State-of-the-art and prospects for intense red radiation from core–shell InGaN/GaN nanorods

Core–shell nanorods (NRs) with InGaN/GaN quantum wells (QWs) are promising for monolithic white light-emitting diodes and multi-color displays. Such applications, however, are still a challenge because intensity of the red band is too weak compared with blue and green. To clarify this problem, we measured photoluminescence of different NRs, depending on power and temperature, as well as with time resolution. These studies have shown that dominant emission bands come from nonpolar and semipolar QWs, while a broad yellow-red band arises mainly from defects in the GaN core. An emission from polar QWs located at the NR tip is indistinguishable against the background of defect-related luminescence. Our calculations of electromagnetic field distribution inside the NRs show a low density of photon states at the tip, which additionally suppresses the radiation of polar QWs. We propose placing polar QWs inside a cylindrical part of the core, where the density of photon states is higher and the well area is much larger. Such a hybrid design, in which the excess of blue radiation from shell QWs is converted to red radiation in core wells, can help solve the urgent problem of red light for many applications of NRs.


II.
Power-dependent µ-PL in the NRs Figure S2. Power-dependent µ-PL spectra measured at room temperature (RT) in the NR sample A1 excited by a 325-nm cw-laser line. Figure S3. Dependence of µ-PL intensity (a, b, c) and peak energy (d, e, f) of peak 1, peak 2, and the defect-related yellow line (YL) in the NRs A1, B1, and C1, respectively, on the excitation power (Pexc). In the legend of figures (a-c), the values of the coefficient n in the formula I~(Pexc) n are shown, which was extracted from the power dependence of the integral intensity of PL for the two minimum and two maximum values of Pexc. Fitting of the original spectra was done by Gaussian functions. Bars in (d-f) show FWHM of the Gaussian functions. The µ-PL spectra were measured at RT, with excitation by a 325 nm cw-laser line. Figure S4. Power-dependent µ-PL spectra measured at RT in the NRs samples A2, B2, and C2 excited by a 325-nm cw-laser line. Figure S4 shows the µ-PL spectra of the NRs series A2-C2. As can be seen, the peak2 occurs only at maximum excitation powers, and it is weaker than that in the spectra of the nanorods A1-C1 with a larger diameter, which are shown in Fig. S2 and Fig. 3 of the main text. This fact indicates the origin of the peak2 from the semipolar or polar QWs, the areas of which strongly decrease in the NRs of the A2-C2 series.

III.
PL in the planar samples  Figure S5 shows the spectra of µ-PL measured in planar samples A, B, and C at RT. The spectra are modulated by an interference pattern of Fabry-Perot modes. The corresponding spectral positions of QW-related PL are at a wavelength of about 450, 505, and 570 nm, respectively. With the above-barrier excitation (λexc = 325 nm), QW-related PL in samples A and B appears only at sufficiently high Pexc. At low Pexc, emission at the absorption edge (near-band-edge emission, NBE) and the yellow luminescence (YL) band associated with defects prevail in the spectra. PL of sample C dominates by broad defect bands and NBE in the all used range of Pexc ( Figure S5 (c)). On the contrary, in the case of quasi-resonant (under-barrier) excitation, the QW-related PL is visible even at a relatively small Pexc ( Figure S5   At the low temperatures (LT), TRPL measurements showed decay times of 50-150 ns in the planar QWs. Such a slow PL decay is commonly explained by a small e-h overlap because of the presence of an electric field across the InGaN/GaN polar QWs, which induces the QCSE. At RT, the PL decay is characterized by a sub-nanosecond decay time, the value of which depends on the Pexc. Figure S5 shows the PL decay curves measured in the planar sample B with two different excitation powers -1 mW (a) and 0.05 mW (b). At the higher Pexc, the PL decay time is longer (~0.8 ns), while it is shorter (~0.16 ns) at the smaller Pexc. We explain such variation by the fact that the decay time is controlled by a fast nonradiative recombination channel which dominates at the smaller Pexc. The saturation of nonradiative centers at the higher Pexc leads to the increase in decay time. Internal quantum efficiency (IQE) of PL in sample B at a wavelength of 500 nm, evaluated as a ratio I(RT)/I(LT), is 0.28% (λexc=377 nm, Pexc=15 mW), where I is the integral PL intensity.

Calculation of the electromagnetic field distribution
We consider the NR as a microcavity, where the value of the radiative recombination rate can be increased or decreased due to the Purcell effect under conditions of weak coupling between the confined optical mode and optical transitions inside the cavity. It works by analogy with the Fermi's "golden rule" and depends on the density of photon states and the correspondence of the frequencies of optical and material resonances [1]. A possible modification of the radiative recombination rate due to the Purcell effect for a single cavity mode (wavelength ) can be expressed as [2] where τ rad and τ are the intrinsic and changed radiative recombination times, respectively, Δλ is the spectral width of the resonant mode, E(r) is the electromagnetic field distribution, FP is the Purcell factor that depends on the characteristics of the resonator [3] where = / is the quality factor of the mode, n is the refractive index of the medium and Veff is the effective mode volume.
The photon density of states can be visualized by calculating the electromagnetic field distribution in a cavity of a certain geometry. As it was previously reported, such a distribution can be complex and inhomogeneous in space inside a monolithic microcavity [4][5][6]. An increase in the radiative radiation rate (1/τ) allows observing the increase in radiation intensity. On the other hand, the intensity can quench when the photon density is low, e.g., when a cavity size is less than a radiation wavelength [1].
We have studied the electromagnetic field distribution inside the structures which are similar to the NRs A1 and A2. The simulations were implemented via the finite-difference timedomain (FDTD) method using Comsol Multiphysics software. We replace the hexagonal structure by a cylindrical one, which does not drastically influence the mode composition [7]. The real size cavity was located inside the large cylinder "box" of air with scattering boundaries. This boundary condition allowed us to avoid scattering waves from the "box", which could create additional interference patterns. The refractive index was chosen to be where n1 -refractive index of GaN and n2 -refractive index of In0.15Ga0.85N; V1 and V2 are respective volumes. However, this value is very close to n1 because of the small volume of QWs.