Interaction between conduction band edge and nitrogen states probed by carrier effective-mass measurements in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$

The electron effective mass, $m_{\mathrm{e}}$, has been determined by magnetophotoluminescence in as-grown and hydrogenated $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ samples for a wide range of nitrogen concentrations (from $x<0.01\%$ to $x=1.78\%$). A modified $\mathbf{k}\mathbf{\bullet }\mathbf{p}$ model, which takes into account hybridization effects between N cluster states and the conduction band edge, reproduces quantitatively the experimental $m_{\mathrm{e}}$ values up to $x⩽0.6\%$. Experimental and theoretical evidence is provided for the N complexes responsible for the nonmonotonic and initially puzzling compositional dependence of the electron mass.

Figure 1

Photoluminescence spectra of three $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ samples ($x=0.043\%$, 0.095%, and 0.14%) at $T=20\mathrm{K}$. $E_{\mathrm{exc}}$ and $(e,\mathrm{C})$ indicate free-exciton recombination, and free-electron to neutral-carbon recombination, respectively. NC labels several recombination bands due to carriers localized on different N clusters. The vertical dashed lines labeled by NP and ${\mathrm{C}}_{\mathrm{S}}$ indicate the calculated energy positions of N pairs and triplets, respectively.

Figure 2

Magnetic-field induced shift of the $(e,\mathrm{C})$ recombination band for $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ samples as measured at $20\mathrm{K}$. Continuous lines are fits to the data through the formula of the first electron Landau level $\Delta E=(\hslash e∕2m_{\mathrm{e}})B$, where $m_{\mathrm{e}}$ is the only fitting parameter.

Figure 3

Measured values of the electron effective mass as a function of the N concentration. Several untreated (full circles) and H-irradiated (full diamonds) samples are considered. Error bars indicate the uncertainty on the mass values (in some case the uncertainty is within the symbol size). Open squares are the calculated effective mass values, the dotted line is a guide to the eye. An abscissa axis break at $x=0.7\%$ is introduced for ease of comparison.

Figure 4

Calculated distribution of N cluster-state energies ${\epsilon }_l$ near to the GaAs CB edge, weighted by the square of their interaction ${\mid V_{\mathit{N}l}\mid }^2$ with the unperturbed conduction band edge wavefunction, ${\psi }_c$. Downward vertical arrows show the calculated position of the alloy CB edge energy $E_{-}$ at each composition $x$. Dashed and dotted lines mark calculated energies of an isolated N pair (NP) and of ${\mathrm{C}}_{\mathrm{s}}$ triplet states, respectively. Insets show the LCINS spectrum projected onto ${\psi }_c$ for each composition considered.