P. I. Cohen

Diffraction from stepped surfaces: I. reversible surfaces

Abstract In electron or atom diffraction experiments on surfaces, the angular shapes of the diffracted beams depend upon the distribution of steps over the surface. In this paper we analyze diffracted beam profiles from stepped surfaces that are reversible. A reversible surface is one in which the pair correlation function over the surface is symmetric with respect to positive and negative directions. We show that the intensity profile across a diffracted beam can be separated into a sharp central spike due to the limit of the correlation function at large separation plus wings or shoulders due to the finite extent of the step disorder. Simple functional expressions for these angular profiles are obtained by a Markov method of treating a one-dimensional geometric distribution of steps. The result explicitly displays the deep structure found for the general case. The method reduces the calculation to a simple eigenvalue problem so that even the continuously changing step distributions that occur in epitaxial growth can be treated easily. As in the general case, the resulting intensity profile is a sharp central spike plus a step-broadened term which now is a sum of Lorentzians. The widths of the Lorentzians are the logarithms of the eigenvalues of the matrix of probabilities which describe the step distribution over the surface. This matrix method, which treats the surface as a Markov chain, also points the correct way to account for correlations between surface atoms for two-dimensional distributions of steps. For a two-dimensional surface one must consider a Markov Random Field as opposed to a simple multiplication of two one-dimensional results. We compare the results of the general calculation to the Si epitaxy experiments of Gronwald and Henzler. The coverage and momentum transfer dependencies of the shapes of the calculated profiles agree with their measurements. The calculation is also applied to the RHEED measurements of Van Hove et al. during GaAs MBE. The measured intensity oscillations can be accounted for by a cyclically changing one-dimensional geometric distribution of steps among three layers in which the third-layer scattering increases with time.

Damped oscillations in reflection high energy electron diffraction during GaAs MBE

Oscillations in the time evolution of electron diffraction during MBE growth of GaAs are shown to be related to periodic variations in the step distributions on GaAs surfaces during epitaxial growth. Unintentionally doped GaAs surfaces were first prepared by MBE. Then the Ga flux is interrupted until an instrument limited diffraction pattern was obtained. During this process the angular width of the specular beam was measured versus time. When the Ga flux there are intensity oscillations that are weak near the Bragg angle. At the Bragg angle, where the diffraction is insensitive to surface steps, the length of the specular RHEED streak does not change. At angles between the Bragg angles, where steps lengthen the streaks, there are periodic variations in the streak length. We interpret the results in terms of a model in which a partially completed surface has a step distribution with smaller average terrace lengths than a completed surface.

Birth-death models of epitaxy: I. Diffraction oscillations from low index surfaces

Abstract Simple mathematical modes are presented that exhibit features observed in reflection high-energy electron diffraction (RHEED) studies of crystal growth by molecular beam epitaxy. These models are based on a birth-death analysis of growth on low-index surfaces. These are mean field models which after an initial transient give RHEED intensity oscillations with varying degrees of damping. For moderate values of interlayer transfer the oscillations are nearly sinusoidal with maxima that do not necessarily correspond to the deposition of integral numbers of layers. As the transfer is increased, the oscillations become more cusp-like, as would be expected for perfect layer-by-layer growth. The results agree qualitatively with the intensity oscillations that are observed on low-index surfaces.

Relaxation of strained InGaAs during molecular beam epitaxy

Relaxation of strained InxGa1−xAs films grown on GaAs substrates has been measured in situ during molecular beam epitaxy growth by reflection high‐energy electron diffraction (RHEED). Growth is found to be layer by layer up to a strain‐dependent ‘‘critical’’ thickness where three‐dimensional clusters with {114} facets form. The onset of cluster growth is simultaneous with lattice relaxation as measured by RHEED. The relaxation during growth is compared with the Dodson–Tsao model for strained‐layer relaxation [Appl. Phys. Lett. 53, 1325 (1987)]. Two distinct mechanisms for relaxation were found depending on film strain. An activation energy for relaxation was measured to be 4.4 eV for a film strain of 2.3%. The relaxation deviated from the Dodson–Tsao model for nongrowth conditions.

Reflection high energy electron diffraction measurement of surface diffusion during the growth of gallium arsenide by MBE

Oscillations in both the intensity and width of reflection high energy electron diffraction (RHEED) are observed to depend upon most MBE growth parameters. Previously, we reported that oscillations in the width of the specular RHEED beam could be used to measure the mean island size occuring during growth. From the mean island size, the diffusion length of adatoms on the surface was estimated. On a GaAs(100) surface the measurements are extended to determine the dependence of the surface diffusion of Ga on Ga arrival rate, As4 flux, crystal misorientation, and substrate temperature. At temperatures where Ga evaporation is not significant, but still high enough to be in the 1×1 surface phase region, we find the diffusion length decreases as the square root of the Ga arrival rate. For fixed Ga arrival rate, the correlation length was measured as a function of temperature and as the As4 flux was varied. These results are compared to those obtained by Neave et al. [Appl. Phys. Letters 47 (1985) 100].

Mass‐action control of AlGaAs and GaAs growth in molecular beam epitaxy

GaAs evaporation during molecular beam epitaxy (MBE) is measured using reflection high‐energy electron diffraction (RHEED). On the (001) surface there is a first‐order phase transition from a 2 × 4 to 1 × 1 reconstruction. Upon crossing the phase boundary into the 1 × 1 structure, layer‐by‐layer evaporation of GaAs is observed. This evaporation affects the rate of growth of GaAs and AlxGa1−xAs by MBE. The dependence of the growth rate on substrate temperature and on As, Al, and Ga fluxes is followed by measuring RHEED intensity oscillations. The results agree quantitatively with the mass‐action analysis of Heckingbottom [R. Heckingbottom, J. Vac. Sci. Technol. B 3, 572 (1985)]. At substrate temperatures above 850 K no differences between As2 and As4 incident fluxes are observed.

Multilayer step formation after As adsorption on Si (100): Nucleation of GaAs on vicinal Si

We have used reflection high‐energy electron diffraction to characterize the initial surface of misoriented Si (100) and then to follow the nucleation of GaAs. Measurement of the diffracted intensity along the length of the specular streak shows sharp structure due to an ordered array of steps. The initial surface contains monolayer steps. However, after exposing to an As4 flux above 650 °C, the surface morphology changes to multilayer steps with four times the original period. In contrast, below 650 °C, surface migration is inhibited and monolayer steps are retained. Subsequent growth of GaAs on either the monolayer‐ or multilayer‐stepped surfaces yields single domain films. However, GaAs grown on the monolayer steps is misoriented toward the (111)A while GaAs grown on the multilayer steps is misoriented toward the (111)B.

Suppression of antiphase domains in the growth of GaAs on Ge(100) by molecular beam epitaxy

Abstract We have used reflection high energy electron diffraction (RHEED) to determine the step structure on Ge and GaAs surfaces. The results show the key role that inequivalent steps on Ge substrates play in suppressing antiphase domain formation at the GaAs/Ge(100) interface. For Ge surfaces misoriented toward the [011] direction and exposed to an As flux, a mass migration causing a four-monolayer step periodicity is observed. If a Ga flux is then applied, a single domain of GaAs is formed. The single domain is observed at the start of growth with weak half order streaks appearing in only one azimuth. In contrast, for surfaces misoriented exactly toward the [010]. RHEED measurements show a different distribution of multilayer step heights with no clearly predominant even or odd layer step height. GaAs grown on this surface shows a reconstruction consisting of two domains.

The meandering of steps on GaAs(100)

Abstract The zincblende structure of GaAs gives rise to two types of steps on a GaAs(100) surface. In a model using abrupt bulk-termination, these steps would be labelled A or B, depending upon whether they are As or Ga terminated, and in the [011] or [011] directions, respectively. Since these steps are structurally and chemically different, one expects them to have different roles in epitaxy. We have used reflection high-energy electron diffraction (RHEED) to study the morphology of each of these two types of steps on surfaces prepared by molecular beam epitaxy (MBE). The results show large differences in the qualitative and quantitative structural disorder of these two step configurations. During static conditions of no growth, but with an As 4 flux provided, the A-steps were straight over long distances. However the terraces between them exhibit large fluctuations in length. Conversely, the B-steps are highly kinked, but are seperated by terraces which show little length variation. For the A-steps, the terrace length fluctuations are greatly reduced by changing the reconstruction from the 2×4 or 1×1 or by initiating growth. During growth, the difference between RHEED intensity oscillations on the two surfaces is striking. For identically prepared and simultaneously mounted wafers that had been oriented 2° from the (100), the A-surface showed intensity oscillations over a range in temperatures. By contrast, the B-surface exhibited only faint oscillations that were rapidly damped. In addition, during growth of GaAs on stepped Si(100) surfaces, growth on surfaces prepared to yield A-steps gave much smoother morphologies than on surfaces prepared to yield B-steps.

Structure and composition of GaN(0001) A and B surfaces

Homoepitaxial, GaN films on both c-plane surfaces of bulk GaN crystals were examined using reflection high-energy electron diffraction (RHEED). Differences in the RHEED pattern, time development of the RHEED intensity, and surface reconstructions were observed. The substrate surfaces were prepared either by mechanical polishing [GaN(0001)A] or by chemo-mechanically polishing [GaN(0001)B]. Then films were grown by molecular beam epitaxy; Ga was provide by a Knudsen cell and nitrogen from NH3. On the B surface, the Ga rich reconstructions reported by Smith and co-workers [Phys. Rev. Lett. 79, 3934 (1997)] were observed. On the A surface, a (2×2) reconstruction was observed. Both reconstructions were much sharper than those seen on GaN films grown on sapphire. RHEED measurements of the specular intensity vs time showed that two different surface terminations could be maintained on the B surface, one of which is a stable, gallided surface, while the other is a nitrided surface, which is unstable in vacuum. I...