An excitonic model for the electron\u2013hole plasma relaxation in proton-irradiated insulators

Lorenzo Stella,Jonathan Smyth,Brendan Dromey,Jorge Kohanoff

doi:10.1140/epjd/s10053-021-00215-3

Abstract

The relaxation of free electron–hole pairs generated after proton irradiation is modelled by means of a simplified set of hydrodynamic equations. The model describes the coupled evolution of the electron–hole pair and self-trapped exciton (STE) densities, along with the electronic and lattice temperatures. The equilibration of the electronic and lattice excitations is based on the two-temperature model, while two mechanisms for the relaxation of free electron–hole pairs are considered: STE formation and Auger recombination. Coulomb screening and band gap renormalisation are also taken into account. Our numerical results show an ultrafast ({ll },{mathrm {1}} ps) free electron–hole pair relaxation time in amorphous {{mathrm {SiO}}_{mathrm {2}}} for initial carrier densities either below or above the exciton Mott transition. Coulomb screening alone is not found to yield the long relaxation time ({mathrm {gg }}{mathrm {10}} ps) experimentally observed in amorphous {{mathrm {SiO}}_{mathrm {2}}} and borosilicate crown glass BK7 irradiated with high-intensity laser pulses or BK7 irradiated by short proton pulses. Another mechanism, e.g. thermal detrapping of STEs, is required to correctly model the long free electron–hole pair relaxation time observed experimentally.Graphical

Highlights

The passage of swift ions through semiconductors or insulators generates a large density of electron–hole pairs, which eventually recombine either radiatively or non-radiatively
We have solved numerically the simplified hydrodynamic equations (5) to assess the consequences of Coulomb screening and band gap renormalisation (BGR) in the evolution of the electron–hole plasma generated upon proton irradiation of a-SiO2
The twotemperature relaxation time is set to a typical value of τ = 0.1 ps [5,6], while self-trapped exciton (STE) formation time is set to τ2ste = 1/k2 = 150 fs [12,13,14]

Summary

Introduction

The passage of swift ions through semiconductors or insulators generates a large density of electron–hole pairs, which eventually recombine either radiatively or non-radiatively. 220 fs, suggesting a longer free electron–hole pair relaxation time as the laser intensity is increased [15,16]. Grojo et al [17] observed an abrupt increase of the free electron–hole pair relaxation time in a-SiO2 as the charge density exceeds 1020 cm−3. Critical examination of the experimental conditions and modelling suggests that relaxation to STEs may not be the dominant mechanism for electron–hole densities as large as 1022 cm−3 [18]. Since for large electron–hole pair densities Coulomb screening is known to hinder the formation of free excitons—which are the precursor of STEs—Auger recombination will become dominant [19,20]. The transition from a gas of free excitons to an electron–hole plasma driven by Coulomb screening is known as the exciton Mott transition (EMT) [21,22,23]

Results

Discussion

Conclusion