VOLUME 85, NUMBER 5 PHYSICAL REVIEW LETTERS 31 JULY 2000 Imaging the Wave-Function Amplitudes in Cleaved Semiconductor Quantum Boxes B. Grandidier,* Y.M. Niquet, B. Legrand, J.P. Nys, C. Priester, and D. Stiévenard Institut d’Electronique et de Microélectronique du Nord, IEMN, (CNRS, UMR 8520), Département ISEN, 41 boulevard Vauban, 59046 Lille Cédex, France J.M. Gérard and V. Thierry-Mieg Groupement Scientifique CNET-CNRS, 196 avenue H. Ravera, 92220 Bagneux, France (Received 30 December 1999) We have investigated the electronic structure of the conduction band states in InAs quantum boxes embedded in GaAs. Using cross-sectional scanning tunneling microscopy and spectroscopy, we report the direct observation of standing wave patterns in the boxes at room temperature. Electronic struc- ture calculation of similar cleaved boxes allows the identification of the standing waves pattern as the probability density of the ground and first excited states. Their spatial distribution in the (001) plane is significantly affected by the strain relaxation due to the cleavage of the boxes. PACS numbers: 73.20.–r, 61.16.Ch, 71.24.+q Semiconductor zero-dimensional (0D) quantum struc- tures, or quantum boxes (QB), exhibit a three dimensional confinement with a d-function-like electronic density of states. In the past years, self-assembled QB have shown very rich spectroscopic signatures [1]. As their optical properties depend on the wave functions of the electron and hole confined in the box, the knowledge of the shape, the extent, and the overlapping of the different wave functions is therefore of prime interest. So far, to glean details of the wave functions in such 0D structures, a growing number of theoretical works have been achieved. The electronic structure of semiconductor boxes with different sizes and facet orientations, embedded or not in an overlayer, have been calculated [2]. But the charge densities associated with the confined wave functions have not yet been resolved experimentally. Even though some experimental results, in electroluminescence and magnetophotoluminescence, have been obtained on the average spatial extent or symmetry of the hole or electron wave functions for an array of boxes [3,4], a detailed analysis of the wave functions in a single box is still missing. In recent years, scanning tunneling microscopy (STM) and spectroscopy have provided unique means to charac- terize low dimensional structures. These techniques have allowed the determination of the energy level structure and the observation of the charge densities in artificial struc- tures like the quantum corral [5] or on natural scatter- ing centers like surface steps [6] and nanoscale islands [7]. Since the temperature imposes a limit of the spec- troscopic resolution of the STM, most of the experiments were achieved at low temperatures. Indeed, at room tem- perature, the energy separation between electron levels must be in the range of a few kT, to resolve each of them individually. In the case of 0D semiconductor nanostruc- tures, this requirement is fulfilled. Such nanostructures can be formed by the controlled growth of InAs on a GaAs substrate in the Stransky- Krastanow growth mode. Recently, cross-sectional STM studies of InAs QB buried in GaAs have been achieved on the (110) face of cleaved samples to determine the shape and size of individual boxes at an atomic resolution [8]. Here, we investigate the conduction band (CB) states of InAs quantum boxes embedded in GaAs with the spec- troscopic ability of the STM. We observe at room tem- perature, for the first time, standing wave patterns in the InAs boxes associated with the lowest CB states. For comparison, within the single band effective mass approxi- mation, we calculate the electronic structure of the box according to its shape given by the STM image. This calculation enables us to determine unambiguously the spatial distribution of the states in the (110) plane of a truncated box. The InAs quantum boxes were grown by molecular beam epitaxy on a (001) oriented GaAs substrate, with a residual p-type concentration. The active part of the samples consists of 15 arrays of InAs boxes separated by 15 nm GaAs barriers. The whole structure is covered by a 140 nm GaAs overlayer. In order to build each box array, 2.3 monolayers of InAs were deposited on the GaAs layer within 20 s at a temperature of 520 ± C. They were immedi- ately buried with GaAs. Samples cut from the wafer were cleaved in situ at a pressure below 5 3 10 211 Torr. Poly- crystalline tungsten tips were prepared by electrochemical etching. The tips were then cleaned by heating and sharp- ened by a self-sputtering process in UHV. Topographic STM images were acquired with a 120 pA current and positive sample biases. In Fig. 1, we display a cross-sectional topographic STM image of a stack of self-aligned QB along the [001] growth direction. The QB appear bright and the GaAs layers dark. The four boxes are lying on bright layers which corre- spond to the wetting layers. We may expect the boxes that show the largest sizes and the highest contrast to be cleaved near the dot center, leaving one-half of the boxes under- neath the cleavage plane. We will now focus on such 1068 0031-9007 00  85(5)  1068(4)$15.00 © 2000 The American Physical Society