Thermalization and non-radiative transitions

Non-radiative transitions invariably involve the conversion of excitation energy into phonons. Thermalization involves many inelastic transitions between states in the band or band tails. Three mechanisms of thermalization apply to a-Si H. Carriers in extended states lose energy by the emission of single phonons as they scatter from one state to another. Transitions between localized states occur either by direct tunneling or by the multiple trapping mechanism in which the carrier is excited to the mobility edge and recaptured by a different tail state. 

The rate of loss of energy of a carrier at an energy by a single phonon is calculated to be (Mott and Davis 1979), 

Thermalization in the band tail at low temperature occurs by tunneling between localized states. The low temperature only permits transitions to states of lower energy. The transition probability to a neighboring site contains the same overlap factor as for the radiative transitions. 

The thermalization rate of carriers from above the exponential tail is shown in Fig. 8.5 for two assumed band tail widths, corresponding to the conduction and valence bands of a-Si H. The rate decreases very rapidly and, for practical purposes, thermalization stops at an energy 5kTf, below the mobility edge. 

At elevated temperatures, thermalization also occurs by thermal emission out of the traps to the mobility edge, followed by retrapping. This is the familiar multiple trapping mechanism which governs the dispersive carrier drift mobility and which is analyzed in Section 3.2.1. 

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