Transmission electron microscopy investigation of segregation and critical floating-layer content of indium for island formation in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$

We have investigated ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ layers grown by molecular-beam epitaxy on $\mathrm{GaAs}\left(001\right)$ by transmission electron microscopy (TEM) and photoluminescence spectroscopy. $\mathrm{InGaAs}$ layers with In concentrations of 16, 25, and $28\%$ and respective thicknesses of 20, 22, and 23 monolayers were deposited at $535°\mathrm{C}$. The parameters were chosen to grow layers slightly above and below the transition between the two- and three-dimensional growth mode. In-concentration profiles were obtained from high-resolution TEM images by composition evaluation by lattice fringe analysis. The measured profiles can be well described applying the segregation model of Muraki et al. [Appl. Phys. Lett. 61, 557 (1992)]. Calculated photoluminescence peak positions on the basis of the measured concentration profiles are in good agreement with the experimental ones. Evaluating experimental In-concentration profiles it is found that the transition from the two-dimensional to the three-dimensional growth mode occurs if the indium content in the In floating layer exceeds $1.1\pm 0.2$ monolayers. The measured exponential decrease of the In concentration within the cap layer on top of the islands reveals that the In floating layer is not consumed during island formation. In addition, ${\mathrm{In}}_{0.25}{\mathrm{Ga}}_{0.75}\mathrm{As}$ quantum wells were grown at different temperatures between $500°\mathrm{C}$ and $550°\mathrm{C}$. The evaluation of concentration profiles shows that the segregation efficiency increases from $R=0.65$ to $R=0.83$. The strong increase of $R$ with the growth temperature is explained by the large growth rate of $1.5\mathrm{ML}∕\mathrm{s}$. Comparison with the temperature dependence of published segregation efficiencies obtained at lower growth rates reveals increasing temperature dependence and decreasing segregation efficiency with increasing growth rate.

Figure 1

(a) Bright-field TEM plan-view image of the multilayer sample, (b), (c) dark-field TEM images of a [010] cross-section of the multilayer sample with (b) $g=\left(002\right)$ and (c) $g=\left(200\right)$.

Figure 2

PL spectra of the multilayer sample recorded at $5\mathrm{K}$. The three emission lines are labeled with the nominal In concentration of the respective $\mathrm{InGaAs}$ layers.

Figure 3

(a) Gray-scale coded map of the In concentration in the first (bottom) and second (top) layers in the multilayer sample, obtained from a cross-section HRTEM lattice-fringe image with CELFA. (b), (c) In-concentration profiles averaged along the [100] direction as a function of the distance in growth direction in units of ML (b) for layer 2 (squares) and layer 3 (circles) and (c) for the island 1 (circles). The triangles correspond to an island from another image not shown here. The solid curves are fit curves computed according to the segregation model of Muraki et al. (Ref. 5). The error bars give the standard deviation obtained by averaging along the respective lattice plane.

Figure 4

(a) Concentration profiles computed for layer 3 according to the segregation models of Muraki et al. (Ref. 5) (solid line) and Dehaese et al. (Ref. 3) (bars). For the Muraki model, we employed the parameters $R=0.8$, $N=22\mathrm{ML}$, and $x_0=0.25$. The parameters for the Dehaese model were taken from Ref. 3. (b) Amount of In in the In floating layer during growth plotted vs the distance in growth direction. For the calculation with the Muraki model, we used Eq. (2). The curves at the left-hand side were computed according to the nominal parameters of layer 1, whereas the curves at the right-hand side correspond to layer 3. As the 2D-3D transition is clearly exceeded in layer 1, we estimate that the critical amount of In lies close to 1 which is marked by a dashed line.

Figure 5

Segregation efficiency $R$ as function of the growth temperature $T$ for $\mathrm{InGaAs}$ QW layers with nominally $x_0=0.25$ and $22\mathrm{ML}$ thickness.

Figure 6

Plot of $\ln \left(R\right)$ as a function of growth temperature for the values measured in this work, compared with results of Muraki et al. (Ref. 5) and Kaspi and Evans (Ref. 25).

Figure 7

Schematic illustration of plan-view and cross-section samples with the island in the middle (dark region) for the discussion of the measured In-concentration profile for the island 1 in Fig. 3c.