Silicon Photonics: Fundamentals and Devices

5.2 Optical Processes in QWs

A theory of optical processes in QWs may be developed along the same lines as used for bulk materials [1–5]. There are some modifications due to quantum confinement. We present in the following subsections the theory of absorption due to interband as well as intersubband transitions.

5.2.1 Absorption in Direct-gap QW

We consider that the band alignment is type I, so that both the electron and hole wavefunctions are confined in the well material. Therefore, in calculating the absorption coefficient, the transitions occurring in the well are to be considered. The initial- and final-state wavefunctions, respectively, for the mth subband in the valence band and the nth subband in the conduction band are given by

(5.1)

(5.2)

In the above, U's are cell-periodic parts of the Bloch function; 's are envelope functions; r and k denote, respectively, the two-dimensional (2D) position and wave vectors; A is the area; and L is the width of the QW. The matrix element for transition may be evaluated by assuming that momentum is conserved in the QW layer plane, that is,

(5.3)

Since the motion is quantized along the z-direction, there is no selection rule for the conservation ...