We have examined the validity of the kinematical approximation in Ge growth at low temperatures, using the camera and framegrabber to simultaneously ana- lyze various features in the diffraction pattern. The decay in the intensity of the specular spot during low temperature growth is shown in Figure 6.13. As the tem- perature is lowered, the decay approaches the value associated with a statistical surface. We expect this limit at low temperature, since surface diffusion becomes negligible and the random deposition of atoms dominates the evolution. This ex- ponentially decay has previously been observed by Chason et al. [9]. Also notice that after an initial decay, the RHEED intensity reaches a steady state value. We see this steady-state intensity over the range of temperatures studied, and observe that it is not consistent with the two-level or stochastic interpretations mapping intensity to coverage.
In our interpretation of the specular spot intensity, we must be sure that other diffraction features are not impinging on the specular spot and artificially con- tributing to the measured intensity. We investigate this issue by collecting line scans through the specular spot during growth at 125◦C in the same run shown in Figure 6.13. A horizontal line scan reveals the contribution of the background to the measured intensity, while a vertical line scan shows the relative intensity of the specular spot and the Bragg rods, which might impinge upon the specular spot during growth. Line scans at the beginning and end of growth are given in Figure 6.14. In both scans, the intensity of the specular spot is large, while the surround- ing intensity is within a few bits of zero. We conclude that even at the lowest
−5 0 5 10 15 0 0.2 0.4 0.6 0.8 1 time (s) normalized intensity 210° C 125 ° C exp(−4θ)
Figure 6.13: Decay of the integrated intensity of the RHEED specular spot during growth at 125◦C and 210◦C at a rate of 0.4 ˚A/s. Growth proceeds for 10 s, after which the shutter is closed. The decay is compared to the decay for stochastic growth for an equivalent monolayer coverage Θ, using 1.4 ˚A = 1 mL. As the temperature is lowered, the decay approaches the stochastic limit, but retains a small nonzero steady-state component for the temperatures considered.
0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 position (pixels) normalized intensity (a) initial final 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 position (pixels) normalized intensity (b) initial final
Figure 6.14: Line scans through the specular spot for the growth at 125◦C shown in Figure 6.13: (a) line oriented vertically, along the Bragg rods; (b) line oriented horizontally, perpendicular to the Bragg rods. The Bragg rod and background do not contribute significant intensity to the measured specular spot intensity.
temperature growth considered, the intensity of the specular spot is not corrupted by other diffraction features. However, in our photodiode measurements of the spectral spot intensity, we continue to measure and subtract off the background intensity for each growth run.
We now continue on with the kinematical interpretation, and consider the evolution of the specular spot first during growth, and then during subsequent recovery, as pictured in Figure 6.6. The main features in this plot are the decay in intensity during growth and the subsequent signal recovery. This recovery is not consistent with a straightforward mapping between surface coverage and signal intensity. Post-growth, the coverage is not changing, but the intensity is increasing. During this recovery phase, we expect the surface atoms to rearrange through adatom diffusion and detachment from islands, leading to island coarsening.
In the kinematical approximation, the RHEED pattern is ideally the Fourier transform of the surface autocorrelation function. However, imperfections in the measurement system result in a smoothening of the features, primarily via diver- gence of the electron beam. In some situations, this loss of spatial coherence is modeled by convolving the RHEED pattern with a Gaussian instrument response function. The width of the Gaussian corresponds to a critical distance on the sur- face at which the electron beam is no longer coherent [24]. The effect of convolution with the Gaussian eliminates contributions to the RHEED pattern that originate from atoms at distances greater than the transfer width. However, in our inter- pretation, we consider a nominal intensity resulting from pure reflection, which is diminished when electron waves interfere destructively from layers differing by an atomic layer. In this interpretation, we do not wish to eliminate the contribution from sites that are far apart. Instead, we should do exactly the opposite and sub- tract out destructive interference only from sites that arewithinthe transfer width. This interpretation is clearly tied to a very different view of the RHEED specular spot intensity, which is that the intensity decay is proportional to the density of steps on the surface [54]. If we consider destructive interference only within some region surrounding the step edges, we obtain the same result. A consistent picture
includes two limits: when steps are close together, the interference model is valid, but when terraces between steps are large, the step density model is appropriate. In the intermediate regime, we expect intensity to be inversely correlated with step density.
6.4.2 Simulation of experimental conditions