Role of strain and properties of N clusters at the onset of the alloy limit in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$

In $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$, the band gap energy decreases very rapidly with $x$ and the electron effective mass shows a quite unusual compositional dependence characterized by a sudden doubling for $x\cong 0.1\%$. In this work, we investigate the origin of this behavior by photoluminescence measurements under hydrostatic pressure in as-grown and hydrogenated $\mathrm{Ga}{\mathrm{As}}_{0.9989}{\mathrm{N}}_{0.0011}$ samples. First, we show that two nitrogen pair states emitting at 1.488 and $1.508\mathrm{eV}$ contribute mainly, but to a different extent, in determining the steep increase in the electron mass observed for $x\cong 0.1\%$. Tight-binding supercell calculations assign the $1.488\mathrm{eV}$ levels to isolated N pairs and the $1.508\mathrm{eV}$ states to N pairs perturbed by a nearby N atom, in disagreement with previous attributions but consistent with the electron mass data. Second, photoluminescence at high hydrostatic pressure discloses that these N pair states show quite different rates of passivation by hydrogen. By combining these findings with the calculated lattice energies associated with each N complex, we conclude that strain relaxation is a key mechanism driving the interaction of hydrogen with N atoms in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$.

Figure 1

Percentage variation of the electron effective mass $m_e$ in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ as a function of the N concentration as measured by magnetophotoluminescence (see Ref. 9). Gray circles refer to untreated samples and black circles refer to the $x=0.11\%$ sample hydrogenated with different H doses ($\mathrm{H}1=3.5\times {10}^{18}{\mathrm{cm}}^{-2}$, $\mathrm{H}2=4.5\times {10}^{18}{\mathrm{cm}}^{-2}$, and $\mathrm{H}3=5.0\times {10}^{18}{\mathrm{cm}}^{-2}$). The open circle indicates the GaAs reference sample. The open squares are the calculated values of $\Delta m_e∕m_e$ (the solid line is a guide to the eyes).

Figure 2

Photoluminescence spectra at low temperature of untreated and H-irradiated $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ samples ($\mathrm{H}1=3.5\times {10}^{18}{\mathrm{cm}}^{-2}$, $\mathrm{H}2=4.5\times {10}^{18}{\mathrm{cm}}^{-2}$, and $\mathrm{H}3=5.0\times {10}^{18}{\mathrm{cm}}^{-2}$) except for the topmost dotted-line spectrum, which is recorded on a GaAs reference. FE and $(e,C)$ indicate the free exciton and the free electron to neutral-carbon recombination bands, respectively. NN is due to carrier recombination on a N pair complex. NC indicates a nearly continuum of states due to excitons recombining on various nitrogen complexes. The thick line highlights a sample whose PL spectra under hydrostatic pressure are shown in the next figure.

Figure 3

Photoluminescence spectra at low temperature of the $\mathrm{Ga}{\mathrm{As}}_{0.9989}{\mathrm{N}}_{0.0011}$ sample hydrogenated at a dose $\mathrm{H}1=3.5\times {10}^{18}{\mathrm{cm}}^{-2}$. The spectra were recorded under different hydrostatic pressure $P$. FE and $(e,C)$ indicate the free exciton and the free electron to neutral-carbon recombination bands, respectively. NN and $\mathrm{N}{\mathrm{N}}^{*}$ refer to carrier recombination on different N pair complexes (see text); $\mathrm{N}{\mathrm{N}}^{*}\text{−}\mathrm{TA}∕\mathrm{LO}$ are the phonon replica of the $\mathrm{N}{\mathrm{N}}^{*}$ band. The NN and $\mathrm{N}{\mathrm{N}}^{*}$ bands are highlighted by thick lines.

Figure 4

Pressure dependence of the peak energy of the bands related to NN and $\mathrm{N}{\mathrm{N}}^{*}$ pair complexes (full triangles). Open symbols at ambient pressure refer to free-exciton recombination in the samples whose PL spectra are shown in Fig. 2. The lines are linear fits to the data: NN and $\mathrm{N}{\mathrm{N}}^{*}$ have pressure coefficient ${\beta }_{P,E}=4.5$ and $4.3\mathrm{meV}∕\mathrm{kbar}$ and extrapolate at 1.484 and $1.508\mathrm{eV}$, respectively.

Figure 5

Calculated distribution of the energy of N complex states for $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ with $x=0.05\%$ at ambient pressure. The distribution is weighted by the interaction potential with the conduction band minimum. The arrows indicate specific perturbed N pair states reported in the table of Fig. 6.

Figure 6

(Color online) Upper part: Sketch of the NN (left) and $\mathrm{N}{\mathrm{N}}^{*}$ (right) nitrogen complexes discussed in the text. $2a$ indicates the size of the conventional cubic cell of the $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ lattice. N1 and N2 are the nitrogen atoms of the pair, while N3 indicates the third nitrogen atom, which perturbs the N pair. Notice that the sketches refer only to the complexes highlighted by bold characters in the table of the lower part of the figure. Lower part: the table reports the calculated energy levels of the perturbed N pairs. $r$ indicates the distances (in units of $a$) between the different atoms forming each complex in the unrelaxed lattice. The components of the distance vectors $r$ are given as absolute values. Bold characters refer exclusively to the two complexes sketched in the upper part. Notice that lattice relaxation (see text) renders energetically inequivalent N pairs having the same $r\left(\mathrm{N}3\text{−}\mathrm{N}1\right)$ and $r\left(\mathrm{N}3\text{−}\mathrm{N}2\right)$.

Figure 7

Photoluminescence spectra at low temperature and high hydrostatic pressure $(P=8.5\mathrm{kbar})$ of the untreated and H-irradiated $x=0.11\%$ $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ sample ($\mathrm{H}1=3.5\times {10}^{18}{\mathrm{cm}}^{-2}$, $\mathrm{H}2=4.5\times {10}^{18}{\mathrm{cm}}^{-2}$, and $\mathrm{H}3=5.0\times {10}^{18}{\mathrm{cm}}^{-2}$). The upper and lower panels refer, respectively, to lower and higher laser power densities. FE and $(e,C)$ indicate the free exciton and the free electron to neutral-carbon recombination bands, respectively. NN and $\mathrm{N}{\mathrm{N}}^{*}$ refer to carrier recombination on different N pair complexes (see text); $\mathrm{N}{\mathrm{N}}^{*}\text{−}\mathrm{TA}∕\mathrm{LO}$ are the phonon replica of the $\mathrm{N}{\mathrm{N}}^{*}$ band. The NN and $\mathrm{N}{\mathrm{N}}^{*}$ bands are highlighted by thick lines. Notice the much higher passivation rate by hydrogen of the NN band with respect to the $\mathrm{N}{\mathrm{N}}^{*}$ band as evidenced by vertical dashed lines. The inset in the upper panel is meant to better highlight the $\mathrm{N}{\mathrm{N}}^{*}$ contribution to the PL spectrum of the untreated sample.