EXACT 4X4 BLOCK DIAGONALIZATION OF THE 8-BAND K-CENTER-DOT-P HAMILTONIAN MATRIX FOR TETRAHEDRAL SEMICONDUCTORS AND ITS APPLICATION TO STRAINED QUANTUM-WELLS
P. Enders et M. Woerner, EXACT 4X4 BLOCK DIAGONALIZATION OF THE 8-BAND K-CENTER-DOT-P HAMILTONIAN MATRIX FOR TETRAHEDRAL SEMICONDUCTORS AND ITS APPLICATION TO STRAINED QUANTUM-WELLS, Semiconductor science and technology, 11(7), 1996, pp. 983-988
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.