Article pubs.acs.org/Langmuir
Optical Extinction Spectra of Silicon Nanocrystals: Size Dependence upon the Lowest Direct Transition Ryan Gresback,† Yoichi Murakami,‡ Yi Ding,† Riku Yamada,† Ken Okazaki,† and Tomohiro Nozaki*,† †
Department of Mechanical and Control Engineering, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan ‡ Global Edge Institute, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan S Supporting Information *
ABSTRACT: We investigate the size-dependent optical extinction properties of colloidal silicon nanocrystals (Si NCs) from the near infrared (NIR) to the ultraviolet (UV). Experimental results are compared to the Mie solution to Maxwell’s equations using the same refractive index as bulk Si to evaluate the deviation from bulk properties. We find that the energy for the lowest direct transition (E1) continuously blueshifts from near bulk-like at ∼3.4 eV in large NCs (16 nm) to ∼3.6 eV for small NCs (3.9 nm), contrary to the Mie solution. The extinction cross-section of NCs on a per atom basis was found to be independent of the NC size, within our experimental resolution. The results suggest that quantum confinement effects strongly influence excitons associated with the E1 transition.
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INTRODUCTION Silicon nanocrystals (Si NCs) are the subject of intense research because of their size-dependent optical and electronic properties for various proposed applications, including photovoltaic devices1,2 and biological tagging.3 To efficiently use Si NCs in such applications, quantitative information on the absorption cross-section is essential. To date, there is limited quantitative knowledge on the absorption cross-section and its size dependence. This is likely due to the difficultly in determining the concentration of NCs. Several studies have investigated the NC cross-section using a variety of techniques, such as photoluminescence (PL) saturation techniques,4 gravimetric analysis,5 and a combination of transmission electron microscopy (TEM) and Si content measurements.6−8 However, there are quantitative discrepancies in the reported results that are further clouded by the wide variety of synthesis techniques and resulting form of nanostructured Si, including porous Si,4 Si NCs in an oxide matrix,6−8 and colloidal Si NCs terminated by organic ligands.5 The absorption cross-section from the near infrared (NIR) to the ultraviolet (UV) can provide essential information on interand intraband transitions. Bulk Si has a number of important interband transitions. The lowest energy transition (E0) is indirect corresponding to the highest valence band at the Γ point of the Brillouin zone to the lowest conduction band near the X point, while the lowest energy direct transition (E1) is at the Γ point, as shown in the inset in Figure 1.9 In bulk Si, these transitions have energies of ∼1.1 and ∼3.4 eV for E0 and E1, respectively.10 Additionally, the NIR intraband transitions from free-carrier absorption become significant with high concentrations of excess carriers.11 © 2013 American Chemical Society
Figure 1. (a) Bulk refractive index of Si: n (left axis) and k (right axis) from refs 9 and 42. (b) Mie solution of Maxwell’s equations for the extinction (solid), scattering (dash), and absorption (dot) crosssections on a per atom basis for different size (see the legend) spherical Si particles. (Inset) Bulk band structure of Si.
Received: October 24, 2012 Revised: December 4, 2012 Published: January 15, 2013 1802
dx.doi.org/10.1021/la3042082 | Langmuir 2013, 29, 1802−1807
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Si NCs onto a glass slide directly after the plasma in the gas phase similar to ref 37. After fabrication, the films were allowed to oxidize in air for 2 weeks. 1-Dodecene-treated Si NCs were prepared by nonthermal plasma synthesis using silane (SiH4), thermally reacted with 1-dodecene in mesitylene (1:5 by volume) then dried, and dispersed in anhydrous toluene (Sigma-Aldrich) as previously described.38,39 Unless otherwise noted, synthesis, handling, and measurements were performed without exposure to air or moisture. A UV−vis−NIR spectrophotometer (Shimadzu UV-3600) was employed on dilute colloids (0.05 and 0.1−0.6 mg/mL above and below 2.3 eV, respectively) in quartz cuvettes with a path length of 10 mm with a 1 nm step size. Several higher concentrations (up to 2 mg/ mL) were also measured to ensure spectra shape and values scaled appropriately with concentration. The size of Si NCs was measured using both atomic force microscopy (AFM, Shimadzu SPM-9600 with a cantilever, Olympus OMCL-AC240TS-C3) and X-ray diffraction (XRD, Bruker Discover D8). XRD allows for a volume average determination of the mean crystalline size, while AFM allows for a determination of the distribution of individual and agglomerated NCs. Samples for AFM were prepared by spin-coating Si NCs with mass concentrations between 0.1 and 1 mg/mL onto pieces of a polished Si wafer with a native oxide at 2000 rpm. Both techniques are susceptible to oxidation, which is especially difficult to minimize for the NCs examined here.34 AFM measurements were performed with minimal air exposure (
