1. Introduction

Surface plasmons (SPs) couple the excitations of photons and mobile charge carriers on the surface of metals or doped semiconductors and can control the electromagnetic energy in nanometer-scale [1,2]. SPs provide both strong electric field localization and high enhancement, which are accompanied by an appreciable wavelength reduction relative to that in free-space condition. Graphene has been identified as a nanoscale platform supporting variable SPs with tunable Fermi levels [1–4]. Specifically, SPs in graphene are collective oscillations of Dirac quasi-particles revealing strong confinement, electrostatic tunability, long lifetimes and relatively low loss [3–7]. In addition, SPs propagate along the graphene sheet and the confinement is expected to be much larger than that in conventional metallic structures due to the two-dimensional (2D) collective plasmon excitations. One key advantage that enables graphene as an excellent platform for plasmonic devices is its large tunability through carrier doping which cannot be achieved in general noble metals. More importantly, SPs in graphene hold promising applications in a wide frequency regime from the terahertz to the infrared [8–11].

Biosensing in mid-IR is a research area where graphene can fully utilize its unique tunability and light localization. Taking advantage of the mid-IR structural vibrations in molecules that precisely identify their chemical properties [12, 13], the mid-IR regime is well suited for biosensing. Generally, the dimensions of the molecules are much smaller than the optical wavelengths, and the corresponding interaction with light is extremely weak. High sensitivity is expected through utilizing resonant metallic nanostructures [14–16]. However, this is ultimately limited by the relatively poor field confinement of metals in the mid-IR waveband [17]. On the contrary, the significant spatial confinement of the electromagnetic fields in graphene mid-IR SPs makes them particularly attractive for enhanced mid-IR light-matter interactions. Some studies about graphene plasmonic biosensor have been reported recently [12, 18]. Due to the large wavevector mismatch compared to free-space photons, graphene SPs can be launched by metal antenna [6], metalized tip [11], tapered waveguide [19] or diffractive grating [20].

In this work, we propose a graphene nanoribbon based tunable mid-IR biosensor and demonstrate its high sensitivity for detecting the optical properties of protein. The Fermi level is modified to realize resonant localized SPs with both high electromagnetic confinement and enhancement. Resonant spectra of the device are acquired using finite-element method with incident electric field polarized perpendicular to the nanoribbon plane. The tunable localized resonant SPs in graphene nanoribbon structure with mid-IR excitation are then employed to detect the protein permittivity. The strong optical field confinement provided by the tunable resonant SPs with extremely small mode volume enhances the light-protein interaction, leading to high molecule sensitivity.

2. Resonant graphene plasmonic modes

There are some aspects on which graphene SPs are superior to metal SPs. First, SPs frequencies of doped graphene can be tuned using electrical gating or chemical doping techniques. Second, the spectra of individual SPs can be stimulated in the mid-IR regime. The optical conductivity of graphene determines the corresponding plasmonic properties. Under the condition that the absolute value of the Fermi level is tuned above the threshold value, i.e., $\left|E_F\right|>\frac{0.25117({\epsilon }_1+{\epsilon }_2)\hslash \omega }{\sqrt{{\epsilon }_1+{\epsilon }_2+1}-1}$ [11, 20, 21], graphene exhibits metallic optical response and supports transverse magnetic (TM) polarized SPs. ${\epsilon }_1$ and ${\epsilon }_2$ are the relative permittivity of two sides cladded layers, $\omega$ is the angular frequency of the incident light. Therefore, as long as $\left|E_F\right|$ is larger than 0.24 eV, it is possible to excite TM SPs in graphene layer cladded by silicon (${\epsilon }_1=11.7$) and air (${\epsilon }_2=1$) at a fixed mid-IR incident wavelength of 6 µm. In fact, the Fermi level of graphene can be tuned flexibly in practice by applying a bias voltage. Taken the permittivity of the substrate ${\epsilon }_1$ and the above surface layer ${\epsilon }_2$ into consideration, the effective index of the guided plasmon mode in graphene can be evaluated as [11, 20–22]:

To understand the physical mechanisms of the guided graphene SPs and their strong light localization and high field enhancement in the mid-IR regime, we first calculate the electric field intensity distribution with different nanoribbon widths and Fermi levels. The excitation wavelength is fixed to be 6 µm in this part. We study the plasmon properties of the graphene nanoribbon with different widths on a silicon substrate surrounded by air as the structure schematic shown in Fig. 1. For the sample fabrication, first, monolayer graphene grown by chemical vapor deposition (CVD) technique on a copper foil can be transferred onto a silicon substrate. Second, monolayer graphene is spin coated with electron beam resist and then exposed using electron beam lithography (EBL) followed by a resist development and an oxygen plasma cleaning. Resist stripping is done in acetone, followed by IPA and DI water rinsing. The metalized tip is used to launch the graphene SPs and the silicon substrate offers high dielectric permittivity to significantly enhance the field localization from Eq. (1). We use TM polarized incident light by means of eigenmode solver of the finite element method for the 2D cross section geometry as indicated in Fig. 1. During the simulation, the complex permittivity of the graphene layer is modeled with complex conductivity from Kubo formula [22] by considering monolayer thickness of 0.5 nm. The complex refractive index of the silicon [23] is also taken into consideration. According to Eq. (1), with large Fermi level (larger than the threshold value of 0.24 eV at 6 µm), graphene plasmon modes emerge.

 

Fig. 1 Schematic of the graphene nanoribbon with width of W on a silicon (Si) substrate. The protein layer is immobilized on top of graphene. Cross section is depicted.

Download Full Size | PDF

The near-field intensity images for different ribbon widths with EF = −0.3 eV is shown in Figs. 2(a)-2(d), indicating the guided mode features at wide and narrow ribbons. The near-field intensity amplitude is a direct measurement of the square of the z-component field amplitude ($\left|E_z^2(\omega )\right|$). Stronger field intensity occurs close to the boundary regions which is due to the constructive interference between multiple boundary-reflected SPs. The induced plasmon is scattered by the graphene edges, which produce reflected fields. The stronger intensity close to the edge can also be attributed to the strong concentration of electromagnetic field included in the local density of optical states model [11]. The graphene SPs confined in the ribbon is equivalent to a Fabry-Perot model with zero-phase reflection [24, 25]. The decay field intensity inside the ribbon is caused by the mode damping effect, which results from a combination of substrate loss and intrinsic graphene loss. The intrinsic graphene layer acts as a primary source of loss due to the interband absorption. The plasmon damping induced by the interband excitation occurs at small carrier densities and could be suppressed when $\left|E_F\right|>E_P$, E_P is the SPs energy. As the ribbon width W decreases, the total number of distinct intensity peaks reduces and consequently the two edge peaks move close to each other. Strongest enhancement of the plasmon intensity occurs when the two principal peaks move inward and merge at the ribbon center, as depicted in Fig. 2(c). This mode is regarded as a localized plasmonic mode (1-st order resonance) with high resonant enhanced near-field intensity. Its field amplitude appears to be the sum of the two principal peak amplitudes close to the boundaries, and the corresponding maximum plasmon intensity is about four times larger than that of the two separately boundary peaks in wider ribbons. In Fig. 2(d), we provide another resonant near-field intensity image where the ribbon width is W = 8 nm. This mode is a 0-th order localized resonant plasmonic mode. We define the wavelength of maxima interference of forward and backward propagating SPs to be λ_p, which can be directly obtained by measuring two adjacent peaks from the field intensity image. We can numerically find resonant plasmon mode in a graphene ribbon at wavelength λ_p = λ₀/n_eff, which is about n_eff times smaller than the wavelength of free-space excitation. The remarkable strong reduction in the guided plasmon wavelength can be directly attributed to the 2D nature and the unique conductance properties of graphene. Based on our calculation, n_eff = 375.57 + 5.0777i and 326.17 + 5.8709i are obtained for the 0-th order resonant SPs mode in Fig. 2(d) and 1-st order resonant SPs mode in Fig. 2(c).

 

Fig. 2 Near-field intensity image of the guided resonant graphene SPs in the nanoribbon graphene-silicon waveguide with ribbon width of (a) 100 nm, (b) 50 nm, (c) 16.5 nm and (d) 8 nm under TM polarization illumination. (e) The maximum intensity enhancement distribution at different ribbon width conditions with a fixed incident light wavelength of 6 µm and Fermi level of −0.3 eV. (f) Nanoribbon width distribution of the two SPs modes as a function of Fermi level to satisfy the resonant condition. (g) λ_P and W/λ_P with different Fermi levels at resonances. Solid lines correspond to λ_P. Dashed lines correspond to W/λ_P. Black lines denote the 0-th order resonant SPs mode and red lines denote the 1-st order resonant SPs mode in (f) and (g).

Download Full Size | PDF

With a fixed Fermi level, the SPs resonance in graphene nanoribbon depends on the incident wavelength λ₀ and ribbon width W. We observe the peak enhancements for the two lowest-order resonant SPs modes at W = 8 nm and W = 16.5 nm in Fig. 2(e), when the incident wavelength is fixed to be 6 µm with increasing W. Figure 2(f) indicates the ribbon width as a function of the absolute value of the Fermi level for the two lowest-order resonant SPs modes. By increasing |E_F|, the two resonances still exist for wider nanoribbons. At resonant condition, the wavelength λ_P of the two plasmonic modes in Fig. 2(e) and the corresponding value of ribbon width W normalized to the λ_P are depicted in Fig. 2(g). We extract the resonant conditions to be W ≈0.5 λ_P and 0.9 λ_P for the 0-th and the 1-st order resonant SPs modes, respectively. For the two resonant modes, the calculated λ_P and the corresponding ribbon widths with different Fermi levels as shown in Fig. 2(g) are in reasonable agreement with the theoretical prediction from Eq. (1) and the field intensity image distribution in Figs. 2(a)-2(d). Note that, the optical conductivity of the graphene ribbon layer used here for the dispersion calculation is obtained with the random phase approximation method where the Fermi level is the only variable.

3. Protein permittivity sensing

We validate the proposed nanoribbon graphene-silicon waveguide as a highly sensitive mid-IR biosensor to detect nanoscale thick protein molecules. For the graphene nanoribbon, the guided SPs in the atomic-thick structure leads to significant field confinement and large spatial overlap with the above-cladded analyte. As known to all, protein molecules are the primary material of life which enable most of the biological functions. Here, we use recombinant protein A/G and goat anti-mouse immunoglobulin G (IgG) bilayer to act as the sensing analyte. The protein layer is induced as an 8 nm thick layer possessing Lorentzian complex permittivity [12]. We model mid-IR sensitivity of the protein permittivity above the surface of the graphene nanoribbon structure under the assumption that the ribbon response is dominated by the two lowest-order resonant modes, i.e., 0-th and 1-st order resonant SPs modes, with different Fermi levels.

The maximum intensity enhancements of the two resonant SPs modes at W = 8 nm and W = 16.5 nm of the graphene ribbon with various incident wavelengths are presented in Fig. 3(a) before (solid curves) and after (dashed curves) protein formation, showing significant changes upon protein immobilization. The first observed prominent effect in Fig. 3(a) is the red shift of the plasmonic resonance as a consequence of the variation in the refractive index at the sensor surface. Despite the nanometric-scale protein layer, wavelength red shift of 78 nm and 99 nm for the 0-th (W = 8 nm) and 1-st (W = 16.5 nm) order resonant SPs modes are achieved, upon protein immobilization above with Fermi level of −0.3 eV. The second prominent effect is the severe decrement of the field intensity resulting from the non-perfectly resonant condition and the loss induced by the protein. We expect that this decrement can be utilized to reveal the chemical vibrational modes of the protein. We set the incident wavelength to be 6 µm and turn the Fermi level merely to achieve tunable refractive index sensitivity as plotted in Fig. 3(b). The wavelength shift decreases as Fermi level increases for both of the two resonant conditions. As a result, the sensitivity decreases with increasing Fermi levels. Table 1 summarizes the effective mode indices of the two resonant plasmonic modes without protein layer, which indicates that narrow graphene ribbon is favorable to confine light down to extremely small volume. The strongest reduction in the guided plasmon wavelength occurs at λ_p≈λ₀/375.6, when EF = −0.3 eV and W = 8 nm. This strong electromagnetic field concentration offers increased near-field signal intensity, enhanced forward and backward reflected plasmon interaction and therefore better sensing performance.

 

Fig. 3 (a) Maximum intensity enhancement of the 0-th order resonant SPs mode at W = 8 nm and the 1-st order resonant SPs mode at W = 16.5 nm as a function of the incident wavelength before (solid curves) and after (dashed curves) protein layer formation. (b) At resonant conditions, the wavelength shifts for the two SPs modes with different absolute value of Fermi levels.

Download Full Size | PDF

Table 1. Effective mode index distribution of the guided resonant graphene SPs with different absolute values of Fermi level.

View Table

To extract the capability of graphene SPs in controlling the nanoscale molecule sensing in situ, we set the ribbon width to be 8 nm and 16.5 nm and engineer the Fermi level from −0.3 eV to −0.7 eV at first. For the 0-th order resonant SPs mode at W = 8 nm in Fig. 4(a), with increasing |E_F| from 0.3 eV to 0.7 eV, the resonant wavelength is turned continuously from 6 µm to 3.794 µm. And the wavelength shift (due to the immobilized protein layer) decreases from 78 nm to 54 nm accordingly. For the 1-st order resonant SPs mode at W = 16.5 nm in Fig. 4(a), the resonant wavelength is turned continuously from 6 µm to 3.782 µm and the corresponding wavelength shift decreases from 99 nm to 52 nm. Therefore, the resonant wavelengths of the two resonant SPs modes can both be tuned continuously and the sensitivity reaches to the maximum with Fermi level of −0.3 eV for the 1-st order resonant SPs mode. The above dynamic tunability enables a broad spectrum of biosensing applications over a single graphene ribbon at mid-IR regime by precisely tuning the Fermi levels of graphene.

 

Fig. 4 Resonant wavelength (solid line) and the corresponding wavelength red shift (dash line, due to the above-immobilized protein layer) as a function of |E_F| with dimensions of (a) W = 8 nm, and 16.5 nm and (b) W = 17.6 nm and 36.2 nm. (c)/(d) The distribution of ratio ${\left|E_{\max }^{\text{'}}/E_{\max }\right|}^2$between the two maximum intensity enhancements with and without protein immobilization for the two resonant modes in (a)/(b) at different Fermi levels.

Download Full Size | PDF

Then we further study the sensitivity of the protein chemical vibrations upon the tunable graphene SPs. The ribbon width of W = 8 nm, and 16.5 nm with Fermi level tuned from −0.3 eV to −0.7 eV can only probe the amide II band of the protein. Therefore, we set the Fermi level to be −0.5 eV and the incident wavelength to be 6.5 µm, and calculate the yielded resonant ribbon width of W = 17.6 nm (0-th order resonant SPs mode), and 36.2 nm (1-st order resonant SPs mode) to meet the resonant graphene SPs. With ribbon width of 17.6 nm and 36.2 nm, Fig. 4(b) gives the distributions of the resonant wavelengths and the corresponding wavelength shifts due to the protein formation at different Fermi levels. The variation trend of the resonant wavelength and the corresponding wavelength shift with various Fermi levels are consistent in Figs. 4(a) and 4(b). To probe the protein vibrational modes, we take advantage of intensity decrement induced by the resonant coupling between the resonant graphene SPs and the molecular vibrations. Figures 4(c) and 4(d) show the ratio between the maximum intensity enhancement with and without the protein immobilization for the two resonant SPs modes in Figs. 4(a) and 4(b), respectively. In Fig. 4(d), two apparent dips of intensity enhancement ratio occur at |E_F| of 0.5 eV and 0.6 eV which correspond to the resonant wavelengths (with protein) of 6.56 µm and 5.956 µm for W = 17.6 nm and W = 36.2 nm, as shown in Fig. 4(b). These two additional decrements are induced by the protein vibrational modes as a result of the resonant coupling between the resonant graphene SPs and the molecular vibrations. The two dips at 6.56 µm and 5.956 µm match the amide I (6.527 µm) and II (5.995 µm) bands of the protein [6], explicitly revealing the presence of the protein compounds in a chemically specific manner. Figure 4(c) also confirms that the chemical manner of the protein layer can be detected through slightly tuning the Fermi level of the graphene nanoribbon. The intensity enhancement ratio dip at |E_F| of 0.3 eV in Fig. 4(c) reproduces the amide II band of the protein. Therefore, the proposed resonant graphene SPs biosensor recognize unique protein chemical specificity in mid-IR spectroscopy and provide an extra degree of freedom in the design of graphene-enabled electron-optical tunability for biomolecule sensing.

4. Conclusion

In conclusion, tunable resonant graphene SPs with strong optical field localization and confinement are exploited to resolve the absorbed nanoscale protein molecules. The graphene 2D structure leads to high electric field confinement and large spatial overlap between the mid-IR SPs and the biomolecules. The large resonant spectral shifts and intensity enhancement ratio dips confirm the high sensitivity of the graphene nanoribbon biosensor to the complex permittivity of the nanometric-scale targeted protein molecule. Fermi level controlled resonant SPs in graphene nanostructure and the corresponding sensitivity on the chemical vibrations provide a solution to facilitate the design and miniaturization of the future development of nanoscale biosensing devices with enhanced sensitivity.