Atomic scale annealing effects on In${}_x$Ga${}_{1-x}$N${}_y$As${}_{1-y}$ studied by TEM three-beam imaging

A transmission electron microscopy (TEM) method for simultaneous measurement of indium and nitrogen content in InGaNAs at atomic scale is introduced, tested, and applied to investigate thermal annealing effects on structural properties. Our technique is based on the extraction of strain and chemical sensitive contrast from a single three-beam TEM lattice fringe image by subsequent decomposition into $220$ and $020$ two-beam fringe images, being free of nonlinear imaging artifacts. From comparison with simulated strain and $020$ fringe amplitude, concentration maps and profiles are derived. For this purpose, the Bloch-wave approach is used with structure factors adapted for chemical bonding, static atomic displacements, as well as diffuse losses due to static and thermal disorder. Application to In${}_{0.28}$Ga${}_{0.72}$N${}_{0.025}$As${}_{0.975}$ before and after annealing at $670\hspace{0.5em}{}^{°}$C yields dissolution of In-rich islands and N-rich clusters and formation of a quantum well with nearly constant thickness and homogeneous elemental distributions, resulting in symmetric profiles along growth direction. To verify that these structural transitions are indeed correlated with typically observed changes of optical properties during thermal annealing, photoluminescence spectra are presented, revealing an increase in intensity by a factor of 20 and a strong blue shift of 60 meV.

Figure 1

Decomposition of an experimental three-beam image (a) acquired near zone axis $[001]$ with a Laue circle center at $(4.2\hspace{0.5em}0\hspace{0.5em}0)$. Via Fourier filtering, 220 and 020 fringe images (b) and (c) are obtained by keeping the primary beam and a circular area around the respective reflection in the diffractogram shown as an inset in (a). The lower half of the image corresponds to pure GaAs, evolving to an In${}_{0.28}$Ga${}_{0.72}$N${}_{0.025}$As${}_{0.975}$ quantum well in the upper half. The chemically sensitive 020 fringe amplitude obtained by keeping only frequencies close to the 020 reflection in the diffractogram and inverse Fourier transformation is shown in part (d). Contrast has been adjusted for better visibility.

Figure 2

Two quarters of a GaN${}_{0.06}$As${}_{0.94}$ diffraction pattern in an exact $[001]$ zone axis orientation for 300-kV electrons, simulated[19] with the multislice approach in the frozen lattice approximation. In quarter (a), the diffuse background stems from SAD only, whereas both SAD and thermal displacements according to $300\hspace{0.5em}$K from Schowalter et al.[20] are applied for part (b).

Figure 3

Pendellösung plots of diffracted beam amplitudes for a strain relaxed In${}_{0.25}$Ga${}_{0.75}$N${}_{0.05}$As${}_{0.95}$ cell using multislice (MS) and Bloch-wave (BW) methods for 300-kV electrons incident exactly along $[001]$ zone axis. The MS graphs were obtained from 10 thermal displacement configurations and by mapping the amplitude in the pixels that correspond to the respective Bragg beam. Atomic scattering amplitudes were taken from Weickenmeier and Kohl[22] in all three cases. The BW simulations contain absorptive form factors due to thermal (dashed curve), as well as both thermal and static (circles) disorders, respectively.

Figure 4

Histograms of SAD in the $x$ direction for individual atomic species in a strain relaxed 100-nm-thick $10\times 10$ In${}_{0.25}$Ga${}_{0.75}$N${}_{0.05}$As${}_{0.95}$ supercell (bars) with respective Gaussian least-squares fits (solid lines). Mean displacements are derived from the standard deviations in the $x$, $y$, and $z$ directions and serve for the calculation of absorptive form factors analogous to those for mean thermal displacements from Ref. 22.

Figure 5

On the thickness dependence of $a_N(\mathrm{c⃗}=(h\hspace{0.5em}k\hspace{0.5em}0),t,x=0.08,y=0.03)$ as a function of specimen tilt. The standard deviation ${\sigma }_t(h,k)$ derived from thickness characteristics of $a_N(t)$ was normalized to $a_N$(1 nm) and is depicted color-coded, showing that tilts with $h>3$ significantly minimize dependence on thickness.

Figure 6

Reference values for ${\varepsilon }_{[010]}$ (dashed white isolines) and normalized $020$ fringe amplitude $a_N$ as a function of indium concentration $x$ and nitrogen concentration $y$ for a Laue circle center $\mathrm{c⃗}=(4.2\hspace{0.5em}0\hspace{0.5em}0)$ and for a thickness of 30 nm. Bonding and SAD are accounted for as proposed by Müller et al.,[15] except for the additional absorptive form factor due to SAD diffuse losses dealt with in Sec. 4a.

Figure 7

The 020 dark-field overview images of samples Ia (annealed, top) and Ib (as-grown, bottom) that qualitatively show the effect of thermal annealing on layer morphology that roughly follows the null of the 020 structure factor. Both images were taken off-zone with a Laue circle center at $(20\hspace{0.5em}1\hspace{0.5em}0)$.

Figure 8

Experimental maps for the local fringe distance (normalized to GaAs) ${\varepsilon }_{[010]}$ (left) and chemically sensitive fringe amplitude $a_N$ (right) for sample Ia. Both maps have been extracted from the same three-beam TEM image by evaluation of local 220 fringe distances and Eq. (2) and 020 fringe amplitude. The Laue circle center was set at $(4.2\hspace{0.5em}0\hspace{0.5em}0)$.

Figure 9

(a) Local indium- and (b) local nitrogen concentration for sample Ia. (c) Profiles obtained by averaging horizontallly in (a) and (b). Error bars indicate statistical fluctuations, and the gray corridor is a measure of error due to inaccurate knowledge of the specimen thickness. Three-beam images had been taken in zone axis [001] with the Laue circle center at $(4.2\hspace{0.5em}0\hspace{0.5em}0)$.

Figure 10

(a) Local indium- and (b) local nitrogen concentration for sample Ib. (c) Profiles obtained by averaging horizontallly in the regions indicated in (a). Three-beam images had been taken in zone axis [001] with the Laue circle center at $(4.2\hspace{0.5em}0\hspace{0.5em}0)$.

Figure 11

Photoluminescence spectra for the laser structures investigated by TEM. After $15\hspace{0.5em}$min of thermal annealing under ${\mathrm{N}}_2$ stabilization, the PL peak intensity increases by a factor of $20$ but shifts about 65 nm toward higher energies. Spectra were recorded at room temperature.

Figure 12

Concentration evaluation yielding (a) local indium and (b) local nitrogen distribution for sample II exemplarily for a thickness of 30 nm. (c) Respective profiles obtained by averaging horizontallly in (a) and (b). Error bars are drawn each 2 nm only and indicate statistical fluctuations, and the gray corridor is a measure of error due to inaccurate knowledge of the specimen thickness. Three-beam images had been taken in zone axis [001] with the Laue circle center at $(4.2\hspace{0.5em}0\hspace{0.5em}0)$.

Figure 13

Simulation of the 220 fringe phase dependence on In content $x$ and nitrogen content $y$ (gray corridor) according to Eq. (1). A constant specimen thickness of 30 nm was assumed. The influence of ${\phi }_{13}$ on composition measurement at interfaces is estimated in the text.