Thermal shift of the resonance between an electron gas and quantum dots: what is the origin?

Abstract

The operation of quantum dots (QDs) at highest possible temperatures is desirable for many applications. Capacitance-voltage spectroscopy (C(V )-spectroscopy) measurements are an established instrument to analyse the electronic structure and energy levels of self-assembled QDs. We perform C(V ) in the dark and C(V ) under the influence of non-resonant illumination, probing exciton states up to + X 4 on InAs QDs embedded in a GaAs matrix for temperatures ranging from 2.5 to 120 K. While a small shift in the charging spectra resonance is observed for the two spin degenerate electron s-state charging voltages with increasing temperature, a huge shift is visible for the electron-hole excitonic states resonance voltages. The s 2 -peak moves to slightly higher, the s 1 -peak to slightly lower charging voltages. In contrast, the excitonic states are surprisingly charged at much lower voltages upon increasing temperature. We derive a rate-model allowing to attribute and value different contributions to these shifts. Resonant tunnelling, state degeneracy and hole generation rate in combination with the Fermi distribution function turn out to be of great importance for the observed effects. The differences in the shifting behaviour is connected to different equilibria schemes for the peaks-s-peaks arise when tunnelling-in-and out-rates become equal, while excitonic peaks occur, when electron tunnelling-in-and hole-generation rates are balanced.

Illumination-induced nonequilibrium charge states in self-assembled quantum dots

“…In particular, it explains the occurrence of electronic and excitonic peaks in the C(V) spectrum as well as their respective height. Furthermore, it captures the thermal shift of peak positions connected to the degeneracy of states [17]. In addition, our model also describes and refines the frequency-dependent suppression of peaks which has been reported, e.g., in the work of Luyken [15].…”

“…We identify these arXiv:1710.07545v2 [cond-mat.mes-hall] 14 Dec 2017 peaks with electrons tunneling into nonequilibrium s-, p-, and d-states which are usually inaccessible via the slow DC-sweep in our C(V) spectroscopy. While the simple model of Brinks et al [17] describes the observed quasiequilibrium C(V)-measurement features, we expand this to an extended theoretical model including electron elimination by holes, offering an excellent quantitative agreement with the observed features in the measurements.…”

“…In the following, we present a theoretical model of C(V) spectroscopy based on a master equation approach [21]. Our theory provides a significant extension of the simple model of Brinks et al [17]. In particular, it explains the occurrence of electronic and excitonic peaks in the C(V) spectrum as well as their respective height.…”

“…The according hole generation process in the quantum dots is expected to be proportional to the LED current [16]. Brinks et al found a hole generation rate per quantum dot of 400 Hz for an LED current of 2 mA [17].…”

“…In order to model this effect, we assume different tunnel coupling strengths Γ s,p for tunneling into s-and p-states. A more realistic treatment which models the energy dependency of tunneling rates via the WKB approximation [17] would be required to obtain a quantitative agreement between the experimental and theoretical peak height which is beyond the scope of the present work. Furthermore, degeneracy factors for tunneling in and out of different states are taken into account properly.…”