Abstract
Semiconductor nanocrystals (NCs) experience stress and charge transfer by embedding materials or ligands and impurity atoms. In return, the environment of NCs experiences a NC stress response which may lead to matrix deformation and propagated strain. Up to now, there is no universal gauge to evaluate the stress impact on NCs and their response as a function of NC size dNC. I deduce geometrical number series as analytical tools to obtain the number of NC atoms NNC(dNC[i]), bonds between NC atoms Nbnd(dNC[i]) and interface bonds NIF(dNC[i]) for seven high symmetry zinc-blende (zb) NCs with low-index faceting: {001} cubes, {111} octahedra, {110} dodecahedra, {001}-{111} pyramids, {111} tetrahedra, {111}-{001} quatrodecahedra and {001}-{111} quadrodecahedra. The fundamental insights into NC structures revealed here allow for major advancements in data interpretation and understanding of zb- and diamond-lattice based nanomaterials. The analytical number series can serve as a standard procedure for stress evaluation in solid state spectroscopy due to their deterministic nature, easy use and general applicability over a wide range of spectroscopy methods as well as NC sizes, forms and materials.
Highlights
It is well known that the electronic structure and optical response of NCs is a function of mechanical stress in the form of lattice strain
Mechanical stress is routinely measured by Ramanand Fourier-Transformation InfraRed (FT-IR) spectroscopy which probe the phononic spectra of NCs.[1,2,3,4,5]
The average coordination number per NC atom NNcoCord is twice the value of Nbnd/NNC with the asymptotic limit limi→ ∞(NNcoCord = 2 × Nbnd[i]/NNC[i]) = 4 describing the bulk case. Such coordination numbers were determined by Schuppler et al using Near Edge X-ray Absorption Fine Structure (NEXAFS) spectroscopy for Si NCs from 3.4 to 1.23 nm with different shapes and faceting.[32]
Summary
It is well known that the electronic structure and optical response of NCs is a function of mechanical stress in the form of lattice strain. Mechanical stress is routinely measured by Ramanand Fourier-Transformation InfraRed (FT-IR) spectroscopy which probe the phononic spectra of NCs.[1,2,3,4,5] Such spectra are very sensitive to changes of stress induced by lattice pressure which is a function of the material via Young’s modulus.[6] Changes in compressive or expansive stress were shown to modify the optical response of NCs by fluorescence[7] or photoluminescence (PL).[8,9] Stranski-Krastanov growth[10,11] of NCs in epitaxial films depends critically on balanced stress to avoid stacking faults which deteriotate electronic NC properties.[12,13,14,15] Attempts to place phosphorus atoms as donors onto lattice sites in free-standing Si NCs were shown to fail increasingly with shrinking NC diameter,[16,17] revealing a transition region from low to virtually zero doping of 20 to 10 nm These findings were confirmed recently in theory and experiment for SiO2-embedded Si NCs.[18,19] Several research groups have shown that self-purification, a Si NC-internal build-up of stress counteracting external stress due to dopant incorporation, causes impurity doping to fail.[20,21,22,23]. Since NCs are often described as spherical, we use dNC for spherical NCs which allows to compare different NC shapes as function of dNC: dNC[i]
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