Appendix D
Multi-Phonon Emission

Based on Chapter 8.3 the forward and reverse barriers of the radiative multi-phonon emission (MPE) and the non-radiative multi-phonon (NMP) model will be deduced from the harmonic oscillator of the form

V1(q) =  1M ω2(q − q1)2 + E1                        (D.1 )
         2   1
V (q) =  1M ω2(q − q )2 + E ,                       (D.2 )
 2       2   2      2     2
where E1   and E2   denote the defect states in thermal equilibrium at V1(q1)  and V2(q2)  . The vibronic frequencies ω1   and ω2   set the curvature of the harmonic potentials.
 D.1 Radiative Multi-Phonon Emission
 D.2 Non-Radiative Multi-Phonon Process