Silicon Photonics: Fundamentals and Devices

6.4 Band Structure Engineering Using Alloys

As mentioned already, a momentum-conserving agent is needed in order to complete the recombination of excess EHPs in an indirect band gap semiconductor. It has been stated that quantized lattice vibrations, that is, phonons, may provide the required momentum in materials like silicon. Defects or disorder may also provide the momentum needed for a recombination process to occur. An example of defect is the alloy disorder in an alloy semiconductor. For example, in Si_1−xGe_x, the atomic potentials are different at the Si and Ge sites. If one assigns an average potential V_alloy to a virtual crystal, then deviations amounting to will be found respectively at the Si and Ge sites. It is usual to assume this fluctuation as a spherical square well potential, the Fourier transform of which may be written as

(6.6)

If , the required momentum may be obtained from this alloy disorder potential. Following the theory of absorption in an indirect gap as outlined in Chapter 4, the expression for absorption coefficient due to alloy disorder becomes

(6.7)

where ...