Step-by-step capping and strain state of $\mathrm{GaN}∕\mathrm{AlN}$ quantum dots studied by grazing-incidence diffraction anomalous fine structure

The investigation of small-size embedded nanostructures, by a combination of complementary anomalous diffraction techniques, is reported. $\mathrm{GaN}$ quantum dots (QD’s), grown by molecular beam epitaxy in a modified Stranski-Krastanow mode, are studied in terms of strain and local environment, as a function of the $\mathrm{AlN}$ cap layer thickness, by means of grazing-incidence anomalous diffraction. That is, the x-ray photon energy is tuned across the Ga absorption $K$ edge which makes diffraction chemically selective. Measurement of $hkl$ scans, close to the $\mathrm{AlN}$ $\left(30\overline{3}0\right)$ Bragg reflection, at several energies across the $\mathrm{Ga}K$ edge, allows the extraction of the Ga partial structure factor, from which the in-plane strain of $\mathrm{GaN}$ QD’s is deduced. From the fixed-$\mathit{Q}$ energy-dependent diffracted intensity spectra, measured for diffraction-selected isostrain regions corresponding to the average in-plane strain state of the QD’s, quantitative information regarding the composition and out-of-plane strain has been obtained. We recover the in-plane and out-of-plane strains in the dots. The comparison to the biaxial elastic strain in a pseudomorphic layer indicates a tendency to an overstrained regime.

Figure 1

$1\text{−}\mathrm{\mu }{\mathrm{m}}^2$ AFM images of uncapped $\mathrm{GaN}$ QD’s grown in the modified SK mode.

Figure 2

(Color online) rms roughness evolution as a function of the $\mathrm{AlN}$ deposit amount.

Figure 3

Grazing-incidence geometry for a in-plane reflection $\left(30\overline{3}0\right)$. See text for details.

Figure 4

(a), (c), (e) $\sqrt{I_{exp}}$ measured at $10.317\mathrm{keV}$ ($50\mathrm{eV}$ below the $\mathrm{Ga}K$ edge), $\parallel F_{\mathrm{Ga}}\parallel$ and $\parallel F_T\parallel$ extracted for a 0-ML (a), a 5-ML (c), and a 10-ML (e) $\mathrm{AlN}$ coverage. (b), (d), (f) experimental square-root intensities $\sqrt{I_{exp}}$ measured below ($-100$ and $-50\mathrm{eV}$), at (edge), and above $(+5\mathrm{eV})$ the $\mathrm{Ga}K$ edge for a 0-ML (b), a 5-ML (d), and a 10-ML (f) $\mathrm{AlN}$ coverage.

Figure 5

Schematic representation in the complex plane of the structure factor $F$ as a function of $F_T$, $F_{A=\mathrm{Ga}}$, and ${\phi }_T-{\phi }_{A=\mathrm{Ga}}$ (see text). $F_N$ represents the partial structure factor of nonresonant atoms (Al, N).

Figure 6

In-plane lattice parameter $a_{\mathrm{GaN},GIXRD}$ and strain (relative to bulk $\mathrm{GaN}$) in $\mathrm{GaN}$ deduced from the position of the $F_{\mathrm{Ga}}$ maximum. Bulk $\mathrm{GaN}$ gives ${\epsilon }_{xx,GIXRD}=0\%$ with $a_{\mathrm{GaN},bulk}=3.189\mathrm{\AA }$ while bulk $\mathrm{AlN}$ gives ${\epsilon }_{xx,GIXRD}=-2.4\%$ with $a_{\mathrm{AlN}}=3.112\mathrm{\AA }$.

Figure 7

(a) Experimental EDAFS for the free-standing QD sample, compared with the best-fit result and (b) $R$-space experimental curve for free-standing QD’s compared with the best fit.

Figure 8

Scheme of $\mathrm{GaN}$ wurzite structure; the most relevant virtual phoelectron scattering paths used for the EDAFS simulation are represented: (1) in-plane $I$-shell $(\mathrm{Ga}\text{−}\mathrm{N}{)}_{\Vert }$, (2) out-of-plane $I$-shell $(\mathrm{Ga}\text{−}\mathrm{N}{)}_{\perp }$, (3) out-of-plane II-shell $(\mathrm{Ga}\text{−}\mathrm{Ga}{)}_{\perp }$, (4) III shell $\mathrm{Ga}\text{−}\mathrm{N}$ along $c$, (5) nearly in-plane IV-shell $\mathrm{Ga}\text{−}\mathrm{N}$, MS $\mathrm{Ga}\text{−}\mathrm{N}\text{−}\mathrm{N}$, and $\mathrm{Ga}\text{−}\mathrm{N}\text{−}\mathrm{Ga}$. Ga atoms are represented by white spheres, N by black ones.

Figure 9

$\mathrm{GaN}$ QD strain ${\epsilon }_{xx}=(a_{\mathrm{GaN},GIXRD}-a_{\mathrm{GaN},bulk})∕a_{\mathrm{GaN},bulk}$ vs ${\epsilon }_{zz}=(c_{\mathrm{GaN},GIDAFS}-c_{\mathrm{GaN},bulk})∕c_{\mathrm{GaN},bulk}$ values for all the samples studied compared with elastic biaxial strain of a pseudomorphic $\mathrm{GaN}$ thin film.

Figure 10

(Color online) (a) GIDAFS spectra for 0-, 2-, 5-, and 10-ML $\mathrm{AlN}$ capping, measured at maximum of $F_A$ and (b) crystallographic best fit for the $10\mathrm{ML}$ $\mathrm{AlN}$ sample. Open circle: experiment. Solid line: simulation performed with experimental $f_{\mathrm{Ga}}^{\prime }$ and $f_{\mathrm{Ga}}^{″}$ of a $\mathrm{GaN}$ thin film.

Figure 11

(Color online) Al-atoms occupation factor $x$ of the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ isostrain region selected by diffraction (maximum of $F_{\mathrm{Ga}}$), as a function of $\mathrm{AlN}$ coverage. Inset: evolution of the $\mathrm{AlN}$ thickness on top of the dots plotted as a function of the nominal $\mathrm{AlN}$ deposit (see text). The dashed straight line of slope 1 corresponds to an $\mathrm{AlN}$ quantity on dots equal to the nominal $\mathrm{AlN}$ deposit.