Journal Name

Supporting information for: “Resonant SiliconNanoparticles with Controllable Crystalline State andNonlinear Optical Response”

Sergey Makarov, Lada Kolotova, Sergey Starikov, Urs Zywietz, Boris Chichkov

1 Laser printing on a gold substrateIn order to study the effect of substrate thermal conductivity onthe printed nanoparticles shape and properties, we carried out alaser printing of silicon nanoparticles on the boarder of a goldfilm and bare glass substrate. In this case, the distance betweensubstrates was the same (z=10 µm), owing to the small region ofanalysis.

The obtained SEM images (Fig 1a) and Raman spectrum(Fig 1b) result in several important conclusions:

(i) at the distance z=10 µm, the droplet falls in liquid state,because of splashing of the particles on the gold substrate withtwo orders of magnitude higher thermal conductivity than thatfor glass.

(ii) Since the measured Raman spectra from the nanoparti-cles on gold reveal their almost complete amorphization at thedistance z=10 µm, we believe that cooling rate is much higherthan that of glass substrate and exceeds the threshold value ofKth=0.8 ps/K.

(iii) From the comparison of our results with our previousworks on laser transfer of silicon nanoparticles on gold surfaceat distance around z=50 µm1, where the particles were in crys-talline phase, one can conclude that the crystallization in air oc-curs somewhere between 10 and 50 µm, depending on nanopar-ticles size (see Fig.5 in the main text).

2 Analysis of nanoparticles ordering at dif-ferent distances

The experimental data were digitized to obtain precise infor-mation on the experimental NPs displacement in the horizontalplane. The directions of the basis vectors i, j of an ideal simplesquare lattice are evaluated by the mean values for the lowest andthe leftmost silicon NP positions, respectively. The length of thevectors corresponds to an average distance between NP L=5 µm.The positions of the lattice sites are calculated as Rid = N·i +M·j, where N and M are integers. The coordinates X and Y of NP

Au film

glass

splashed Si NPs

spherical Si NPs

z = 10 mm

-1Raman shift (cm )

200 300 400 500 600

Ra

ma

n s

ign

al (

co

un

ts)

splashed Si NP

(a)

(b)

Fig. 1 (a) SEM image of silicon nanoparticles printed on glass and goldsurfaces at the distance between donor and receiver substratesz=10 µm. (b) Raman spectrum of the silicon nanoparticle printed on thegold surface.

Journal Name, [year], [vol.], 1–2 | 1

Electronic Supplementary Material (ESI) for Nanoscale.This journal is © The Royal Society of Chemistry 2018

themselves are determined from the following condition Rreal =X·i + Y·j. The mean square of the displacement of particles fromthe nodes of the ideal lattice can be estimated as:

< ∆L2 >=< (Rreal−Rid)2 >=< (X−N)2 > i2+< (Y−M)2 > j2. (1)

Figure 2 shows the dependence of NP mean-squared displace-ment <∆L>ms/L on distance z between substrates. The reason forthe disorder of particles at distances greater than 20 µm can bethe fluctuation in the angle of NP motion. In this case <∆L>ms =<∆ϕ>·z. The average value <∆ϕ> ≈ 4o is obtained from the lin-ear approximation of the experimental dependence data for thefirst 5 distances (5-20 µm). It should be noted that in the case ofcompletely disordered arrangement of NPs, the maximum devia-tion of NP’s position from the lattice site ∆Lmax = L

√2/2 which

results in the mean-squared displacement <∆L>ms ≤ 0.3L. Thisfact causes the absence of values <∆L>ms/L greater than ∼ 0.3in figure 2. Thus, the deviation of NP motion angle from the thevertical direction by 4o can explain the gradual transition fromthe ordered NP structure at small distances to the substrate todisordered structure at the distances to the substrate larger than40 µm. It should be noticed that sub-100-nm Si nanoparticlesoften accompany controllably printed larger particles (Fig. 3).

Fig. 2 Nanoparticles ordering. Experimental normalized dependenceof silicon nanoparticles mean-squared displacement on the distancebetween substrates (z).

Fig. 3 SEM image of a silicon nanoparticle printed on glass surfaces atthe distance between donor and receiver substrates z=10 µm.

References

1 V. Milichko, D. Zuev, D. Baranov, G. Zograf, K. Volodina,A. Krasilin, I. Mukhin, P. Dmitriev, V. Vinogradov, S. Makarovand B. P.A., Laser & Photonics Reviews, 2018, 12, 1700227.

2 | 1–2Journal Name, [year], [vol.],