Contrasting anisotropy of light absorption and emission by

Jan 29, 2019 - Photon absorption and emission play a key role in our understanding of how light interacts with matter. An attractive system to explore...
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Contrasting anisotropy of light absorption and emission by semiconductor nanoparticles Yera Ye. Ussembayev, Zeger Hens, and Kristiaan Neyts ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01405 • Publication Date (Web): 29 Jan 2019 Downloaded from http://pubs.acs.org on February 4, 2019

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ACS Photonics

Contrasting anisotropy of light absorption and emission by semiconductor nanoparticles Yera Ye. Ussembayev1, Zeger Hens2, Kristiaan Neyts1* 1ELIS Department, Ghent University, Technologiepark 15, 9052 Gent, Belgium 2PCN research group, Ghent University, Krijgslaan 281, 9000 Gent, Belgium *corresponding author: [email protected] Abstract Photon absorption and emission play a key role in our understanding of how light interacts with matter. An attractive system to explore these processes are semiconductor nanoparticles (SNP) with their distinguishable photoluminescence, which makes them widely applied in optoelectronics, laser technology and biophotonics. In current implementations of SNP, there is only partial control over anisotropy in absorption or in emission, which limits their applicability in photonics. An emerging strategy to attain a certain degree of anisotropy is to embed quantum dot in semiconductor shell structure. Here, we report how designing the shell geometry and the position of the quantum dot enables extended control over the anisotropy in absorption and emission by a core/shell nanoparticle in a solvent. Based on the dielectric effect, our approach provides an accessible route to achieve sharply contrasting anisotropies that may even have opposite sign. Using this unique feature, we propose cross particles to transform unpolarized blue light into polarized red and green light for liquid crystal backlights, and thumbtack particles to absorb sunlight and efficiently emit photons in a solar concentrator. The strong anisotropic contrast between absorption and emission of SNP may advance energy-efficient technology, biodiagnostics and quantum information as well as offer new insights on light-matter interaction at the nanoscale. Keywords: nanooptics, anisotropic absorption, anisotropic emission, core/shell nanoparticles, quantum dots

Semiconductor nanoparticles serve as a versatile platform to study different phenomena of light-matter interaction. Besides having distinct quantum and nonlinear optical properties, these nanocrystals exhibit sizetunable absorption1,2 and optically stable emission1,2. Such characteristics have led them to diverse applications, ranging from living cell labeling3 and biosensing3 to single-photon light sources4,5, light-emitting diodes2, displays6,7 and solar energy devices8,9. However, the lack of freedom to control the polarization anisotropy and wave vector anisotropy for absorption and emission of photons by SNP still limits their efficient implementation in these fields. To date, there are several methods to induce anisotropic light absorption and emission using SNP. The most sophisticated one is to place the quantum dot (QD) in a cavity4, including micropillars, microdisks and photonic crystals, which effectively governs the direction and polarization of the emitted light. However, due to the technical complexity in realization, these resonators are hard to adopt on a large scale. Plasmonics offer another way to manipulate QD emission by employing nanoantennas10, but these, unfortunately, still suffer from losses due to coupling in the near field. An alternative strategy is to sculpture the semiconducting material into non-spherical shapes, such as wires11–13 and platelets14,15. These particles have strong absorption and emission directionality but the resulting anisotropies are coupled, thus, restricting their independent control. A similar approach is to incorporate the quantum emitter into a non-spherical shell structure of a different

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semiconductor material. The ongoing progress in colloidal chemistry facilitates the formation of such core/shell heterostructures, including dot-in-rod16, rod-in-rod17 and core-crown18. These core/shell particles have several distinct advantages over uniform SNP. First, the encapsulation reduces the losses that originate from recombination at the core surface19, hence, improving the photoluminescent quantum efficiency. Furthermore, core/shell engineering provides a favorable opportunity to create SNPs with exotic shell geometries20,21 and well-defined positioning of the QDs22. Such design flexibility unlocks considerable potential to manipulate the anisotropy of light absorption and emission utilizing core/shell SNP. In this work, we investigate how the design of nanoparticle shape and the position of the embedded QD impact the anisotropy in absorption and emission, to gain broader control over these optical properties. We employ the analysis of anisotropic dielectric screening23–26, based on the following justifications. For the absorption of photons with energy above the bandgap of the shell, we neglect the presence of the (much smaller) QD and consider a homogeneous particle with known dielectric constant23. For the emission, we assume that the QD acts as an elementary electrical dipole emitter with random orientation, thereby neglecting anisotropies of quantum-mechanical origin related to the crystal structure and stress17,27,28. The motivation for this approach is that the spherical QD is small, has limited anisotropy and has a dielectric constant that is similar to that of the semiconducting shell. In addition, we also neglect losses related to the transfer29 of the electron-hole pair, from the place where it is generated to QD. Results and discussion When a single particle with real, isotropic and homogeneous dielectric constant p is placed in an external medium with dielectric constant m and homogeneous static electric field Ee, the magnitude and the orientation of the electric field Ei inside the particle depend on the position r. The relation between the field components inside the particle and the external field components is linear and described by a tensor (r):   xx  r   xy  r   xz  r     Εi  r     r  Εe    yx  r   yy  r   yz  r   Εe . (1)   r   r   r   zy zz  zx  The amplitude of the oscillating electric field Ei(r) inside a particle, due to an incident electromagnetic plane wave with amplitude Ee(r) can be approximated by this tensor when absorption is weak and when the particle is much smaller than the wavelength. The absorption per unit volume in the particle is then given by 1/ Im( )|E (r)|2. If the external field E is, for example, oriented along the z-axis, then the absorption is 2 p i e proportional to the quadratic field factor z2, with: (2)  z2 r   xz2 r   yz2 r   zz2 r .









The total particle absorption is proportional to the volume integral of the quadratic field factors ||2 or 2 (for fields resp. parallel or perpendicular to the principle axis), shown in Fig. 1b. The anisotropy in the absorption cross-section  of a particle (due to the anisotropic shape) for || versus  polarized light is defined as a:  P2   2  dV .  V a  (3)  P2   2  dV



V

For spheroidal particles, there is an analytical expression for this factor30: 2 2  m  N    p   m     m  NP   p   m       a , spheroidal  2 2  m  N    p   m     m  NP   p   m      

(4)

with (N, N||) the depolarization factors (Methods) perpendicular and parallel to the main axis23,30: for a sphere (1/3,1/3); for a flat disc (0,1); for a long needle (1/2,0). The quadratic field factor 2(r), its volume average 2 and the anisotropy factor a are shown in Fig. 1a and b for spheroidal particles with m/p=0.375 (Methods).

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Figure 1| Simulated absorption properties of nanoparticles. a. Distribution of the quadratic field factor 2(r) in different particles with the external field (blue arrow) parallel and perpendicular to the main axis, with m/p=0.375. First and second row: nanowires. Third and fourth row: nanoplatelets. The values are shown in a vertical cross-section and on the particle surface. b, c, Volume-average of 2 for particles with different edges (b) and different cross-sections (c) as a function of the aspect ratio L/d and L/(2h), respectively. Inset graphs show the absorption anisotropy a.

Advances in the colloidal synthesis of nanocrystals have led to synthesis methods that yield particles with a large variety of sizes and shapes16–18,20,21,27,28. In particular, the hexagonal or cubic symmetry of the crystal lattice can be imposed on the overall SNP geometry, resulting in the formation of rods and platelets when the atoms are arranged in a hexagonal or cubic lattice21, respectively (Fig. 1a, hexagon and block). In addition, chemical synthesis strategies may introduce structural modifications at the edges and tips of the particles as exemplified in Fig. 1a (pill-shape and cylinder). Therefore, it is important to evaluate the effect of the particle geometry on the field factor. We use finite element modeling (Methods) to calculate the quadratic field factor 2(r), the volume average 2 and the anisotropy factor for the different shapes. Fig. 1a illustrates that for spheroidal particles (nanowires or nanoplatelets) the field inside the particle is homogeneous, while for the other particles the field is higher near the surfaces that are parallel to the applied field and lower near the surfaces that are perpendicular to the applied field. Fig. 1b and Fig. 1c illustrate that the aspect ratio L/d or L/2h (with h the apothem of the hexagon or block cross-section) is a key parameter for the anisotropy factor a. The absorption anisotropy remains similar for all these geometries (Fig. 1b, c, inset), being negative for platelets and positive for wires.

Figure 2| Simulated emission properties of nanoparticles. a, b. Finite element electromagnetic simulations for elementary electrical dipoles in a nanowire. Electric field intensity (brightness) for dipole emitters parallel to the particle’s long axis at three locations in a spheroidal (a left) or cylindrical (a right) nanowire. Radial far-field emission patterns for dipoles parallel to the particle’s long axis at three locations in the spheroidal (b left) and cylindrical (b right) nanowire, and for a randomly oriented dipole (b left, black line). c. Anisotropy of the emission ap as a function of the aspect ratio and the location of the emitter in a spheroidal (left) or cylinder (right) particle. All calculations are performed with m/p=0.375.

Next, we consider the down-converted emission of a photon from the QD in a nanoparticle, after absorption of a photon. The electric field (Fig. 2a) and far-field radiation patterns (Fig. 2b) for elementary electrical dipoles parallel to the particle’s long axis, obtained with electromagnetic simulations (Supplementary), show the strongest emission in the plane perpendicular to the particle’s long axis. Note that for the cylindrical nanowire the emission is reduced when the QD is located close to the tip (axial position ±L/2), while for the spheroidal nanowire the emission is independent of the location. For a randomly oriented dipole emitter (obtained as the incoherent average for three orthogonal elementary electrical dipoles) in a spheroidal particle, the emission is not isotropic due to the dielectric effect, with the highest intensity observed perpendicular to the nanowire (black line in Fig. 2b). The reciprocity theorem31 requires that the external dipole moment pe that describes the emission, is linked to the internal dipole moment pi by the same tensor  given in eq. (1), now obtained for the down-converted photon energy. The polarization anisotropy for photoluminescence (parallel versus perpendicular) observed in a particular direction, for a randomly oriented dipole in the location r of QD is then given by the factor ap (Supplementary):

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ap 

P2  r    2  r  . P2  r    2  r 

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(5)

The photoluminescence anisotropy for a randomly oriented dipole emitter at different locations in a spheroidal and cylindrical SNP with different aspect ratios, is summarized in Fig. 2c. These diagrams illustrate that the emission anisotropy for a cylindrical nanowire decreases when the quantum dot is positioned near the tip. Thus, for non-spheroidal particles (Supplementary) the emission depends on the location of the embedded QD, which in combination with the particle length, enables fine-tuning of the emission anisotropy.

Figure 3| Dependency of the photoluminescence polarization anisotropy ap on the aspect ratio (horizontal axis) and dielectric contrast m/p (color) for spheroids (solid lines), cylinder and block particles (colored areas), including a comparison between measurements (filled markers) and simulations (open markers). The solid lines represent the analytical formula for spheroidal particles for three values of m/p. The colored areas represent numerically calculated values of ap for particles in which the QD position varies between r=0 (at the center) and r=L/2 for block (blue area, aspect ratio W/L) and cylinder (red and purple areas, aspect ratio L/d) particles. The filled markers represent experimental results: downward triangles for rectangular nanoplatelets14 with m/p=0.5; purple circle32 and upward triangles22 for cylinder particles with m/p=0.375 (see also the inset); red filled squares28 for cylinder particles with m/p=0.167. The open markers show the calculated emission anisotropy for the parameters corresponding to the experiments (Supplementary).

To assess the validity of the developed model for different core/shell SNP geometries and sizes, we compare numerically calculated emission anisotropies with reported experimental results14,22,28,32. Fig. 3 shows the photoluminescence anisotropy ap as a function of the aspect ratio (W/L for block particles with fixed thickness and L/d for spheroids and cylinders) for different dielectric contrasts (Supplementary). The blue, purple and red solid lines correspond to the analytical expression (eq. (5)) for the emission anisotropy for spheroids with m/p = 0.5, m/p = 0.375 and m/p = 0.167, respectively. For cylinder and rectangular block particles the emission anisotropy depends on the QD position r, which varies between r = 0 (center of the particle) and r = L/2, leading to the blue, purple and red areas in Fig. 3. The figure illustrates that assuming a spheroidal shape can lead to an overestimation of the emission anisotropy when the QD is located closer to the tip of the cylinder (r = L/2). In ref. 22 (filled purple upward triangles) both the QD position r and the photoluminescence anisotropy is provided, which allows to make a detailed comparison with the simulated ap (open purple upward triangles). The inset in Fig. 3 shows excellent agreement. The position r of the embedded QDs is not provided in refs. 14, 28 and 32, and the measured anisotropies remain within the corresponding shaded areas. The good agreement between existing experiments and simulations warrants the use of the numerical model to estimate the emission anisotropy of SNPs with different shapes. We now address our primary question of whether the absorption and emission anisotropies can be manipulated by designing the core/shell SNP to acquire the desired directionality and polarization. We first select cross (Fig. 4a, top) and thumbtack (Fig. 4a, bottom) nanoparticles. A cross particle consists of two cylinders with length L and diameter darm=d whereas a thumbtack particle has a cylindrical head with diameter dhead=L and length Lhead=d and a cylindrical leg with inversed dimensions (Lleg=L, dleg=d), with typically d