First principles study of Ge∕Si exchange mechanisms at the Si(001) surface

Abstract

Based on density functional theory calculations, we show that an isolated Ge adatom on Si͑001͒ triggers an exchange mechanism involving three atoms, which leads to the formation of a Si adatom and a mixed SiGe surface dimer. The activation energy calculated from first principles is sufficiently low ͑0.8 eV͒ to make such a process viable down to the lowest temperature ͑330 K͒ at which intermixing was reported. A second mechanism, with a higher barrier, is also proposed and shown to possibly contribute to the incorporation of Ge into deeper layers as experimentally observed at higher temperatures. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2926683͔ Deposition of Ge on Si leads to a wealth of interesting phenomena of great technological relevance. Both flat Gerich films and three-dimensional ͑3D͒ structures grown in the Stransky-Krastanow regime have been extensively studied and exploited for present and next-generation microelectronics devices.1,2 In these systems, Ge/ Si intermixing has been soon recognized as a key factor, since it affects the formation of sharp interfaces, 3 the release of strain behind the formation, stability, and evolution of 3D Ge islands, 4-10 and the reconstruction of wetting layers. 11,12Although Ge would tend to segregate at the surface due to its lower surface energy, entropy would lead to Si/ Ge intermixing also in a Ge capping layer on Si. To which extent thermodynamic equilibrium would be reached during heterostructures growth is still a matter of debate. High-resolution photoemission data showed the formation of mixed SiGe dimers by depositing Ge on Si͑001͒ at 623 K, 13 while scanning tunneling microscopy measurements 14 revealed the formation of GeSi mixed dimers down to 330 K. Elementary processes leading to Si/ Ge intermixing have been theoretically investigated within density functional theory ͑DFT͒ as well.15-18 An activation energy of 1.6 eV was calculated for a Si/ Ge exchange between the first and the second surface layer, 16 while exchanges between adatoms and surface atoms are predicted to have barriers of 1.6 eV ͓for Ge adatom on Si͑001͔͒ 15 or 1.5 eV ͓for Si adatom on Ge͑001͔͒. 16 Starting from a stable ad-dimer, intermixing with surface atoms would occur with calculated activation energies of 1.2 eV for a SiGe turning into a SiSi or 1.4 eV for the reverse mechanism. 18 Clearly, activation energies in the range of 1.4-1.6 eV ͑Ref. 19͒ are incompatible with intermixing at 330 K as reported in Ref. 14.In this letter, based on DFT calculations, we shall show that isolated Ge adatoms on Si͑001͒ are able to trigger exchange processes through a three-atom mechanism down to the lowest temperature ͑330 K͒ at which intermixing was observed.14 By combining our results with previously reported ones, we show that theory and experiments seem to be in good agreement for a wide set of observed phenomena. Spin unrestricted calculations were performed with gradient corrected exchange and correlation ͑xc͒ functional, 20 plane waves expansion of Kohn-Sham orbitals up to an ener...

Aspect-ratio-dependent driving force for nonuniform alloying in Stranski-Krastanow islands

“…At the same time, also further Ge atoms reach the island, partially relieving strain by intermixing with Si, and partially climbing along the exposed facets and reaching the top regions, which are energetically favored. With this respect, the higher Ge content in the central, internal region of the island could be a reminiscence of the initial stages of formation, the actual profile being caused by the progressive reshaping allowed for by Si/Ge exchanges, limited, however, to the very outermost layers 12,35 where kinetic barriers are sufficiently low. For islands grown at higher temperatures, instead, it looks like the c min profile deviates more substantially from the experimental one ͑compare Fig.…”

Shaping the composition profiles in heteroepitaxial quantum dots: Interplay of thermodynamic and kinetic effects

“…[22][23][24][25][26] These range, on average, from few tenths of an eV for events on the (100) surface to ∼2 eV for diffusion down to the sixth subsurface layer. 25 The effect of the reconstruction stress field is taken into account in the estimation of barriers.…”

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

“…The fourth contribution comes from the entropic term and favours alloying. As demonstrated by ab initio calculations [32,33], all mechanisms of atomic exchange responsible for intermixing are possible only within the first few atomic layers at the surface. In the bulk below, the activation barriers for atomic motions are too high and bulk diffusion is hindered.…”

“…Intermixing takes place also in InGaAs/GaAs [31], but the effect is less dramatic due to the non-negligible enthalpy of mixing. It is important to point out that, at the typical temperatures of interest, intermixing occurs only at the surface (or, at the subsurface) [32][33][34], as bulk diffusion is kinetically hindered. This observation is key, as, for any miscible system, deposition of a thin film on a thick substrate would lead to full dilution of the former in the latter, as determined by entropy maximization.…”