Supporting Information. Silicon Nanocrystal Superlattice Nucleation and Growth

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1 Supporting Information Silicon Nanocrystal Superlattice Nucleation and Growth Adrien Guillaussier, Yixuan Yu, Vikas Reddy Voggu, Willi Aigner, Camila Saez Cabezas, Daniel W. Houck, Tushti Shah, Detlef-M. Smilgies, Rui N. Pereira,, ǁ Martin Stutzmann, Brian A. Korgel * McKetta Department of Chemical Engineering, Texas Materials Institute, The University of Texas at Austin, Austin, Texas , USA. Technische Universität München, Walter Schottky Institut Am Coulombwall 4, Garching beimünchen, Germany Cornell High Energy Synchrotron Source (CHESS), Cornell University, Ithaca, NY 14853, United States. ǁ Institute for Nanostructures, Nanomodelling and Nanofabrication, Department of Physics, University of Aveiro, Aveiro, Portugal *Corresponding Author: (T) ; (F) ; korgel@che.utexas.edu Silicon nanocrystal size determination by small angle X-ray scattering (SAXS). Figure S1a shows a transmission electron microscopy (TEM) image of the Si nanocrystals used in the study. The nanocrystals exhibit a spherical shape. The average nanocrystal size and size distribution were determined by small angle X-ray scattering (SAXS). Figure S1b shows SAXS data obtained from a dispersion of Si nanocrystals dispersed in hexane. The X-ray scattering is dominated by the crystalline Si core of the nanocrystals and an analysis of the scattering pattern provides a measure of the nanocrystal size. For a collection of nanocrystals with varying radius R, the intensity of the scattered radiation, is: 1 (1) In Eqn (1), q is the scattering wave vector, 4 sin 2, where is the scattering angle and is the X-ray wavelength. is the shape factor, taken here as a sphere of radius R: 3 (2) The number distribution of the nanocrystals,, is assumed to be Gaussian with an average radius, and standard deviation of : (3) Fitting Eqns (1)-(3) to the SAXS data in Figure S1b gives 6.11 nm and 0.4 nm. S-1

2 Figure S1. (a) TEM image of the Si nanocrystals used for these studies. (b) SAXS data acquired from the nanocrystals dispersed in hexane fit to Eqns (1)-(3) to obtain the average radius of the nanocrystals and the standard deviation. The data are shown in blue and the best fit of Eqns (1)- (3) to these data are shown in red. Additional GISAXS Pattern Analysis Figure S2 shows GISAXS patterns obtained from Si nanocrystals deposited on silicon substrates by drying dispersions in either hexane or chloroform for 2 hr. Figure S2a corresponds to Figure 2e and Figures S2b and S2c are both same GISAXS pattern as Figure 1e with spot indexing for two different superlattice orientations on the substrate. All three diffraction patterns index to face centered cubic (FCC) superlattices with a superlattice constant of 21.5 nm. The GISAXS pattern in Figure S2a from the superlattice deposited from hexane indexes to a superlattice oriented with (111) SL planes on the substrate. The diffraction spot pattern obtained from the superlattice formed by evaporating chloroform indexes to an FCC superlattice as in Figure S2a; however, there is a mixture of superlattice orientations: (111) SL and (100) SL. Figure S2b shows the (111) SL orientation indexing and Figure S2c shows the with (100) SL orientation indexing. The spots corresponding to the (111) SL orientation are more predominant but the pattern shows that both (111) SL and (100) SL orientations are present. S-2

3 Figure S2. GISAXS patterns obtained from Si nanocrystals. (a) Si nanocrystals dried from a hexane dispersion at room temperature for 2 hr. The diffraction spots are indexed to an FCC superlattice with (111) SL orientation and a superlattice constant of 21.5 nm. (b,c) Si nanocrystals dried from chloroform for 2 hr at room temperature. The patterns in (b) and (c) are indexed to FCC superlattices with superlattice constant 21.5 nm, but with two different superlattice orientations on the substrate. The indexing in (b) corresponds to a (111) SL orientation and (c) corresponds to a (100) SL orientation. The superlattice assembly exhibits a mixture of both of these superlattice orientations. Figure S3 shows the GISAXS pattern in Figure 2d of the disordered assembly of Si nanocrystals obtained by depositing the nanocrystals from hexane with a 30 min drying time. The radial integration of the 2D diffraction pattern shows the expected diffraction peaks corresponding to an amorphous assembly of nanocrystals. Figure S3. (Left) 2D GISAXS pattern obtained from Si nanocrystals deposited on a silicon substrate by drying hexane for 30 min at room temperature and a radial integration of I(q) is shown on the right. SEM images of Si nanocrystals deposited from hexane at room temperature and 55 o C. Figure S4 shows SEM images of Si nanocrystals deposited on substrates by evaporating hexane for 2 hr at room temperature and 55 o C. There is a clear difference in the film morphology. The nanocrystals clump into mounds when deposited at room temperature. When S-3

4 deposited at 55 o C, the nanocrystals form a non-uniform film ont the substrate, but the film is relatively continuous and does not exhibit the spherical mounds observed when deposited at room temperature. Figure S4. SEM images of Si nanocrystals deposited on substrates by evaporation from hexane for 2 hr at (a) room temperature and (b) 55 o C. The black regions in the images correspond to regions of bare substrate. In (a), the nanocrystals deposit as mounds with a circular shape. In (b), the nanocrystals deposit as continuous ribbon shapes the nanocrystals do not form mounds as in (a). Pair interaction potential calculations. Hamaker constant. The Hamaker constants for Si nanocrystals dispersed in hexane (A121) and chloroform (A131) were determined using the following relationship: 2 (4) The subscripts 1, 2, and 3 correspond to silicon, chloroform, and hexane, respectively. A 11 is the Hamaker constant of Si across vacuum (A 11 = J), 2 and A 22 is the Hamaker constant of chloroform across vacuum. A 33 is the Hamaker constant of hexane across vacuum. The Hamaker constants for hexane and chloroform, A 22 and A 33, were estimated using a simplification of the Lifshitz theory: 3 S-4

5 (5) where k is Boltzmann s constant, T is the temperature, is the dielectric constant, h is Planck s constant, e is the electronic UV adsorption, and n is the refractive index. A 131 is found to be 0.33 ev, and A 121 has a value of 0.24 ev. These values are significantly lower than the Hamaker constants of alkanethiol-capped Au nanocrystals dispersed in organic solvents. For example, values of 1.36 ev for A 131 and 1.16 ev for A 121 were obtained for Au nanocrystals in hexane and chloroform by Sigman, Saunders and Korgel. 3 Model for the pair interaction potential. The interaction potential between two Si nanocrystals in a dispersion was estimated by adding the contributions of their Van der Waals attraction, and steric repulsion (osmotic, and elastic ): 3 In Eqn (6), (6) (7) 2 2 (8) 2 (9) (10) R is the radius of the nanocrystals, k is Boltzmann s constant, T is the temperature, φ is the ligand fraction profile, ν solv is the molecular volume of the solvent, χ is the Flory-Huggins parameter and is taken to be zero for good solvents such as hexane and chloroform, l is the ligand length, c is the core-to-core distance, ρ and MW 2 are the ligand density and molecular weight, respectively. 3 Figure S5 shows total calculated for Si nanocrystals dispersed in hexane and chloroform. The values of total at room temperature and 55 o C overlap. S-5

6 Figure S5. Pair interaction potentials total, calculated using Eqns (6)-(10) for 12.2 nm diameter Si nanocrystals capped with 1-dodecene dispersed in hexane (blue curve) or chloroform (red curve). Instances of (110) SL orientations observed. In a few rare instances, the Si nanocrystal superlattices were observed with (110) SL orientation when the nanocrystals were dried from chloroform. Figure S6 shows and SEM image and Figure S7 shows a TEM image of superlattices with (110) SL orientation. The indexing of the fast Fourier transform (FFT) of the TEM image in Figure S7 is consistent with an FCC superlattice with (110) SL orientation. 100 Figure S6. SEM image of a Si nanocrystal superlattice domain with (110) SL orientation. The nanocrystals were deposited from chloroform. S-6

7 Figure S7. (Bottom) TEM image of a Si nanocrystal superlattice domain with (110) SL orientation. (Top) FFT of the TEM image indexed to an FCC superlattice with (110) SL orientation. The nanocrystals were deposited from chloroform. S-7

8 References (1) Korgel, B.A.; Fitzmaurice, D. Small-angle x-ray-scattering study of silver-nanocrystal disorder-order phase transitions. Phys. Rev. B 1999, 59, (2) Israelachvili, J. (2011). Intermolecular and Surface Forces. Santa Barbara, CA: AcademicPress. (3) Sigman, M. B.; Saunders, A. E.; Korgel, B. A. Metal Nanocrystal Superlattice Nucleation and Growth. Langmuir 2004, 20, S-8