Charged Excitons in Self-assembled Quantum Dots

We have succeeded in generating highly charged excitons in InAs self-assembled quantum dots by embedding the dots in a field-effect heterostructure. We discover an excitonic Coulomb blockage: over large regions of gate voltage, the exciton charge remains constant. We present here a summary of the emission properties of the charged excitons. INTRODUCTION An exciton is the elementary excitation in a semiconductor consisting of an electron and a valence level hole, bound together by the Coulomb potential. The exciton decays by photon emission when the electron recombines with the hole, which is a strong optical process because the exciton and vacuum states are connected by the electric dipole operator. The exciton ionization energy can be increased in a quantum well relative to that in bulk material by the quantum confinement. An increase up to about 10 meV from a bulk value of about 4 meV is possible in a GaAs quantum well [1]. A charged exciton, consisting of two electrons and a hole, is just bound in a quantum well. More highly-charged excitons are however unbound and do not exist. This state-of-affairs changes in a self-assembled quantum dot where in addition to a vertical confinement, there is also a lateral confinement arising from the nanometer-sized dot. In this case, the exciton binding energy (defined as the energy required to separate an electron and a hole and place them in identical but well separated quantum dots) increases to, say, 30 meV for an InAs/GaAs quantum dot [2]. In fact, the quantum confinement is so strong in these systems that it is more accurate to refer to a highly-confined electron-hole pair rather than an exciton. The strong confinement in a self-assembled quantum dot opens up the possibility for the first time of investigating highly-charged excitons because even excitons with several excess electrons are stable. We have shown how it is possible to generate these highly-charged excitons in a single self-assembled quantum dots by embedding the quantum dots in an appropriate field-effect heterostructure [3]. We label the excitons with Xn− where n is the excess charge. We have detected photoluminescence (PL) from the neutral exciton X up to the quadruply-charged exciton X4−. Each time an exciton gains an additional electron, its PL red-shifts through the Coulomb interaction, with the jumps in wavelength revealing a shell structure. Furthermore, for the X2− and X2−, splittings arise, related to electron-hole exchange effects in the initial states, and electron-electron exchange effects in the final states. In this paper, we summarize the behavior of charged excitons in self-assembled quantum dots. HETEROSTRUCTURE DESIGN In our field-effect heterostructure, the InAs quantum dots are self-assembled on undoped GaAs, 25 nm above an n-region, the back contact. The dots are capped with a total of 150 nm of GaAs/AlAs. We make contacts to the n-layer and deposit a semi-transparent NiCr gate on the sample surface. A voltage Vg is applied to the gate, with the back contact grounded. At large negative Vg, the ground state of a particular dot lies above the Fermi energy and so the dot is unoccupied at low temperature. At a more positive Vg, there is a resonance between the dot’s ground state and the Fermi level in the back contact allowing an electron to tunnel in and out. A further increase in Vg traps an electron on the dot, and a Coulomb blockade results: a significantly larger voltage is required to induce tunneling of a second electron from the back contact into the dot. The Coulomb blockade is particularly pronounced because the quantum dots are so small, resulting in large Coulomb energies. We perform PL measurements on individual dots at 4.2 K, recording the PL as a function of Vg. In all the experiments, the excitation (between 820 and 850 nm wavelength) is kept low enough that the biexciton-related features are much weaker than the exciton-related features. NEUTRAL AND SINGLY-CHARGED EXCITONS A color scale plot of the PL versus Vg is shown in Fig. for a particular quantum dot. It can be seen that there are large regions of voltage where PL from only one charge state is observed. In the transition regions, there is a transfer of intensity from one charge state to the next; the transition is not completely abrupt because of thermal occupation of the higher energy state. In other words, an exciton in this sample always has sufficient time to find the charge state with the minimum energy before recombination occurs. This can be termed an excitonic Coulomb blockade. At large and negative Vg, the lowest energy state is an empty dot and for this reason there is no PL. At less negative Vg however, the exciton is stable, and we resolve a sharp PL line typical of the neutral exciton in a single dot at low temperature. At ∼ −0.5 V, the PL from the dot in Fig. jumps to the red. This is the transition from a neutral exciton to a charged exciton: the voltage is positive enough that the exciton with the lowest energy is X1−, not X. The red-shift occurs because, on adding an electron to a neutral exciton, the Coulomb attraction of the electron and hole is larger than the Coulomb repulsion of the two electrons. This is a consequence of the fact that the hole has a wave function with a smaller lateral extent than the electron [2]. An obvious feature in Fig. is that the X1− exists over a larger range in Vg than the X. The reason for this is that the width of the X plateau is determined by a Coulomb energy, but the X1− plateau width is determined not only by the Coulomb energy but also by the quantization energy: in order to form an X2−, an electron must tunnel into the excited state. DOUBLY-CHARGED EXCITONS: EXCHANGE INTERACTIONS For the X2−, the PL exhibits not a single line, but, at first glance, two peaks separated by ∼ 5 meV (Fig.s and ). The origin of this splitting is an exchange interaction in the final state. The initial state has electron spin S = 1 2 ; the final state has spin S = 1 or S = 0. The possible configurations, labelling the electron ground state orbital s and the first excited orbital p in analogy to atomic physics, are shown in Fig. . The final states are split by twice the exchange energy between an s and a p electron. A very marked feature of the PL is that the higher energy emission into the S = 1 state has a sharp line, whereas the emission into -0.6 -0.4 -0.2 0.0 0.2 0.4 1.265 1.270 1.275 1.280 1.285 1.290 1.295