Variational Method Applied to Determine the Lattice Parameter Profiles in Semiconductor Heterostructures Articles uri icon

publication date

  • August 2009

start page

  • 1604

end page

  • 1610


  • 8


  • 41

International Standard Serial Number (ISSN)

  • 1386-9477

Electronic International Standard Serial Number (EISSN)

  • 1873-1759


  • We have obtained the lattice parameter profiles for Ge/Si (1 1 n) and InAs/GaAs (1 1 n)
    heterostructures using the elasticity continuum theory in the linear
    approximation. In our model we assume that a small fraction of the substrate
    participates in the heterostructures relaxation in the non-rigid approximation.
    Minimization of the free energy by the Euler&-Lagrange method allows us to
    predict the evolution of the lattice parameter with the film coverage. A
    sigmoidal-like law for the lattice parameter profile is observed in the rigid
    and non-rigid approximations. This behaviour is qualitatively similar to that
    obtained for lower Miller indices in Ge/Si and InAs/GaAs heterostructures. As
    the aspect ratio changes, we observed a significant dependence of the lattice
    parameter slope basically for higher aspect ratio values. Therefore, the
    difference in the depletion parameter does not sensitively affect the lattice
    parameter changes for higher aspect ratios in some range of investigated
    materials. So the aspect ratio is seen to play a key role in relaxation
    mechanisms and can explain different shapes observed in the formation of
    heterostructures. From these results, we have deduced that the aspect ratio and
    subsequently the misfit strain and substrate orientations are the key parameters
    in relaxation processes, since they define changes in the lattice parameter with
    the height of deposited film.