The coupling between localized surface plasmons and excitons via Purcell effect
 Feng Wang^{1},
 Dongsheng Li^{1}Email author,
 Deren Yang^{1} and
 Duanlin Que^{1}
DOI: 10.1186/1556276X7669
© Wang et al.; licensee Springer. 2012
Received: 17 October 2012
Accepted: 22 November 2012
Published: 7 December 2012
Abstract
The coupling between localized surface plasmons (LSPs) within silver nanostructures and excitons in a siliconrich silicon nitride (SiN_{ x }) matrix has been demonstrated via the Purcell effect. A simple model is employed for the estimation of the Purcell factor as well as the average position of excitons within a luminescence matrix. The estimated average position of the excitons is located at approximately 40 nm beneath the top surface of the SiN_{ x } films. The approaches for further improving the optoelectrical properties of the luminescence matrix are anticipated based on the model we adopted. The optimization of the thickness of the luminescence matrix as well as the size and shape of metal nanostructures may be the alternative approaches. Besides, the application of multilayers with the luminescence matrix inserted between barrier layers (we defined it as confined structures here) may be also an available choice. Our work may provide a deep comprehension on the coupling between LSPs and excitons, which is not limited to a certain luminescence material but with unconfined structures.
Keywords
Localized surface plasmons Siliconrich silicon nitride Silver nanostructures Average position of excitons LuminescenceBackground
As an effective approach to overcome the diffraction limit of classical optics due to the mismatch of energy and momentum between electrons and photons, localized surface plasmons (LSPs) referring to the collective electronic oscillations within the metallic nanostructures excited by the external radiation have captured much research interest [1–8]. The confinement of electromagnetic field at the subwavelength volume as well as the Purcell enhancement of this field on the order of the quality factor (Q) of the LSP resonance is achieved by the adoption of these polariton modes [9, 10]. This Purcell enhancement effect is similar to the Purcell effect in a microcavity with a quality factor Q, where the coupling between an exciton and a microcavity mode is allowed by the field confinement within an ultrasmall volume V[10, 11]. This effect can enhance the density of photon states, which is proportional to the spontaneous emission decay rate, leading to the Purcell factor (F_{p}) enhancement of luminescence [10, 12]. Obviously, this F_{p} can characterize the coupling efficiency indirectly, which is influenced especially by the sizes and species of metallic nanostructures, the energy of emitted photons (hν_{D} = hc/λ_{D}), and the distance (d) between LSPs and excitons in a luminescence matrix [13]. The effects of these parameters on F_{p} as well as the estimation of the average position of excitons within the luminescence matrix are particularly important for the further optimization of the luminescence properties of the active matrix.
In this letter, an amorphous siliconrich silicon nitride (SiN_{ x }) film, a promising candidate material of siliconbased light sources due to its superior photophysical properties [12, 14–18], is employed as the luminescence matrix investigated here. Silver (Ag) nanostructures are used for the demonstration of the coupling between LSPs and excitons in SiN_{ x } due to their lowest absorption losses and a superior enhancement of the local electromagnetic field among all the metals with plasmon resonances at visible frequency, which is near the luminescence wavelength of SiN_{ x } films. Both the relationships between F_{p} and λ_{D} and the estimation of the average position (d) of the excitons within SiN_{ x } are provided based on a simple model.
Methods
SiN_{ x } films with a thickness of approximately 50 nm were deposited using a plasmaenhanced chemical vapor deposition technique onto the substrates of ptype Si (100) or quartz for various measurements. The preparation of SiN_{ x } films has been described in detail in our previous paper [12]. After the deposition of SiN_{ x }, a Ag layer was deposited by magnetron sputtering, with the thickness regulated by the sputtering time (20, 40, 60, and 80 s). To form the Ag nanostructures with various dimensions and surface morphologies, a rapid thermal annealing (RTA) in argon at 500°C for 60 s was employed subsequently. We label the samples by the sputtering time of the Ag layer, e.g., Ag40 refers to the sample with the sputtering time of the Ag layer of 40 s. A SiN_{ x } film without Ag was also fabricated as the reference sample (Ag0).
The ellipsometric parameters ψ and Δ can be obtained from the ellipsometric measurement (M2000D, J. A. Woollam Co. Inc., Lincoln, NE, USA), from which the complex index of refraction (n) can be calculated using the equation of $n=\frac{\left[\sqrt{14{sin}^{2}\left({\theta}_{0}\right)tan\left(\psi \right){e}^{\mathit{j\Delta}}+2tan\left(\psi \right){e}^{\mathit{j\Delta}}+{tan}^{2}\left(\psi \right){e}^{\mathit{j\Delta}}}\right]{n}_{0}sin\left({\theta}_{0}\right)}{cos\left({\theta}_{0}\right)\left[1+tan\left(\psi \right){e}^{\mathit{j\Delta}}\right]}$, where θ_{0} and n_{0} stand for the angle of incidence and the complex refractive index of the ambient, respectively [19]. Meanwhile, the film thickness (t) can be obtained from the equation of $t=\frac{j\mathrm{ln}\left({e}^{j2\beta}\right)\lambda}{4\mathrm{\pi}ncos\left({\theta}_{1}\right)}$, where $\beta =2\mathrm{\pi}\frac{t}{\lambda}\sqrt{{n}^{2}{n}_{0}^{2}{sin}^{2}\left({\theta}_{0}\right)}$ and θ_{1} represents the angle of refraction [19]. All these calculations, including the determination of the extinction coefficient (k) as a function of wavelength, have been integrated into the ellipsometric measurement system. Consequently, we can acquire the data of t, n, and k directly from ellipsometry by scanning over the angle (θ_{0}) range from 65° to 75° in steps of 5° with the spectral (λ) range from 400 to 800 nm. The extinction spectra of the samples with and without Ag nanostructures were obtained using a Hitachi U4100 spectrophotometer (Hitachi, Ltd., Chiyoda, Tokyo, Japan). The photoluminescence (PL) spectra of all the samples were excited by a 325nm HeCd laser using an Acton SpectraPro2500i monochrometer (Acton Research Corporation, Acton, MA, USA).
Results and discussion
Coupling between localized surface plasmons and excitons via Purcell effect
For the sample without the coverage of Ag nanostructures, the excitons generated in SiN_{ x } films by optical or electrical pumping are terminated by radiative or nonradiative recombination with the internal quantum efficiency (η_{int}) determined by the ratio of the radiative recombination rates (κ_{rad}) to the nonradiative recombination rates (κ_{nrad}) as η_{int} = κ_{rad} / (κ_{rad} + κ_{nrad}) = τ_{rad}^{−1}/(τ_{rad}^{−1} + τ_{nrad}^{−1}). After the addition of Ag nanostructures, the interaction between LSPs and excitons can be treated as a twostep process (shown in Figure 2). When the energy (ћω_{ex}) of excitons is close to the electron vibration energy (ћω_{SP}) of LSPs, the excitons transfer their energies to the LSP modes with the radiative recombination rates (κ_{rad}) enhanced by the Purcell factor F_{p}[4, 11]. This process will compete with the nonradiative decay and enhance the PL decay rate (κ_{PL}) significantly due to the large electromagnetic fields introduced by the high mode density in LSPs [21]. For the second step, the energy from the LSP mode will be outcoupled to radiated photons with the rate γ_{rad}, as shown in Figure 2. This coupling will compete with the nonradiative loss (γ_{nrad}) due to the absorption of Ag nanostructures, where the coupling efficiency can be defined as η_{c} = γ_{rad} / (γ_{rad} + γ_{nrad}) [22]. This efficiency (η_{c}) can be optimized via the modulation of the parameters of metal nanostructures, such as the size, shape, density, and the distance between metal nanostructures [22].
Average position of excitons in SiN_{ x }matrix
To find out the relationship between F_{p} and F_{PL}, the originations of these two factors are considered. Both of them mainly result from the enhancement of the spontaneous emission rate, where the value of F_{p} can be rewritten as F_{p}(ω) = κ_{PL}^{*}(ω)/κ_{PL}(ω), with κ_{PL}(ω) and κ_{PL}^{*}(ω) standing for the original and enhanced PL decay rates, respectively [25] . Consequently, the approximation relation between F_{p} and F_{PL} (F_{P} ≈ F_{PL}) can be employed for the estimation of the average position of excitons (d) in SiN_{ x } by plotting the curves of F_{p}vs. d at the wavelength where the enhancement of dipole resonance occurred, as shown in Figure 4d. The average position of excitons is located at 43 to 45 nm beneath the top surface of the SiN_{ x } films. Consequently, the optimized luminescence properties can be achieved via the optimization of parameters in the Equation 5 by the modulation of the sizes and shape of the Ag nanostructures. Both the optimal PL and electroluminescence efficiency of a SiN_{ x }based lightemitting device are achieved by the addition of Ag nanostructures with the radii of approximately 50 nm from our experimental results (not shown here). Further attentions can be paid to the decrease of the distance between LSPs and excitons, which may be achieved via the optimization of the thickness of the luminescence matrix as well as the appropriate design of the luminescence structure. Multilayers with the active matrix inserted between barrier layers may be also an available choice.
Conclusions
The coupling between LSPs and excitons in SiN_{ x } has been demonstrated via the Purcell effect. When the energy of the excitons is close to the electron vibration energy of LSPs, the excitons can transfer their energy to the LSPs, in which the radiative recombination rates are enhanced by the Purcell factor. The relationships between the Purcell factors and the deposition parameters are illustrated, including the size of the Ag nanostructures, the energy of the emitted photons, and the distance between the LSPs and excitons in the SiN_{ x } matrix. Further improvement on the luminescence efficiency can be achieved by decreasing the distance between LSPs and excitons and/or modulating the parameters of the metal nanostructures.
Abbreviations
 Ag:

silver
 F _{PL} :

PL enhancement factor
 F _{p} :

Purcell factor
 LSPs:

localized surface plasmons
 PL:

photoluminescence
 RTA:

rapid thermal annealing
 SEM:

scanning electron microscopy
 SiN_{ x }:

siliconrich silicon nitride
 SiO_{ x }:

silicon oxide.
Declarations
Acknowledgments
The authors thank the National Natural Science Foundation of China (no. 61176117), the 863 Program (no. 2011AA050517), and the Innovation Team Project of Zhejiang Province (no. 2009R5005).
Authors’ Affiliations
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