Absorption of Ultrashort Electromagnetic Pulses by ITO Nanoparticles

Article pubs.acs.org/JPCC

Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

Absorption of Ultrashort Electromagnetic Pulses by ITO Nanoparticles V. A. Astapenko,† S. V. Sakhno,† O. J. Ilegbusi,*,‡ and L. I. Trakhtenberg†,§ †

Moscow Institute of Physics and Technology, 9 Institutsky Lane, Dolgoprudny 141700, Moscow Region, Russia University of Central Florida, 4000 Central Florida Boulevard, Orlando, Florida 32816-2450, United States of America § Semenov Institute of Chemical Physics, Russian Academy of Sciences, 4 Kosygin Str., Moscow 119991, Russia ‡

ABSTRACT: The paper investigates the cross-section and probability of absorption of ultrashort electromagnetic pulses by ITO nanoparticles in a dielectric matrix. It discusses the suitability of using the total probability of photoabsorption instead of the probability per unit time for such pulses. It is shown that in the case of negative detuning of the pulse carrier frequency from the plasmon resonance frequency, the photoabsorption probability is a nonlinear function of the pulse duration. For detuning with sufficiently large magnitude, the formation of a maximum is possible in this functional relationship, the position of which depends on the refractive index of the matrix. A method is proposed for measurement of environmental parameters by the analysis of time dependence of this photoprocess. Calculations are performed for a corrected Gaussian pulse and ITO nanoparticles with different doping levels.

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INTRODUCTION Advances in the experimental generation of ultrashort electromagnetic pulses (USP) have resulted in the production of pulses with a duration of tens of attoseconds,1−3 which approaches the atomic unit of time (24 as). This makes it possible to observe atomic and molecular processes in real time.4 In such a situation, there is the potential to form and control pulses with predetermined characteristics. These advances have necessitated the study of the characteristics of USP interaction with various targets. There are currently a number of theoretical and experimental studies of USP interaction with various targets including atoms of noble gases,5,6 fullerenes,7 metal clusters,8 etc. Of special interest is the study of USP interaction with semiconductor nanoparticles since surface plasmons may appear on the nanoparticles. The frequency of this process varies over a wide range: from the terahertz region to the near-IR region, which is achieved as a result of a change in the doping level. This makes it possible to produce semiconductor nanoparticles with a specified plasmon resonance frequency as well as adjust plasmon frequency thereafter. Such features provide opportunities for use of semiconductor nanomaterials as sensory materials, which indeed has been done.9−11 In the present study, another mechanism of the sensory effect on tin-doped In2O3 (ITO) semiconductor nanoparticles is proposed. The mechanism is based on the relationship between the time dependence of the probability of electromagnetic pulse absorption by a plasmon nanoparticle, and the refractive index of the surrounding medium. It should be noted © XXXX American Chemical Society

that In2O3 nanoparticles have a number of interesting service properties: good electrical conduction, transparency to sunlight, and high reactivity with some molecules of toxic gases. These properties make the use of In2O3 films attractive, for example, in manufacturing solar cells12 and optoelectronic devices.13,14 In addition, nanostructured In2O3 films are an important material for semiconductor gas sensors.9−11,15 The thermoelectric effect on a thin ITO film with different tin doping levels has also been studied.16 The conductance and the Seebeck coefficients at different temperatures of heated sample were analyzed. The cross sections of photoabsorption in the IR range by In2O3 nanoparticles were calculated.17 These studies used as initial data, the number of electrons in traps and distribution of conduction electrons over the nanoparticle radius.18 In the present study, the probability of photoabsorption of ultrashort electromagnetic pulses is calculated, and a description is given of the method used for measuring the refractive index of the surrounding medium in which an ITO nanoparticle is placed. This approach, utilizing the measurement of time dependence of photoprocess probabilities, provides the potential for creation of a new class of sensors, namely, optical plasmon sensors based on semiconductor nanoparticles. Received: November 3, 2017 Revised: December 5, 2017 Published: December 6, 2017 A

DOI: 10.1021/acs.jpcc.7b10890 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

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PROBABILITY OF USP PHOTOABSORPTION The concept of photoprocess probability per unit time is traditionally used in describing the process of radiation interaction with a substance within the framework of applicability of the perturbation theory, thus: w=

∫ σ(ω′) Iℏ(ωω′′) dω′

x=

∫0

∝

|E(ω′, τ )|2 σ(ω′) dω′ ℏω′

bn(ω) =

(6)

π J (z), hn(2)(z) = 2z z + 1/2

π (2) Hn + 1/2(z) 2z

σsc(ω) = πr 2Q sc(ω)

(7)

where Qsc(ω) is the scattering efficiency Q sc(ω) =

2 x2

(2)

21

given by

∞

∑ (2n + 1)(|an(ω)|2 + |bn(ω)|2 ) n=1

(8)

The parameters Qext(ω) and Qsc(ω) in eq 4 and eq 7 are expressed as expansions in terms of multipoles: to n = 1 corresponding to dipole expansion, to n = 2 corresponding to quadrupole expansion, etc. The photoabsorption cross-section σabs(ω) is equal to the difference between the cross sections of extinction in eq 3 and scattering in eq 7 thus: σabs(ω) = πr 2(Q ext(ω) − Q sc(ω))

(9)

The dielectric permittivity of a nanoparticle ε(ω) in the case under consideration can be described by the Drude classical model22,23 that was initially proposed24,25 for metals: ε(ω) = ε∞ −

ωp 2 ω 2 + iωγ

(10)

where ε∞ is the high-frequency dielectric permittivity of a substance, γ is the relaxation constant for conduction electrons, and ωp is the plasma frequency. Using the expression in eq 10 is correct for substances in which the concentration of free charge carriers reaches values comparable to the corresponding concentrations in metals.26 The value of this concentration is equal to 6 × 1020 cm−3 for ITO.27 The function ε(ω) calculated for the ITO nanoparticles in the Drude model is in a good agreement with the experimental data28 in the wavelength range 500−2200 nm. Substituting the formula in eq 10 in the expressions of eqs 5 and 6, we calculate the Mie coefficients an(ω) and bn(ω). The valuesof the plasmon resonance parameters, ε∞, γ, and ωp are obtained from the experimental data.29 Knowing the Mie coefficients, we find the efficiencies of extinction Qext(ω) and scattering Qsc(ω) and, with the use of eq 9, calculate the required photoabsorption cross-section σabs(ω).

(3)

∞

n=1

m(ω)ψn′(y)ζn(x) − ψn(y)ζn′(x)

Here Jz+1/2(z) is the Bessel function of the first kind and H(2) n+1/2 is the Hankel function of the second kind, m(ω) = ε(ω)/εm , y(ω) = 2πr εm m(ω)/λ . The expression for the scattering cross-section σsc(ω) is

Here r is the target radius, and Qext(ω) is the extinction efficiency determined from the relation,,

∑ (2n + 1)Re(an(ω) + bn(ω))

(5)

m(ω)ψn′(y)ψn(x) − ψn(y)ψn′(x)

jn (z) =

PHOTOABSORPTION CROSS SECTION The cross-section of photoabsorption for a semiconductor nanoparticle σ(ω) has been calculated within the framework of the Mie theory.20,21 The target is assumed to be spherical and homogeneous with well-defined boundary, and its optical properties are fully described by the dielectric permittivity ε(ω). The target is in turn placed in a uniform and isotropic medium with dielectric permittivity εm(ω). According to the Mie theory, the extinction cross-section is of the form,

2 x2

ψn′(y)ζn(x) − m(ω)ψn(y)ζn′(x)

ψn(z) = zjn (z), ζn(z) = zhn(2)(z)

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Q ext(ω) =

ψn′(y)ψn(x) − m(ω)ψn(y)ψn′(x)

an(ω) =

(1)

where c is the speed of light, and E(ω′,τ) is the Fourier transform of the strength of the electric field in the USP. Naturally, it is assumed that W < 1, that is, a restriction is imposed on the electromagnetic field amplitude and the pulse duration. The formula in eq 2 was derived using the standard quantum-mechanical formulation of the first-order perturbation theory as well as the relationship between the target dipole moment correlator and the cross-section of target photoionization.19 Thus, for calculation of the photoabsorption probability using the expression in eq 2 it is necessary to know the photoabsorption cross-section and the Fourier transform of the electric field in the USP.

σext(ω) = πr 2Q ext(ω)

λ

where an(ω) and bn(ω) are the Mie coefficients, and λ is the wavelength of light in vacuum. The Mie coefficients are expressed21 thus:

Here σ(ω′) is the photoprocess cross-section, ω′ is the current frequency, I(ω′) is the spectral intensity of radiation, and integration with respect to ω′ allows for the nonmonochromaticity of real radiation. It should be emphasized that the formula in eq 1 is true if the spectrum of an electromagnetic pulse is considerably narrower than the spectrum width of the photoprocess cross-section Δ, that is, for pulses of duration τ ≫ 1/Δ. Besides, the concept of spectral intensity of radiation itself is well-defined if τ ≫ T, where T is the period corresponding to the pulse carrier frequency ω = 2π/T. From the definition of the probability per unit time it follows that the total probability increases linearly with pulse duration. The results of the present study indicate this is generally not the case. For ultrashort pulses when at least one of the above conditions is not fulfilled, it is necessary to use the probability over the complete duration of a pulse (total probability), W to describe the photoprocess. The total probability of photoabsorption W in the dipole approximation is expressed19 as c W (τ ) = 4π 2

2πr εm

(4) B

DOI: 10.1021/acs.jpcc.7b10890 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C The absorption spectrum for ITO nanoparticles with different tin doping levels has been determined experimentally.29 Using these experimental data, the parameters γ, and ωp are readily determined. The absorption spectrum calculated by the Mie theory was fitted to the experimental data29 by proper selection of the parameters γ, and ωp (see Figure 1 and Table 1).

Ecor (ω′, ωcτ , φ) = iE0τ

2 2 π ω′2 τ 2 {e−iφ − (ωc − ω ′) τ /2 2 2 2 1 + ωc τ 2 2

− eiφ − (ωc − ω ′) τ

/2

}

(11)

Here E0 is the amplitude of the strength of the electric field in a pulse, ωc is the pulse carrier frequency, τ is the USP duration, and φ is the carrier frequency phase with respect to the pulse envelope. The value of phase φ has no effect on the probability of absorption of single-cycle and longer pulses,32 so we will henceforth assume that φ = 0. For description of the USP absorption spectrum, we will introduce the dimensionless frequency detuning parameter ξ: ω − ωmax ξ= c × 100% ωmax (12) where ωmax is the frequency of the maximum of the ITO nanoparticle absorption spectrum (see Table 1).

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RESULTS AND DISCUSSION To calculate the photoabsorption probability, we will substitute the expression for the photoabsorption cross-section in eq 9 and the expression for the Fourier transform of the strength of the electric field in a CGP of eq 11 in the formula of eq 2. Presented in Figure 2 are the results of the numerical calculation of function Wabs(τ) using the formula in eq 2 for ITO nanoparticles with different doping levels and frequency detuning parameters ξ for E0 = 10−5 au (atomic units) and εm = 1. Figure 2 shows that the behavior of the function W(τ) essentially depends on the value of ξ. This function at ξ ≥ 0% (zero and positive ξ) increases monotonically and subsequently becomes linear at sufficiently long τ (on the order of 4 fs and higher) (Figure 2a). A different situation is observed in the case of negative detunings ξ. The dependence becomes nonmonotonical and can have a maximum. This is the consequence of the asymmetry of the absorption spectrum. In general, the appearance of maximum in the W(τ) dependence is due to the change in the intersection of pulse spectrum with absorption spectrum as pulse duration increases, as evident from the expression for absorption probability in eq 2. The necessary condition for appearance of a maximum is detuning of pulse carrier frequency from the central frequency of absorption spectrum. However, this condition is not sufficient. Sufficient condition includes the requirement of an adequately rapid decrease in the absorption cross section with increasing frequency detuning. This condition is not fulfilled in the case of asymmetric absorption spectrum for positive frequency detuning, which is evident from a recalculation of the absorption cross section in Figure 1 as a function of frequency. On the other hand, for negative frequency detuning the decrease of absorption spectrum is rapid and a maximum appears in the function W(τ). Therefore, for negative detunings that are relatively small in magnitude (|ξ| < 20%), a nonlinearity appears that, with further increase in the magnitude of ξ reaches a maximum. The degree of ITO doping influences the position of this maximum. In the case of 5% doping, the value of the amplitude at the maximum is larger, and the maximum is shifted to the region of longer pulses compared with the cases of 8% and 10% doping (Figure 2d). The use of total probability to describe the photoprocess in the USP field is validated in particular by Figure 2 since the nonlinearity of the dependence of W(τ) on

Figure 1. Photoabsorption cross-section calculated within the framework of the Mie theory and the results of the experiment29 for ITO nanoparticles with different tin doping levels.

Table 1. Parameters of the Photoabsorption Cross-Section for ITO Nanoparticles with Different Doping Levels Sn, % ωp, eV γ, eV ωmax eV λmax, nm

5 1.56 0.21 0.639 1941

8 1.73 0.22 0.701 1769

10 1.89 0.15 0.77 1610

Figure 1 shows that the theoretical model adequately describes the experimental data. This finding confirms it is appropriate to apply the Mie theory with the use of the Drude model for calculation of the photoabsorption cross-section for ITO semiconductor nanoparticles. The parameters of the photoabsorption cross-section were selected for ε∞ = 4.1,30 and the ITO nanoparticles were assumed to be in air (εm = 1). Three levels of ITO tin doping were considered in this study: 5, 8, and 10%. The results obtained from fitting of the data are summarized in Table 1. Thus, using the parameters ωp, and γ from Table 1, with the Drude model and the Mie theory it is possible to calculate the absorption cross-section σabs(ω) that will be used for further calculations. It should be noted that for the ITO nanoparticles under consideration, the maximum of the spectral cross-section is shifted to the short-wave region when the doping level increases, (see Figure 1 and Table 1).

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CORRECTED GAUSSIAN PULSE

As USP we will consider the so-called corrected Gaussian pulse (CGP).31 The Fourier transform of the strength of the electric field in this pulse is expressed thus: C

DOI: 10.1021/acs.jpcc.7b10890 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 2. Probability of USP photoabsorption by ITO nanoparticles with different tin doping levels and ξ.

the maximum of the function W(τ) on the refractive index of a medium in which an ITO nanoparticle is placed. Let us consider how the extent of ITO doping influences the shift of the maximum of W(τ), all other conditions being the same. This can be readily done by plotting the function Δτmax(n), which represents the difference between the position of the maxima of Wabs(τ, n) and the position of the maximum for Wabs(τ, n = 1):

the pulse duration cannot be obtained within the framework of the standard approach based on the process probability per unit time. The presence of maxima in the dependence of photoabsorption probabilities on the pulse duration makes it possible to propose a new method of measuring the refractive index, n of a medium. This method is based on the measurement of the relative shift of the maximum of the function W(τ) as n changes. Presented in Figure 3 are the plots of the function W(τ) with ξ = −70% for ITO with 10% tin doping for different values of the refractive index n = εm . It is seen that an increase in n results in an increase in the amplitude at the maximum and a shift of the latter to the region of longer pulses τ. Thus, a new effect is predicted, namely, the dependence of the position of

Δτmax(n) = τmax(n) − τmax(n = 1)

(13)

The results of the calculation of Δτmax(n) for ITO with 5%, 8%, and 10% tin doping and ξ = −70% are presented in Figure 4.

Figure 4. Dependence of the shift of the maximum Δτmax(n) of the probability of USP photoabsorption by ITO nanoparticles with different doping, ξ = −70%.

Figure 3. Probability of USP photoabsorption by ITO nanoparticles (10% tin doping), ξ = −70%, for different values of the refractive index n. D

DOI: 10.1021/acs.jpcc.7b10890 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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(6) Gets, A. V.; Krainov, V. P. Interaction of Atomic Clusters with Intense Attosecond Pulses. Contrib. Plasma Phys. 2011, 51, 471−481. (7) Shchatsinin, I.; Laarmann, T.; Zhavoronkov, N.; Schulz, C. P.; Hertel, I. H. Ultrafast Energy Redistribution in C60 Fullerenes: A Real Time Study By Two-Color Femtosecond Spectroscopy. J. Chem. Phys. 2008, 129, 204308. (8) Astapenko, V. A.; Sakhno, S. V. Scattering of Ultrashort Electromagnetic Pulses on Metal Clusters. J. Exp. Theor. Phys. 2016, 123, 963−966. (9) Faucheaux, J. A.; Stanton, A. L. D.; Jain, P. K. Plasmon Resonances of Semiconductor Nanocrystals: Physical Principles and New Opportunities. J. Phys. Chem. Lett. 2014, 5, 976−985. (10) Wang, F.; Hu, S. Electrochemical Sensors Based on Metal and Semiconductor Nanoparticles. Microchim. Acta 2009, 165, 1−22. (11) Luo, X.; Morrin, A.; Killard, A. J.; Smyth, M. R. Application of Nanoparticles in Electrochemical Sensors and Biosensors. Electroanalysis 2006, 18, 319−326. (12) Granqvist, C. G. Transparent Conductive Electrodes for Electrochromic Devices: A Review. Appl. Phys. A: Solids Surf. 1993, 57, 19−24. (13) Bierwagen, O. Indium Oxide − A Transparent, Wide-Band Gap Semiconductor for (Opto) Electronic Applications. Semicond. Sci. Technol. 2015, 30, 024001. (14) Golan, G.; Axelevitch, A.; Gorenstein, G.; Peled, A. Novel Type Of Indium Oxide Thin Films Sputtering For Opto-Electronic Applications. Appl. Surf. Sci. 2007, 253, 6608−6611. (15) Gerasimov, G. N.; Gromov, V. F.; Ilegbusi, O. J.; Trakhtenberg, L. I. The Mechanisms of Sensory Phenomena in Binary Metal-Oxide Nanocomposites. Sens. Actuators, B 2017, 240, 613−624. (16) Brinzari, V.; Damaskin, I.; Trakhtenberg, L.; Cho, B. K.; Korotcenkov, G. Thermoelectrical Properties of Spray Pyrolyzed Indium Oxide Thin Films Doped by Tin. Thin Solid Films 2014, 552, 225−231. (17) Trakhtenberg, L. I.; Astapenko, V. A.; Sakhno, S. V.; Kozhushner, M. A.; Posvyanskii, V. S.; Ilegbusi, O. J. Absorption of Infrared Radiation by an Electronic Subsystem of Semiconductor Nanoparticles. J. Phys. Chem. C 2016, 120, 23851−23857. (18) Kozhushner, M. A.; Lidskii, B. V.; Oleynik, I. I.; Posvyanskii, V. S.; Trakhtenberg, L. I. Inhomogeneous Charge Distribution in Semiconductor Nanoparticles. J. Phys. Chem. C 2015, 119, 16286− 16292. (19) Astapenko, V. A. Simple Formula for Photoprocesses in Ultrashort Electromagnetic Field. Phys. Lett. A 2010, 374, 1585−1590. (20) Mie, G. Beiträge Zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen. Ann. Phys. 1908, 330, 377−445. (21) Hulst, H. C. Light Scattering by Small Particle; John Wiley and Sons: New York, 1957. (22) Kuttge, M.; Kurz, H.; Rivas, J. G.; Sánchez-Gil, J. A.; Bolívar, P. H. Analysis of the Propagation of Terahertz Surface Plasmon Polaritons on Semiconductor Groove Gratings. J. Appl. Phys. 2007, 101, 023707. (23) West, P. R.; Ishii, S.; Naik, G. V.; Emani, N. K.; Shalaev, V. M.; Boltasseva, A. Searching for Better Plasmonic Materials. Laser Photonics 2010, 4, 795−808. (24) Fox, M. Optical Properties of Solids, 2nd ed.; Oxford University Press: Oxford, U.K., 2010; pp 33−44. (25) Chuang, S. Physics of Photonic Devices, 2nd ed.; Wiley: New York, 2009; pp 193−196. (26) IAENG Transactions on Engineering Technologies; Special Issue of the World Congress on Engineering and Computer Science 2012, Springer: The Netherlands, 2014; p 247. (27) Fan, J. C. C.; Bachner, F. J.; Foley, G. H. Effect of O2 Pressure During Deposition on Properties of rf-Sputtered Sn-Doped In2O3 Films. Appl. Phys. Lett. 1977, 31, 773−775. (28) Holman, Z.; Filipic, M.; Descoeudres, A.; De Wolf, S.; Smole, F.; Topic, M.; Ballif, C. Infrared Light Management in High-Efficiency Silicon Heterojunction and Rear-Passivated Solar Cells. J. Appl. Phys. 2013, 113, 013107.

Figure 4 indicates that the shift of the maximum of Wabs(τ, n) assumes the maximum value in the case of 5% doping among the three cases considered. In addition, this figure demonstrates the possibility to measure the refractive index by the shift Δτmax. For this purpose, it will suffice to calculate the inverse function n(Δτmax) and use it to determine the value n of the substance (matrix) under consideration.

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CONCLUSIONS The paper describes the probability of USP photoabsorption during the interaction of a pulse with an ITO semiconductor nanoparticle. The results are presented for a corrected Gaussian pulse and ITO with different doping levels, and analyzed with the Mie theory and the Drude model. It was found that the sign of the frequency detuning parameter ξ defines the function W(τ). In the case with ξ = 0, there is a monotonic increase of W(τ), which becomes linear at large values of pulse duration, τ. In the case of positive frequency detuning (ξ > 0), W(τ) exhibits a nonlinearity at small τ (there is an inflection of the plotted function); however, with increasing pulse duration there is also a transformation to the linear mode. In the case of negative detuning (ξ < 0) and small τ, a nonlinearity of W(τ) is also observed, which with increasing τ similarly transforms to the linear mode. A new effect was demonstrated, which is that the position of the maximum in the function W(τ) is defined by the value of the refractive index n of the medium in which a nanoparticle is placed. An increase in the refractive index results in a shift of the maximum of W(τ) to the region of longer pulse duration τ, as well as an increase in the amplitude. By using the value of the shift of this maximum, it is possible to measure the medium parameters, for example, the refractive index n itself, or to determine the concentration of a substance under consideration.

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AUTHOR INFORMATION

Corresponding Author

*(O.J.I.) E-mail: [email protected]. ORCID

O. J. Ilegbusi: 0000-0001-5927-8320 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was supported by the Government order of the RF Ministry of Education and Science (Project No. 3.9890.2017/8.9)

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DOI: 10.1021/acs.jpcc.7b10890 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.7b10890 J. Phys. Chem. C XXXX, XXX, XXX−XXX