Capacitance-Voltage Spectroscopy of InAs Quantum Dots

Abstract

Semiconductor quantum dots (QDs) have been studied intensively in the past [1, 2] as model systems for three-dimensional carrier confinement as well as building blocks of novel devices. Because they can be fabricated in high quality and provide strong confinement for electrons and holes, self-assembled InAs QDs – mostly grown by molecular beam epitaxy – are arguably the most intensively studied QD system. One of the most important consequences of the complete carrier confinement are the atomically sharp energy levels due to three-dimensional quantization. The detailed knowledge of the energy level structure, which determines the electrical and optical properties of the QDs, is very interesting from a fundamental point of view as well as for possible applications. Compared to the single particle picture, the energetic situation becomes more complicated, if the QDs are charged with more than one carrier because then interaction energies have to be taken into account [3, 4]. If the confinement length is small, as for example in InAs QDs, the interaction energies can be comparable or even larger than the quantization energies. To study the energy level structure in QDs, several methods have been employed. On the one hand, there are optical methods [2] with photoluminescence (PL) as the most prominent one and on the other hand electrical methods as tunneling spectroscopy [5–8] and capacitance-voltage (C-V) spectroscopy [9–38]. The optical methods give a wealth of information but measure in general the conduction and the valence band system together. Also, the investigated QDs are in general electrically neutral although optical investigations of charge-tuneable QDs are possible in special heterostructures [39]. In contrast, electrical methods give information of the conduction or the valance band level structure separately. Also, the interaction of carriers in few-carrier QDs can be studied. One of the most widely used electrical characterisation methods is C-V spectroscopy, for which several variations exist [9–38]. In general, the QDs have to be embedded into a doped heterostructure, so the charge in the QDs can be tuned by an external gate bias. Either p-n-junctions [27–29], n[3, 9, 11–20, 28–37] as well as p-type [21–26] Schottky diodes or n-i-n structures [38] have been employed.