Electron temperature dependences of nonradiative multiphonon hot-electron capture coefficients of deep traps in semiconductors—I: Small lattice relaxation

Abstract

Generalizing the theory of nonradiative multiphonon capture of thermal electrons for cases where the effective temperature T e of conduction electrons differs from lattice temperature T L , we develop a corresponding theory of hot electron capture. Its principal novelty is due to an exponential decrease ∝ exp(− E/ k B τ) of the efficiency of this energy loss mechanism, at increasing electron energy E, for the usual regime of small lattice relaxation characterized by a corresponding “capture extinction temperature” τ. The resulting T e -dependences of hot electron capture coefficients at sufficiently low T e ( ▪ τ, i.e. in the “Sommerfeld factor regime”) are controlled by the net charge of the centre which means C( T e ) ∝ C(T e) ∝ T e − 1 2 , ∝ T e 0, or ∝ T e 2 3 exp [−3·(θ/T e) 1 3 ] in cases of attraction, neutrality, and repulsion, respectively. At high T e ▪ τ, i.e. in the “energy-loss factor regime”) these relations reduce to the form C( T e ) ∝ T e − 3 2 which is simply due to an increasing depopulation of the relevant region of low-lying band states. This theory is applied to electron capture by a singly charged repulsive gold centre and a doubly charged repulsive copper centre in germanium. The corresponding theoretical maximum values C max. (−1) = 5.2 · 10 −11 cm 3 s −1 and ifC ( rnmax.) (−2) = 2.4 · 10 −12 cm 3 s −1 of hot electron capture coefficients are in good agreement with experimen observations.