Strong phase separation of strained In${}_x$Ga${}_{1-x}$N layers due to spinodal and binodal decomposition: Formation of stable quantum dots

InGaN quantum dots were grown by metal-organic vapor phase epitaxy using a phase-separation process based on spinodal and binodal decomposition. Uncapped structures were grown which show InGaN phases with two different In contents on the surface. The high-In-content phase accumulates to huge islands while the low-In content phase forms flat meander and quantum-dot-like structures on the surface. The dissolution of the high-In-containing phase is very sensitive to the growth temperature of the GaN capping while there is no significant change of the InGaN quantum dot structures. The samples were investigated with transmission and scanning electron microscopy, photoluminescence measurements, and x-ray diffraction. A narrow growth window concerning the In${}_x$Ga${}_{1-x}$N composition was found in which the formation of quantum dots takes place. This growth window is in good agreement with the InGaN miscibility gap calculated for a strained InGaN layer. A detailed theoretical discussion is presented and the quantum dot and island formation will be explained by a strain-modified spinodal and binodal decomposition model.

Figure 1

Composition $x$ in the In${}_x$Ga${}_{1-x}$N solid plotted versus the gas-phase ratio for temperatures from 600 to 800 ${}^{°}$C. With a gas-phase ratio of $\text{In}/(\text{In}+\text{Ga})=0.82$, nearly the same composition is expected in the solid for growth temperatures below 700 ${}^{°}$C.

Figure 2

Spinodal (black) and binodal (gray) lines calculated for different strain states of the InGaN layer on a GaN substrate. A strain state of 100% corresponds to pseudomorphic material grown on GaN, whereas 0% means completely relaxed material. With increasing strain in the InGaN layer, the critical temperature decreases and shifts toward higher $x$. Nevertheless, a miscibility gap exists for growth temperatures below 713 ${}^{°}$C.

Figure 3

General pattern after phase separation calculated for different time steps and for different initial $x$ inside the unstable region (near the left border, in the center, near the right border). For the InGaN case the white regions would correspond to ${\mathrm{In}}_{x_{\mathrm{low}}}{\mathrm{Ga}}_{1-x_{\mathrm{low}}}\mathrm{N}$ and the black regions to ${\mathrm{In}}_{x_{\mathrm{high}}}{\mathrm{Ga}}_{1-x_{\mathrm{high}}}\mathrm{N}$. For relatively higher and lower temperatures the number of time steps would decrease and increase, respectively, to obtain similar results.

Figure 4

Strain distribution for pseudomorphic In${}_{0.648}$Ga${}_{0.352}$N QD protruding from a GaN substrate as a function of aspect ratio. Due to the symmetry, the right half is displayed only. The strain distribution is displayed in a gray scale between 0% and 100%. Due to the strain dependence of the spinodal region (Fig. 2) the decomposition has to be considered concerning the local strain.

Figure 5

SEM pictures ($1\hspace{0.5em}\mu \text{m}\times 500$ nm) of the surface of phase-separated InGaN layers with different annealing steps after growth (see also Table ).

Figure 6

STEM $Z$-contrast measurement of sample C. One of the large islands of truncated pyramidal shape with a high-In content (in the middle of the image) as well as the flat dot-like structures with a low-In content (marked with arrows) are visible on top of the GaN substrate.

Figure 7

RT-PL of the uncapped InGaN layers A–D. Strong PL from the QDs is visible from 2.3 to 2.7 eV, superposed by Fabry-Perot oscillations. At the low-energy side, sparse PL is visible originating from the yellow luminescence band.

Figure 8

XRD 2$\Theta$-$\omega$ measurements along the (0002) reflex of the uncapped InGaN samples. InGaN with high-In content can be determined for each sample.

Figure 9

HRSTEM $Z$-contrast images (left) and the evaluated In-concentration maps (right) of GaN-capped phase-separated InGaN structures. Sample E (upper row) and F (lower row) were capped at 700 and 750 ${}^{°}$C, respectively.

Figure 10

$\mu$-PL (left panel) and the normalized LT-PL to RT-PL comparison (right panel) of samples E and F. Sharp emission lines from the QDs can be identified in $\mu$-PL. For each sample, broad yellow defect luminescence (YL) around 2.2 eV is visible. At LT, neutral-donor-bound exciton (D${}^0\mathrm{X}$) emission at 3.47 eV as well as donor-acceptor-pair recombination (DAP) at 3.25 eV and near-band-edge emission (NBE) at RT around 3.4 eV[28] are detectable.

Figure 11

AFM of a phase-separated InGaN layer grown at 650 ${}^{°}$C. The high-In-containing islands have a height of 20 nm. The scale height was set to 5 nm to have a better contrast for the flat and small dots on the surface.

Figure 12

RT-PL of samples with different growth temperatures for the InGaN layer.

Figure 13

(a) PL spectra recorded at RT for samples G–K with different $x$ in the In${}_x$Ga${}_{1-x}$N layer. (b) Corresponding temperature-dependent integrated PL intensity.

Figure 14

QD formation model based on spinodal decomposition and relaxation of coherent dots or islands. Each step of the model is explained in the text.