Band structure and interband optical transitions in the sawtooth superlattice

The band structure and interband matrix elements of the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As sawtooth superlattice are analyzed. We have shown that the envelope wave functions may be expressed as integrals of elementary functions. Numerical results are given for a superlattice with maximal mole fraction $x_{\max }$=0.3, and period equal to 14 nm. A comparison of our results with those obtained via the pseudopotential method is given. Also, the possibility of determining the conduction-band offset Δ$E_c$ from optical measurements, based on strong dependence of the transition matrix elements on Δ$E_c$, is discussed.