CC BY
10
УДК 535.131
Self-Assembly of Nanoparticles Controlled by Resonant Laser Light
Aleksey S. Tsipotan* Vitaliy V. SlabW
Institute of Engineering Physics and Radio Electronics
Siberian Federal University Kirenskogo, 26, Krasnoyarsk, 660026
Russia
Aleksandr S. Aleksandrovsky*
Kirensky Institute of Physics SB RAS Akademgorodok, Krasnoyarsk, 660036
Russia
Nina V. Abuzova§
Institute of Engineering Physics and Radio Electronics
Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041
Russia
Received 10.09.2014, received in revised form 01.10.2014, accepted 10.11.2014 The paper presents theoretical justification for the possibility of formation of nanoparticle structures with the predefined configuration. The process of formation is the self-organized aggregation of nanoparticles under the action of external resonant laser field. The formation of various nanostructures that contain metallic and semiconducting nanoparticles with resonances in the visible spectrum is considered in the dipole-dipole approximation.
Keywords: interaction of laser radiation with matter, dipole-dipole interaction, nanoparticles, nanostruc-tures.
Introduction
Construction of nanoscale objects, study of their properties and application of these objects in electronics and photonics are presently among the main trends of both fundamental and applied research. The main disadvantage of using traditional technologies of microelectronics to produce nanostructures is the limit imposed by photolithographic copying. This makes cheap and mass production of nanostructures impossible [1]. It is worthwhile to mention here the review articles [2,3]. They describe the methods of formation of nanoparticles and nanostructures with the use of laser radiation. However, these methods have disadvantages of photolithography mentioned above. Therefore, the use of self-organization phenomena is attractive because it can provide the basis for development of relatively cheap technology of complex nanoscale objects production. Self-organization phenomena that are based on intermolecular interactions are the
*cipotana@mail.ru tvslabko49@mail.ru taleksandrovsky@kirensky.ru §sci_box@mail.ru © Siberian Federal University. All rights reserved
most attractive. These phenomena allow the formation of extremely complicated structures without using any technological processes. One should note that the majority of studies devoted to self-organized nanostructures formation is based on the chemical interactions and employs selective interactions between molecules from which the nanostructures are to be formed [4-8]. It seems promising to use physical fields, laser radiation in particular, for controlled self-organization of nanoobjects into clusters. The shape and properties of clusters are imposed in the process of their formation. Under the action of laser radiation atoms, molecules and other microparticles become polarized and they interact with the laser radiation. This produces the so-called radiation forces. These forces allow one to control particles movement and to form structures with the size of order of radiation wavelength [9]. Laser induced polarization leads to the interparticle interaction if the average distance between particles is much smaller than the wavelength. This can be treated as the near field effect.
The use of laser irradiation of nanoparticles produces various effects that are known to turn the assembly of nanoparticles to either disordered or ordered structures. For instance, mesoscale filaments of carbon and gold nanoparticles are irreversibly obtained under laser irradiation with the use of optical trapping, hydro-thermal and chemical effects [10]. Light-controlled assembly of CdTe nanoparticles in helical structures [11] was ascribed to the production of photogenerated charges. Another prospective approach implies the modification of potential energy of the particles in the non-resonant electromagnetic field of the light wave due to particle interactions [12]. Self-assembly of nanoparticles under the action of non-resonant electromagnetic field in the wide frequency range was also investigated [13]. When nanoparticles resonantly interact with the electromagnetic field, this interaction gives new opportunities for selective manipulation of nanoparticles [14]. One should note that optical and spectral properties of silver nanoparticles with a surface plasmon resonance in the visible spectrum were extensively studied [15-22]. Nonlinear optical properties of fractal aggregates of such nanoparticles were experimentally studied [15,16]. The influence of electromagnetic interaction between particles on spectral properties of their aggregates was also investigated [17-18]. Photochromic effects due to photostimulated aggregation were described [19-21] and the origin of these effects were discussed [22]. All these studies are devoted mainly to the study of spectral properties observed for weak electromagnetic field. The most interesting phenomena are expected in the case of action of strong laser field on the resonant particles. The energy of their electromagnetic interaction may exceed not only the energy of their thermal motion but also, in a number of cases, the energy of chemical bond.
It was theoretically shown that in the case of plasmon-resonant metallic and semiconductor nanoparticles the action of proper frequency electromagnetic field affects the geometry of the produced structures [23,24]. It was found that interaction of particles in the laser field leads to the shift of their resonant frequencies. This shift depends on the distance between particles and particles orientation with respect to the laser field polarization. The given configuration of the aggregate of particles can be obtained only when laser field induces the attraction of particles. This is achieved by proper choice of the frequency and polarization of laser field.
The formation of one geometry of nanostructure or another strongly depends on the resonance linewidth of individual nanoparticle. Since plasmon resonances of metallic nanoparticles are rather wide it is interesting to consider the light-controlled aggregation of nanoparticles with narrower resonances. Such resonances can be found in semiconducting nanoparticles [25, 26] and in doped dielectric nanoparticles [27]. The formation of heterogeneous nanostructures that consist of different materials (dielectric, semiconducting and conducting nanoparticles) is also of great interest. A special feature of heterogeneous systems is the presence of several resonances with non-coinciding frequencies and linewidths. In the present paper we summarize the theoretical results obtained in dipole-dipole approximation on resonant light-controlled effects on formation of nanostructures that contain semiconducting and metal nanoparticles or just semiconducting nanoparticles. The influence of phases of induced dipoles on the interaction energy of particles is considered in detail.
1. Mathematical model of the process of interaction between nanoparticles
When metal or semiconductor nanoparticles in the state of Brownian motion interact with laser field then they acquire induced electric dipole moment due to polarization effect. Interaction of this dipole with laser field results in optical trapping in the regions with the dimensions of order of wavelength. Increased density of nanoparticles results in increased aggregation rate within an optical trap. The produced aggregates are disordered on the nanoscale but they can bear the signs of ordering on the sub-wavelength scale due to a variety of processes that depend on the medium containing nanoparicles [10,28]. When several particles in the course of Brownian motion occasionally appear closely enough to each other then dipole-dipole interaction takes place. This is one of the manifestations of near-field effect. If the energy of electromagnetic interaction between nanoparticles exceeds the energy of thermal motion kT and the energy of a barrier preventing the aggregation then irreversible formation of nanostructures happens.
Let us consider an ensemble of N nanoparticles with coordinates r». The interaction between nanoparticles is dipole-dipole interaction and dipole moments of nanoparticles are induced by laser field. The size of the ensemble is supposed to be much less than the wavelength of laser radiation. Then external field strength can be considered homogeneous within the ensemble. It is assumed that electric field strength depends only on time: E = 1/2Eoexp(wt) + c.c. Local field acting on every nanoparticle is a sum of external field and the fields induced by all other particles. In the dipole-dipole interaction approximation the dipole moment vector induced on i-th particle at given frequency w is
di = xo(E + £ Ej). (1)
j = i
Here x0 = |Pi2|2 /h(Q + ¿r») is the linear polarizability of isolated nanoparticle, |P12|2 is the squared magnitude of electric dipole moment of the transition between ground (1) and excited (2) states for i-th particle, Q = w0j — w is the resonance detuning, h is the Planck constant, r» is the homogeneous width of transition and Ej is the field produced by j-th nanoparticle in the position of ¿-th particle [29]:
3(dj ry )r»j — dj rj Ej = --' (2)
»j
where r»j = r» — rj is the distance between particles. Interaction energy of ¿-th and j-th particles with excited dipole polarization is [12]
w , 3(dj r»j )r»j — rj dj (d»dj )r2j — 3(d»rij )(dj r»j)
Wdij = —di--~5-— = -—5- • (3)
»j »j
Therefore, calculation of interaction energy between particles requires solution of system of N equations with dipole moments of every particle X defined by expression (1). Renormalised linear polarizability of every particle can be also obtained. In general, it is a tensor that relates dipole moment vector induced on ¿-th particle to the vector of electric field strength: d» = XjE. Imaginary part of renormalized polarizability is responsible for the absorption of light by i-th particle. Let us consider the binary interaction of two particles with different resonant frequencies in the dipole approximation. As an example let us choose silver nanoparticle [29] and semiconductor nanoparticle of CdSe [25, 26]. The optical properties of these nanoparticles are well studied.
Using relation (1) and introducing the frequency shift of ¿-th particle resonance due to interaction with neighbor particle ws» = |P12|2 /hr3, we obtain expressions for d1x(x||r12) and
diy (y±ri2) components of induced dipole moments of a pair of nanoparticles:
dix = r3Ews1 cos a
(»2 + 2^S2)(Oi »2-rir2-4^si^s2)+r2(0ir2 + »2 ri)
(»i»2-rir2 - 4wsi^s2 )2 + (№ +^2ri)2
+
-rir2-4^si^s2)-(02 +2^s2)(Oir2 + »2^)
diy = r3Ewsi sin a
+
d2x = r3Ewsi cos a
d2y = r3EiMsi sin
(»i»2 -rir2 - 4^si^s2)2 + (»^2 + »2^)2 " (»2)(»i»2-rir2-^sj^s2) + ^(»^2 + »2^)
T2(»i»2-rir2-Wsi^s2)-(02 +2^s2)(Oir2 + »2^ )
—I— i_
. (»i»2 - rir2 - ^i^)2 + (№ + »2^)2
■(»i + 2^si )(»i»2-rir2-4^si^s2) + ri (»^2 + »2^)
(»i»2 -rir2-4^si^s2)2 + (»ir2 + »2ri)2 , ,ri(»i»2-rir2-4wsiws2)-(»i +2^si)(»ir2 +»2ri)
—I— i-
^ (»i»2 - rir2 - 4^si^s2)2 + (»ir2 + »2^)2
(»i - ^Si)(»i»2 - rir - + ri(»ir2 + »2^) (»i»2 - № - ^i^)2 + (»ir2 + »2ri)2
eiwi + c.c,
eiwi + c.c,
+
eiwi + c.c,
+
+i
Ti(»i »2-ri r2 -wsi^s2)-(»i + 2wsi)(»ir2 +»2ri)
(»i»2 - № - ^si^s2)2 + (»ir2 + »2ri)2
(4)
eiwi + c.c.
Here a is the angle between the line connecting the centers of nanoparticles and the vector E (Fig. 1).
It is convenient to present the expression for the energy of dipole-dipole interaction in terms of the amplitudes and phases of induced dipole moments of every particle. Then, after averaging over time, expression (3) takes the form
W :
|diy | |d2y | cos(^iy - ^2y)sin2 a - 2 |dix| |d2x| cos(^ix - ^2x)cos2 a
2r3 '
(5)
where diy, d2y, dix, d2x are magnitudes and ^>iy, ^2y, ^ix, ^2x are phases of y and x components of time-averaged dipole moments of the first and the second particles.
a
2. Results and Discussion
2.1. One metallic and one semiconductor particles
The dependence of imaginary part of (d1x + d2x)/E cos a and (d1y + d2y)/E sin a on the external field wavelength is shown in Fig. 1 (solid line) for x (a) and y (b) components of electromagnetic field, respectively. This part is responsible for the absorption of the whole system consisting of two particles.
Dependencies of dipole-dipole interaction energy normalized by room temperature thermal energy kT on the laser wavelength are shown in Fig. 1 (dashed lines) for angles a = 00 (Fig. 1a) and a = 900 (Fig. 1b). The following parameters were used in the calculation. For semiconducting CdSe nanoparticle we take into account only most prominent long-wavelength exci-ton transition with resonant wavelength A0i = 590 nm that corresponds to w10, the linewidth AAi = 3 nm, the radius R1 =5 nm and squared magnitude of electric dipole moment of the transition |P12|2 = 1.91 • 10-31erg-cm3 [7,8]. For silver nanoparticle corresponding values are A02 = 420 nm, AA12= 90 nm, R2 = 6 nm and |P12|2 = 3.12 • 10-3erg-cm3 [29]. The external
field strength is E = 200 ESU (106W/cm2), temperature of the medium is T = 300 K and the distance between particles is r12 = 13 nm.
Fig. 1. Wavelength dependence of imaginary part of polarizability for pair of nanoparticles (solid line) x and normalized dipole-dipole interaction energy of particles (dashed line). Vertical lines are resonant wavelengths of non-interacting nanoparticles. External field is directed at (a) a = 00 and (b) a = 900
As can be seen from expression (4) and Fig. 1, wavelength dependence of imaginary part of susceptibility responsible for the absorption noticeably differs from that for non-interacting particles for both field components x and y. One can see that x component has two prominent maxima with the positions shifted from the centers of non-perturbed resonances. This shift is due to the particle interaction and it depends on the resonances widths Г, Г2, resonant frequencies of non-interacting particles and squared magnitudes of electric dipole moments |P12 and |P12|2. Characteristic feature is the existence of a dip in the area of 600 nm for imaginary part of polarizability for y field component (Fig. 1b). This dip is the Fano-like resonance and it reflects the interference nature of the particles pair interaction when particles have different resonant frequencies and linewidths [30,31]. Spectral dependence of nanoparticles interaction energy at a = 00 has the potential well (Fig. 1a dashed line) and the well depth considerably exceeds the energy of thermal motion. If the height of a potential barrier hindering the aggregation is smaller than this depth the formation of a stable pair of nanoparticles becomes possible. This pair of particles is oriented at the angle a = 00 to the vector of electromagnetic field. The stability of the pair is sustained by either van der Waals or Coulomb forces. The latter are due to electron transfer between semiconductor quantum dot and metallic nanoparticle [32]. The dependence of
imaginary part of susceptibility at a = 900 also has the minimum (Fig. 1b) but minimal energy remains positive in this case.
2.2. Three particles
Let us consider now the possibility to form such potential well that allows one to join a third particle at a given angle 0 to a pair of particles. It can be accomplished by varying the radiation frequency and the angle a between the polarization plane of the radiation and the radius-vector r12 (see Fig. 2). Let us consider the case of formation of a structure consisting of 3 metallic particles. In this case, it is assumed that the pair of particles 1 and 2 acts as a single whole and that r12 can be oriented in space using auxiliary laser radiation. Analytical solution of Eqs. (1) and (2) for three particles is very cumbersome and it is not presented here. The distance between the particles of the pair is r12 = 2R = 12 nm. In Fig. 2, r23 is the distance between the second and third particles and 0 is the angle between the straight lines r12 and r23. The polarization of the external light field is directed at an angle a to the straight line that connects the centers of the first two particles and it is parallel to the x axis. Fig. 2 shows the dependence of the energy of the dipole-dipole interaction of the third particle with the two others on frequency and the angle a. The values of the particle radius, the external field strength and temperature are the same as in the above case with two interacting particles. The distance between the pair of aggregated particles and the third particle is r23 = 15 nm. The angle of arrangement of the third particle is equal to 0 = 900. It is seen from Fig. 2a that the minimum value of the dipole-dipole interaction energy is about -1.7 kT and it is attained at the angle of orientation of the external field polarization a « 650 ° and at the radiation wavelength A « 500 nm. Similarly to the above case of two interacting particles, when the particles approach each other the potential well becomes deeper and the resonance frequency is shifted toward the IR range. For example, for the particle arrangement shown in Fig. 2b, i.e., at 0 = 1200 and r23 = 12 nm, the minimum of the potential well at A « 1600 nm is about -6.9 kT. The field in this case should be oriented at the angle a = 900. This is consistent with qualitative analysis. In addition, numerical calculation shows that a decrease in the angle 0 also leads to the shift of the resonance frequency toward the IR range, to the small deepening of the potential well and to its shift towards smaller angles a. Thus, the calculated minimum is -2.2 kT at and it is observed at r23 = 15 nm, 0 = 00, A « 3500 nm and a = 00.
a K (mill h X (nm)
Fig. 2. Energy of interaction of a third particle with two other particles in electromagnetic field in relation to the orientation angle of the field polarization and the wavelength; the angle 0 = 900 (a) and 0 = 1200 (b)
Calculations for various configurations of nanoparticles in a nanostructure, that is, for different values of angle 6 , show that not all configurations are equally controllable through the change of wavelength, laser intensity and polarization. As one can see from figures, the potential well depth in the case of interaction of metal particles is of order of several kT at the field intensity close to (106W/cm2). Besides, the large spectral width of these wells attracts attention. This is because the large width of plasmon resonance of individual particles.
For comparison, let us compare results for heterogeneous structures with the case of homogeneous structure formation when semiconductor particle takes on a pair of already aggregated semiconductor particles. The resonance width of semiconductor particle is much smaller than that of metallic particle. Fig. 3 presents the dependence of interaction energy on the laser wavelength and angle a for 6 = 1200.
Fig. 3. The dependence of the energy of normalized dipole-dipole interaction between semiconducting particle and the pair of aggregated semiconducting particles on the laser wavelength and electric field direction angle
Individual resonant frequency of every aggregated particle is chosen to be corresponding to the wavelength 590 nm, while for the third particle it corresponds to 510 nm. The particle radius is r3 = 3 nm. Linewidths of isolated nanoparticles and laser field strength are the same as in previous calculations. As can be seen from Fig. 3, two potential wells exist at a = 900 and a = 200. The well depths are 63 kT and 43 kT at wavelengths 595 nm and 655 nm. Figs. 4a and 4b show the dependence of interaction energy on wavelength at a = 00 and a = 90° for different angles 6. For a = 900 configurations are possible either with 6 = 1200 (the wavelength is 593 nm) or with 6 = 900 (the wavelength is 554 nm). While suitable potential wells for 6 = 00 and for 6 = 450 are absent.
When laser field polarization angle a = 00, the formation of configurations with 6 = 1200, 900, 450, 00 is possible since all of them have suitable potential wells at 655, 615, 685 and 710 nm, respectively. The accuracy of positioning the particle at the desired angle 60 can be found from the dependence of the energy of interaction between particle and two aggregated
900
Fig. 4. The dependence of the normalized energy of dipole-dipole interaction between semiconductor particle and two aggregated semiconducting particles on the laser wavelength for different configurations of the nanostructure: 6 = 1200 (dash), 900 (thick solid), and 00 (thin solid); (a) — a = 900 and (b) — a = 00
particles on the angle 6 in the vicinity of 60. This dependence is presented in Fig. 5 for three different sets of particles.
The possibility to build structure with desired configuration (60) can be quantitatively described by the angular width A6 of the potential well on the level that is 1 kT higher than the value of potential well minimum. Evidently, A6 can characterize the angular selectivity of desirable structure under conditions of thermodynamic equilibrium with the surrounding medium. As can be found from Fig. 5 for 60 = 90°, A6 = 2.70 for three semiconducting particles and a = 00. While for a = 900 and two semiconducting and one metallic particles A6 = 16.90. For the case of two metallic and one semiconductor particles the minimum at 60 = 900 is absent, as it was already mentioned in the analysis of spectral dependencies. The highest selectivity (A6 below 10) is expected for three semiconducting particles for both a = 900 and a = 00. The A6 values and corresponding potential well depths |Wmin | (in kT units) for two metallic and one semiconductor particles (mms), two semiconductor and one metallic particles (ssm) and three semiconductor particles (sss) are presented in Tab. 1 for laser intensity 106 W/cm2. As can be seen, for (a = 900) stable configurations with 6 = 00 are nonexistent for all particle sets because of the absence of potential wells for all considered wavelengths. For mms set, for both a = 900 and a = 00, and for ssm set and a = 00 the configuration 60 = 900 possesses potential wells, but stable configurations are absent as well as in the cases mms90 and ssm0 for 60 = 1200.
Of course, the A6 values depend not only on the structure configuration but also on the
Fig. 5. Dependence of potential energy of interaction on the angle 9 for a = 900: 1 - three semiconducting nanoparticles, 2 — two semiconducting and one metallic nanoparticles, 3 — two metallic and one semiconducting nanoparticles
intensity of laser radiation. They decrease with the increase of the laser radiation. Joint consideration of spectral and angular widths of potential wells allows one to evaluate the possibility of light-controlled formation of nanostructures.
Table 1. Angular widths AO and potential well depths for various particle sets, particle configurations Oq and light polarizations a
Qq mms ssm sss
a = 0° a = 90° a = 0° a = 90° a = 0° a = 90°
0° AO 7.38° - 12.46° - 4.718° -
1 Wmin 1 4.117 - 20.84 - 112.7 -
90° AO - - - 16.89° 2.739° 1.031°
IWminl 0.591 5.47 1.41 6.49 10.04 61.2
120° AO 3.44° - - 2.1° 0.19° 0.22°
IWminl 1.634 23.35 1.311 5.411 41.55 71.84
2.3. The influence of phases of induced dipole moments on the energy of dipole-dipole interaction
The results presented above indicate fundamental difference in the interaction between identical particles and between particles with different linewidths, resonant wavelengths and dipole moments. One can observe the occurrence of additional maxima and minima in the spectral dependence of interaction energy. For example, in distinction to a pair of metallic particles [23], calculations show (see Figs. 2 and 3) the occurrence of additional spectral minima in the interaction energy. This can be connected with phase relations of dipole moment oscillations induced on
individual particles. If electric dipole moments of transitions, linewidths or resonant frequencies of particles are different and the phases of induced dipole moment oscillations are different then situation may occur when phase difference is close to n/2 at the angle a = 900. This results in occurrence of additional minima or maxima in the interaction energy [24]. Using (4), one can obtain the following expression for phases of dipole moment oscillations
, = . r2(»i- № - 4^^) - + 2^2X^2 + fl2ri) <ix arc g (^2 + 2^2X^2 - rir2 - 4^S1 ^2) + ^(0^2 + №) '
ri(fii^2 - rir2 - 4^si^2) - (fii + 2^si)(^ir2 + ^i)
<i2 = arctg
<iy = arctg <2 y = arctg
(fii + 2^si)(niQ2 - rir2 - 4^^) + ri(^2 + ^i) ' ^(0^2 - rir2 - Wsi^s2) - (O2 - Ws2)(Oir2 + O2ri)
(^2 - Ws2)(0i^2 - rir - Wsi^s2) + ^(^iT + O2ri) '
ri(^i^2 - rir2 - ^si^s2) - (0i - ^siX^i^ + ^2^) (0i - Wsi)(ni^2 - rir2 - WsiWs2) + ri^ir + ^2^)
(6)
As one can see from expression (5), the energy of dipole-dipole interaction for polarization angles a = 00 ( x component) and a = 900 (y component) consists of just one term. Expression (6) shows how the phases of dipole moment oscillations depend on linewidths and resonant frequencies of interacting particles. Therefore, in the case of interaction of identical particles the phase difference in expression (6) is always zero and the cosine function in the expression (5) is always unity. One should note that in the case of stationary electric field the situation is completely the same. However, when parameters of individual interacting particles are different, cosine function can change its sign. This results in additional resonances mentioned above [24]. These resonances occur only in the case of oscillating polarization of particles.
The results of numerical calculations of phases of induced dipole moments oscillations and dipole-dipole interaction energy normalized to the energy of thermal motion are presented in Figs. 6 and 7 as a function of angle a and external field frequency. The following values of the quantities entering the equations are used: external field E=200 ESU (106W/cm2), temperature T=300 K, distance between particles r12=14 nm.
As one can see from Fig. 6b, induced dipole moments of metallic particles always oscillate with the same phase. The wavelength region around 800 nm corresponds to the interaction energy well and the well depth is equal to -6.6 kT. This means that stable aggregate of a pair of particles is formed. At the wavelengths from 400 to 550 nm the interaction energy of a pair of metallic and semiconducting particles experiences maximum of order of 0.6 kT that corresponds to particles repulsion (Fig. 6c) and the difference between oscillation phases of individual particles is close to n. In the region of 620 nm the potential well arises and the well depth is equal to -1 1.2 kT. This corresponds to attraction of particles and the phase difference equals zero.
For angle a = 900 (y component of induced dipole moment) the dipole-dipole interaction energy of two identical particles (Fig. 7a) exhibits maximum at 350 nm that corresponds to repulsion of particles and phase oscillations of induced dipole moments are observed (Fig. 7b). The variation in phase of the value close to n takes place when wavelength is tuned over the resonance. More complicated situation occurs in the case of interaction of metallic and semiconducting particles. When phase difference of induced dipole moments oscillations becomes close to n (Fig. 7d), additional minimum in the energy of dipole-dipole interaction occurs. This minimum corresponds to weak attraction (the well depth equals -0.03 kT ) and it lies in the region of 590 nm (Fig. 7c). Therefore, the occurrence of attraction between particles at a = 900 is due to the phase shift of induced dipole moments of metal and semiconducting particles and the shift value is close to n.
X, nm X, nm
Fig. 6. The dipole-dipole interaction and phases of induced dipole moments: a, b are two metallic particles; c, d are metallic and semiconducting particles, angle a = 0q. 1 is the phase of induced dipole moment of metallic particle, 2 is the phase of induced dipole moment of semiconducting particle
_01i-,-.-,-.-,-.-,-, --out—,-.-,-.-,-.-,-,
С 200 400 600 800 d 200 400 600 800
X, nm X, nm
Fig. 7. The dipole-dipole interaction energy and phases of induced dipole moments: a,b are two metallic particles, c,d are metallic and semiconducting particles, angle a = 90q . 1 is the phase of induced dipole moment of metal particle, 2 is the phase of induced dipole moment of semiconducting particle
3. Conclusions
We theoretically show the possibility to control the self-organized aggregation of nanoparticles in order to form the structures with predefined geometry with the help of external resonant field of laser radiation. The basic idea of controllable aggregation is that interaction between particles
in a group under the action of external electromagnetic field depends on both the frequency and the polarization orientation of the field. As this takes place, either attraction or repulsion of particles is possible. If the potential well depth exceeds the threshold that prevents spontaneous aggregation then particles fall into the potential well. The formed structure is preserved due to action of van der Waals forces because the energy of interaction considerably exceeds the energy of thermal motion. The spatial configuration of the formed nanostructure can be predefined with the proper choice of frequency and polarization of the field. Nanostructures consisting of metallic and semiconducting nanoparticles with optical resonances in the visible spectrum are considered. The possibility of formation of such nanostructures is examined in dipole-dipole approximation. The choice of such nanostructures is dictated mainly by the fact that they form the basis for elements of micro- and nanoelectronics. In our study the following particles parameters are taken into account: resonant frequencies, resonance widths and electric dipole moments. Numerical analysis shows that for the commonly accepted values of the parameters the interaction energy between particles can achieve values comparable with the chemical bond energy in the laser field with the intensity below particle destruction threshold. The numerical algorithm is presented that allows one to choose the particles and field parameters that are necessary for formation of predefined nanostructures.
This research was supported by Siberian Federal University under the grant F12 and by the Ministry of Education and Science of Russian Federation under the contract 14-А18.21.1942.
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Самоорганизация наночастиц, контролируемая резонансным лазерным полем
Алексей С. Ципотан Виталий В. Слабко Александр С. Александровский Нина В. Абузова
Теоретически показана возможность формирования структур из наночастиц с заранее заданной конфигурацией. Это возможно благодаря явлению самоорганизации наночастиц под действием внешнего резонансного поля лазерного излучения. Формирование различных наноструктур, содержащих металлические и полупроводниковые наночастицы с резонансной длиной волны в видимой области, считалось в диполь-дипольном приближении.
Ключевые слова: взаимодействие лазерного излучения с веществом, дипольное взаимодействие, наночастицы, наноструктуры.
