Surface morphology of GaAs during molecular beam epitaxy growth: Comparison of experimental data with simulations based on continuum growth equations

Abstract

Using atomic force microscopy and in situ elastic light scattering we show that the surface of molecular beam epitaxy ͑MBE͒ grown GaAs tends towards an equilibrium roughness independent of the initial condition, as predicted by kinetic roughening theory. Two separate continuum growth equations are consistent with the observed equilibrium roughness, namely, the Kardar-Parisi-Zhang ͑KPZ͒ equation ‫ץ‬h/‫ץ‬tϭٌ 2 hϩ(/2) ϫ(ٌh) 2 ϩ, where h is the surface height and represents nonconservative noise, and the MBE equation ‫ץ‬h/‫ץ‬tϭϪٌ 4 hϪ(⌳/2)ٌ 2 (ٌh) 2 ϩ c , where c represents conservative noise. These equations represent different physical smoothing mechanisms, so to distinguish between them we have numerically solved both equations. A novel geometric implementation of the nonlinear terms avoids instabilities associated with stiffness of the equations. We find that the time and length scale dependence of the smoothing of initially rough substrates is consistent with the KPZ equation but not the MBE equation. As the growth temperature is increased the coefficient increases relative to , but the KPZ description remains valid over the entire measured temperature range of 550-600°C. Reducing the As overpressure increases the anisotropy of the surface morphology. We provide a physical interpretation of the KPZ equation in which the incorporation rate of mobile adatoms on the surface is governed by evaporation/condensation type dynamics. These results provide important insight into the MBE growth mechanism of GaAs.

Studies of oxide desorption from GaAs substrates via Ga2O3 to Ga2O conversion by exposure to Ga flux

“…Such morphology is consistent with other literature reports. [1][2][3]6 Figure 3͑c͒ shows the morphology of a wafer where approximately 70% of the oxide was removed with Ga exposure, while the rest was evaporated during the following temperature ramp. Although some pitting is still present, the improvement in morphology compared to standard desorption is dramatic.…”

“…Typically, upon oxide desorption, very high densities of surface pits are formed, many of which are deeper than 20 nm. [1][2][3] For many applications such morphology is not acceptable. Although a combination of smoothing superlattices and thick GaAs buffer layers can effectively planarize the surface, their deposition takes time, consumes elements, and could be undesirable for a variety of other reasons.…”

Renormalization of stochastic lattice models: Epitaxial surfaces

“…(48) and (49). Upon making the transformation u → u + F τ this yields the EW equation (45) with a smoothed Gaussian noise ξ(x, τ ) which has zero mean and the covariance in Eq.…”

“…Moreover, experiments and computer simulations only access transient regimes of morphological evolution, whereas universality, which is often invoked [10,11] to justify a particular continuum equation for a given experimental setup, is appropriate only in the limit of infinitely large length and time scales. Indeed, the difficulties encountered with the description of recent computer simulations [45][46][47] and experiments [30][31][32][33][48][49][50] of homoepitaxial growth in terms of the standard equations of surface growth show that this program remains problematic. This is exacerbated by the fact that, from a technological perspective [29][30][31][32][33], the initial, rather than the asymptotic behavior of homoepitaxial surfaces, is of primary interest.…”

Model parameter estimation and feedback control of surface roughness in a sputtering process

“…Stochastic PDEs contain the surface morphology information of thin films, and thus, they may be used for the purpose of feedback controller design. For example, it has been experimentally verified that the Kardar-Parisi-Zhang (KPZ) equation (Kardar et al, 1986) can describe the evolution of the surface morphology of GaAs thin films which is consistent with the surface morphology measured by atomic force microscopy (AFM) (Ballestad et al, 2002;Kan et al, 2004).…”