Superlattices and Microstructures, Vol. 4, No. 415, 1988 511 ELECTRONIC STRlJCTlJRE OF STRAINED LAYER Si/GexSil_x SlJPERUITICES FROM TIGBT BINDING TBEORY H.Riicker. F.Bechstedt(*), R.Enderlein, D.Hennigand S.Wilke (**) Sektion Physik,Humboldt-Universitiit zu Berlin, G.D.R.. (*) Friedrich-Schiller-Universitiit Jena, G.D.R., (**) Czechoslovak Academy of Sciences,Prague, CSSR (Received31 August 1987) The electronicstructureof strainedlayer Si/Ge Sil_x superlattices is calculatedby means of the empiricaltight bind& mathod. Coherently strainedSi/Ge superlattices grown on Ge Si are considered?'~~"&?fect substrates of strain (y). band gff&s(!?)layer thick- nesses on superlattice bandstructures and wave functionsis studied.A strain-induced type I - type II transition is obtained. 1. Introduction Strained layer (SL's) grown on Ge Si rent compositions ZIrelZKallenging new systems for experimental and theoretical investiga- tions. Among the various experimental fin- dings the strong effect of lattice misfit strain on transportproperties is the most exciting one'. Theoretical studies of the electronic structureof Si/Ge Si SL's were first performed by Morrison fndl-jarosr who used the pseudopotential approachand simu- lated strain by displacing atoms in appro- priate way. In the present paper we continue such studies by extending our former inve- stigations) on the electronic structure of GaAs/AlxGal_x theory SL's within tight binding (TB) to strained layer Si/GexS;~;~os~~p;; Strain is included either in a way by adopting strain dependent atomic po- sitions or in a phenomenological way by ex- ploiting experimental deformation potentials. 2. Method Si/Ge consi,e2~;G.SSL'~ on GeySil_ substrates are consisting of Nsi itomic layers of sumed to be free of dislocations but cohe- rently strained due to the lattice misfit between the three materials involved. Atoms in a strained SL are displaced compared to unstrained bulk crystals. The displacements are determined as follows. Each SL slab undergoes a tetragonal distortion which leads to different lattice constants parallel and perpendicular to a SL plane. The two pa- rallel latticeconstantsare set equal to the substrate lattice constant where the lat- ter one is taken accordingto Vegard'srule. The parallel strain components then are immediately known, and the perpendicular components can be calculated by means of elastostatics. The two strain components result in elastic displacements which are part of the strain-induced atomic displace- ments on which the internalatomic displace- ments are superimposed". In our case the latter ones vanish for reasonsof symmetry. The TB method is applied in two different versions. First we consideran sp3 basis set and include first and second nearest neighbour interactions (2BW). Strain dependent atomic positions are used to specify the TB interaction matrix elements. The dependencies of the latter ones on interatomic distancesare taken according to Li and Lin-Chung" The (Ge,Si) alloy is treated in VCA. The natural valenceband (VB) offset AE =E (Ge)-E (Si) between unstrained Ge and ST exters tile first TB versionas an experimental parameter. By directly diago- lixi;i&;I-I; i:$h;e;BFgiSg)) we 5 (g-Hamiltonian as well as the SL wave functions C" ($ depending on subband index n,wave vect!!? k of first SL-BZ, layer index m and orbital index a(s,p .P ,P 1. In o?der to control uncertainties which are inherent to any TB method and to the descrip- tion of strain on a microscopiclevel, we use still another TB calculation scheme which complements the first one in a certain sense. In the second versionan sp3s* basis set is applied and only first nearest neighbour in- teractions (1RR) are taken into account. The interaction integrals are chosen such that lNTU bands are reproduced in the case of bulk materials6 . This parametrization fixes the 0749-6036/88/040511+03$02.00/0 0 1988 Academic Press Limited