Model System: Germanium Homoepitaxy
6.4 Comparison with simulation
6.4.3 Simulation of alternative growth strategies
value of Edif,0 reported previously [42], we ultimately arrive at parameter values of Edif,0 = 0.65±0.05 eV and ∆E = 0.20±0.05 eV.
We further compare our activation energies to an annealing study on Ge(001) [11], in which the activation energy for smoothening of large surface features is reported as 1.9±0.25 eV. This energy is argued to be the sum of the formation and diffusion energies for the mobile species. In our microscopic model, the formation energy for an adatom from a kink site is 1.05 eV, while its activation energy for surface diffusion is 0.65 eV, for a total of 1.70 eV—consistent with the annealing study.
Multilayer growth
We now use the parameters previously obtained for the cubic lattice model to make predictions about growth strategies based on time-varying conditions. First the conditions of the two of runs of Figure 6.9 are simulated, with corresponding step densities plotted in Figure 6.18. In both cases, the step density decays during growth and recovers when the source is shuttered. The decay of the higher growth rate is greater, but in both cases, the surfaces remain smooth and do not show any overall decay or recovery over multiple pulses.
We also simulate growth under the conditions shown in Figures 6.10 and 6.11 in which persistent RHEED oscillations are seen. Step edge density is plotted in Figure 6.19 for growth under continuous flux, and with one-monolayer pulses sep- arated by 5 s pauses. In the simulations, the surface remains smooth, as measured by the oscillations, during both strategies, so one would not expect the pauses in growth to substantially alter evolution—in the simulations, both growth strategies result in growth by two-dimensional island nucleation and coalescence.
0 100 200 300 400 500
−0.05 0
time (s)
−step edge density
F = 0.4 Ang/s F = 0.05 Ang/s
Figure 6.18: Kinetic Monte Carlo simulations of multilayer pulsed growth. The physical parameters are those determine previously for Ge(001): ν = 1013s−1, Edif,0 = 0.65 eV, and ∆E= 0.20 eV. The growth conditions correspond to experi- mental conditions of T = 230◦C and F = 0.4 and 0.05 ˚A/s. Pulse times of 2 s and 16 s, respectively, result in the deposition of approximately half a monolayer per pulse. Ten pulsing cycles are simulated, with 40 s pauses between the pulses. The faster growth rate results in a slightly higher step density.
0 10 20 30 40 50 60 70 80
−0.04
−0.03
−0.02
−0.01 0
(a)
time (s)
−step edge density
0 10 20 30 40 50 60 70 80
−0.04
−0.03
−0.02
−0.01 0
(b)
time (s)
−step edge density
Figure 6.19: Kinetic Monte Carlo simulation of roughness evolution at 0.3 ˚A/s and 270◦C, withEdif,0 = 0.65 eV, ∆E = 0.20 eV, andν = 1013s−1. The growth condi- tions match those of the experiments of Figures 6.10 and 6.11, while the physical parameters are those determined for Ge(001) from the submonolayer experiments:
(a) continuous flux (b) 5 s pauses after each of the first five monolayers.
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)
(a)
75°C 100°C 125°C 150°C
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)
(b)
continuous flux pulsed MBE
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)
(c)
150°C synchr
Figure 6.20: Kinetic Monte Carlo simulations of roughness evolution at a mean flux of 1 mL/s and temperatures between 75 and 150◦C. The physical parameters are those identified for Ge(001): Edif,0= 0.65 eV, ∆E= 0.20 eV, andν= 1013s−1. In (a), the temperature is held constant throughout growth, while in (b) contin- uous growth is compared to a pulsed-MBE strategy in which 1 mL is deposited during the first 0.2 s, with the remaining 0.8 s having no flux. In (c) constant tem- perature growth is compared to a temperature synchronization strategy, in which the temperature is lowered to 75◦C during the first 0.2 s of each layer, after which it is raised to 150◦C.
150◦C. We first simulate growth under constant conditions, with a flux of 1 mL/s and a range of temperatures, as shown in Figure 6.20(a). At the highest temper- ature, roughness oscillations are seen, which indicate a smooth two-dimensional surface. These oscillations decay as growth proceeds. However, note that the maximum remains near 0.5, indicating that at a coverage of 0.5, the surface is still two-dimensional. We next compare continuous growth to a pulsing strategy like those used in the experiments, in which a dose of one monolayer is deposited, fol- lowed by a pause in which the flux is zero. A comparion is made in Figure 6.20(b) for growth at 150◦C between a continuous flux of 1 mL/s, and a pulsed flux with 1 mL deposited in 0.2 s, follow by a pause of 0.8 s. There is no substantial change in the final roughness after 10 layers are deposited, indicating that the evolution under pulsed flux is not significantly different than under continuous flux.
We next make a comparison between continuous growth and growth under a different pulsing strategy, in which either temperature is lowered at the begin- ning of each layer, or alternatively the flux is raised. Either method can lead to smoothing by increasing island density, thereby reducing three-dimensional nucle- ation. Figure 6.20(c) demonstrates this effect. We compare continuous growth at 150◦C to growth in which the temperature is lowered to 75◦C during the first 0.2 s of each layer, after which it is raised to 150◦C. The final thickness under this synchronized nucleation strategy is substantially lower than under continous growth. However, in both cases the roughness at 1/2 mL coverage is 0.5, so at half coverage, in both cases the surface is two-dimensional. The benefit of the synchronization strategy is to reduce island density and delay the initiation of a new layer before the active one has been completed, providing a surface closer to an atomically flat one after the deposition of an integer number of monolayers.
A final comparison is made between continuous flux and a periodic flux profile reminiscent of pulsed laser deposition. One motivation for this study was to test the hypothesis [58] that the time-varying flux is generally roughening, and that the smoothening effect observed in PLD is the result of energetic effects. Based on the experiments, and the simulations of the experiments, we see no evidence
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.