thick GaN quantum barrier, but with different thicknesses (2, 3, or 5 nm) of In\({}_{0.1}\)Ga\({}_{0.9}\)N QWs. Later, an electron-blocking layer of 40 nm thickness and a Mg-doped p-GaN layer of 150 nm thickness were deposited. LEDs with specific circular mesas and pixel diameters of 120, 90 and 60 \(\upmu\)m were manufactured to validate whether the modulation bandwidth is constrained by the carrier lifetime. Figure 1a displays the time-resolved photoluminescence spectra (TRPL) at room temperature for LEDs with three different QWs of 2, 3, and 5 nm thicknesses. The LED with 2 nm QW thickness is found to have the longest carrier lifetime as compared to other LEDs with QW thicknesses of 3 and 5 nm. Since localized carriers are trapped within the QWs, they have a much longer decay time, and, hence, carrier lifetime can be correlated with the carrier localization effect in QWs. The carrier localization effect causes the carriers to be trapped within the QWs, and this effect inhibits the carriers from moving to non-radiative recombination centers, thereby increasing the carrier lifetime [43; 44]. The slow decay times for the three LEDs have been extracted from the TRPL curves as a function of photon energy to reflect the degree of carrier localization, as shown in the inset in Figure 1a. The slow decay time is related to the depth of carrier localization, as shown in Equation (8). \[\tau_{slow}(E)=\frac{\tau}{1+\exp[\frac{E-E_{\text{nr}}}{E_{0}}]} \tag{8}\]where \(\tau\) is the carrier lifetime, \(E_{o}\) represents the depth of the carrier localization with the MWQs. The energy \(E_{o}\) for LEDs with QWs thickness of 2, 3, and 5 nm is derived using the experimental data to be 57, 29, and 3 meV, respectively.