Direct-Bandgap InAs Quantum-Dots Have Long-Range Electron−Hole Exchange whereas Indirect Gap Si Dots Have Short-Range Exchange

Abstract

Excitons in quantum dots manifest a lower-energy spin-forbidden "dark" state below a spin-allowed "bright" state; this splitting originates from electron-hole (e-h) exchange interactions, which are strongly enhanced by quantum confinement. The e-h exchange interaction may have both a short-range and a long-range component. Calculating numerically the e-h exchange energies from atomistic pseudopotential wave functions, we show here that in direct-gap quantum dots (such as InAs) the e-h exchange interaction is dominated by the long-range component, whereas in indirect-gap quantum dots (such as Si) only the short-range component survives. As a result, the exciton dark/bright splitting scales as 1/R(2) in InAs dots and 1/R(3) in Si dots, where R is the quantum-dot radius.

Strained Interface Defects in Silicon Nanocrystals

“…The electron states of Si NCs are obtained from solving the Schrodinger equation,37

where {ϵ i , ψ i } are energy and wavefunction of state i , m is the bare electron mass, and is the Planck constant. The crystal potential

is a superposition of screened atomic potentials $ \hat v_\alpha $ of atom type α located at atomic site

within the primitive unit cell n :38–40

thus forcing upon us the correct atomically resolved symmetry. The construction of the screened atomic potentials $ \hat v_\alpha $ is the key to accuracy and realism.…”

The Effect of pH on the Photoluminescent Properties of Silicon Nanoparticles

“…6,7 As a result, indirect band gap semiconductors require more energy to generate PL emissions, and as a result, are typically slower and less efficient. 6,8 The separation of the electron and electron hole (together, called an exciton) results in the formation of current, a product of the electron and electron hole freely traversing the material. This is a property harvested in modern semiconductor devices and commonly seen in bulk materials resulting from the absence of spatial confinement exerted upon the exciton, thus allowing the electron and electron hole to overcome their electrostatic attraction.…”

“…The PL from H-SiNPs has previously been reported to result from recombination across the indirect band gap, and is believed to be in good agreement with the QCE. 8 Examination of the IR spectrum reveals strong peaks present at approximately 2100 cm -1 , 900 cm -1 , and 600 cm -1 (Figure 8). These are all indicative of Si-H stretching, which is expected immediately following HF etching.…”

“…They postulated this discrepancy to be the result of the presence of low-density traps from nitrogen impurities on the surface of the NPs 11. Other reports have indicated that non-QC PL emissions may be the result of differences between the radiative mechanisms of direct and indirect band gap semiconductors, as well as the presence of surface traps 7,8,[12][13][14].…”

Dissecting biexciton wave functions of self-assembled quantum dots by double-quantum-coherence optical spectroscopy

“…This approach naturally includes both long-and short-range exchange. 47,48 Once the many-body wave functions of multiexcitons are solved from above equations, the dipole transition matrix elements will be readily obtained. The linear absorption spectra, calculated according to Fermi's golden rule with a broadening parameter γ = 1 meV, of transitions…”