First-principles calculation of the effect of strain on the diffusion of Ge adatoms on Si and Ge (001) surfaces
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First-principles calculation of the effect of strain on the diffusion of Ge adatoms on Si and Ge (001) surfaces A. van de Walle, M. Asta, and P. W. Voorhees Materials Science & Engineering Department, Northwestern University, Evanston, IL 60208-3108 2/10/2003 Abstract First-principles calculations are used to calculate the strain dependencies of the binding and diffusion-activation energies for Ge adatoms on both Si(001) and Ge(001) c(4x2) reconstructed surfaces. Our calculations reveal that over the range of strains typically sampled during quantum dot self-assembly (0 to 1% compressive strain) the binding and activation energies on a strained Ge(001) surface increase and decrease, respectively, by ° 0.21 eV and 0.12 eV. For a growth temperature of 600 C, these strain-dependencies give rise to a 16-fold increase in adatom density and a 5-fold decrease in adatom diffusivity in the region of compressive strain surrounding a Ge island with a characteristic size of 10 nm lying on top of a Si substrate covered by a Ge wetting layer.
In heteroepitaxial growth of lattice-mismatched thin films, the Stranski-Krastanov (SK) growth mode has been widely investigated as a basis for self-assembling arrays of coherent nanostructured islands, commonly referred to as quantum dots (QDs).[3] The need for highly monodisperse QD arrays in semiconductor optoelectronic device applications has motivated extensive research into the microscopic mechanisms influencing the evolution of island size distributions during SK growth. While the stabilizing thermodynamic effects associated with the elastic interactions between strained islands have been investigated in some detail (e.g., Refs. [30,2], and references cited therein), the role of various proposed kinetic mechanisms on the development of island size distributions remains less clear. Within a self-consistent mean-field rate theory, Koduvely and Zangwill [9] demonstrated that with decreasing island-island separation, a strain-mediated decrease in the barrier for adatom-island detachment leads to a reduction in the mean island size, with an associated narrowing of the size distribution. These findings are qualitatively consistent with experimental observations [8] in InAs/GaAs. Madhukar [14] and Penev, Kratzer and Scheffler [10,23] have considered the growth of InAs QDs on GaAs, where increasing island size leads to a buildup of compressive elastic strains in the surrounding substrate.[22] Within simplified models of diffusion-limited growth these authors demonstrated that, in the InAs/GaAs heteroepitaxial system, the strain-dependence of the parameters governing adatom diffusion gives rise to a reduction in the flux of adatoms reaching larger islands relative to small ones, leading to a reduced rate of coarsening and an associated narrowing of the size distribution. While the potentially important consequences for island growth kinetics arising from strain dependencies in adatom binding and migration energies have been clearly demonstrated, attempts to determine the magnitude o
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