Abstract

We have examined graphene absorption in a range of graphene-based infrared devices that combine either monolayer or bilayer graphene with three different gate dielectrics. Electromagnetic simulations show that the optical absorption in graphene in these devices, an important factor in a functional graphene-based detector, is strongly dielectric-dependent. These simulations reveal that plasmonic excitation in graphene can significantly influence the percentage of light absorbed in the entire device, as well as the graphene layer itself, with graphene absorption exceeding 25% in regions where plasmonic excitation occurs. Notably, the dielectric environment of graphene has a dramatic influence on the strength and wavelength range over which the plasmons can be excited, making dielectric choice paramount to final detector tunability and sensitivity.

© 2017 Optical Society of America

1. Introduction

On-chip hyperspectral detection necessitates spectrally-selective sensing. In many cases, this is achieved through the integration of two separate elements: a tunable filter component and a conventional broadband detector [1]. Simplification of this detection paradigm is achievable through the combination of these two elements into a single structure, which performs both sensing and tuning. Owing to its malleable optical response [2,3], graphene presents a direct path towards creation of such a detector where these elements are one and the same, enabling creation of a simplified multispectral solid-state sensor [4–6]. However, as photodetector sensitivity is defined by the magnitude of absorption within the active material, graphene’s atomic thickness, and therefore limited absorption, presents a challenge to creation of a practical graphene-based detector.

To this end, previous studies have demonstrated substantial increases in the photoresponse of graphene detectors through implementation of metallic gratings on the graphene surface [7–10]. Currents excited in these structures yield confined fields at the metal edges concentrating the incident long-wavelength light into the far sub-wavelength graphene thickness. While gratings alone can enhance graphene absorption, they do not directly enable tunability of the resonant response as this is fixed by the geometry of the grating dimensions. However, through careful design of the metallic patterns, external light can be coupled into graphene’s plasmonic response, both further increasing graphene absorption and enabling significant tunability of the wavelength of this absorption [11–14]. Importantly, the plasmonic response is strongly dependent on the graphene carrier concentration, as well as the dielectric environment surrounding graphene, allowing for shifting of the absorption peak through modification of the Fermi-level dependent plasmon dispersion [13,15–19].

In spite of the breadth of work that has been undertaken regarding graphene-based detection, a heuristic design process for multispectral detector optimization has not been presented. In response, we examine tunable absorption using monolayer (MLG) and bilayer (BLG) graphene in conjunction with three different gate dielectrics: SiO2, HfO2, and MgO, to determine how changes to the graphene-dielectric system modify the magnitude and tunability of graphene absorption. Since active material absorption is generally correlated with photodetector sensitivity, we assume that graphene absorption is the primary factor in determining detector capabilities. Simulations of the graphene absorption in each of these devices show that selection of the graphene layer number and gate dielectric is paramount to the design of an effective graphene detector, as interplay between all aspects of the stack ultimately defines device sensitivity and potential for tunability.

2. Simulations

Electromagnetic simulations of a periodic detector structure were performed using COMSOL Multiphysics. One period of the simulated device stack is shown in the inset of Fig. 1. This simple grating-like structure is ideal for comparing the effectiveness of each graphene/dielectric combination and can be used as a guide in designing more complex devices. In all simulations, a dielectric thickness of 50 nm was used with gold contact thickness of 100 nm. An additional benefit of this structure is that, with application of a small bias between alternating gold features, the grating can function as the source and drain electrodes for carrier extraction from the graphene layer. The period of the device was assumed to be 1.2 μm with a graphene channel width of 200 nm. In all simulations, the normally incident light is polarized such that the electric field is perpendicular to the graphene channel. Fully dispersive optical properties of the oxides (shown in Fig. 5), p-doped silicon [20], and gold were measured using spectroscopic ellipsometry while the conductivities of MLG and BLG were calculated using the random phase approximation (RPA) and Slonczewski-Weiss-McClure [17,21–24] models, respectively. While the graphene doping density in graphene devices may not be uniform across the channel due to contact induced doping or non-idealities in the device as compared to a simple parallel plate capacitor, the resulting effects are beyond the scope of this work which focuses on the interaction of graphene plasmonic devices with their dielectric environment. Previous works have examined the influence of non-uniformities in graphene on photocurrent in similar devices [25]. Both MLG and BLG were represented by conductive surface layers at the interface between the dielectric and air, a method that dramatically reduces computation time. A comparison of results employing this surface conductivity model with graphene simulated as a layer of finite thickness showed good agreement, both with each other and with analytical calculations for grating-free planar geometries, supporting the use of this simplified model. The infrared conductivities of MLG and BLG used in our simulations are shown in Fig. 6 for the range of Fermi levels achievable with the examined gate dielectrics, taking into account dielectric DC permittivity and breakdown electric fields, which are presented in Table 1.

 

Fig. 1 Definition of optimization metric variables with graphene absorption plots for Fermi levels of EF = 0.3 and 0.6 eV (black and red respectively) on an MgO gate dielectric. (Inset) Schematic of one period of the simulated device. Graphene is represented by a surface current on the top surface of dielectric.

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Tables Icon

Table 1. Zero-frequency dielectric properties employed in our simulations [26–29]

In the simulated structure, graphene functions as the active material for sensing incident radiation with the two metal pads that define the 200 nm wide graphene channel acting as source and drain contacts for carrier collection. As a result, it is important to quantify the absorption in the graphene layer itself, rather than device absorption. For example, high losses in the metallic elements of the device (gold and doped silicon) can dramatically alter the perceived functionality through increased total absorption. The graphene absorption in our model (Ag) is determined through integration of loss in the graphene layer given by

Ag=1Pinc12σ1(ω)|E(ω)|2da
where σ1 is the real part of the MLG or BLG conductance, E is the electric field at the graphene surface, Pinc is the power incident on the device, and the integral is taken over the entire graphene surface. For a device employing MLG with an SiO2 gate dielectric, the modeled total and graphene absorption are shown in Fig. 2(a) for Fermi levels EF = 0 and 0.4 eV. The percent change in total absorption, A, within the device ΔA/A = (A0.4eV-A0eV)/A0eV is shown in Fig. 2(b) demonstrating the significant effects graphene can have on the total device optical behavior. These results illustrate the importance of directly extracting graphene absorption in the modeling of a graphene detector, as less than 30% of the total absorption occurs in graphene itself, with maxima in graphene absorption for EF = 0.4 eV correlating with local minima in total absorption.

 

Fig. 2 (a) Comparison of the total (solid) and MLG (dotted) absorption in the simulated device at two different graphene Fermi levels of 0 and 0.4 eV. (b) Percent change in total absorption in the device for data shown in (a).

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Using the model described above, we simulate the expected absorption for MLG and BLG as a function of wavelength and graphene Fermi level, as shown in Fig. 3. While these plots display the same range of EF for each dielectric, the realistically achievable Fermi level is limited by remnant charge impurities on the graphene and dielectric surface on the lower end, and by the DC dielectric permittivity and breakdown field on the upper end. The range of accessible Fermi levels are shown by the horizontal white dotted lines in the absorption maps with the impurity concentration being estimated from previous studies and the upper limit being calculated from an ideal capacitive model of the system using the parameters in Table 1 [30]. Present in all maps are peaks of high absorption present at Fermi levels greater than 0.2 eV. These dispersive peaks in absorption are suggestive of plasmon excitation in graphene. To verify the origin of the maxima, we examine the plasmon dispersion of graphene on each of our substrates, which is determined from the momentum- and frequency-dependent reflection coefficient for the stack in the absence of gold contacts. Poles observed in the imaginary part of this reflection coefficient are indicative of collective mode excitation (e.g. graphene plasmons) [31]. The results of these calculations are shown in Fig. 7 for a graphene Fermi level of 0.5 eV. In our structure, the accessible plasmon momentum (qp) is defined by the width of the graphene ribbon, wg, as qp ≈mπ/wg where m is an integer [12]. While previous studies have observed a phase shift at the edges of graphene ribbons, the presence of gold contacts appears to eliminate this phase shift resulting in the momentum noted above. This momentum, for m = 2, is shown as the vertical dotted line in the dispersion plots and defines the plasmon excitation frequency for each Fermi level and dielectric. The Fermi level-dependent absorption peak wavelengths show good agreement with the calculated plasmon dispersions (gray dots in Figs. 3(a)-3(c) and Figs. 5(a)-5(c)), supporting the conclusion of plasmon enhanced absorption.

 

Fig. 3 Maps of the variation in MLG (a)-(c) and BLG (d)-(f) absorption as a function of wavelength and Fermi level with three gate dielectrics: SiO2, HfO2, and MgO. Horizontal white dotted lines show the range of Fermi levels which are expected to be achievable with a given dielectric. Bright features seen in each image are indicative of graphene plasmon excitation and a resulting increase in graphene absorption. Gray dots in the MLG plots indicate the wavelength of plasmon excitation for EF = 0.5 eV corresponding to the plots of the reflection coefficient in the figure below.

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Of note in the dispersion maps are the regions where the plasmonic response is either very weak or absent. These regions are a result of the phonon response of the dielectrics beneath graphene. Plasmon mode splitting occurs at the dielectric phonon frequencies creating an anti-crossing, as seen most clearly in the calculated plasmon dispersion on SiO2, which possesses two phonons in the wavelength range of interest at λ ≈8.4 and 9.4 μm. The presence of these phonons prevents SiO2 from serving as a useful gate dielectric for graphene-plasmon-enabled photodetection in the long-wave IR, creating a “dead zone” from 8 to 10 μm where graphene absorption is minimized (See Figs. 3(a) and 3(d)). In contrast, the highest energy optically active phonons in both HfO2 and MgO are at wavelengths greater than ∼14 μm allowing for a strong graphene plasmonic response throughout the examined infrared range.

3. Analysis

Having established the origin of the absorption peaks, we can examine several key points demonstrated in the maps of Fig. 3. First, MLG absorbs a greater percentage of incident energy than BLG. Second, absorption within the graphene itself can be increased significantly through harnessing of its plasmonic response. Third, dielectric selection dramatically influences the functional operational wavelengths through the interplay between dielectric phonons and the graphene plasmon, with HfO2 devices underperforming SiO2 and MgO devices due to decreased plasmon absorption. Finally, examination of the dispersion of the peaks in Fig. 3 shows that through modification of the graphene Fermi level, the peak absorption can be shifted by more than 2 μm while the magnitude of the absorption stays relatively constant, suggesting the possibility of future creation of a dynamically tunable detector structure.

To more closely inspect each point mentioned above, it is useful to extract horizontal cuts from the maps in Fig. 3. Plots for each graphene-dielectric combination are shown in Fig. 4 for the range of accessible Fermi levels. In this discussion, we focus on SiO2 (Figs. 3(a) and 3(d)) and MgO (Figs. 3(c) and 3(f)) based devices as these show significantly higher graphene absorption than those based on HfO2 (Figs. 3(b) and 3(e)). Prior to discussing these data in detail, we establish the following important parameters: 1) The graphene absorption Apeak, 2) The tunability range Δλpeak, and 3) The full width at half maximum (FWHM), which determines the ability for tuning to discriminate different spectral lines. Each of these parameters, shown in Fig. 1, is vital to the functionality of a tunable detector. For the discussion below we assume that, for creation of a functional tunable photodetector, sensitivity (graphene absorption) must be greater than 10% for reasonable detection efficiency, with a tuning range of ~1 μm.

 

Fig. 4 Cuts of MLG (a)-(c) or BLG (d)-(f) absorption taken horizontally across maps in Fig. 3 demonstrating the resonance wavelength tuning that is achievable when coupling into the graphene plasmon. Differences in magnitude and spectral range are due to the effects of the dielectric on the plasmon excitation wavelength.

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Both monolayer and bilayer graphene have been previously employed in the creation of detector structures [7,32,33]. The full benefits of employing BLG necessitates fabrication of continuously Bernal stacked samples, which allow for opening of an energy gap in the otherwise gapless BLG upon the application of a transverse electric field [17]. Creation of a band gap yields tunability by blocking transitions at light energies smaller than the gap. Unfortunately, in a large-area device as is required for a multi-pixel detector array, such a uniformly stacked BLG sample remains difficult to realize [34]. Given this complication to BLG use, it is necessary to determine what benefits, if any, it contributes as compared to MLG. From the data shown in Fig. 4, it is apparent that no concrete benefits exist to drive development of plasmon-enabled BLG detectors over MLG. Specifically, the simulated absorption of BLG lags behind that of MLG while giving a similar tuning range. This drawback, in combination with the challenges of growing uniform Bernal-stacked BLG, make MLG a more attractive solution for plasmon-enabled graphene detectors. For this reason, we focus on the response of the MLG-based devices shown in Figs. 4 (a)-4(c) for the remainder of this discussion.

For a continuous sheet of graphene (no metallic resonators or patterning of graphene), the graphene absorption is limited to several percent for wavelengths shorter than ~20 μm. However, with the addition of gold structures on the graphene surface, a dramatic increase in absorption is observed. The MLG/SiO2 structure shows the largest enhancement in graphene absorption. As noted above, the phonons present in SiO2 at ~9 μm prevent a strong plasmonic response in the 8-10 μm range. Additionally, plasmonic damping from SiO2 at longer wavelengths results in limited graphene absorption in the lower frequency plasmon branch, with peak absorption of 8% and a FWHM greater than 1 μm, suggesting a weak detector response. In contrast, the shorter wavelength high-frequency plasmon mode displays higher peak absorption with a total tuning range of ~1 μm for accessible Fermi levels. Over this range, graphene absorption remains above 10% with a FWHM of 0.4-0.5 μm. This mode shows high contrast between resonances with variable EF, resulting from the narrow width of this resonance. It is important to note that the FWHM results discussed here may be modified by the inclusion of a non-uniform Fermi level in the graphene sheet, which can result in excitation of graphene plasmons at a range of free-space wavelengths at a given momentum. These characteristics give the SiO2-gated detector greater spectral selectivity than the MgO-based device discussed below, but also limit its effective wavelength range.

While MgO-based devices show weaker absorption than those based on SiO2 they also yield a broader tuning range with resonance variation from 7.2 μm to 9.25 μm, again with graphene absorption greater than 10% and a FWHM of 0.8-1.0 μm. While these parameters suggest that the MgO-based detector may be less sensitive than that based on SiO2, the use of MgO enables access to a wavelength range unachievable with SiO2. Together, these results indicate that for a mid-wave infrared detector SiO2 is the optimal dielectric of choice, while in the long-wave, alternatives, such as MgO, must be considered. Thus, in spite of the superior characteristics of the SiO2-based device, the final choice of dielectric is dependent upon the wavelength range of interest.

4. Conclusion

While the device geometry studied in this work is simple, it allows us to demonstrate a path towards design of improved graphene-based detectors. Such simple devices can be employed as testing grounds for more complicated structures while easing simulation and fabrication loads. Our results demonstrate the importance of the graphene environment and detector structure on the overall functionality including sensitivity and tuning range. This work builds towards future development of enhanced sensing and tunable detector paradigms enabled by the unique properties of graphene.

Appendix A Dielectric properties

The zero-frequency dielectric properties of SiO2, HfO2, and MgO are shown in Table 1. These parameters were used to calculate the maximum possible Fermi level (EF) achievable in MLG for each dielectric. In all cases, a perfect capacitive model of the system was employed where n is given by

n=κε0qdV=κε0qE=EF2π2vF2
with κ being the dielectric constant of the gate oxide, ϵ0 the vacuum permittivity, q the electron charge, and d the thickness of the oxide, V the applied voltage, E is the electric field across the dielectric, ℏ is the reduced Plank constant, and vF is the graphene Fermi velocity. For frequency-dependent calculations (i.e. plasmon dispersion calculations), the ellipsometrically measured frequency-dependent optical properties shown in Fig. 5 were used.

 

Fig. 5 Measured real part of the optical permittivity of the three dielectrics used in our simulations.

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Appendix B Graphene conductivity

For monolayer graphene, the optical conductivity was calculated using the random phase approximation with a scattering rate of 90 cm−1, corresponding to a mobility μ∼2000 cm2/V⋅s. This scattering rate was chosen as a representative value of what is achievable for chemical-vapor-deposition-grown graphene on granular dielectrics where topographic variation can have a deleterious effect on the graphene mobility and scattering time. For the case of bilayer graphene, the optical conductivity was calculated using the Slonczewski-Weiss-McClure model as described in [23]. The complex optical conductivities calculated from these models are shown in Fig. 6.

 

Fig. 6 Real optical conductivity for MLG (a) and BLG (b). Imaginary optical conductivity for MLG (c) and BLG (d).

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Appendix C Plasmon dispersion

The expected plasmon dispersion of our graphene/dielectric system was visualized by calculating the momentum-dependent imaginary part of the reflection coefficient of the device. Poles in these maps determine the frequency-momentum dispersion of collective modes in the system corresponding to plasmonic excitation [31]. The calculated reflection coefficients for p-polarized light with each dielectric are shown in Fig. 7 for graphene with a Fermi energy EF = 0.5 eV.

 

Fig. 7 Maps of the reflection coefficient for (a) SiO2, (b) HfO2, and (c) MgO with maxima corresponding to graphene plasmon excitation with graphene EF = 0.5 eV. The vertical dotted lines indicate the momentum excited in our system due to graphene’s finite width. Gray dots correspond to the wavelength of plasmon excitation expected for a device with a graphene channel width of 200 nm where qp = 2π/wg where wg is the graphene channel width.

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Funding

Sandia National Laboratories (DE-NA0003525).

Acknowledgment

The authors wish to acknowledge L.M. Zhang for theoretical support. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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References

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  1. N. Gat, “Imaging spectroscopy using tunable filters: A review,” Proc. SPIE 4056, 50–64 (2000).
    [Crossref]
  2. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
    [Crossref]
  3. K. F. Mak, L. Ju, F. Wang, and T. F. Heinz, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
    [Crossref]
  4. F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
    [Crossref] [PubMed]
  5. D. E. Aznakayeva, F. J. Rodriguez, O. P. Marshall, and A. N. Grigorenko, “Graphene light modulators working at near-infrared wavelengths,” Opt. Express 25(9), 10255–10260 (2017).
    [Crossref] [PubMed]
  6. Y. Su, Z. Guo, W. Huang, Z. Liu, T. Gong, Y. He, and B. Yu, “Ultra-sensitive graphene photodetector with plasmonic structure,” Appl. Phys. Lett. 109(17), 173107 (2016).
    [Crossref]
  7. F. H. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
    [Crossref] [PubMed]
  8. Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
    [Crossref] [PubMed]
  9. T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
    [Crossref] [PubMed]
  10. Y. Wu, J. Niu, M. Danesh, J. Liu, Y. Chen, L. Ke, C. Qiu, and H. Yang, “Localized surface plasmon resonance in graphene nanomesh with Au nanostructures,” Appl. Phys. Lett. 109(4), 041106 (2016).
    [Crossref]
  11. V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
    [Crossref] [PubMed]
  12. V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
    [Crossref] [PubMed]
  13. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
    [PubMed]
  14. H.-J. Li, L.-L. Wang, B. Sun, Z.-R. Huang, and X. Zhai, “Tunable mid-infrared plasmonic band-pass filter based on a single graphene sheet with cavities,” J. Appl. Phys. 116(22), 224505 (2014).
    [Crossref]
  15. M. D. Goldflam, G. X. Ni, K. W. Post, Z. Fei, Y. Yeo, J. Y. Tan, A. S. Rodin, B. C. Chapler, B. Özyilmaz, A. H. Castro Neto, M. M. Fogler, and D. N. Basov, “Tuning and Persistent Switching of Graphene Plasmons on a Ferroelectric Substrate,” Nano Lett. 15(8), 4859–4864 (2015).
    [Crossref] [PubMed]
  16. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
    [PubMed]
  17. Z. Fei, E. G. Iwinski, G. X. Ni, L. M. Zhang, W. Bao, A. S. Rodin, Y. Lee, M. Wagner, M. K. Liu, S. Dai, M. D. Goldflam, M. Thiemens, F. Keilmann, C. N. Lau, A. H. Castro-Neto, M. M. Fogler, and D. N. Basov, “Tunneling Plasmonics in Bilayer Graphene,” Nano Lett. 15(8), 4973–4978 (2015).
    [Crossref] [PubMed]
  18. M. Jablan and D. E. Chang, “Multiplasmon Absorption in Graphene,” Phys. Rev. Lett. 114(23), 236801 (2015).
    [Crossref] [PubMed]
  19. H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
    [Crossref]
  20. J. C. Ginn, R. L. Jarecki, E. A. Shaner, and P. S. Davids, “Infrared plasmons on heavily-doped silicon,” J. Appl. Phys. 110(4), 043110 (2011).
    [Crossref]
  21. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007).
    [Crossref]
  22. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8(12), 318 (2006).
    [Crossref]
  23. L. M. Zhang, Z. Q. Li, D. N. Basov, M. M. Fogler, Z. Hao, and M. C. Martin, “Determination of the electronic structure of bilayer graphene from infrared spectroscopy,” Phys. Rev. B 78(23), 235408 (2008).
    [Crossref]
  24. L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
    [Crossref]
  25. F. Léonard, C. D. Spataru, M. Goldflam, D. W. Peters, and T. E. Beechem, “Dynamic Wavelength-Tunable Photodetector Using Subwavelength Graphene Field-Effect Transistors,” Sci. Rep. 8, 45873 (2017).
    [Crossref] [PubMed]
  26. J. Robertson, “High dielectric constant oxides,” Eur. Phys. J. Appl. Phys. 28(3), 265–291 (2004).
    [Crossref]
  27. G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
    [Crossref]
  28. J. Yota, H. Shen, and R. Ramanathan, “Characterization of atomic layer deposition HfO2, Al2O3, and plasma-enhanced chemical vapor deposition Si3N4 as metal-insulator-metal capacitor dielectric for GaAs HBT technology,” J. Vac. Sci. Technol. A 31(1), 01A134 (2013).
    [Crossref]
  29. M. A. Subramanian, R. D. Shannon, B. H. T. Chai, M. M. Abraham, and M. C. Wintersgill, “Dielectric constants of BeO, MgO, and CaO using the two-terminal method,” Phys. Chem. Miner. 16(8), 741–746 (1989).
    [Crossref]
  30. S. Adam, E. H. Hwang, V. M. Galitski, and S. Das Sarma, “A self-consistent theory for graphene transport,” Proc. Natl. Acad. Sci. U.S.A. 104(47), 18392–18397 (2007).
    [Crossref] [PubMed]
  31. Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, S. M. A. C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO(2) interface,” Nano Lett. 11, 4701–4705 (2011).
    [Crossref] [PubMed]
  32. V. Ryzhii and M. Ryzhii, “Graphene bilayer field-effect phototransistor for terahertz and infrared detection,” Phys. Rev. B 79(24), 245311 (2009).
    [Crossref]
  33. F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
    [Crossref] [PubMed]
  34. Y. Hao, L. Wang, Y. Liu, H. Chen, X. Wang, C. Tan, S. Nie, J. W. Suk, T. Jiang, T. Liang, J. Xiao, W. Ye, C. R. Dean, B. I. Yakobson, K. F. McCarty, P. Kim, J. Hone, L. Colombo, and R. S. Ruoff, “Oxygen-activated growth and bandgap tunability of large single-crystal bilayer graphene,” Nat. Nanotechnol. 11(5), 426–431 (2016).
    [Crossref] [PubMed]

2017 (2)

D. E. Aznakayeva, F. J. Rodriguez, O. P. Marshall, and A. N. Grigorenko, “Graphene light modulators working at near-infrared wavelengths,” Opt. Express 25(9), 10255–10260 (2017).
[Crossref] [PubMed]

F. Léonard, C. D. Spataru, M. Goldflam, D. W. Peters, and T. E. Beechem, “Dynamic Wavelength-Tunable Photodetector Using Subwavelength Graphene Field-Effect Transistors,” Sci. Rep. 8, 45873 (2017).
[Crossref] [PubMed]

2016 (3)

Y. Hao, L. Wang, Y. Liu, H. Chen, X. Wang, C. Tan, S. Nie, J. W. Suk, T. Jiang, T. Liang, J. Xiao, W. Ye, C. R. Dean, B. I. Yakobson, K. F. McCarty, P. Kim, J. Hone, L. Colombo, and R. S. Ruoff, “Oxygen-activated growth and bandgap tunability of large single-crystal bilayer graphene,” Nat. Nanotechnol. 11(5), 426–431 (2016).
[Crossref] [PubMed]

Y. Su, Z. Guo, W. Huang, Z. Liu, T. Gong, Y. He, and B. Yu, “Ultra-sensitive graphene photodetector with plasmonic structure,” Appl. Phys. Lett. 109(17), 173107 (2016).
[Crossref]

Y. Wu, J. Niu, M. Danesh, J. Liu, Y. Chen, L. Ke, C. Qiu, and H. Yang, “Localized surface plasmon resonance in graphene nanomesh with Au nanostructures,” Appl. Phys. Lett. 109(4), 041106 (2016).
[Crossref]

2015 (3)

Z. Fei, E. G. Iwinski, G. X. Ni, L. M. Zhang, W. Bao, A. S. Rodin, Y. Lee, M. Wagner, M. K. Liu, S. Dai, M. D. Goldflam, M. Thiemens, F. Keilmann, C. N. Lau, A. H. Castro-Neto, M. M. Fogler, and D. N. Basov, “Tunneling Plasmonics in Bilayer Graphene,” Nano Lett. 15(8), 4973–4978 (2015).
[Crossref] [PubMed]

M. Jablan and D. E. Chang, “Multiplasmon Absorption in Graphene,” Phys. Rev. Lett. 114(23), 236801 (2015).
[Crossref] [PubMed]

M. D. Goldflam, G. X. Ni, K. W. Post, Z. Fei, Y. Yeo, J. Y. Tan, A. S. Rodin, B. C. Chapler, B. Özyilmaz, A. H. Castro Neto, M. M. Fogler, and D. N. Basov, “Tuning and Persistent Switching of Graphene Plasmons on a Ferroelectric Substrate,” Nano Lett. 15(8), 4859–4864 (2015).
[Crossref] [PubMed]

2014 (3)

H.-J. Li, L.-L. Wang, B. Sun, Z.-R. Huang, and X. Zhai, “Tunable mid-infrared plasmonic band-pass filter based on a single graphene sheet with cavities,” J. Appl. Phys. 116(22), 224505 (2014).
[Crossref]

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

F. H. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
[Crossref] [PubMed]

2013 (3)

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
[Crossref] [PubMed]

H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

J. Yota, H. Shen, and R. Ramanathan, “Characterization of atomic layer deposition HfO2, Al2O3, and plasma-enhanced chemical vapor deposition Si3N4 as metal-insulator-metal capacitor dielectric for GaAs HBT technology,” J. Vac. Sci. Technol. A 31(1), 01A134 (2013).
[Crossref]

2012 (3)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

K. F. Mak, L. Ju, F. Wang, and T. F. Heinz, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
[Crossref]

2011 (5)

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
[Crossref] [PubMed]

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref] [PubMed]

J. C. Ginn, R. L. Jarecki, E. A. Shaner, and P. S. Davids, “Infrared plasmons on heavily-doped silicon,” J. Appl. Phys. 110(4), 043110 (2011).
[Crossref]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, S. M. A. C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO(2) interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

2009 (2)

V. Ryzhii and M. Ryzhii, “Graphene bilayer field-effect phototransistor for terahertz and infrared detection,” Phys. Rev. B 79(24), 245311 (2009).
[Crossref]

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

2008 (3)

L. M. Zhang, Z. Q. Li, D. N. Basov, M. M. Fogler, Z. Hao, and M. C. Martin, “Determination of the electronic structure of bilayer graphene from infrared spectroscopy,” Phys. Rev. B 78(23), 235408 (2008).
[Crossref]

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

2007 (2)

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007).
[Crossref]

S. Adam, E. H. Hwang, V. M. Galitski, and S. Das Sarma, “A self-consistent theory for graphene transport,” Proc. Natl. Acad. Sci. U.S.A. 104(47), 18392–18397 (2007).
[Crossref] [PubMed]

2006 (1)

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8(12), 318 (2006).
[Crossref]

2004 (1)

J. Robertson, “High dielectric constant oxides,” Eur. Phys. J. Appl. Phys. 28(3), 265–291 (2004).
[Crossref]

2001 (1)

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
[Crossref]

2000 (1)

N. Gat, “Imaging spectroscopy using tunable filters: A review,” Proc. SPIE 4056, 50–64 (2000).
[Crossref]

1989 (1)

M. A. Subramanian, R. D. Shannon, B. H. T. Chai, M. M. Abraham, and M. C. Wintersgill, “Dielectric constants of BeO, MgO, and CaO using the two-terminal method,” Phys. Chem. Miner. 16(8), 741–746 (1989).
[Crossref]

Abraham, M. M.

M. A. Subramanian, R. D. Shannon, B. H. T. Chai, M. M. Abraham, and M. C. Wintersgill, “Dielectric constants of BeO, MgO, and CaO using the two-terminal method,” Phys. Chem. Miner. 16(8), 741–746 (1989).
[Crossref]

Adam, S.

S. Adam, E. H. Hwang, V. M. Galitski, and S. Das Sarma, “A self-consistent theory for graphene transport,” Proc. Natl. Acad. Sci. U.S.A. 104(47), 18392–18397 (2007).
[Crossref] [PubMed]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, S. M. A. C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO(2) interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Anthony, J. M.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” J. Appl. Phys. 89(10), 5243–5275 (2001).
[Crossref]

Atwater, H.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
[Crossref] [PubMed]

Avouris, P.

F. H. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
[Crossref] [PubMed]

H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

Aznakayeva, D. E.

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Bai, J.

Y. Liu, R. Cheng, L. Liao, H. Zhou, J. Bai, G. Liu, L. Liu, Y. Huang, and X. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2, 579 (2011).
[Crossref] [PubMed]

Bao, W.

Z. Fei, E. G. Iwinski, G. X. Ni, L. M. Zhang, W. Bao, A. S. Rodin, Y. Lee, M. Wagner, M. K. Liu, S. Dai, M. D. Goldflam, M. Thiemens, F. Keilmann, C. N. Lau, A. H. Castro-Neto, M. M. Fogler, and D. N. Basov, “Tunneling Plasmonics in Bilayer Graphene,” Nano Lett. 15(8), 4973–4978 (2015).
[Crossref] [PubMed]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, S. M. A. C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO(2) interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Basov, D. N.

M. D. Goldflam, G. X. Ni, K. W. Post, Z. Fei, Y. Yeo, J. Y. Tan, A. S. Rodin, B. C. Chapler, B. Özyilmaz, A. H. Castro Neto, M. M. Fogler, and D. N. Basov, “Tuning and Persistent Switching of Graphene Plasmons on a Ferroelectric Substrate,” Nano Lett. 15(8), 4859–4864 (2015).
[Crossref] [PubMed]

Z. Fei, E. G. Iwinski, G. X. Ni, L. M. Zhang, W. Bao, A. S. Rodin, Y. Lee, M. Wagner, M. K. Liu, S. Dai, M. D. Goldflam, M. Thiemens, F. Keilmann, C. N. Lau, A. H. Castro-Neto, M. M. Fogler, and D. N. Basov, “Tunneling Plasmonics in Bilayer Graphene,” Nano Lett. 15(8), 4973–4978 (2015).
[Crossref] [PubMed]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, S. M. A. C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO(2) interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

L. M. Zhang, Z. Q. Li, D. N. Basov, M. M. Fogler, Z. Hao, and M. C. Martin, “Determination of the electronic structure of bilayer graphene from infrared spectroscopy,” Phys. Rev. B 78(23), 235408 (2008).
[Crossref]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Beechem, T. E.

F. Léonard, C. D. Spataru, M. Goldflam, D. W. Peters, and T. E. Beechem, “Dynamic Wavelength-Tunable Photodetector Using Subwavelength Graphene Field-Effect Transistors,” Sci. Rep. 8, 45873 (2017).
[Crossref] [PubMed]

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
[Crossref] [PubMed]

Britnell, L.

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
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Camara, N.

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Y. Wu, J. Niu, M. Danesh, J. Liu, Y. Chen, L. Ke, C. Qiu, and H. Yang, “Localized surface plasmon resonance in graphene nanomesh with Au nanostructures,” Appl. Phys. Lett. 109(4), 041106 (2016).
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V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
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H. G. Yan, T. Low, W. J. Zhu, Y. Q. Wu, M. Freitag, X. S. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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K. F. Mak, L. Ju, F. Wang, and T. F. Heinz, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
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Martin, M. C.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
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F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
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Figures (7)

Fig. 1
Fig. 1 Definition of optimization metric variables with graphene absorption plots for Fermi levels of EF = 0.3 and 0.6 eV (black and red respectively) on an MgO gate dielectric. (Inset) Schematic of one period of the simulated device. Graphene is represented by a surface current on the top surface of dielectric.
Fig. 2
Fig. 2 (a) Comparison of the total (solid) and MLG (dotted) absorption in the simulated device at two different graphene Fermi levels of 0 and 0.4 eV. (b) Percent change in total absorption in the device for data shown in (a).
Fig. 3
Fig. 3 Maps of the variation in MLG (a)-(c) and BLG (d)-(f) absorption as a function of wavelength and Fermi level with three gate dielectrics: SiO2, HfO2, and MgO. Horizontal white dotted lines show the range of Fermi levels which are expected to be achievable with a given dielectric. Bright features seen in each image are indicative of graphene plasmon excitation and a resulting increase in graphene absorption. Gray dots in the MLG plots indicate the wavelength of plasmon excitation for EF = 0.5 eV corresponding to the plots of the reflection coefficient in the figure below.
Fig. 4
Fig. 4 Cuts of MLG (a)-(c) or BLG (d)-(f) absorption taken horizontally across maps in Fig. 3 demonstrating the resonance wavelength tuning that is achievable when coupling into the graphene plasmon. Differences in magnitude and spectral range are due to the effects of the dielectric on the plasmon excitation wavelength.
Fig. 5
Fig. 5 Measured real part of the optical permittivity of the three dielectrics used in our simulations.
Fig. 6
Fig. 6 Real optical conductivity for MLG (a) and BLG (b). Imaginary optical conductivity for MLG (c) and BLG (d).
Fig. 7
Fig. 7 Maps of the reflection coefficient for (a) SiO2, (b) HfO2, and (c) MgO with maxima corresponding to graphene plasmon excitation with graphene EF = 0.5 eV. The vertical dotted lines indicate the momentum excited in our system due to graphene’s finite width. Gray dots correspond to the wavelength of plasmon excitation expected for a device with a graphene channel width of 200 nm where qp = 2π/wg where wg is the graphene channel width.

Tables (1)

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Table 1 Zero-frequency dielectric properties employed in our simulations [26–29]

Equations (2)

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A g= 1 P inc 1 2 σ 1 (ω)| E (ω) | 2 da
n= κ ε 0 qd V= κ ε 0 q E= E F 2 π 2 v F 2

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