Eur. Phys. J. B 35, 209–216 (2003) DOI: 10.1140/epjb/e2003-00270-8 T HE EUROPEAN P HYSICAL JOURNAL B Far-infrared probe of size dispersion and population fluctuations in doped self-assembled quantum dots J.N. Isaia 1 , L.A. de Vaulchier 1, a , S. Hameau 1 , R. Ferreira 1 , Y. Guldner 1 , E. Deleporte 1, b , J. Zeman 2 , V. Thierry-Mieg 3 , and J.M. G´ erard 3, c 1 Laboratoire de Physique de la Mati` ere Condens´ ee, ´ Ecole Normale Sup´ erieure, 24 rue Lhomond, 75231 Paris Cedex 05, France 2 Grenoble High Magnetic Field Laboratory, CNRS/MPI, 25 avenue des Martyrs, 38042 Grenoble Cedex 9, France 3 Laboratoire de Photonique et Nanostructures, Route de Nozay, 91460 Marcoussis, France Received 7 May 2003 / Received in final form 22 July 2003 Published online 2 October 2003 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2003 Abstract. We investigate the FIR magneto-optical transitions in doped self-assembled InAs quantum dots with an average filling ranging from 0.6 to 6 electrons per dot. Significant changes in the magnetic field dispersion, the line-width and the amplitude of the transitions are observed as the doping level is varied, in agreement with our theoretical calculations. We show that our technique is an effective tool to obtain informations regarding the dot size homogeneity and the electron filling uniformity. PACS. 73.21.La Quantum dots – 78.20.Ls Magnetooptical effects – 78.30.Fs III-V and II-VI semiconductors – 78.67.Hc Quantum dots 1 Introduction Doped self-assembled InAs/GaAs quantum dots (QD) open new perspectives both in fundamental physics (for instance the strong coupling regime between electrons and optical phonons [1–3]) and for device applications (for instance QD far-infrared photodetectors [4–8] or solid- state qubits for quantum computing [9,10]). For basic physics and for device design, it is crucial to obtain in- formation regarding the QD electron filling uniformity. Spatial variations of the QD filling can originate from various effects: composition fluctuations, statistical dis- tribution of the dopants, size dispersion of the QD. The far-infrared (FIR) magneto-absorption technique is an ef- fective tool to investigate the electronic excitations in QD [1,3,11]. Previous theoretical calculations predicted that FIR magneto-absorption spectra should depend sig- nificantly on the QD filling [12] and FIR spectroscopy was used to study the electronic excitation as a function of the QD filling [13]. But to date, there was no investiga- tion of the influence of the QD filling fluctuations on the a e-mail: Louis-Anne.deVaulchier@lpmc.ens.fr b Present address: Laboratoire de Photonique Quantique et Moleculaire, ´ Ecole Normale Superieure de Cachan, 94235 Cachan Cedex, France c Present address: CEA-Grenoble DRFMC/SP2M/PSC, Laboratoire de Physique des semiconducteurs, 38054 Greno- ble, France FIR magneto-spectra. We report here an investigation of the far-infrared (FIR) magneto-optical transitions up to B = 28 teslas at T = 2 K in samples with increasing dop- ing levels in order to transfer, on average, N =0.6 to 6 electrons per dot and to populate the s and p states (states with an angular momentum projection along the growth axis L z =0, ±). Significant changes in the disper- sion, the line-width and the amplitude of the FIR transi- tions are observed as the doping level is varied. The energy positions of the observed resonances are consistent with our theoretical calculations of the electronic levels. Using a realistic QD shape, we predict that up to six electrons can be confined at low temperature. Nevertheless the ex- periments evidence a delocalization of some electrons in the wetting layer for a filling N = 6. We also show that the resonance lineshape can be accounted by the filling fluctuations resulting from the QD size dispersion. The QD size distribution is evaluated from the analysis of the FIR magnetotransmission and PL results measured on the samples with lowest doping levels. We then evaluate the resulting fluctuations of the QD filling for each sample. Fi- nally, we simulate the lineshape of the resonances observed in samples with various doping. The simulation reproduce rather well the intensities and lineshape of the experimen- tal resonances. We also evaluate the line broadening aris- ing from the statistical distribution of the dopants and we conclude that the size dispersion constitutes the dominant effect which governs the filling uniformity in our samples.