Effect of Varying Three-Dimensional Strain on the Emission Properties of Light-Emitting Diodes Based on (In,Ga)N/GaN Nanowires

In the experimental electroluminescence (EL) spectra of light-emitting diodes (LEDs) based on N-polar (In,Ga)N/GaN nanowires (NWs), we observe a double-peak structure. The relative intensity of the two peaks evolves in a peculiar way with injected current. Spatially and spectrally resolved EL maps confirm the presence of two main transitions in the spectra and suggest that they are emitted by a majority of the single nano LEDs. In order to elucidate the physical origin of this effect, we perform theoretical calculations of the strain, electric field, and charge-density distributions for both planar LEDs and NW LEDs. On this basis, we simulate also the EL spectra of these devices, which exhibit a double-peak structure for N-polar heterostructures, in both the NW and the planar case. By contrast, this feature is not observed when Ga-polar planar LEDs are simulated. We find that the physical origin of the double-peak structure is a stronger quantum-confined Stark effect occurring in the first and last quantum well of the N-polar heterostructures. The peculiar evolution of the relative peak intensities with injected current, seen only in the case of the NW LED, is attributed to the three-dimensional strain variation resulting from elastic relaxation at the free sidewalls of the NWs. Therefore, this study provides important insights on the working principle of N-polar LEDs based on both planar and NW heterostructures.

Figure 1

Illustrative sketch of the active region of a NW LED. Note that the different dimensions are not to scale. The crystallographic directions are shown at the bottom-left corner.

Figure 2

(a) EL spectra of the NW ensemble for the total injected current from 0.001 to 50 mA, plotted on a semilogarithmic scale. The magenta arrows are guides for the eye which sketch the evolution of the two main transitions. (b)–(d) Exemplary EL spectra (data points) and fits obtained by means of two Gaussians labeled peak 1 and peak 2; see the red and green solid curves, respectively. The yellow dashed lines depict the cumulative fits, namely, the algebraic sum of the two Gaussians. The data are plotted on a linear scale and refer to injected currents of (b) 0.001, (c) 0.1, and (d) 10 mA.

Figure 3

Monochromatic false-color top-view EL maps of the NW LED for emission energies of (a) 2.29 and (b) 2.38 eV acquired under a total injected current of 20 mA. The emission energies correspond to the two main peaks observed in the EL spectra of Fig. 2. (c)–(e) Spectra extracted from two different single-emission spots on the EL maps, attributed to individual NWs (NW1 and NW2), for injected currents of 0.05, 1, and 10 mA. The solid and dashed lines represent the two Gaussians used to fit the data points of NW1 and NW2, respectively.

Figure 4

Simulation of (a) in-plane and (b) out-of-plane strain distributions along the central $[000\overline{1}]$ $z$ axis of the employed LED structure. Solid and dashed lines represent the planar and NW cases, respectively. The origin of the central $z$ axis is placed at the lower interface of QW1.

Figure 5

Simulation of the electric-field distribution along the central $[000\overline{1}]$ $z$ axis of the employed LED structure calculated for an injected current density of $180\mathrm{A}{\mathrm{cm}}^{-2}$. Solid and dashed lines depict the data for the planar and NW cases, respectively. The vectors represent the direction and the magnitude of spontaneous polarization (${\mathbf{P}}_s$) and piezoelectric polarization (${\mathbf{P}}_{\mathrm{pe}}$). The positive- or negative-charge accumulation due to ionized donors and acceptors, namely, ${\mathrm{Si}}^{+}$ and ${\mathrm{Mg}}^{-}$ atoms, is indicated by $++++$ and $----$, respectively. The origin of the central $z$ axis is placed at the lower interface of QW1.

Figure 6

Simulation of room-temperature EL spectra in the case of (a) N-polar planar LEDs and (b) N-polar NW LEDs calculated for three different injected current densities ($J$): 1.8, 54, and $180\mathrm{A}{\mathrm{cm}}^{-2}$. The dotted lines represent the emission from each single QW, whereas the solid lines are the cumulative spectra, namely, the sum of the different contributions.

Figure 7

Simulations of the quantum charge-density maps on the $x\text{−}y$ plane of the NW, calculated for (a) QW4 and (b) QW1 at two different injected currents: 10 pA and 10 nA. The maps on the left-hand side refer to electrons (el), and the ones on the right-hand side to holes (hl). The intensity is color coded as indicated by the scale bars. Profiles of the quantum charge density, (c) and (d), along the $x$ axis, namely, the $[11\overline{2}0]$ direction, extracted from the charge-density maps in (a) and (b) along the dashed arrows for QW4 and QW1, respectively. Solid and dashed lines depict the profiles of electron and hole densities, respectively. The origin of the $x$ axis is placed at the center of the NW.

Figure 8

Comparison between simulated and measured optoelectronic properties of the NW LEDs; see the dashed and solid lines, respectively. (a) EL intensity and (b) energy position of the two main peaks plotted vs the average current per NW.