Time-resolved photoluminescence of type-I and type-II $\left(\mathrm{GaIn}\right)\mathrm{As}∕\mathrm{Ga}\left(\mathrm{NAs}\right)$ heterostructures

A set of ${(\mathrm{Ga}}_{0.77}{\mathrm{In}}_{0.23})\mathrm{As}∕\mathrm{Ga}({\mathrm{N}}_x{\mathrm{As}}_{1-x})$ heterostructures is studied by time-resolved photoluminescence. Four samples with nitrogen concentrations from $x=0.48\%$ up to $x=2.2\%$ are investigated at different temperatures and with different excitation densities. The experiments suggest that the heterostructure band offset is type I for $x=0.48\%$ and type II for $x=2.2\%$. The situation is more complex for $x=0.72\%$ and $x=1.25\%$, since these samples are close to the transition from type I to type II. The experimental findings are analyzed using a detailed microscopic theory. Numerical calculations describe the measured data well. In particular, the interpretation of the experimental results concerning the band alignment is confirmed by the theoretical analysis.

Figure 1

(Color) Overview of the time-resolved PL data for the samples with 0.48%, 0.72%, and 1.25% nitrogen concentration in the $\mathrm{Ga}\left(\mathrm{NAs}\right)$ layers, respectively. The various images have the time scale as abscissa and the energy scale as ordinate. The normalized intensity is given in colors. For each sample, the results are ordered in columns according to increasing lattice temperature from top to bottom and in rows according to excitation intensity. The arrow in the top panel of the rightmost column indicates the onset of the incident laser pulse. The inset for each sample depicts schematically the type of heterostructure band offset for the samples, i.e., one of the important results of our following analysis.

Figure 2

Time dependence of the spectrally integrated PL signal for the samples with $0.48\%(∎)$, $0.72\%(엯)$, $1.25\%\left(▵\right)$, and $2.2\%\left(▿\right)$ nitrogen concentration.

Figure 3

Time-integrated PL spectra for different excitation densities at $10\mathrm{K}$ for the samples with $0.48\%(∎)$, $0.72\%(엯)$, $1.25\%\left(▵\right)$, and $2.2\%\left(▿\right)$ nitrogen concentration.

Figure 4

Time-resolved PL for different excitation densities at $10\mathrm{K}$ for the samples with $0.48\%(∎)$, $0.72\%(엯)$, $1.25\%\left(▵\right)$, and $2.2\%\left(▿\right)$ nitrogen concentration.

Figure 5

Peak position of the measured PL as a function of temperature at an excitation density of $33\mathrm{W}∕{\mathrm{cm}}^2$ for the samples with $0.48\%(∎)$, $0.72\%(엯)$, $1.25\%\left(▵\right)$, and $2.2\%\left(▿\right)$ nitrogen concentration.

Figure 6

Band alignment between the central $\left({\mathrm{Ga}}_{0.77}{\mathrm{In}}_{0.23}\right)\mathrm{As}$ QWs and the $\mathrm{Ga}\left({\mathrm{N}}_x{\mathrm{As}}_{1-x}\right)$ barriers for the samples with nitrogen concentrations of $x=0.72\%$ (left) and 1.25% (right) (Ref. 25). A flat conduction band occurs for an $x$ in between 0.72% and 1.25%.

Figure 7

Comparison between calculated (solid line) and measured (dotted line) time-dependent PL. The excitation density in the experiment is $74\mathrm{W}∕{\mathrm{cm}}^2$ and the temperature is $40\mathrm{K}$. At the time of excitation, the carrier densities in the numerical evaluations are $\rho =2.66\times {10}^9∕{\mathrm{cm}}^2$ for $x=0.72\%$, $\rho =1.19\times {10}^{10}∕{\mathrm{cm}}^2$ for $x=1.25\%$, and $\rho =1.06\times {10}^{11}∕{\mathrm{cm}}^2$ for $x=2.2\%$, respectively.

Figure 8

Calculated total luminescence $I_{\mathrm{pl}}\left(\rho \right)$ as function of the carrier density $\rho$ for nitrogen concentrations of $x=0.48\%$ (dotted), $x=0.72\%$ (dashed), $x=1.25\%$ (solid), and $x=2.2\%$ (dash-dotted), respectively. The temperature is $40\mathrm{K}$.

Figure 9

Calculated decay time $\tau$ as function of the carrier density $\rho$ (see text for an explanation). The inset shows $\tau$ values at a carrier density of ${10}^9{\mathrm{cm}}^{-2}$ plotted vs nitrogen concentration.