Anomalous composition dependence of the band gap pressure coefficients in In-containing nitride semiconductors

The pressure-induced changes in the electronic band structures of In-containing nitride alloys, ${\text{In}}_x{\text{Ga}}_{1\text{−}x}\text{N}$ and ${\text{In}}_x{\text{Al}}_{1\text{−}x}\text{N}$ are examined experimentally as well as by ab initio calculations. It is found that the band gap pressure coefficients, $d{E}_g/dp$, exhibit very large bowing with $x$, and calculations with simulation of clustered distributions of the In atoms over the cation sites show a strong enhancement of this effect. This relates well to the experimental data obtained from pressure dependent photoluminescence measurements for ${\text{In}}_x{\text{Ga}}_{1\text{−}x}\text{N}$ and ${\text{In}}_x{\text{Al}}_{1\text{−}x}\text{N}$ layers, performed in this work, and combined with existing data for ${\text{In}}_x{\text{Ga}}_{1\text{−}x}\text{N}$ layers. We discuss possible explanations of the anomalously large magnitude of the $d{E}_g/dp$ bowing in these nitride alloys.

Figure 1

Calculated bulk modulus as a function of $x$, for two kinds of ${\text{In}}_x{\text{Ga}}_{1\text{−}x}\text{N}$ alloys; uniform and clustered distribution of indium atoms, respectively.

Figure 2

Calculated bulk modulus as a function of $x$, for two kinds of ${\text{In}}_x{\text{Al}}_{1\text{−}x}\text{N}$ alloys; uniform and clustered distribution of indium atoms, respectively.

Figure 3

(Color online) Pressure dependence of the luminescence spectra of InGaN layer measured at $T=77\text{K}$. The spectra are shifted along the vertical axis for clarity.

Figure 4

(Color online) Hydrostatic pressure dependences of the PL peak energies of the ${\text{In}}_{0.10}{\text{Ga}}_{0.90}\text{N}$ sample and the GaN epilayer. The slopes of linear fits to the experimental data are equal to PL pressure coefficients.

Figure 5

(Color online) Normalized ambient-pressure PL spectra of ${\text{In}}_x{\text{Al}}_{1\text{−}x}\text{N}$ layers, recorded at 10 K. The strong, relatively narrow lines visible at the energy 3.48 eV originate from the GaN template. The spectra are shifted along the vertical axis for clarity.

Figure 6

(Color online) Pressure dependence of the photoluminescence spectra of ${\text{In}}_x{\text{Al}}_{1\text{−}x}\text{N}$ layer measured at $T=10\text{K}$. The spectra are shifted along the vertical axis for clarity.

Figure 7

(Color online) Hydrostatic pressure dependences of the PL peak energies of the ${\text{In}}_{0.18}{\text{Al}}_{0.82}\text{N}$ sample and the GaN epilayer. The slopes of linear fits to the experimental data define PL pressure coefficients.

Figure 8

$d{E}_g/dp$ as functions of $x$ for ${\text{In}}_x{\text{Ga}}_{1\text{−}x}\text{N}$. Open diamonds are our experimental values. Theoretical results are illustrated for uniform (solid lines) and clustered (dotted lines) arrangement of In atoms. Other experimental values are from ref. a (Ref. 19).

Figure 9

$d{E}_g/dp$ as functions of $x$ for ${\text{In}}_x{\text{Al}}_{1\text{−}x}\text{N}$. Open and filled stars are our experimental values. Theoretical results are illustrated for uniform (solid lines) and clustered (dotted lines) arrangement of In atoms. The experimental data for InN and AlN are from ref. a (Ref. 19) and ref. b (Ref. 21), respectively.