Direct Measurement of the Binding Energy and Bohr Radius of a Single Hydrogenic Defect in a Semiconductor Quantum Well

Simon Perraud, Kiyoshi Kanisawa, Zhao-Zhong Wang, and Toshimasa Fujisawa

Physical Science LaboratoryImpurities are fundamentally important for semiconductor device fabrication. In the simplest approximation, an impurity, or a point defect, inside a semiconductor is described as a hydrogen atom. The two essential properties of such impurity are the binding energy and the Bohr radius (

a_{B1}). Impurities in quantum wells (QWs) are affected by the confining potential ifa_{B1}>l, wherelis the QW thickness. (111)A-oriented, nominally undoped In_{0.53}Ga_{0.47}As surface QWs were grown by molecular beam epitaxy (MBE) [1]. We used the scanning tunneling microscope (STM) and the spectroscopy (STS) at the low-temperature (5 K) to study point defects behaving like donor impurities, which are natively located at the epitaxial surface of a QW. The electronic local density of states (LDOS) was measured with nanoscale resolution in the vicinity of single point defects. By measuring the LDOS in the QW, we are able to determine both the binding energy and the Bohr radius of single defects. Four different QW thicknesses were investigated in this work (l=2, 6, 10, and 14 nm). The obtained spatial dependence as the function of the distanceris well fitted by an exponential decay proportional to exp(-2r/a_{B1}), representing the 1shydrogenic wave function. Figure 1 summarizes the STS data obtained in this work. The smallerl, the larger binding energyE_{1}-ε_{1}, and the smallera_{B1}, i.e. the tighter the electron is bound to the point defect. Here,E_{1}is the bottom of the two-dimensional subband of the QW, andε_{1}is the ground level of the impurity bound states. We clearly observe the influence of quantum confinement on the bound states, as expected in the casea_{B1}>l. If STS data are compared with a calculation of hydrogenic impurity states, the binding energy and the Bohr radius were found to be functions of the quantum well thickness, in quantitative agreement with variational calculations of hydrogenic impurity states [2]. It is remarkable that this calculation requires no adjustable parameter. The increase ofE_{1}-ε_{1}(or, equivalently, the decrease ofa_{B1}) with decreasinglis enhanced by the conduction band nonparabolicity.[1] S. Perraud, K. Kanisawa, Z.-Z. Wang, and T. Fujisawa, Phys. Rev. B

76(2007) 195333.

[2] G. Bastard, Phys. Rev. B24(1981) 4714.

Fig. 1. Binding energy E_{1}-ε_{1}and Bohr radiusa_{B1}as a function of QW thicknessl: STS data (each circle corresponds to a single point defect at the In_{0.53}Ga_{0.47}As QW surface), and hydrogenic model (solid curves).

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