Carrier-density-dependent recombination dynamics of excitons and electron-hole plasma in $m$-plane InGaN/GaN quantum wells

We study the carrier-density-dependent recombination dynamics in $m$-plane InGaN/GaN multiple quantum wells in the presence of $n$-type background doping by time-resolved photoluminescence. Based on Fermi's golden rule and Saha's equation, we decompose the radiative recombination channel into an excitonic and an electron-hole pair contribution, and extract the injected carrier-density-dependent bimolecular recombination coefficients. Contrary to the standard electron-hole picture, our results confirm the strong influence of excitons even at room temperature. Indeed, at 300 K, excitons represent up to 63 ± 6% of the photoexcited carriers. In addition, following the Shockley-Read-Hall model, we extract the electron and hole capture rates by deep levels and demonstrate that the increase in the effective lifetime with injected carrier density is due to asymmetric capture rates in presence of an $n$-type background doping. Thanks to the proper determination of the density-dependent recombination coefficients up to high injection densities, our method provides a way to evaluate the importance of Auger recombination.

Figure 1

Impact of different $n$-type background doping concentrations ($n_0$) on the lifetimes of SRH (solid curves) and Auger (dashed curves) recombinations at 300 K, obtained with the following parameters: hole capture time of defects ${\tau }_{p0}=1.4\times {10}^{-9}\mathrm{s}$, electron capture time of defects ${\tau }_{n0}=6\times {10}^{-9}\mathrm{s}$, and Auger recombination coefficient $C_{\mathrm{Auger}}=1\times {10}^{-31}\mathrm{c}{\mathrm{m}}^6{\mathrm{s}}^{-1}$.

Figure 2

(a) Injected carrier-density-dependent ${\tau }_{r,\mathrm{e}-\mathrm{h}}$ for different $n$-type background concentrations ($n_0$) at 300 K, with the average recombination time ${\tau }_0=6.2\times {10}^{-6}\mathrm{s}$. (b) Corresponding injected carrier-density-dependent PL intensity given by $I_{\mathrm{pl}}\propto n_{\mathrm{e}-\mathrm{h}}/{\tau }_{r,\mathrm{e}-\mathrm{h}}$.

Figure 3

(a) Computed phase diagrams of the exciton fraction vs total photoexcited carrier density in the QWs without $n$-type background doping, with the parameters: $n_{\mathrm{Mott}}=1\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}, E_{b0}=42\mathrm{meV}$. (b) Computed phase diagrams of the fraction of exciton PL intensity vs total PL intensity without $n$-type background doping, with the parameters: $n_{\mathrm{Mott}}=1\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}, E_{b0}=42\mathrm{meV}$. For simplicity, ${\tau }_{r,x}$ has been chosen to vary linearly between $1.7\times {10}^{-8}\mathrm{s}$ at 300 K and $5.0\times {10}^{-10}\mathrm{s}$ at 4 K, and ${\tau }_{r,\mathrm{e}-\mathrm{h}}$ linearly decreases from $5\times {10}^{-6}\mathrm{s}$ at 300 to 4 K. Those values are extracted from our experiments (see Sec. 5). (c) and (d) Corresponding phase diagrams with an $n$-type background doping $n_0=1\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$.

Figure 4

(a) Power-dependent PL spectra at early time delay (between 0 and 20 ps) at 4 K for various laser fluences on the sample ranging from 0.0075 to $22\mu \mathrm{J}\mathrm{c}{\mathrm{m}}^{-2}$. (b) Corresponding power-dependent peak energies (black dots) and the upper and lower limits of the FWHM (red dots) of the PL spectra measured at initial delay.

Figure 5

(a) and (b) Power-dependent decay curves integrated over the whole energy range of QW emission spectra measured at 4 and 300 K under conditions otherwise identical for laser fluences on the sample ranging from 0.0075 to $22\mu \mathrm{J}\mathrm{c}{\mathrm{m}}^{-2}$.

Figure 6

(a) Injected carrier-density-dependent PL intensity at the initial delay $I_{\mathrm{pl}}\left(t=0\right)$ measured at 4 K (black dots) and 300 K (red dots) extracted from the decay curves shown in Fig. 5 and related fits deduced from modeling with and without Saha's equation. The black solid line is the fit obtained by assuming that pure excitonic recombination is at play at 4 K. Modeling with Saha's equation at 300 K, the red solid curve is the total $I_{\mathrm{pl}}\left(t=0\right)$ containing the recombination of excitons and that of the e-h plasma, the green dashed curve is the e-h plasma $I_{\mathrm{pl},\mathrm{e}-\mathrm{h}}\left(t=0\right)$, while the green solid curve is the exciton one $I_{\mathrm{pl},x}\left(t=0\right)$. The blue dashed curve is the result of modeling without Saha's equation at 300 K, namely, a pure e-h plasma system. (b) Corresponding injected carrier-density-dependent effective lifetimes ${\tau }_{\mathrm{eff},4\mathrm{K}}$ (black dots) at 4 K, ${\tau }_{\mathrm{eff},200\mathrm{K}}$ (blue dots) at 200 K, ${\tau }_{\mathrm{eff},300\mathrm{K}}$ (red dots) at 300 K, and the estimated radiative lifetime at 300 K ${\tau }_{r,300\mathrm{K}}$ (green shaded region). The solid curves are the related fits deduced from modeling using Saha's equation. The dashed curves are the related fits based on the modeling without Saha's equation. The error bar of the injected carrier density is $\sim 40\%$. It is mainly coming from the estimation of the excitation spot diameter and the uncertainty on the injection efficiency ${\eta }_{\mathrm{inj}}$ at room temperature. Concerning the precision on the effective lifetime, we estimate the error to be less than 10%, due to the nonzero time windows (1 ns) to estimate the effective lifetime at early delays.

Figure 7

(a) Injected carrier-density-dependent internal quantum efficiency derived from $\mathrm{IQE}={\tau }_{\mathrm{eff},300\mathrm{K}}/{\tau }_{r,300\mathrm{K}}$ (red shaded region). The red solid and red dashed curves are fits based on models with and without Saha's equation, the fitting parameters of which are the same as the fits shown in Fig. 6. The green solid curve and the green dashed curve are the fits based on models with and without Saha's equation, keeping the same fitting parameters as for the previous fits except for $C_{\mathrm{Auger}}=0$. (b) Injected carrier-density-dependent $B$ coefficients (red curves) and $A$ coefficients (black curves) extracted from the experimental data shown in Fig. 6. The solid (dashed) curves are fits based on the model with and without Saha's equation, respectively.