This work was part of the research programme of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). Authors of this work thank M. J. F. van de Sande for skillful technical assistance, M. A. Verheijen for TEM images, and the group of Tom Gregorkiewicz for PL measurements.

1. Planning of the Experiments
<ol>
	<li>Synthesize or obtain the nanocrystals of interest13 (Figure 1a).</li>
	<li>Avoid any confusion with the background signal by making sure that the substrate material does not have overlapping peaks in the Raman spectrum of the nanocrystals (Figure 1a).</li>
	<li>Turn on the laser of the Raman spectroscopy setup. Wait enough time (approximately 15 min) for the laser intensity to stabilize.</li>
	<li>Measure a bulk reference of the nanom...

<ol>
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First discussion point is the critical steps within the protocol. In order not to have overlapping peaks with the material of interest, it is important to use another type of substrate material as mentioned in step 1.2. For instance, if Si-NCs are of interest, do not use silicon substrate for the Raman measurements. In Figure 1a, for instance, Si-NCs were synthesized on plexiglass substrates, which has completely flat signal roughly around the range of interest, i.e....

Semiconductor nanocrystals draw attention as their electronic and optical properties can be tuned by simply changing their size in the range compared to their respective exciton-Bohr radii.1 These unique size-dependent features make these nanocrystals relevant for various technological applications. For instance, carrier multiplication effects, observed when a high energy photon is absorbed by the nanocrystals of CdSe, Si, and Ge, can be used in the concept of spectrum conversion in solar cell applications;2&#8211;4 or size-dependent optical emission from PbS-NCs and Si-NCs can be used in the light emitting diode (LED) applications.5,6 A precise knowledge and control on the nanocrystal size distribution will therefore play a determinant role on the reliability and the performance of these technological applications based on nanocrystals.
The commonly used techniques for the size distribution and morphology analysis of nanocrystals can be listed as X-ray diffraction (XRD), transmission electron microscopy (TEM), photoluminescence spectroscopy (PL), and Raman spectroscopy. XRD is a crystallographic technique that reveals morphological information of the analyzed material. From the broadening of the diffraction peak, estimation of the nanocrystal size is possible,7 however, obtaining a clear data is usually time consuming. Moreover, XRD can only enable the calculation of average of the nanocrystal size distribution. In the existence of multi-modal size distributions, size analysis with XRD can be misleading and result in wrong interpretations. TEM is a powerful technique that enables imaging of the nanocrystals.8 Although TEM is able to reveal the presence of individual distributions in a multi-modal size distribution, sample preparation issue is always an effort to be spent before the measurements. In addition, working on densely packed nanocrystal ensembles with different sizes is challenging because of the difficulty of individual nanocrystal imaging. Photoluminescence spectroscopy (PL) is an optical analysis technique, and optically active nanocrystals can be diagnosed. Nanocrystal size distribution is obtained from the size-dependent emission.9 Due to their poor optical properties of indirect band gap nanoparticles, large nanocrystals that are not subject to confinement effects, and defect-rich small nanocrystals cannot be detected by PL and the observed size distribution is only limited to nanocrystals with good optical properties. Although each of these abovementioned techniques has its own advantages, none of them have the capability of meeting the expectations (that is, being fast, non-destructive, and reliable) from and idealized size analysis technique.
Another means of size distribution analysis of nanocrystals is Raman spectroscopy. Raman spectroscopy is widely available in most of the labs, and it is a fast and non-destructive technique. In addition, in most cases, sample preparation is not required. Raman spectroscopy is a vibrational technique, which can be used to obtain information on different morphologies (crystalline or amorphous), and size-related information (from the size-dependent shift in the phonon modes that appear in the frequency spectrum) of the analyzed material.10 The unique feature of Raman spectroscopy is that, while size-dependent changes are observed as a shift in the frequency spectrum, the shape of the phonon peak (broadening, asymmetry) gives information on the shape of the nanocrystal size distribution. Therefore it is in principle possible to extract the necessary information, i.e., the mean size and the shape factor, from Raman spectrum to obtain the size distribution of nanocrystals analyzed. In the case of multi-modal size distributions sub-distributions can also be separately identified via deconvolution of the experimental Raman spectrum.
In the literature, two theories are commonly referred to model the effect of nanocrystal size distribution on the shape of the Raman spectrum. The bond polarizability model (BPM)11 describes the polarizability of a nanocrystal from the contributions of all the bonds within that size. The one-particle phonon confinement model (PCM)10 uses size-dependent physical variables, i.e., crystal momentum, phonon frequency and dispersion, and the degree of confinement, to define the Raman spectrum of a nanocrystal with a specific size. Since these physical variables depend on the size, an analytical representation of the PCM that can be explicitly formulized as a function of nanocrystal size can be defined. Projecting this expression on a generic size distribution function will therefore be able to account for the effect of size distribution within the PCM, which can be used to determine the nanocrystal size distribution from the experimental Raman spectrum.12

<table border="0" cellpadding="0" cellspacing="0">
	<tbody>
		<tr>
			<td>Raman Spectroscopy</td>
			<td>Renishaw</td>
			<td>In Via</td>
			<td>Equipped with 514 nm Ar ion laser</td>
		</tr>
		<tr>
			<td>Wire 3.0</td>
			<td>Renishaw</td>
			<td></td>
			<td>Raman spectroscopy record tool</td>
		</tr>
		<tr>
			<td>Mathematica</td>
			<td>Wolfram</td>
			<td></td>
			<td>For fitting function and size determination</td>
		</tr>
		<tr>
			<td>Substrate</td>
			<td></td>
			<td></td>
			<td>Plexiglass (to avoid signal coincidence with Si-NCs)</td>
		</tr>
		<tr>
			<td>Si wafer</td>
			<td></td>
			<td></td>
			<td>Reference to Si-NC peak position</td>
		</tr>
		<tr>
			<td>Photoluminescence Spectroscopy</td>
			<td></td>
			<td></td>
			<td>334 nm Ar laser. For optical size distribution.</td>
		</tr>
		<tr>
			<td>Transmission Electron Microscopy</td>
			<td></td>
			<td></td>
			<td>Beam intensity 300 kV. For nanocrystal size and morphology determination.</td>
		</tr>
	</tbody>
</table>

characterization of nanocrystal size distribution using raman spectroscopy with a multi-particle phonon confinement model

Analysis of the size distribution of nanocrystals is a critical requirement for the processing and optimization of their size-dependent properties. The common techniques used for the size analysis are transmission electron microscopy (TEM), X-ray diffraction (XRD) and photoluminescence spectroscopy (PL). These techniques, however, are not suitable for analyzing the nanocrystal size distribution in a fast, non-destructive and a reliable manner at the same time. Our aim in this work is to demonstrate that size distribution of semiconductor nanocrystals that are subject to size-dependent phonon confinement effects, can be quantitatively estimated in a non-destructive, fast and reliable manner using Raman spectroscopy. Moreover, mixed size distributions can be separately probed, and their respective volumetric ratios can be estimated using this technique. In order to analyze the size distribution, we have formulized an analytical expression of one-particle PCM and projected it onto a generic distribution function that will represent the size distribution of analyzed nanocrystal. As a model experiment, we have analyzed the size distribution of free-standing silicon nanocrystals (Si-NCs) with multi-modal size distributions. The estimated size distributions are in excellent agreement with TEM and PL results, revealing the reliability of our model.

For using Raman spectroscopy as a size analysis tool, a model to extract the size-related information from a measured Raman spectrum is needed. Figure 2 summarizes the analytical multi-particle phonon confinement model.12 All-size-dependent phonon confinement function (Figure 2c) is projected onto a generic size distribution function (Figure 2b), which is chosen as a lognormal...

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Characterization of Nanocrystal Size Distribution using Raman Spectroscopy with a Multi-particle Phonon Confinement Model

We demonstrate how to determine the size distribution of semiconductor nanocrystals in a quantitative manner using Raman spectroscopy employing an analytically defined multi-particle phonon confinement model. Results obtained are in excellent agreement with the other size analysis techniques like transmission electron microscopy and photoluminescence spectroscopy.

Analysis of the size distribution of nanocrystals is a critical requirement for the processing and optimization of their size-dependent properties. The ...

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13.4K Views.  Eindhoven University of Technology. We demonstrate how to determine the size distribution of semiconductor nanocrystals in a quantitative manner using Raman spectroscopy employing an analytically defined multi-particle phonon confinement model. Results obtained are in excellent agreement with the other size analysis techniques like transmission electron microscopy and photoluminescence spectroscopy.