Interband optical absorption in thin semiconducting quantum well wires

We have calculated the optical absorption coefficient due to interband transitions between quantized subbands in the valence and conduction bands of a thin semiconducting quantum well wire having a direct energy band gap Eg. The model we have used in our calculations assumes electron wave functions and energy eigenvalues of the particle in a box type for the motion of the carriers in the direction perpendicular to the axis of the thin semiconducting wire. The threshold for the optical absorption due to interband transitions is shifted to shorter wavelengths as the cross-sectional area of the wire decreases. Above the threshold, the absorption is an oscillatory function of the photon energy when the transverse dimensions of the wire are fixed. For allowed transitions, the selection rules allow transitions only between those subbands in the conduction and valence bands having the same set of quantum numbers. In this case, the absorption coefficient has peaks whenever the photon energy is such that transitions can take place between new pairs of subbands in the valence and conduction bands. The absorption coefficient for such allowed transitions is directly proportional to the density of states of the carriers in the valence and conduction bands. For forbidden transitions, the threshold for the beginning of absorption is also shifted towards shorter wavelengths because of size quantization and the absorption is an oscillatory function of photon energy for fixed transverse dimensions of the wire, but the selection rules for transitions allow transitions to states where the quantum numbers of the quantized subbands can be different in the conduction and valence bands. Also, when the transitions are forbidden, the behavior of the absorption depends upon the polarization of the radiation relative to the axis of the quantum well wire.