EXACT 4X4 BLOCK DIAGONALIZATION OF THE 8-BAND K-CENTER-DOT-P HAMILTONIAN MATRIX FOR TETRAHEDRAL SEMICONDUCTORS AND ITS APPLICATION TO STRAINED QUANTUM-WELLS

In its commonly used form, the eight-band k . p Hamiltonian for tetrah edral semiconductors exhibits a two-fold (Kramers) degenerate spectrum throughout the Brillouin zone (BZ). We present an exact and general ( valid for all k-vectors) block diagonalization of this 8 x 8 Hamiltoni an matrix into two 4 x 4 blocks each having the same eigenvalues as th e 8 x 8 matrix. The 4 x 4 blocks exhibit a relatively simple dependenc e on the k-vector and include arbitrary strain along the cubic crystal axes. The spin-orbit interaction is now an 'effective' one, depending on the k-vector and the strain. For the application to QWS, the goal is to get for the 4 x 4 blocks a dependence on k(z) which is no more c omplicated than that of the 8 x 8 matrix. This is achieved for k(t) pa rallel to 0 [10], k(t) parallel to [01] (arbitrary strain) and k(t) pa rallel to [11] (only biaxial strain in the layer plane). For general k (t)-vectors only a minor approximation is necessary, as shown by numer ical examples.