Some Considerations Concerning the Detection of Excitons by Field Ionization in a Schottky Barrier

Abstract

Dedicated to Professor Dr. Roland Zimmermann on the occasion of his 60th birthdayThe possibility of Bose-Einstein condensation of excitons in semiconductors and/or their superfluid transport are long-standing, still controversially discussed problems. In a recent series of experiments by E. Fortin and coworkers [1-3] [phys. stat. sol. (b) 191, 345 (1995); Phys. Rev. Lett. 77, 896 (1996); and Proc. Internat. Conf. Exciton Processes in Condensed Matter, World Scientific, Singapore 2000, respectively], (para-)excitons in Cu 2 O have been detected electrically by their field ionization in a Schottky barrier. We analyze the electric field in the Schottky barrier and its screening by the holes remaining after field ionization and find serious screening and saturation effects of this Schottky-barrier exciton detector under the excitation conditions of the experiment. These findings make a reinterpretation of the data very likely. IntroductionExcitons are the quanta of the collective excitation of the electron system in semiconductors and insulators. This excitation can be described to a very good approximation as a two-particle state, consisting of an electron in the conduction band and of the hole left behind in the valence band plus Coulomb and exchange interaction between these two particles. In so far the problem is closely related to the hydrogen or the positronium atom (see, e.g., [4,5], and references therein). Obviously the exciton is an electrically neutral quasiparticle with integer spin, but it is composed of two fermions, namely electron and hole. As a consequence of this fact, the commutation relations between exciton creation and annihilation operators are those of bosons at low densities, but with a deviation from ideal boson character via a term which increases with the density of excitons [4].The interplay of bosonic character and fermionic constituents triggered a lot of research over several decades about what happens with excitons at the highest densities. In the following we summarize shortly the present situation for bulk semiconductors. It became clear that at the highest densities a transition to a metallic electron-hole plasma (EHP) occurs [4][5][6]. Depending on the material parameters and excitation conditions such as carrier lifetime, excitation density, and carrier temperature, the plasma may even undergo a first-order phase transition to a liquid-like state, the analogon to molten metallic hydrogen. This is even true in CuCl [7] in spite of its large exciton binding energy and small Bohr radius, shifting the density for the occurrence of an EHP (also called Mott density) from values below 10 17 cm À3 , e.g., for Ge to very high values around 10 20 cm À3 . Experimental investigations and the theoretical modelling of the electron-hole plasma have been pushed by many research groups world-wide as can be seen, e.g., from the references in reviews and textbooks like [4,5]. These refer-

Comment on “Some considerations concerning the detection of excitons by field ionization in a Schottky barrier” – [phys. stat. sol. (b) 234, No. 1, 23–35 (2002)]

“…Drawing from this conclusion, the authors revisit our data and their interpretation, and then propose their own interpretation. We disagree with the conclusions of reference [1] and show in this paper that our detection method is indeed valid.…”

“…A recent manuscript [1] addresses the issue of exciton detection by the voltaic effect in Cu 2 O. Based on theoretical considerations, the authors of reference [1] conclude that this type of detector, which was used by our group to report anomalous transport of high density excitons in Cu 2 O [2][3][4] is not adequate since it must necessarily be in a strong saturated regime. Drawing from this conclusion, the authors revisit our data and their interpretation, and then propose their own interpretation.…”

“…For the sake of clarity, we start by briefly describing again the principle of the exciton detector itself, since the authors of [1] have apparently overlooked reference [5] where we had previously discussed its use at low particle densities. Paper [5] was triggered by the observation of a photovoltaic signal in Cu 2 O at low temperature.…”

“…Above threshold for BEC, a sublinear dependence of the ballistic signal upon laser intensity was observed, an effect associated with the excess energy imparted to the excitonic particles during their optical injection, as discussed below. In reference [1], it was argued instead that saturation of the detector was responsible for the change of voltaic signal shape. Because of the extensive range of exciton densities created under pulsed excitation, it is of course important that the exciton detector be linear in its response.…”

“…Because of the extensive range of exciton densities created under pulsed excitation, it is of course important that the exciton detector be linear in its response. We had verified in references [2,3] the linearity of the detector by creating high density excitons directly in the vicinity of the detector plane, by shining light on the back surface containing the electrodes, a procedure questioned in reference [1]. We therefore revisit this problem here.…”