Steps on (001) silicon surfaces

Abstract

We investigate a topological method of eliminating antiphase domains in zinc-blende semiconductors heteroepitaxially grown on (001) Si substrates. Antiphase domains cannot occur if only one of the two atomic species of the polar overlayer bonds directly to the substrate at the heteroepitaxial interface (As, in the case of GaAs on Si) and if atoms from only one of the two inequivalent sublattices of the substrate form the termination boundary [only biatomic (a0/2) steps present]. We show that thermal equilibrium is a necessary and sufficient condition to realize this condition for (001) Si, a result of a π-bonded step reconstruction that lowers the relative enthalpy of reconstructed [110] biatomic steps by 0.04 eV per step atom for one type of biatomic step, and of correlation, which freezes out the step configuration entropy thereby suppressing the formation of all other types of steps. Our model explains selection rules and dimer orientations observed in infrared absorption, low-energy electron diffraction, and reflection high-energy electron diffraction measurements of vicinal (001) Si surfaces tilted toward (110). For general vicinal surfaces, competition from the non-π-bonded sides of the atomically flat terraces weakens the thermodynamic driving force. For surfaces tilted toward (100) it vanishes completely, indicating that antiphase-free polar material cannot be grown on these surfaces, in agreement with experiment. If a minimum threshold energy is needed per terrace to form a primitive (001) surface, then the boundaries between antiphase-free and antiphase-dominated regions for spherically figured surfaces should be parabolic. The minimum energy estimated from the results of Akiyama et al. on spherically figured surfaces suggests that terrace–terrace correlations are also important factors in forming the primitive surface.