No abstract

Surface diffusion of Ge on Si͑111͒ at high temperatures has been examined experimentally by secondharmonic microscopy and computationally by molecular-dynamics simulations with a Stillinger-Weber potential. Experimentally, the activation energy and preexponential factor for mass-transfer diffusion equalled 2.48Ϯ0.09 eV and 6ϫ10 2Ϯ0.5 cm 2 /s, respectively. Simulational results yielded essentially the same numbers, confirming the utility of the Stillinger-Weber potential for diffusional studies. A previously developed semiempirical correlation also did fairly well. The simulations also provided estimates for the corresponding parameters for intrinsic diffusion and for the enthalpy and entropy of Ge adatom-vacancy pair formation on Si. The simulations further yielded evidence for minor contributions of atom exchange to intrinsic diffusion, as well as the complex high-temperature islanding phenomena on picosecond time scales.

Second harmonic microscopy has been used to quantify the surface diffusion of In on Si(111). At temperatures near 50% of the bulk melting temperature and in the coverage range 0<θ<0.7, the activation energy Ediff and pre-exponential factor D0 lie at 42±0.5 kcal/mol and 3×103±0.3 cm2/s, respectively. These parameters, which are quite large, are explained semiquantitatively by reference to an adatom–vacancy model recently developed for related systems. The present work, when compared with the results of these other systems, offers significant evidence for the effects of adatom–vacancy ionization.

For diffusion-controlled reactions in three dimensions, continuum mechanics provides a quantitative relation between the steady-state reaction rate constant k and the diffusion coefficient D. However, this approach fails in two dimensions, where no steady-state solution exists on an infinite domain. Using both Monte Carlo methods and analytical techniques, we show that previous attempts to circumvent this problem fail under real laboratory conditions, where fractional coverages often exceed 10−3. Instead, we have developed a rigorous and general relation between k and D for all coverages on a square lattice for the reaction A+A→A2. For short times or high coverages, the relation k=πD/γ holds exactly, where γ denotes the two-dimensional packing fraction. For lower coverages, however, k depends on time in both constant-coverage (adsorption allowed) and transient-coverage (adsorption forbidden) regimes. In both cases, k decreases in response to the evolution of nonrandom adsorbate configurations on the surface. These results indicate that diffusion-limited surface reactions may be identified unambiguously in the laboratory and also provide a quantitative link between diffusion parameters and experimentally determined recombination rate parameters. Practical experimental methods highlighting such effects are outlined.

Surface diffision of Sb on Si(ll1) has been studied by second harmonic microscopy, which uses surface second harmonic generation to monitor surface concentration profiles with a 3 pm spatial resolution. At temperatures near 55% of the bulk melting point and in the coverage range 0 < 6 < 0.12, the activation energy, &iff, and pre-exponential factor, DO, were found to be 60 f 3 kcdmol and 6 x 103*0.' cm2/s, respectively. The high prefactor and activation energy indicate that the surface diffusion is governed by a recently developed adatom-vacancy mechanism.