The search for Bose–Einstein condensation of excitons in Cu2O: exciton-Auger recombination versus biexciton formation

James P Wolfe,Joon I Jang

doi:10.1088/1367-2630/16/12/123048

James P Wolfe, Joon I Jang

Open Access

https://doi.org/10.1088/1367-2630/16/12/123048

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Abstract

Excitons in high-purity crystals of Cu2O undergo a density-dependent lifetime that opposes Bose–Einstein condensation (BEC). This rapid decay rate of excitons at a density n has generally been attributed to Auger recombination having the form , where A is an exciton-Auger constant. Various measurements of A, however, have reported values that are orders-of-magnitude larger than the existing theory. In response to this conundrum, recent work has suggested that excitons bind into excitonic molecules, or biexcitons, which are short-lived and expected to be optically inactive. Of particular interest is the case of excitons confined to a parabolic strain well—a method that has recently achieved exciton densities approaching BEC. In this paper we report time- and space-resolved luminescence data that supports the existence of short-lived biexcitons in a strain well, implying an exciton loss rate of the form with a biexciton capture coefficient C(T) proportional to , as predicted by basic thermodynamics. This alternate theory will be considered in relation to recent experiments on the subject.

Highlights

Cuprous oxide (Cu2O) is a thoroughly studied direct-gap semiconductor with long-lived, highly mobile excitons [1]3
In [14] we considered the direct Auger decay process; a phonon-assisted biexciton Auger decay would lead to a linear temperature dependence of the Auger process
In an unstressed high-purity crystal of Cu2O, calibrated measurements of orthoexciton and paraexciton densities following 5 ps excitation pulses are well explained by the biexciton formation model for crystal temperatures between 2 and 200 K

Summary

Introduction

Cuprous oxide (Cu2O) is a thoroughly studied direct-gap semiconductor with long-lived, highly mobile excitons [1]3. The time-resolved luminescence spectrum in figure 2(a) shows the kinetic energy distribution of the exciton gas at a high density. The proximity of e–h pairs in the molecule would cause a much faster Auger decay than that of two free excitons at the thermodynamic gas density In this case, the rapid thermodynamic binding of excitons into molecules would limit the exciton lifetime, and equation (1) is replaced by the following two equations [14]. With the assumption that biexcitons will be created in their para–para state either by the binding of two paraexcitons or by two orthoexcitons of opposite spin alignment, one expects Co = Cp/3 and Cop = 0, which leads to an average capture coefficient C applicable to both temperature regimes and given by:. Theoretical calculations show a small but significant binding energy, of order 3–13 meV10

Strain-confinement of excitons in Cu2O

Discussion of results and relation to other work

Findings

Summary and prospects