Nitrogen scattering
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S-matrix theory
In S-matrix theory, the scattering rate in the presence of a perturbing potential V can be calculated from the matrix element
where |kñ and |y(k)ñ are the eigenstates of the unperturbed and perturbed systems respectively. This approach was first applied to dilute nitrides by Fahy and O'Reilly [1] who found that in the ultra-dilute limit, the S-matrix element was proportional to the rate of change of the conduction band-edge with respect to nitrogen concentration.
Subsequently, Fahy et al [2] again applied S-matrix theory in a model based on resonant scattering using the LCINS model discussed earlier.
The scattering rate
Applying S-matrix theory in conjunction with the Anderson Hamiltonian, we find a scattering rate of [3]
where a0 is the lattice constant, N(E) is the density of states and the other terms are as defined earlier.
References
[1] S. Fahy and E.P. O'Reilly, Appl. Phys. Lett, 83, 3731 (2003) abstract
[2] S. Fahy, A. Lindsay, H. Ouerdane and E. P. O'Reilly, Phys. Rev. B, 74, 035203 (2006) abstract
[3] M.P. Vaughan and B.K. Ridley, Phys. Rev. B, 75, 195205 (2007) abstract; M.P. Vaughan, PhD Thesis, University of Essex (2007)
M.P. Vaughan (2007)