The overall features of the energies and atomic structures of the twist boundaries in Si have been examined by energy-minimization calculations using the transferable semiempirical tight-binding method, and the results have been compared with those of the tilt boundaries in Si. First, the {122} SIGMA = 9 tilt boundary has been dealt with as a typical tilt boundary observed in polycrystalline Si. It has been shown that the configuration consisting of atomic rings without any coordination defects can exist stably with a relatively small interfacial energy, 0.32 J/m2, and with small bond-length and bond-angle distortions within about +/-2% and about +/-20-degrees, similarly to the other tilt boundaries. The twist boundaries with different rotation axes and boundary planes, the [111] SIGMA = 7, and [011] SIGMA = 3, and [001] SIGMA = 5 twist boundaries have been examined against various rigid-body translations parallel to the interface. It has been found that the twist boundaries contain larger bond distortions or more coordination defects, and much larger interfacial energies than those of the tilt boundaries, at least when they are constructed by ideal surfaces. It seems that there do not exist deep or sharp energy minima against the rigid-body translations, differently from the tilt boundaries. About the [111] SIGMA = 7 and [011] SIGMA = 3 boundaries, configurations without any coordination defects can be constructed for proper translations. However, in the [111] SIGMA = 7 boundaries, large bond stretchings are inevitably introduced except at the sites of good coincidence, and the [011] SIGMA = 3 boundary frequently contains four-membered rings with large bond-angle distortions. Thus the most stable configurations of these boundaries contain interfacial energies over three times larger than the value of the SIGMA = 9 tilt boundary, and contain shallow states in the band gap. On the other hand, the [001] SIGMA = 5 boundaries have very complex structures as compared with the other twist boundaries. The interfacial energies are much larger than the other twist boundaries, the configurations frequently contain coordination defects and deep states in the band gap, and there seem to exist many metastable configurations with different bonding networks in a similar energy range, similarly to the results of the same boundaries in Ge by Tarnow et al. [Phys. Rev. B 42, 3644 (1990)]. The present different features of the respective twist boundaries can be explained by the morphology of the respective ideal surfaces. It can be said that stable configurations of the tilt boundaries and other extended defects in Si or Ge are constructed by arranging the structural units consisting of atomic rings without any large bond distortions or coordination defects. For twist boundaries, such stable structural units cannot be easily constructed, which causes the present greater structural disorder and larger interfacial energies. This is the reason why twist boundaries are seldom found in polycrystalline Si as compared with the frequently observed tilt boundaries.
