Silicon Photonics: Fundamentals and Devices

5.7 Optical Processes in QDS

We consider a quantum box of cubic shape with each side length a. The absorption coefficient for this box is expressed as 30

(5.74)

where is the degeneracy of the energy level determined by n². Only transitions satisfying Δn = 0 are allowed. The above equation indicates that the interband absorption will be a series of discrete lines representing the reduced density-of-states function of a zero-dimensional (0D) system. The discrete lines will occur at photon energies

(5.75)

The discrete lines are broadened due to several reasons. As for example, we consider a family of dots whose sides show a fluctuation described by the following Gaussian distribution:

(5.76)

where a₀ is the average side length, and the standard deviation D is given by . Using Eqs. (5.74) and (5.76), the absorption coefficient for a non-uniform dot size distribution is

(5.77)

Let us define ...