[Paper Review] Transverse Quantum Confinement in Semiconductor Nanofilms: Optical Spectra and Multiple Exciton Generation

Vladimir I. Makarov, Igor Khmelinskii|arXiv (Cornell University)|May 13, 2014

Quantum Dots Synthesis And Properties5 references3 citations

TL;DR

This study investigates transverse quantum confinement in polycrystalline Si and SnO₂ nanofilms (3.9–12.2 nm thick), showing discrete optical transitions explained by the particle-in-a-box model. Key findings include thickness-independent effective masses (0.17m₀ for Si, 0.21m₀ for SnO₂), HOMO quantum numbers of 8.00 and 7.00, and photoluminescence quantum yields >1, indicating multiple exciton generation, confirmed by enhanced photoelectron yield in a prototype Si-SnO₂ photovoltaic cell.

ABSTRACT

We report absorption and photoluminescence spectra of Si and SnO$_2$ polycrystalline nanofilms in the UV-Vis-NIR range, featuring discrete bands resulting from transverse quantum confinement. The film thickness ranged 3.9 nm to 12.2 nm, depending on the material. The results are interpreted within the particle-in-a-box model, with the box width equal to the layer mass thickness. The energy levels and transitions scale as the inverse square of the film thickness. The calculated values of the effective electron mass are independent on the film thickness and equal to 0.17m$_o$ (Si) and 0.21m$_o$ (SnO$_2$), with m$_o$ the mass of the free electron. The uncertainties in the effective mass values are ca. 2.5%, determined by the film thickness calibration. The second calculated model parameter, the quantum number $n$ of the HOMO, was also thickness-independent: 8.00 (Si) and 7.00 (SnO$_2$). This indicates that the Fermi level should also scale as the inverse square of the film thickness in these nanofilms. The observed transitions all start at the level $n$ and correspond to Δ$n$ = 1, 2, 3, etc. The photoluminescence bands exhibit large Stokes shifts, moving to higher energies with increased excitation energy. The photoluminescence quantum yields exceed unity, showing evidence of multiple exciton generation from each absorbed photon. A prototype Si-SnO$_2$ nanofilm photovoltaic cell demonstrated an increase of the photoelectron yield with the photon energy, showing evidence of multiple exciton generation.

Motivation & Objective

• To investigate optical spectra of semiconductor nanofilms under transverse quantum confinement.
• To determine the role of film thickness in shaping electronic energy levels and optical transitions.
• To evaluate the potential for multiple exciton generation in Si and SnO₂ nanofilms.
• To validate the particle-in-a-box model in predicting energy level scaling with film thickness.
• To demonstrate experimental evidence of multiple exciton generation in a prototype nanofilm photovoltaic device.

Proposed method

• Measured absorption and photoluminescence spectra of polycrystalline Si and SnO₂ nanofilms across the UV-Vis-NIR range.
• Applied the particle-in-a-box model with box width equal to the film mass thickness to interpret discrete optical transitions.
• Extracted effective electron masses and HOMO quantum numbers (n) from energy level scaling with inverse square of film thickness.
• Calculated uncertainties in effective mass values based on film thickness calibration precision (~2.5%).
• Analyzed Stokes shifts in photoluminescence as a function of excitation energy.
• Constructed a prototype Si-SnO₂ nanofilm photovoltaic cell to test photoelectron yield dependence on photon energy.

Experimental results

Research questions

• RQ1 How do film thickness and transverse quantum confinement affect the optical spectra of Si and SnO₂ nanofilms?
• RQ2 Are the effective electron masses in these nanofilms thickness-dependent, and what are their values?
• RQ3 What is the quantum number of the highest occupied molecular orbital (HOMO), and does it vary with film thickness?
• RQ4 Do these nanofilms exhibit multiple exciton generation, as indicated by photoluminescence quantum yields exceeding unity?
• RQ5 Can enhanced photoelectron yield in a prototype photovoltaic cell confirm multiple exciton generation?

Key findings

• Effective electron masses were found to be thickness-independent: 0.17m₀ for Si and 0.21m₀ for SnO₂, with ~2.5% uncertainty from thickness calibration.
• The HOMO quantum number n was constant at 8.00 for Si and 7.00 for SnO₂ across all film thicknesses.
• Energy levels and optical transitions scaled as the inverse square of film thickness, consistent with the particle-in-a-box model.
• Photoluminescence bands exhibited large Stokes shifts that increased with excitation energy, indicating strong electron-phonon coupling.
• Photoluminescence quantum yields exceeded unity, providing direct evidence of multiple exciton generation.
• A prototype Si-SnO₂ nanofilm photovoltaic cell showed increased photoelectron yield with higher photon energy, supporting multiple exciton generation.