Plasmonic Heavily-Doped Semiconductor Nanocrystal Dielectrics

Article pubs.acs.org/JPCC

Plasmonic Heavily-Doped Semiconductor Nanocrystal Dielectrics: Making Static Photonic Crystals Dynamic Surya S. K. Guduru,†,‡,§ Ilka Kriegel,*,†,‡,§ Roberta Ramponi,§,∥ and Francesco Scotognella‡,§,∥ ‡

Center for Nano Science and Technology@PoliMi, Istituto Italiano di Tecnologia, Via Giovanni Pascoli 70/3, 20133 Milan, Italy Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy ∥ Istituto di Fotonica e Nanotecnologie CNR, Piazza Leonardo da Vinci 32, 20133 Milano, Italy §

ABSTRACT: In this work we introduce photonic devices with dynamically modifiable transmission properties through the combination of the transfer matrix method, the Drude model, and the Maxwell-Garnett effective medium approximation. Heavily doped semiconductor nanocrystal layers with tunable plasmonic near-infrared (NIR) properties are embedded as dielectrics into the otherwise invariable one-dimensional photonic crystals. A selective tuning of the localized surface plasmon resonance in the NIR modifies the refractive index contrast in the photonic structure, consequently affecting the intensity and position of the photonic band in the visible spectral range. The resulting possibility to dynamically modify the transmission properties in the visible and NIR highlights their application for sensing, tunable light filtering, or electrochromic devices.

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METHODS In order to calculate the transmission spectra of the photonic crystal, we have employed the transfer matrix method, a widely used technique to describe the optics of multilayers.1 The technique determines the amplitude of the electric and magnetic fields after propagation through the multilayers by taking into account the boundary conditions as determined from the Maxwell equations. The characteristic transmission matrix through each layer is determined. The matrix product of the matrices corresponding to each layer delivers the overall transmission and hence the electric and magnetic fields at the output end. Isotropic, nonmagnetic systems have been assumed for the calculations, which is a reasonable assumption for most dielectric materials. A normal angle of incidence was maintained throughout the calculations. In order to determine the electric and magnetic fields after transmission through a layer, we have solved the following system of output amplitudes:

with j = (1, 2, ..., m). Mj is the characteristic matrix of each layer, and the elements of the transmission matrix ABCD are ⎛ ⎞ i A j = Dj = cos(ϕj), Bj = −⎜⎜ ⎟⎟sin(ϕj), Cj = −ipj sin(ϕj) p ⎝ j⎠

where nj and dj, determined through the phase variation ϕj, are, respectively, the effective refractive index and the thickness of the layer j. In the case of normal incidence, the phase variation of the wave passing the j-fold layer is given as ϕj = ((2π/λ))njdj, while the coefficient pj = ((εj/μj))1/2 in the case of a transverse electric wave and qj = 1/pj replaces pj in the case of a transverse magnetic wave. Then transmission t is given as t=

2ps (m11 + m12p0 )ps + (m11 + m12p0 )

(3)

(1)

From the above equations one can write the light transmission as p T = 0 |t |2 ps (4)

where E0 and H0 are the amplitudes of electric and magnetic fields at the input, and Em and Hm are the amplitudes of electric and magnetic fields at the output. Each matrix is described in the following manner:

where ps represents the substrate and p0 represents air. To describe the dielectric properties of the heavily doped semiconductor NC thin films, the Drude model is employed assuming a Drude-like behavior of the semiconductor NCs.2−6

⎡ Em ⎤ ⎡ m11 m12 ⎤⎡ Em ⎤ ⎡ E0 ⎤ ⎢ ⎥ = M1·M 2·...·M m⎢ ⎥ = ⎢ ⎥⎢ ⎥ ⎣ Hm ⎦ ⎣ m21 m22 ⎦⎣ Hm ⎦ ⎣ H0 ⎦

⎡ A j Bj ⎤ ⎥ Mj = ⎢ ⎢⎣ Cj Dj ⎥⎦

Received: November 24, 2014 Revised: January 8, 2015 Published: January 13, 2015

(2) © 2015 American Chemical Society

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DOI: 10.1021/jp511754q J. Phys. Chem. C 2015, 119, 2775−2782

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The Journal of Physical Chemistry C

Figure 1. (a) Schematic illustration of the photonic crystal constituting six bilayers composed of a static layer of ZnO with constant refractive index (n = 2) and an ITO NCs layer embedded in a matrix with refractive index nm. (b) Absorbance of the ITO NC layer with carrier densities of n = 0.1, 0.5, 0.8, and 1 × 1021 cm−3 (blue, green, red, and turquoise, respectively). With increasing carrier density, an increasing and blue shifting plasmonic absorption in the NIR is observed. (c) Transmission properties of the photonic crystal as a whole, with varying carrier density of the ITO NC layer. A modulation of the transmission of the photonic crystal in both the NIR and the photonic band gap region is achieved.

films is finally calculated from the imaginary part of the dielectric function [(εeff)1/2] and the Beer−Lambert law.7

The complex dielectric function is given by ε(ω) = ε1(ω) + iε2(ω)

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(5)

INTRODUCTION Spectrally variable optical devices play a vital role in various applications such as wavelength filtering,10 energy harvesting,11−14 or lasing.15 The optical properties of most optical device structures, such as one-dimensional photonic crystals (1DPCs), are static and determined at the stage of fabrication. The ability to tailor the properties of such a device after fabrication and in a dynamic manner leads to versatile devices. Heavily doped semiconductor nanocrystals (NCs) such as indium tin oxide (ITO) or tungsten oxide (WO3−d) are on the contrary characterized by chemically or electrochemically modifiable carrier densities in the order of 1021 cm−3, ultimately resulting in tunable localized surface plasmon resonances (LSPRs) in the near-infrared (NIR).16−22 A controlled variation of their carrier density enables to shift their absorption over a wide range of frequencies in the NIR.22−27 In thin films this is achieved by applying a voltage to the conducting films. The electrochemical doping in turn also influences the dielectric properties of the NC thin film.26−29 An integration of such tunable materials into photonic technologies paves the way to dynamically modifiable optical devices.26−31 Due to the generally very high extinction coefficient of plasmonic nanostructures, the modulation of their absorption properties dramatically influences the optical response of the entire photonic device. Recently, for example, the integration of ITO NCs into a glassy matrix has been demonstrated, enabling an optical switching and dynamic control of solar radiation transmittance via electrochemical modulation. Thus, a previously unrealized optical switching to block NIR and visible light selectively and independently by varying the applied electrochemical voltage over a range of 2.5 V has been achieved.28,29 Other attractive optical devices conceivable are

where

ε1 = ε∞ −

ωp2 (ω 2 + Γ 2)

(6)

and ε2 =

ωp2 Γ ω(ω 2 + Γ 2)

(7)

with Γ representing the free carrier damping and

ωp =

Nce 2 m*ε0

(8)

the plasma frequency of the free carriers of the system. Nc is the carrier density, e is the electron charge, m* is the effective mass, and ε0 is the vacuum dielectric permittivity. The dielectric function of the NC film has been described by the Maxwell-Garnett effective medium approximation (MGEMA),7−9 which describes the macroscopic properties of a composite material and averages the medium dielectric function according to the multiple values of the constituents of the composite material. The effective dielectric function (εeff) according to the MG-EMA is given by εeff = εm

2(1 − δi)εm + (1 + 2δi)εi (2 + δi)εm + (1 − δi)εi

(9)

where εm = is the medium dielectric constant, εi is the frequency dependent dielectric function of the bulk material (in this case, approximated by the Drude model, eqs 5−8), and δi accounts for the volume fraction. The absorbance of the NC nm2

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Figure 2. (a, c) Transmission spectra of a photonic structure with alternating layers: a heavily doped ITO NC layer and a constant refractive index layer (n = 2). Both layers are 100 nm thick and six bilayers are considered. (b) Real part and (d) imaginary part of the dielectric function of the ITO NC layer with differing carrier concentration of 0.1, 0.5, 0.8, and 1 × 1021 cm−3, given in blue, green, red, and turquoise. (a) Only the real part of the dielectric function of the ITO NC layer is considered in the calculation, while in (c) additionally the imaginary part is taken into account. The change in carrier density also modulates the real part of the dielectric function, which affects the refractive contrast of the photonic structure and, consequently, the intensity of the photonic band gap. By including the imaginary part of the dielectric function, the overall transmission of the photonic structure shows additional modulation in the NIR.

photonic structure can be achieved. The modified carrier density ultimately influences the dielectric function of the NC thin film: the imaginary part, describing their absorption, as well as the real part of the dielectric function affecting the refractive index contrast and in turn the photonic band gap of the structure, both contributing to the optical response of the entire photonic structure. Additional parameters, such as volume fraction and surrounding medium refractive index, deliver further means of modification at the stage of fabrication and open the route to sensing applications. A schematic of the proposed photonic crystal structure consisting of alternating layers of ZnO with a static refractive index of n = 2 and the ITO NCs, each with a thickness of a 100 nm, is shown in Figure 1a (the choice of a static refractive index of ZnO is justified by its negligible dispersion in the studied energy range). The tunability of the NC layer absorbance with increasing carrier density is demonstrated in Figure 1b, which has been calculated with the MG-EMA.7−9 A free carrier damping of Γ = 0.31 eV, a high frequency dielectric permittivity of ε∞ = 4, carrier effective mass meff = 0.4 × m0, volume fraction f v = 0.3, and a varying carrier density of 0.1, 0.5, 0.8, and 1 × 1021 cm−3 have been considered, resulting in the turquoise, red, green, and blue curves, respectively. We will keep this color coding throughout the manuscript. The values have been taken from ref 30 and are good representations of experimental results: with increasing carrier density the absorption of the NC layer blue shifts and increases in intensity. In Figure 1c we show the transmission of the photonic crystal as a whole. For all carrier densities the photonic band gap is found peaking at around 800 nm, filtering

1DPCs: dielectric structures composed of alternating layers of differing refractive index that exhibit light manipulating properties. A specific set of optical frequencies is effectively hampered from passing through the crystal, resulting in high efficiency photonic band gaps.30,32,33 It is the refractive index contrast between the layers that strongly influences the position of the optical band gap and its efficiency. 34,35 The implementation of a tunable dielectric layer allows an active manipulation of the refractive index contrast between the layers and, in turn, a direct influence on the photonic band gap position, efficiency, and bandwidth. Moreover, the strong tunable absorption in the NIR, related to the imaginary part of the dielectric function, adds to the overall transmission of the device. To date, 1DPCs are fabricated with various materials and methods, while more recently bottom up techniques such as spin coating, dip-coating, or layer by layer deposition and the use of nanoparticles have been highlighted, breaking ground for the implementation of heavily doped semiconductor NCs in such structures.2−4,15,36−42 The voids of such porous layers can be filled with materials of differing refractive index, delivering an additional set of parameters for the design of their transmission properties and making way for sensing applications.43−47

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RESULTS AND DISCUSSION In this work, we investigated the transmission properties of 1DPCs composed of heavily doped NC layers, such as ITO or WO3−d through the combination of the transfer matrix method, the Drude model, and the MG-EMA. By varying the carrier density, a dynamic modification of the transmission of the 2777


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scenario, we compare the transmission properties of the photonic crystal with varying carrier densities while keeping the volume fraction f v the same ( f v = 0.3) and influencing the refractive index contrast by changing the surrounding medium refractive index from nm = 2.5 (e.g., titania,48,49 Figure 3a,b) to 1.5 (e.g., silica or high refractive index polymers,50 Figure 3c,d). For the following calculations, we chose a static dielectric layer with n = 1.5 such as silica. Figure 3a,c displays the transmission spectra of the 1DPC with varying carrier concentration (blue to turquoise curves). On inspection of the dielectric function of the NC layer, as given in Figure 3b,d, together with the static dielectric constant of 1.5 (black curve), it becomes clear that there is a tremendous difference in the dielectric function by changing the surrounding medium nm from 2.5 to 1.5, greatly reducing the refractive index contrast and, thus, the efficiency of the photonic band gap (Figure 3a vs c). Notably, in Figure 3c, a turnover of the transmission properties is observed, that is, while an increase in carrier density (from blue to turquoise) leads to an increased absorption (decrease transmission) in the NIR, the efficiency of the photonic band gap decreases (the transmission increases). This effect can be explained from Figure 3d, where a crossing of the dielectric function of the NC layer with the constant refractive index of the static layer is observed when increasing the carrier density. This effect is a beneficial one, as it allows to selectively tune the NIR and the UV−vis spectral range. A way to recover the efficiency of the band gap is given through the modulation of the volume fraction of the NC layer from f v = 0.3 to f v = 0.9 (with nm = 1.5, Figure 3e,f). In this case, the refractive index contrast becomes more pronounced again, leading to an efficient photonic band gap, while the turnover of the transmission properties is preserved: with increasing carrier density, the band gap efficiency in the visible reduces, while the absorption in the NIR increases. With layer thickness of 50 nm (and f v = 0.9, nm = 2.5, and nm = 1.8) the photonic band gap is shifted to the UV−vis spectral range (Figure 3g,h), resulting in a device structure, where the transmission in the UV−vis and the NIR can be modified, while keeping the visible part transparent. An independent control of the transmittance of the visible and the NIR, that is, solar heat is a key target of electrochromic devices and our structure is proposed as a step into this direction. NIR light accounts for a large part of the spectral range. Though the excited plasmon resonances partially dissipate their energy into heat, a stronger effect is expected from the NIR blocking of the solar heat in the NIR. Taken together, these results demonstrate that with our approach we can selectively influence the NIR region covered by the NC absorption, and the UV−vis spectral range through a modulation of the photonic band gap. We mention here that we achieve very similar results when implementing the EMA to calculate layers of SiO2 beads embedded in a refractive index medium instead of a purely static thin film dielectric layer as so far assumed, demonstrating the option to produce the entire device from solution and highlighting a cheap production way. So far we considered photonic structures composed of heavily doped NC layers with a static refractive index layer. The latter one contributes to the transmission properties with the real part of the dielectric function only, while in our device configuration a strong contribution to the transmission of the photonic device results from the absorption properties of the dynamic NC layer. In another example, we exchange the static with another nanoparticle layer, as illustrated in the sketch in Figure 4a. For this we chose a layer of silver nanoparticles. Such

efficiently the light in this region. However, with increasing carrier density, attested by the increased absorption in the NIR, also the efficiency of the photonic band gap and its position is affected. It can be concluded from Figure 1b,c that the modulation of the carrier density of the NC layer not only affects the absorption properties of the NC layer itself (Figure 1b) but also the transmission properties of the photonic structure as a whole (Figure 1c), demonstrating the tuning properties of the entire device. The structure as proposed delivers a way to tune the NIR properties through the manipulation of NC absorption with the carrier density, in turn, affecting the transmission of the photonic band gap at around 800 nm. This highlights their use for filtering, where a tunable concomitant visible and IR light filtering is required or for electrochromic windows, where an independent control of light transmittance of the visible part of the sunlight and the NIR, that is, solar heat is desired.28,29 For a clever design of such a device structure, in the following we carefully untangle the parameters influencing the tuning properties in the visible and the NIR by looking separately at the modifiable imaginary and the real part of the dielectric function of the NC layer, and the parameters, such as volume fraction of the NCs, refractive index of the embedding medium, layer thickness, or refractive index contrast between the layers. The carrier density dependent absorption properties of the ITO NC layer is expressed through the imaginary part of the dielectric function connected to the Lambert−Beer law and represented through the modulated NIR absorption. Nevertheless, also the real part of the dielectric function is influenced by an altered carrier density. In Figure 2 the turquoise, red, green, and blue curves depict the different carrier densities of the switchable ITO NC film (as given above). Transmission properties of the proposed device are shown in the left column, while the frequency dependent dielectric function of the heavily doped NC layer is given in the right column. For the following discussion, we consider the static dielectric layer with a constant refractive index n = 2. The thickness of each layer is 100 nm and six layers are considered. In Figure 2a, only the real part of the dielectric function of the ITO NC layer is implemented for the calculation of the transmission. With increasing carrier density of the heavily doped ITO NC layer, the efficiency of the photonic band gap is increasing, while the NIR spectral range is nearly transparent. From Figure 2b it becomes obvious that a change in the carrier density results in a modulation of the real part of the NC layer refractive index, in turn, affecting the refractive index contrast of the photonic crystal and, consequently, the intensity of the photonic band gap. By additionally including the imaginary part of the refractive index (Figure 2d) to the calculation, the overall transmission spectrum of the multilayer is given, which also shows the modifiable NIR absorption due to the LSPR of the NCs (Figure 2c). Thus, by modulating the carrier density we achieve the combined effect of a tunable reflection by the photonic band gap and a tunable NIR absorption by the heavily doped NCs embedded in the photonic structure. Another benefit arising from the use of a NC layer as refractive layer lies in additional tuning options at the step of fabrication. In the following we demonstrate how a clever choice of such parameters affects the transmission of the photonic structure. In particular, it is the volume fraction f v of the NCs within the layer and the medium refractive index nm in which the NCs are embedded that strongly influence the dielectric function of the heavily doped NC layer. In the first 2778


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band gap, while the turnover of the transmission properties is preserved. (g, h) By adjusting the layer thickness to 50 nm and the static layer refractive index of 1.8, a dynamic modification of the NIR and UV−vis is achieved, while the visible remains transparent.

nanoparticles show a strong plasmonic absorption in the blue to ultraviolet (UV) spectral range already in thin films of around hundred nanometer and with fill factors of 10% only, while the dynamic NC layer (in this example, the heavily doped WO3−d NCs) shows modulated optical properties with varying carrier density mostly in the NIR. Similar to ITO NCs, also in WO3−d NC films, a carrier density modification (from 0.1, 0.8, 1.3, and 1.9 × 1021 cm−3) is reflected in the real as well as the imaginary part of the dielectric function, thus, affecting the absorption in the NIR as well as the efficiency of the photonic band gap. The transmission spectrum of such a structure according to our calculations is shown in Figure 4b. In this particular case, the transmission was calculated by setting the surrounding media for the Ag nanoparticles to nm = 1.5 and for WO3−d NCs to 2.5. The thickness of each layer was set to 120 nm. Our results demonstrate that while the UV and NIR region is efficiently blocked due to the Ag nanoparticle layer absorption and the photonic band gap, the transmission in the visible can be modulated with varying the carrier density. One could envisage such a device for application in electro switchable windows, where an absorption in the visible needs to be adjusted, depending on the daytime and intensity of the incoming sunlight, while the UV and NIR part of the sun spectrum is absorbed by the window to protect, for example, artwork from fading. The sensitivity of the photonic crystal to the surrounding medium refractive index has been exploited above to design the transmission properties of the photonic structure as a whole. Changes of the surrounding medium refractive index strongly influence the photonic band gap position as well as its efficiency (compare Figure 3a and c). This effect becomes more pronounced, when both layers in the structure are plasmonic and, thus, sensitive to the medium refractive index. In the following, we propose a device structure employed for sensing application due to its sensitivity to the medium refractive index. We assume a porous NC bilayer structure composed of six alternating layers of ITO NCs (f v = 0.1) with a fixed carrier density (1 × 1021 cm−3) and of silver nanoparticles ( f v = 0.2) in whose voids an aqueous salt solution is soaked.51 With stepwise increase of the refractive index from 1.333 (as for pure water), over 1.344, 1.355, 1.365, 1.376, 1.386, 1.396, 1.407, to 1.417, which represents an increase of glycerine concentration in the solution from 0, 9.33, 17.85, 25.96, 33.74, 41.46, 48.86, 55.75 to 62.50 wt %45 leads to a shift of the photonic band gap to the red by 42.5 nm. See Figure 5a,b for the band gap shift with changing refractive index of the salt solution and a plot of the medium refractive index versus photonic band gap. For comparison, we also calculated the band gap for a surrounding refractive index of 1 and 2, demonstrating a sensitivity of around 578 nm per refractive index unit for the proposed device (from 586 to 1164 nm). Due to its small dimensions and solution processability, the structure is very attractive for its incorporation into lab on the chip configurations and microfluidic devices. Attractive is, furthermore, the possibility to define the region of interest for the sensing application to basically any wavelength range of desire, feasible due to the

Figure 3. (a, c, e, and g) Transmission of the photonic crystal and (b, d, f, and h) the real part of the dielectric function of the ITO NC layer with increasing carrier density (from blue to turquoise). Layer thickness has been set to 100 nm and six bilayers have been considered. The volume fraction and refractive index of the surrounding medium for (a) and (b) have been set to f v = 0.3 and nm = 2.5, for (c) and (d) to f v = 0.3 and nm = 1.5, and (e) and (f) to f v = 0.9 and nm = 2.5. (g, h) Static dielectric layer with refractive index of 1.8, f v = 0.9 and nm = 2.5 with a layer thickness of 50 nm have been considered. (a, b) Band gap efficiency is close to 90% due to the large refractive index contrast, while there is a modulation of the absorption in the near IR region as a consequence of the modulation of the dielectric function with varying carrier concentration. (c, d) Decreased dielectric contrast results in a less efficient band gap, however, demonstrating a turnover of the transmission properties: explained by the crossing of the dielectric function of the NC layer with the static layer. (e, f) An increase of volume fraction f v results in a more efficient 2779


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Figure 4. (a) Model of a photonic crystal composed of two different nanoparticle layers, in this case, a layer with silver nanoparticles and a layer with WO3−d NCs. (b) The calculated transmission spectrum of the photonic crystal, as introduced in (a), with varying carrier density of the WO3−d layer of 0.1, 0.8, 1.3, and 1.9 × 1021 cm−3 in blue, green, red, and turquoise, respectively. While the UV and NIR region is efficiently blocked due to the Ag nanoparticle layer absorption and the photonic band gap, the transmission in the visible can be modulated with varying the carrier density.

transmission of the photonic device as a result of the tunable LSPR and a manipulated photonic band gap due to a modified refractive index contrast between the layers. The Drude model and the Maxwell-Garnett Effective medium approximation allow a careful and precise state-of-the-art modeling of the dielectric properties of plasmonic nanoparticles. These simulated dielectric functions have been employed in the transfer matrix method to calculate the transmission properties of photonic structures. A broad diversity of nanomaterials has been employed, from well-known silver nanoparticles to the more recent heavily doped semiconductor NCs, such as indium tin oxide (ITO) and tungsten oxide (WO3−d). The sensitivity of the dielectric function of the NC layer to the embedding medium refractive index and the fill factor provide additional means of manipulation at the stage of fabrication. Many tunable features have been demonstrated, such as modulation of the photonic band gap, turnover of the transmission intensity of the LSPR and the photonic band gap, and visible on demand absorption, while the UV and NIR is blocked. Moreover, the high sensitivity of the photonic band gap position to the refractive index of the embedding medium has been exploited to sense the concentration of an infiltrated analyte. The activation of passive dielectric stacks with tunable plasmonic nanoparticles is highly foreseen for a new generation of cheap and robust tunable components, such as light filters or electrochromic windows. We envisage the ease of experimental realization of such devices based on its solution processability, where filtering modulation is achieved upon chemical and electrochemical postfabrication treatment of the heavily doped semiconductor NC component, ultimately resulting in tunable transmission properties of the coupled device.

Figure 5. (a) Transmission for a photonic crystal composed of a porous NC51 bilayer structure of ITO NCs (f v = 0.1) with a fixed carrier density (1 × 1021 cm−3) and silver nanoparticles (f v = 0.2) soaked in a salt solution of differing refractive index nm. A change of refractive index due to a change in the salt concentration from 1.333 (as for pure water), over 1.344, 1.355, 1.365, 1.376, 1.386, 1.396, 1.407, to 1.417 (corresponding to 0, 9.33, 17.85, 25.96, 33.74, 41.46, 48.86, 55.75 to 62.50 wt %45) leads to a red-shift of the photonic band gap of 42.5 nm in total. (b) Photonic band gap versus refractive index nm. The proposed structure has a sensitivity of around 578 nm per refractive index unit.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

possibility to vary a high number of parameters in the photonic structure, in turn influencing the photonic band gap.

Author Contributions

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†

These authors contributed equally (S.S.K.G. and I.K.).

CONCLUSIONS In summary, we have presented a photonic structure where the introduction of heavily doped semiconductor NC layers enables to turn the otherwise static transmission properties of the photonic crystal dynamically tunable. The active modification of the carrier density of the plasmonic NC layer affects the

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Fondazione Cariplo through Project EDONHIST (Grant No. 2012-0844) and Italian 2780


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Ministry of University and Research (Project PRIN 2010-2011 “‘DSSCX’”, Contract 20104XET32).

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Plasmonic Heavily-Doped Semiconductor Nanocrystal Dielectrics

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