Calculation of energy characteristics for Si1–xGex–Si structures with single quantum wells

Energy characteristics of Si1–xGex–Si quantum-size structures with single quantum wells were calculated numerically based on a four-band k·p method. Analytical expressions for the Luttinger parameters are obtained as functions of the component composition of Si1–xGex compounds. Analytical expressions for the energy ħω of optical band-to-band transitions are obtained in an effective mass approximation and agree well with numerical calculations by the k·p method. This allows one to determine accurately a range of changes while varying the component compositions and thickness of the active and barrier layers.