Model System: Germanium Homoepitaxy
6.5 Discussion and conclusions
that pulsed MBE creates a significant smootheningor roughening effect. However, simulations with the higher fluxes seen in PLD do generate roughening. The results of this simulation study are shown in Figure 6.21. Simulations are performed for the germanium parameters determined earlier in the chapter, and for the silicon parameters used in [58].
We use a pulse time of 5 µs, as in the PLD simulations of Taylor and At- water [58]. The number of pulses per second is varied, with the instantaneous flux adjusted to maintain a mean growth rate of 1 mL/s. With low pulse rate and high instantaneous flux, a significant roughening effect is seen, which is diminished as the pulse rate is increased. When the pulse rate becomes large, we expect to recover the continuous flux evolution, and do for a pulse rate of 100 pulses/mL, with corresponding instantaneous flux only twice that of continous growth. Our lattice model and simulations are thus consistent with the predictions in [58] that an intense pulsed flux without energetic effects is roughening. We further conclude that at typical temperatures and growth rates of MBE, the maximum instanta- neous flux is not high enough to create significant roughening.
(a)
0 1 2 3 4 5 6 7 8 9 10
0 0.2 0.4 0.6 0.8
time (s)
rms roughness (mL)
1 pulse/s 10 pulse/s 100 pulse/s continuous
(b)
0 1 2 3 4 5 6 7 8 9 10
0 0.5 1 1.5 2 2.5 3
time (s)
rms roughness (mL)
1 pulse/s 10 pulse/s 100 pulse/s continuous
Figure 6.21: Kinetic Monte Carlo simulations of pulsed growth. Growth in pulses of 5 µs is compared to growth with continuous flux. In all cases the mean flux is 1 mL/s. (a) Physical parameters are those for Ge, with a growth temperature is 150◦C. (b) Physical parameters, including step-edge barriers, are taken from Taylor and Atwater [58] to represent silicon. The growth temperature is 400◦C.
appear [42] (our experiments consist of less than 10 monolayers).
We conclude that a straightforward application of the kinematical approxima- tion for RHEED is not warranted based on our data. Instead the analysis of the RHEED data is limited to the submonolayer regime, where the specular spot inten- sity is dependent on both the growth rate and coverage. The intensity is compared for surfaces with equal temperature and equal coverage, and it is observed that the intensity decay is greater when the growth rate is higher. We thus assume only a monotonic dependence between step density and intensity. This enables an esti- mation of bond energy for the cubic lattice KMC simulations, based only on the conjecture that when temperature and coverage are equal, equal intensity implies equal step density. The kinetic Monte Carlo simulations predict a bond energy of 0.20 eV, using a vibrational frequency of ν = 1013 s−1 and an adatom diffusion energy of 0.65 eV. This model is consistent with our data, with previously reported activation energies [11, 42], and with a comparison between our simulations and previously reported data [42].
In the multilayer growth experiments, differences in the RHEED intensity due to changes in the instantaneous flux are not observed over multiple layers of growth, and the interpretation of the RHEED pattern is uncertain in this regime. Sim- ulations of the same experimental conditions were performed, which predict that faster instantaneous growth rates increase the step density slightly, and in all cases two-dimensional nucleation and coalescence is the dominant growth mode. The experiments and simulation are consistent with the explanation that pulsed-MBE does not result in a significant effect.
We also simulated growth under the synchronized nucleation strategy, and under intense flux pulsing characteristic of pulsed laser deposition. A smoother interface is obtained using the synchronization strategy, while intense flux pulsing was roughening. While the pulsed-MBE strategy may not be an effective at gen- erating altered morphology, the simulations do predict that other strategies using time-varying flux and temperature would produce unique surface properties.
At the conclusion of this study, several promising directions for future investi-
gation are suggested. For the purpose of producing smoother films at low temper- atures, our simulations suggest that the synchronized nucleation strategy could be beneficial for Ge(001) at low growth temperatures. Previous studies on Ge(111) [37] show that the synchronization can prolong the existence of RHEED oscilla- tions. Connections between this growth strategy and final surface morphology could be of great utility in germanium, and particularly in silicon, and should be investigated experimentally.
It is also clear from the experimental work that while RHEED is sensitive to surface morphology, and provides real-time information during growth, a straight- forward interpretation based on the kinematical approximation is not justified.
Further development of RHEED models based on multiple scattering would be beneficial, particularly ones that can be run in real-time during growth to en- able feedback control. However, in the absence of such models, calibration of the RHEED signal to STM measurements could also be tremendously useful. Our chamber is not equipped with an STM, and we instead relied on another STM study to complement our RHEED data [42]. It is clear that RHEED and an STM provide different types of information each with its own advantages, and that in a surface study such as ours, the combination of the two would be particularly useful.