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Comment on ``Inverse exciton series in the optical decay of an excitonic molecule''

Tokunaga et al. [Phys. Rev. B Vol. 59, R7837 (1999)] claim the first successful observation of the inverse exciton M series in the emission spectrum of excitonic molecules. We assert that actually such a series was observed as early as 1989 in the beta-ZnP_2 crystal. We show that the objections of Tokunaga et al. against the biexciton nature of the inverse exciton series in beta-ZnP_2 are ungrounded. In particular, their estimations for the ratio of the intensities of M2 and M1 emission lines in this crystal give two order smaller value because they do not take into account the reabsorption of the M1 line photons. We report the observation of additional inverse exciton M' series in the emission spectrum of excitonic molecules in beta-ZnP_2.

Tokunaga et al. [Phys. Rev. B 59, R7837 (1999)] claim the first successful observation of the inverse exciton M series in the emission spectrum of excitonic molecules. We assert that actually such a series was observed as early as 1989 in the β-ZnP2 crystal. We show that the objections of Tokunaga et al. against the biexciton nature of the inverse exciton series in β-ZnP2 are ungrounded. In particular, their estimations for the ratio of the intensities of M 2 and M 1 emission lines in this crystal give two order smaller value because they do not take into account the reabsorption of the M 1 line photons. We report the observation of additional inverse exciton M ′ series in the emission spectrum of excitonic molecules in β − ZnP2.

71.35.-y, 78.55-m
In the recent publication 1 Tokunaga et al. have reported an observation of the inverse exciton M series in the emission spectrum of excitonic molecules in CuCl crystal. They claim that their experiment is the first successful observation of such a series in semiconductors. The aim of our Comment is to show that the above claim is not actual.
To our knowledge the first observation of the emission M series caused by two-electron radiative transitions in a biexciton was reported by some authors of the present Comment ten years ago. M series in β−ZnP 2 is observed at considerably higher temperatures too (fig. 3). This fact confirms high binding energy of the biexciton in β −ZnP 2 and rejects any possible impurity interpretation. β − ZnP 2 is very remarkable in the following. If the direction of the wavevector of emitted photon k is parallel to axis b of crystal (k b) and photon polarization is E a, another inverse exciton M ′ series is observed in emission spectrum of this crystal ( fig. 4). This additional series is symmetric to A series of the free S orthoexciton which is observed in absorption spectrum at E a and k b. 6 Thus, M ′ series is due to the radiative transitions from the excitonic molecule ground state to the S states of orthoexciton. Main M series is symmetric to C series of the free S paraexciton which is observed in absorption and emission spectrum at E c. 6 Respectively, M series is due to the radiative transitions from the biexciton ground state to the S states of paraexciton.
Authors of Ref. 1 see the cause that the previous attempts of biexciton M series observation "were unsuccessful" in fact that "the M n≥2 lines are extremely weak in intensity, requiring for their observation a highly sensitive detection technique and a high-quality sample free from impurity emissions". However, the fact of extremely weak intensities of M series lines in CuCl does not prove the impossibility of that in other materials these intensities can be considerably higher. Indeed, in CuCl intensities of M n≥2 lines are extremely small, since in this material: I 2 /I 1 = 1.4×10 −4 ; I 3 /I 1 = 4.0×10 −5 ; I 4 /I 1 = 1.5 × 10 −5 . In β − ZnP 2 we have more than one order higher values: I 2 /I 1 = 4. This allowed them to reconstruct the internal molecule wave function. However, they did not say that this idea was proposed in Ref. 4. Only the reabsorption of M 1 line photons and the respective saturation of this line did not allow us to reconstruct the biexciton wave function in β − ZnP 2 . However, taking for I 2 /I 1 the extrapolation value obtained above, we can estimate the components C n of the exciton excited states in the biexciton wave function in β − ZnP 2 as following: |C 2 /C 1 | 2 = I 2 /I 1 = 4.3 × 10 −3 ; |C 3 /C 1 | 2 = I 3 /I 1 = 6.0 × 10 −4 ; |C 4 /C 1 | 2 = I 4 /I 1 = 2.6 × 10 −4 .
In conclusion, we assert that the inverse exciton M series in the emission spectrum of excitonic molecules was observed for the first time in β − ZnP 2 crystal in 1989. 2 Besides this series, we have observed in this crystal an additional inverse exciton M ′ emission series which is due to the radiative transitions from the biexciton ground state to the S states of orthoexciton.