Electromagnetic shielding using Anderson localization in nanoparticle–biopolymer composites Open Access

Interaction of radiofrequency/microwave radiation with matter has been the subject of enormous interest for several decades along with the development of electromagnetic interference (EMI) shielding materials.^1,2 Electromagnetic shielding is the designed attenuation of electromagnetic radiation over a certain frequency range. EMI shielding is critical to the operation of a wide range of technologies, including sensors, measurement apparatus, wireless communications, medical equipment, and consumer electronics. In general, EMI shielding is indispensable for any application that requires low noise operation, which depends on isolation from noisy electrical environments. Shielding is most effectively achieved using conductive coating, where a metal reflects most of the incident radiation below its plasma frequency. However, metal coatings suffer from bulkiness and inflexibility. Another approach to EMI is to absorb the incident radiation that occurs in thin films made of biopolymer composites.^3–5 While these composite materials are flexible and overcome the problems posed by metal coatings, their shielding efficacy is far lower, and additionally, the absorption of EM radiation leads to the generation of heat, which is detrimental to the performance of sensitive electronics.

The progress in integrated circuits and the drive toward miniaturization demands new requirements for shielding technologies, where the shielding structures need to follow the increasingly aggressive device-size scaling, while also maintaining shielding efficacy. Here, we present experimental data on a composite film of metal nanoparticles embedded in a novel DNA–CTMA biopolymer, which displays a very high shielding efficacy within a film thickness of just a few micrometers. Our experiments show that the measured attenuation is close to the ideal limit—that of a solid slab of metal. Using high-resolution electromagnetic simulations, we argue that the mechanism responsible for the extremely high EMI shielding of our Ag/DNA–CTMA composite is Anderson localization.

Anderson localization can occur in wave transport in a disordered medium for a sufficiently large disorder (both in strength of scattering and quantity), which marks a transition between propagating and localized modes. It has been demonstrated in a variety of settings in which wave transport is involved, such as electromagnetic (EM) radiation, acoustic waves, gravity waves, electrons, cold atoms, and sound waves.^6–25 The relevant dimensionless parameter is given by kl_mfp, where k = 2 π/λ is the wavenumber of the wave (in our case, the incident radiation) and l_mfp is the mean free path that characterizes the strength/amount of disorder. A transition between propagation and localization is expected to occur at kl_mfp∼ 1, known as the Ioffe–Regel criterion, with kl_mfp < 1 being the localized state. An examination of the components of the dimensionless parameter individually reveals the following: k characterizes the wave nature of the incident radiation. For k → 0, the wave nature dominates, allowing for interference effects. In the opposite limit, k → ∞, ray transport dominates. Now, consider l_mfp → 0, which corresponds to a random scatterer configuration that lacks any ordering. The opposite limit l_mfp → ∞ corresponds to a configuration wherein scatterers are placed in a perfect crystal lattice.

Now, consider the present problem: electromagnetic radiation at 10 GHz has a wavelength of 3 × 10⁴ μm corresponding to k ≈ 2 × 10⁻⁴ μm⁻¹. Further, the particle–polymer composites assume a completely disordered configuration with a typical l_mfp∼ 1 μm for particle weight fractions typically used in experiments. We, thus, have kl_mfp∼ 10⁻⁴ and so there is good reason to expect the system to be in the so-called strong localization regime.

DNA, the building block of life, has been the center of biological research and industries for five decades. However, interest in DNA's electrical properties intensified soon after the discovery of its doublehelix structure. In recent years, the observation of DNA's electrical properties saw renewed attention in the search for new materials for next-generation nanotechnologies and microelectronics.

The raw DNA–CTMA composite was produced by a cationic surfactant reaction. We have studied a wide selection of metal nanoparticle fillers and have experimentally studied their EMI shielding performance and efficiency. Among them, thus far, silver and carbonbased nanoparticles have proved to have the best performance and were, therefore, selected for further investigation. The detailed fabrication process, our careful study of their performance, and our selection process will be published elsewhere.

Ag-based, electrically conductive, nanoparticles with diameters of 1 μm were blended with both the DNA/CTMA biopolymer and the amorphous polymer polymethylmethacrylate (PMMA), for comparison, and cast onto Teflon substrates, which could then be easily removed, to realize free- standing films [Figs. 1(a)–1(c)]. Samples of three different thicknesses were fabricated for both Ag/DNA/CTMA and Ag/PMMA. As can be seen in Fig. 1(b), the Ag/DNA/CTMA-based films are very flexible and pliable, whereas the Ag/PMMA-based films are very fragile and brittle [Fig. 1(c)], and essentially unusable.

The samples were designed in such a way that the “‘effective” shielding layer of the films was approximately 1/3 the total thickness of the films and was electrically conductive, whereas the remaining 2/3 of the samples was electrically insulating. This was done to prevent electrical shorting when used to shield electronic circuits. Figure 1(d) illustrates a scanning electron microscopy (SEM) image of the edge of one of the samples. The thicknesses of the Ag/DNA/CTMA-based thin films were measured using digital thickness calipers. The average total thicknesses of each free-standing film sample measured 198, 213, and 389 μm, respectively, while the “effective” shielding layer thickness of each sample, based on SEM, measured 65, 70, and 128 μm, respectively.

The EMI shielding of the Ag/DNA/CTMA samples was measured over a very broad spectra range of 0.5–26 GHz, which required different sets of measurement methodology [Figs. 2(a)–2(c)]. As stated above, the Ag/PMMA samples were too brittle to withstand EMI measurements. To eliminate stray and spurious RF, the setup was enclosed in an RF-insulating chamber. In order to characterize multilayer-periodic structure samples, the experimental setup was constructed to produce well defined RF EM waves between the RF emitter and the receiver, and the RF generators and spectral analyzers were judiciously chosen to cover their corresponding spectral coverage and data processing software. At lower frequencies, electromagnetic shielding effectiveness measurements were conducted using the horn-type setup with a 7 mm low frequency coax. At higher frequencies, K-band coax-to-waveguide adapters were used, with the samples sandwiched between the flanges of two straight sections of the waveguide. Detailed measurements were performed in groups where all three sample thicknesses were measured in three different places in two orthogonal orientations (not necessarily in the same location). Each group of measurements was preceded by a full 12-term TRL calibration using four averages and an IF bandwidth of 3 Hz. The aluminum foil used for reference was also measured in three different places.

A representative measurement over a frequency range of 500 MHz to 19 GHz of each sample thickness, along with the aluminum foil reference, is presented in Fig. 2(d). As a note, a weight fraction of 0.9 was used for these films. It was discovered that variations in shielding effectiveness measurements of the same sample thicknesses were caused by pinholes. The more pinholes, the lower the shielding effectiveness. In addition, more pinholes appeared to be present in the thinner films than in the thicker films, suggesting that improvements in processing are warranted in future work.

We consider a particle–biopolymer composite consisting of 1 μm metal particles dispersed in a DNA–CTMA biopolymer. We study transmission at 10 GHz for which ℜ(ɛ_metal) ≃ − 1 × 10⁵ɛ₀ (ɛ₀≡ free space permittivity, ɛ_metal≡ permittivity of metal particles) and ℑ(ɛ_metal) ≃ 1 × 10⁸ɛ₀, where we have assumed a Drude model, with a scattering time scale set by DC conductivity for simplicity. For the DNA–CTMA biopolymer, we set ℜ(ɛ_DNA) ≃ 4.6ɛ₀ and ℑ(ɛ_DNA) ≃ 0.2ɛ₀. While we present results for the metal particles embedded in a DNA–CTMA biopolymer, our results are more general and are applicable to metal particles randomly dispersed in biopolymers. The generality arises because the key parameter is the skin depth of the metal that constitutes the particles in the composite, which is less than 1 μm at 10 GHz for a wide range of metals. The biopolymer is passive with regard to the electromagnetic radiation, and its role is to solely provide structural support to the metal particles, which in itself is a crucial issue.

The physical setup is inherently stochastic due to the random nature of the particle configurations. In order to obtain statistically significant results, we need to perform an ensemble average. Therefore, we have performed simulations for a number of different particle configurations for each specific combination of particle diameter, weight fraction, film thickness, and source frequency. As we will see, our results are free of fluctuations arising from sampling different particle configurations when the nanoparticle system is either fully transmitting or reflecting. However, the transition between the transmitting and reflecting states is fluctuation-dominated, and so we consider a much larger ensemble (25 configurations) for each combination of macroscopic parameters during the transition. We use a spatial resolution of 0.1 μm over a domain of 2200 × 18.9 μm² (grid size N_x × N_y = 22 002 × 189) with periodic boundaries along y and perfectly matched layers (PMLs) of thickness of 1000 μm along x to simulate infinite boundaries. A line source for J_y is placed at the left end of the domain and the fields are measured at a line probe around 1000 μm after the film. The power is given by the Poynting vector along x, |S_x| = |E^∗B_z|, and the transmission is computed using $10 log( | S x | / | S x r e f |)$⁠, where $S x r e f$ is the transmitted powerin a reference simulation that contains no film.

The optimization is done with the L-BFGS-B (Limited memory Broyden–Fletcher–Goldfarb–Shanno Bounded) optimizer,^30–32 using the bounds to enforce that the particles remain within the film thickness.

We first examine the effect of disorder by varying the weight fraction a of 1 μm particles in the composite and examining the resulting dependence of the attenuation, as shown in Fig. 3. All configurations have a film thickness of 50 μm, with the source frequency set to 10 GHz and a particle diameter of 1 μm. For each weight fraction a, there are 25 different particle configurations. The transmitted power for each of the individual configurations is shown using a red marker, connected together by a dotted red line. Therefore, the vertical extent of the line indicates the magnitude of the fluctuations. The ensemble average is shown using a black marker. As a is varied, the transmission is almost constant, before abruptly dropping at a ≃ 0.92, marking a transition to a reflecting state. Also note the large variation between various instances of the disorder in the particles, with the onset of the transition in good agreement with the experiment given the large error bars.

The conceptual picture of a transition between two distinct states is further bolstered by examining the fluctuations, which are large precisely during the transition between the transmitting and the reflecting states (Fig. 3). We examine the spatial profiles of the electromagnetic power across the film for an ensemble of particle configurations at a = 0.92 (Fig. 4), where fluctuations are dominant. Notably, the radiation has a highly complex spatial structure at the transition, in contrast to a much simpler profile before and after the state transition. As a increases further, the fluctuations subside, and the system becomes completely reflecting (transmission ≃ − 114 dB).

To quantify the strength of the attenuation, we need a reference value: the maximum possible attenuation that can be achieved. This reference value is given by a solid film made of the same metal that constitutes the particles in the particle–biopolymer composite. For a 50 μm film composed solely of the constituent metal (i.e., a = 1), the transmission is ≈ − 115 dB. We, thus, see that Anderson localization in the disordered film produces the maximum possible attenuation for a fixed film thickness.

We now examine the dependence on film thickness and particle size, fixing the frequency to 10 GHz and metal weight fraction a to 0.95 (i.e., in the reflecting/attenuating state seen in the previous section) in Fig. 5. For particle sizes 0.6–1.1 μm, there is strong attenuation even for the smallest film thickness considered (10 μm), with a modest increase in the attenuation for increasingly thick films. As the particle diameter is increased (e.g., at 1.5 μm), there is again a state transition: for thin films, the system is transmitting all incident power, but becomes attenuating above a critical thickness. As the particle diameter is made much larger than the skin depth (2, 5, and 10 μm), the system is fully transmitting for all thickness considered. We can understand this result within the localization framework: for localization to occur, we require a sufficient number of scatterers. As particle size is increased with the weight fraction kept constant, the number of scatterers decreases, and, thus, there is an absence of localization. Figure 6 shows the spatial profiles of the radiation for varying film thicknesses across the transmitting–reflecting transition.

We have argued that the key physics that governs the attenuation of microwave/RF radiation by metal–biopolymer composites is Anderson localization caused by the disordered configuration of metal particles within the composite. The attenuation is observed to be a spatially nonlocal effect, requiring us to take into account long-range fluctuations in the EM fields. The effect is not reproduced in simulations with a local effective medium approximation. We note that a critical limitation of our study is that our simulations have been limited to two dimensions due to computational constraints. To further advance the idea that the shielding in nanoparticle–biopolymer composites is caused by wave localization, simulations are required in full three dimensions (3D). The main bottleneck to realizing FDTD simulations in 3D is the convergence failure of iterative linear solvers in our attempts so far.

The novel insight of localization physics leads to specific quantitative predictions, which we list point-wise below.

Invoking the conceptual picture provided by localization physics, which requires that scatterers have a sufficient strength, we see that a lower limit on the particle size is set by the requirement that it be greater than the skin depth. Further, we require a sufficient number of scatterers within the film, which then sets an upper limit on the particle size.

Combining the constraints, we find that ∼1–1.5 μm sized particles are ideal for shielding for film thickness beyond a critical lower limit of ≳30 μm.

A critical requirement for localization to set in is that the particle diameter exceeds the skin depth. This requirement is satisfied by a range of metals, for e.g., Al, Cu, and Ag, all of which have a submicron skin depth, making them ideal for shielding. The frequency range of applicability extends well into the terahertz regime, where we calculate that the DNA–CTMA/Ag composite displays an attenuation of ≃37 dB, which is close to the upper limit of ≃39 dB displayed by a solid film of Ag at 1 THz. More broadly, we have a convenient design rule: a composite film in the localization regime can be thought of simply as a solid film made of the same material as the metal particles that constitute the composite.

The attenuation does not exploit any microphysics that arises due to the biopolymer, for, e.g., interfacial polarizations caused by charge transfer at the particle–biopolymer interface. The biopolymer plays a passive role with regard to the electromagnetic wave propagation, and its only role is to provide structural support to the metal particles. Therefore, candidate biopolymers can be assessed based solely on their structural properties when embedded with the metal particles without having to worry about interactions between the biopolymer and the metal.

We have shown that EM attenuation occurs because of a localization transition, for which wave physics is crucial. An entirely different transition is observed in terms of the measured DC resistance across the composite film. For low weight fractions, where there is no pathway for charge transfer across the metal particles, the resistance is set by that of the biopolymer (which is large). As the weight fraction increases, a connected pathway across the metal particles appears and short circuits the charge transport through the composite, leading to a large drop in the resistance. This is known as a percolation threshold and also appears at sufficiently high weight fractions. Clearly, the onset of attenuation of EM propagation and the percolation threshold are correlated, as is well-known in the shielding community.² However, wave attenuation occurs because of Anderson localization, which has a lower weight fraction threshold than the percolation threshold.³³ This new insight allows for the design of shielding composites that exclusively reflect (and so do not heat up) and which are insulating in charge transport.

Finally, contrast our random disordered medium with the ordered dielectric structures of photonic crystals, where propagating modes can be eliminated within a photonic bandgap. However, it is challenging to experimentally realize a photonic crystal that is flexible for the purposes of EMI shielding. In contrast, our DNA–CTMA/Ag composite is easily manufactured and can be sprayed upon the device to be shielded. Further, the bandgap in a photonic crystal may be limited to certain modes and frequencies, while a disordered medium displaying localization will block all modes and frequencies up to the plasma frequency of the metal that constitute the scatterer; beyond the plasma frequency, the metal particles fail to effectively scatter, and the film becomes transmitting. Most importantly, our simulations show that EMI shielding is achievable in metal nanocomposites due to Anderson localization independent of the matrix material; DNA leads to mechanically stable composites, but this finding opens up the pathway for further materials design for EMI shielding.

We thank Professor William A. Goddard, III at Caltech for several stimulating discussions and a review of this manuscript. We are grateful to Professor Michael Fiddy (DARPA) for his support in the initial phase of this work in the prior years. We also would like to thank the technical staff of AFRL for their independent test and verification of our data in the prior years, and Mr. Larry Hurzon, for his technical support and several stimulating discussions. Finally, we are most grateful to Dr. Ben Kelsall from MuEpsln, LLC laboratories, for another series of careful, independent tests, validations, and verifications of our most recent experimental results.

Co-authors James Grote, Gitansh Kataria, Mani Chandra, and Ravishankar Sundararaman dedicate this manuscript to Michael Salour, who recently passed away in an unfortunate airplane accident. His insights and support were immeasurable. He was an outstanding scientist as well as a dear friend and colleague. Rest in peace, Michael. You will be deeply missed.

The authors have no conflicts to disclose.

Michael M. Salour: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). James G. Grote: Conceptualization (equal); Investigation (equal); Validation (equal); Writing – review & editing (supporting). Gitansh Kataria: Investigation (equal). Mani Chandra: Investigation (equal); Methodology (equal); Software (equal); Writing – original draft (equal). Ravishankar Sundararaman: Conceptualization (equal); Methodology (equal); Software (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.