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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25452–25466
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Design and analysis of a silicon-based terahertz plasmonic switch

Mohammad Ali Khorrami and Samir El-Ghazaly  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 25452-25466 (2013)
http://dx.doi.org/10.1364/OE.21.025452


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Abstract

In this paper, a novel terahertz (THz) plasmonic switch is designed and simulated. The device consists of a periodically corrugated n-type doped silicon wafer covered with a metallic layer. Surface plasmon propagation along the structure is controlled by applying a control voltage onto the metal. As will be presented, the applied voltage can effectively alter the width of the depletion layer appeared between the deposited metal and the semiconductor. In this manner, the conductivity of the silicon substrate can be successfully controlled due to the absence of free electrons at the depleted sections. Afterwards, the effectiveness of the proposed plasmonic switch is enhanced by implementing a p++-type doped well beneath the metallic indentation edges. Consequently, a P-Intrinsic-N diode is formed which can manipulate the plasmon propagation by modifying the electron and hole densities inside the intrinsic area. The simulation results are explained very concisely by the help of scattering matrix formalism. Such a representation is essential as employing the switches in the design of complex plasmonic systems with many interacting parts.

© 2013 Optical Society of America

1. Introduction

The terahertz frequency band, located between microwave and optical ranges is considered to be a promising section of the electromagnetic (EM) spectrum. THz radiation with uniquely attractive characteristics has been employed in laboratory demonstrations to identify explosives, find hidden weapons, and detect cancer cells and tooth decays [1

1. C. M. Armstrong, “The truth about terahertz,” IEEE Spectr. 49(9), 36–41 (2012). [CrossRef]

]. In spite of these laboratory level researches, the real world application of THz radiation has proven to be challenging. One of the major pitfalls in the commercial application of THz radiation is the lack of room temperature active devices as modulators, switches, sources and detectors. In recent years, there have been considerable efforts to employ novel devices based on the collective oscillations of electrons mostly called plasmons, in the THz frequency range [2

2. C. W. Berry, N. Wang, M. R. Hashemi, M. Unlu, and M. Jarrahi, “Significant performance enhancement in photoconductive terahertz optoelectronics by incorporating plasmonic contact electrodes,” Nat Commun 4, 1622 (2013). [CrossRef] [PubMed]

8

8. M. A. Khorrami, S. El-Ghazaly, S. Q. Yu, and H. Naseem, “Analytical modeling of THz wave propagation inside ungated two dimensional electron gas layers,” IEEE MTT-S Int. Microwave Symp. Dig.,Baltimore, USA (2011).

]. Specifically, plasmonic materials formed by the periodical texturing of metal or highly doped semiconductor surfaces have been extensively studied and applied in microwave and THz frequency ranges [9

9. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

20

20. Z. Xu, K. Song, and P. Mazumder, “Dynamic terahertz spoof surface plasmon-polariton switch based on resonance and absorption,” IEEE Trans. Electron. Dev. 58(7), 2172–2176 (2011). [CrossRef]

]. These structures can support surface waves which are mostly called Spoofed Surface Plasmon Polaritons (SSPPs), since they mimic the properties of surface plasmon polaritons at visible frequencies. Recently, there has been an increasing interest in exploiting SSPPs because of their unique properties as high field confinement and comparatively low propagation losses [9

9. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

12

12. B. Wang, L. Liu, and S. He, “Propagation loss of terahertz surface plasmon polaritons on a periodically structured Ag surface,” J. Appl. Phys. 104(10), 103531 (2008). [CrossRef]

].

The idea of changing the wave properties of a plasmonic waveguide by heating to modulate plasmons was first coined in [21

21. A. V. Krasavin and N. Zheludev, “Active plasmonics: Controlling signals in Au/Ga waveguide using nanoscale structural transformations,” Appl. Phys. Lett. 84(8), 1416–1418 (2004).

] and applied in the visible frequency range. Subsequently, reversible variations in the waveguide characteristics caused by femto-second optical excitation have been employed to develop faster and more efficient plasmonic switches and modulators [22

22. K. F. MacDoland, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009). [CrossRef]

]. In terahertz frequency range, the optical and thermal control of the SSPP propagation along the surfaces of indented doped semiconductors has been investigated in [16

16. J. Gomez Rivas, J. A. Sanchez-Gil, M. Kuttge, P. H. Bolivar, and H. Kurz, “Optically switchable mirrors for surface plasmon polaritons propagating on semiconductor surfaces,” Phys. Rev. B 74(24), 245324 (2006). [CrossRef]

,17

17. J. A. Sanchez-Gil and J. G. Rivas, “Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces,” Phys. Rev. B 73(20), 205410 (2006). [CrossRef]

]. Recently, a terahertz plasmonic switch implemented inside a metallic surface with a periodic array of grooves filled with an electro-optical material is proposed in [19

19. K. Song and P. Mazmuder, “Active terahertz spoof surface plasmon polariton switch comprising the perfect conductor metamaterial,” IEEE Trans. on Elect. Devices 56(11), 2792–2799 (2009). [CrossRef]

,20

20. Z. Xu, K. Song, and P. Mazumder, “Dynamic terahertz spoof surface plasmon-polariton switch based on resonance and absorption,” IEEE Trans. Electron. Dev. 58(7), 2172–2176 (2011). [CrossRef]

]. It is shown that the incorporation of the electro-optical material such as Nematic Liquid Crystal (LC), with controllable refractive index into the plasmonic gap provides a compact and efficient THz switch. However, the switching speed of the logic blocks developed based on the LC based gates or the ones with the thermally controlled plasmonic waveguides are undesirably low. Besides, the device implementation and wiring of such a gate is difficult [20

20. Z. Xu, K. Song, and P. Mazumder, “Dynamic terahertz spoof surface plasmon-polariton switch based on resonance and absorption,” IEEE Trans. Electron. Dev. 58(7), 2172–2176 (2011). [CrossRef]

]. In spite of short response times, the modulators with optical manipulation of SSPPs require a separate high power source for an efficient operation.

To avoid the above mentioned fabrication difficulties and to increase the switching speed of future terahertz plasmonic active devices, the application of doped semiconductors instead of the LCs is proposed here. As widely known, the conductivity of a semiconductor is dependent upon the number of the free charges which can be controlled by different mechanism as light illumination and electrical doping [23

23. Y. Urzhumov, J. S. Lee, T. Tyler, S. Dhar, V. Nguyen, N. M. Jokerst, P. Schmalenberg, and D. R. Smith, “Electronically reconfigurable metal-on-silicon metamaterial,” Phys. Rev. B 86(7), 075112 (2012). [CrossRef]

]. While photo-doping is a fast and effective approach for many applications, the significant amount of the conductivity modulation required in active plasmonic devices necessitates large incident optical powers which are impractical in many applications. Alternatively, the doping level within a semiconductor can be varied via the application of a voltage across an appropriately designed metal-semiconductor (Schottky) junction [23

23. Y. Urzhumov, J. S. Lee, T. Tyler, S. Dhar, V. Nguyen, N. M. Jokerst, P. Schmalenberg, and D. R. Smith, “Electronically reconfigurable metal-on-silicon metamaterial,” Phys. Rev. B 86(7), 075112 (2012). [CrossRef]

]. This is due to the variations of the depletion region width that exists along the metal-semiconductor interface. In this manner, the conductivity of the semiconductor can be manipulated by changing the bias voltage. The semiconductor conductivity can be regulated more effectively by implanting different doping levels and types (p or n) in various locations within the structure. For instance, depositing a thin layer of highly p++-type doped silicon inside an intrinsic silicon wafer with an n++-type doped back gate can establish a PIN (P-Intrinsic-N) diode. The existence of the PIN diode makes the manipulation of the silicon conductivity possible with the aid of electron and holes, simultaneously.

In this paper, we propose a THz plasmonic modulator implemented inside a corrugated silicon substrate covered with a platinum layer. By applying the bias voltage on the doped silicon-platinum junction, the wave propagation along the waveguide is controlled. The design starts with a finite element solution of the well-known drift-diffusion and Poisson equations to calculate the charge distribution inside the device. Next, Drude model is employed to estimate the doped silicon conductivity from the calculated charge densities. Afterwards, a full wave commercial simulator [24

24. Ansoft HFSS, Ansys Inc., Pittsburg, PA.

] is used to characterize the surface wave propagation along the structure. This simulation is repeated as the silicon conductivity is varied by applying various bias voltages across the junction. This characterization is performed in a wide frequency range located at terahertz regime (200 GHz- 320 GHz). However, the device is aimed to operate efficiently at a specific frequency range (250 GHz – 320 GHz).To concisely present the results, the scattering matrix formulation of the non-TEM plasmonic mode is developed. Finally, a more sophisticated design is introduced that employs a PIN diode to electrically modify the doping density of the silicon substrate.

2. The structure of the proposed THz plasmonic switch

As demonstrated in [9

9. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

12

12. B. Wang, L. Liu, and S. He, “Propagation loss of terahertz surface plasmon polaritons on a periodically structured Ag surface,” J. Appl. Phys. 104(10), 103531 (2008). [CrossRef]

], a periodically corrugated metallic layer is able to carry EM surface waves with TMx mode characteristics at terahertz frequency ranges. An example of this structure is depicted in Fig. 1
Fig. 1 A front view of the proposed plasmonic THz switch and input and output plasmonic waveguides. The switch and the waveguides are respectively designed inside the doped and un-doped sections of a silicon wafer with thickness t1 = 160 µm indented with periodic holes with repetition d = 30 µm, in distances a = 24 µm and height h = 60 µm.
. It includes a silicon wafer (deliberately doped at a specific section) with relative permittivity εr, tailored with linearly spaced grooves which are filled with a metal. The electric and magnetic field components and the wave vector of the TMx mode are also depicted in Fig. 1. Generally, the field variations of the TMx mode at frequency “f”, follows the exponential function exp (jωt – jßx – δ (y–h–t2)); where, ω = 2πf, β and δ, h and t2 are angular frequency, phase and attenuation constants along x and y directions, indentation height and metallic layer thickness, respectively. As proved in [10

10. S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007), pp. 93–100.

] for the case of periodically grooved metal surface with sharp edge indentations, the dispersion relation of the fundamental plasmonic mode is:
β2k2siksi=S20tan(ksih),k=ωεrc
(1)
as λsi a, d and where:
S0=adsinc(β×a2),
(2)
δ=±β2-ksi2and λsi = 2π / ksi. In Eq. (1) and Eq. (2), c and, ksi and λsi are the speed of light in vacuum (m/s) and the phase constant and wavelength of the radiating mode inside the silicon wafer, respectively. Additionally, the TMx mode wave impedance along x is defined as Zx = β / (ω × ε) [25

25. C. A. Balanis, Advanced Engineering Electromagnetics, 1rd edition (John Wiley & Sons, 1989).

], where the silicon permittivity is ε = εr × ε00 ≈8.85 × 10−12 F/m). Using Eq. (1), it can be concluded that SSPPs (with β ≥ ksi) are only allowed to propagate along the grooved metal as tan (ksi × h) > 1. Therefore, SSPPs are not bounded to the metal-semiconductor interface at z = (-h – t2) as f>fr=c/(4hεr), where fr is called the resonant frequency herein. Thus, fr sets the upper limit for the operating frequency bandwidth of the plasmonic structure. As taking Ohmic and dielectric losses into account, the phase constant (j β) within the wave function is substitute with γ = α + j β where, α is the fundamental mode attenuation constants along x. Moreover, the TMx wave impedance along x is re-defined as: Zx = γ / (j ω ε) [25

25. C. A. Balanis, Advanced Engineering Electromagnetics, 1rd edition (John Wiley & Sons, 1989).

]. Considering the well-known Helmholtz equation [25

25. C. A. Balanis, Advanced Engineering Electromagnetics, 1rd edition (John Wiley & Sons, 1989).

]:
γ2+δ2+ω2c2×εr=0,
(3)
it is understood that the fundamental mode is mainly confined in the proximity of the metal edges as λsi λ = 2 × π / β. In addition to the fundamental mode, higher order modes excited due to the wave diffraction at the edges also exist in the proximity of the indented surface.

As shown in Fig. 1, the edges of the holes located inside the wafer are considered to be rounded with radius “r”. The width of the structures along z axis is considered to be at least an order of magnitude larger than the desired plasmonic mode wavelength. Therefore, a 2D solution of the electromagnetic and charge transport equations can obtain accurate results. In order to control the width of the Schottky contact depletion region, an external control voltage Va is applied between the Schottky and Ohmic contacts. In this manner, the conductivity of the doped silicon substrate is externally controlled. As the Schottky diode is under forward bias condition (switch is in the OFF mode), SSPPs suffer from large attenuations as propagating along the device. On the other hand, plasmons face less attenuation as the diode is reversely biased (switch is in the ON mode). To reduce the insertion losses of the switch in the ON mode, it is favorable to increase the width of the depleted area. However, the width is restricted to a maximum allowable reverse voltage. This limit corresponds to the silicon breakdown condition that happens as the total magnitude of electric field is larger than the 3×105 V/cm. The consideration of the rounded edges in the simulation allows us to apply higher reverse bias voltages onto the Schottky junction compared to the right angle ones, without reaching the breakdown limit of the silicon substrate.

3. The simulation details

In order to completely capture the electron-wave interactions inside the proposed plasmonic switch, a set of electronic transport and wave equations ought to be solved. The simulation of the charge transport inside the semiconductor device is accomplished by solving the well-known steady-state Drift-Diffusion equations. Moreover, Maxwell equations can completely describe the wave propagation inside the plasmonic device. In this section, the details of the electronic transport and the full simulations are described.

3.1 The charge transport model

In the developed model, Shockley-Read-Hall formulation with the electron-hole recombination rate:
R=n×pn2iτp(n+ni)+τn(p+ni).
(4)
is employed. In Eq. (4), ni = 1.45 × 1010 cm−3, τn and τp = 10−7 (s) are silicon intrinsic carrier concentration, electron and hole lifetimes, respectively. The set of three differential equations (two drift-diffusion equations for electron and hole densities and the Poisson equation) are solved numerically as considering specific boundary conditions over the computational domain. Here, constant values of electron “n” and hole “p” densities are considered at the location of the Ohmic contact. This is correct as presuming infinite carrier recombination velocities at the contact. Furthermore, the electrostatic potential of the boundaries adjacent to the Ohmic and Schottky contacts are:
φSchottky=Va+kTqln(nni)φBandφOhmic=kTqln(nni),
(5)
respectively. In Eq. (5), T = 300 (K), q = 1.602 × 10−19 (C), φB = 0.83 (eV) and k=1.38×10-23 (J / K) are the room temperature, unit charge, Pt/Si barrier height [23

23. Y. Urzhumov, J. S. Lee, T. Tyler, S. Dhar, V. Nguyen, N. M. Jokerst, P. Schmalenberg, and D. R. Smith, “Electronically reconfigurable metal-on-silicon metamaterial,” Phys. Rev. B 86(7), 075112 (2012). [CrossRef]

] and Boltzmann constant, respectively. The carrier densities beneath the Schottky contacts formed between the deposited Pt layer and the wafer in Fig. 1 are n = Nc × exp(q φB / kT) and p = ni2 / n where, Nc = 2.82 × 1019 (cm−3) is effective density of states at the silicon conduction band. In the other boundaries, vanishing normal components of electron and hole current densities, and electric field are enforced.

3.2. Details of the full wave simulation

3.3 The definition of the scattering parameters for the plasmonic device

Recently, there has been a trend to employ scattering parameters as reporting the properties of novel plasmonic devices [30

30. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008). [CrossRef]

32

32. P. Chen, C. Argyropoulos, and A. Alu, “Terahertz antenna phase shifters using integrally-gated graphene transmission-lines,” IEEE Trans. Antenn. Propag. 61(4), 1528–1537 (2013). [CrossRef]

]. Here, the definition of the characteristic impedance of a non-TEM transmission line, as a plasmonic waveguide is reviewed. Next, the employed method for the S-parameter calculation is detailed. As described in [33

33. D. M. Pozar, Microwave Engineering, 3rd edition (John Wiley & Sons, 2005).

], there are many ways to determine the voltage, current, and the characteristic impedance of a non-TEM transmission line. However, the voltage and current waves are mostly defined for the transverse electric and magnetic fields of a specific mode, respectively. Besides, an arbitrary characteristic impedance may be chosen to relate ± x going voltage and current [33

33. D. M. Pozar, Microwave Engineering, 3rd edition (John Wiley & Sons, 2005).

]. As mentioned, there exist infinite numbers of plasmonic modes inside the designed device, along the interface of the indented metal and the dielectric. However, the fundamental mode extends furthest into the dielectric. Therefore, the characteristic impedance Z0 is selected equal to the real part of the fundamental TMx mode wave impedance Zxr where Zx = Zxr + j Zxi.

In this paper, the simulated plasmonic switches are represented as a two port network. Such a representation of the active device is depicted in Fig. 2(a)
Fig. 2 (a) 2-port demonstration of the plasmonic device terminated with plasmonic waveguides. (b) A schematic showing the details of the initial simulation performed for the calibration.
. In the developed EM model, two plasmonic waveguides with length l1 and l2, are included at the input and output ports of the network to transfer the waves into and out of the switch (see Fig. 2(a)). Moreover, the presence of the waveguides allows that the excitation enforced at x = 0 (planar wave with electric field component Eincy and propagation constant ksi) completely follows the fundamental mode variations as it reaches the switch. In order to avoid wave attenuations inside the waveguides, the corresponding silicon wafers and the deposited metallic layers are assumed to be loss-free. In this manner, the waveguides can handle the TMx mode with real wave impedance Zxr. Here, the reference planes of the reported S-parameter are located at the boundaries of the active device as depicted in Fig. 2(a).

4. Plasmonic switch with the Schottky contact

In order to present a guideline for designing the plasmonic switch in different frequency ranges, the dispersion relation of the described structure (in Fig. 1) with different indentation depths “h”, calculated by the analytical mode (Eq. (1) and Eq. (2)) are shown in Fig. 3
Fig. 3 The TM fundamental mode phase constants calculated by the analytical model (Eq. (1) and Rq. 2) versus frequency as the indentation height h is changing.
. As depicted, the resonance frequency of the plasmonic structure “fr” decreases as the depths of the holes “h” increases. In this manner, the indentation heights “h” can be determined for a specific design with a required maximum working frequency limit. In Fig. 3, the dispersion relation of the radiating mode is also illustrated. Comparing the phase constants of the radiating mode and the TMx modes along the plasmonic structure with different “h” in Fig. 3, it is understood that the SSPPs are not bounded to the metal edges at z = (-h – t2) plane as f<200GHz. This places a minimum operating frequency limit on the plasmonic device since the SSPPs are not restricted inside the silicon wafer as β ksi.

Figure 4
Fig. 4 Variations of the waveguide’s fundamental mode wave impedances Zxr and phase constant, calculated by the full wave solver versus frequency.
represents the fundamental mode wave impedance Zxr and dispersion relation of the input and output waveguides calculated by the full wave simulator as h = 60 µm. To this end, the calibration simulation (detailed in Fig. 2(b)) is performed. In this manner, the phase constant β is first computed for a section of the waveguide with length ld as β = φ / ld where, φ is the phase of the waveguide port 1 to 2 transmission coefficient SWG21 ( = |SWG21| × e(j × φ)). Next, the wave impedance of the fundamental mode is computed as Zxr = β/ ω × ε. As mentioned, the characteristic impedances of the waveguides are chosen equal to their fundamental mode wave impedance Z0 = Zxr. As depicted in Fig. 4, the resonant frequency is located at 320 GHz. The differences between the SSPP characteristics (resonant frequency and maximum achievable phase constant) calculated by the analytical model in Eq. (1) and Eq. (2), and the full wave simulator are due to the consideration of the exact shape of the indentations edges inside the numerical solver. The dispersion relation variations of a corrugated metal with curved-shape edges compared to the one with sharp corners have been also discussed in [12

12. B. Wang, L. Liu, and S. He, “Propagation loss of terahertz surface plasmon polaritons on a periodically structured Ag surface,” J. Appl. Phys. 104(10), 103531 (2008). [CrossRef]

].

To show the effectiveness of the designed switch, the simulation is performed with different applied voltages. Figures 5(a)
Fig. 5 (a) and (b) show the distribution of the electron density inside the doped silicon wafer, and the magnitude of the electric field at f = 300 GHz as Va = 1 V, respectively. (c), (d) similarly present the variations of the charge density and the electric field magnitude at the same frequency as the applied voltage is −80 V.
-5(b) and Figs. 5(c)-5(d) depict the distribution of the electron density logarithm (log10 n) inside the doped silicon wafer and the magnitude of the electric field |E| = (|Ex|2 + |Ey|2)0.5 at f = 300 GHz, throughout the active device as the applied voltages are 1 V and −80 V, respectively. As presented in Fig. 5(a), the depletion layer width is almost negligible as the Schottky diode is forward-biased (Va = 1). In this condition, the plasmons are attenuated as they propagate along the device (see Fig. 5(b)). However, the depletion layer width increases up to 14 µm as the diode is reverse-biased (see Fig. 5(c)). In this case, the switch is operating in the ON mode and SSPPs suffers from small attenuations (see Fig. 5(d)), if they are concentrated inside the depleted region, with small electrical conductivity. Comparing the distribution of the electric field magnitude shown in Figs. 5(b) and 5(d), it is concluded that the wave concentration along the edges of the metallic indentation are kept similar at a single frequency, as the device is operating in the ON and the OFF mode. Applying high reverse voltages in a structure, grooved with sharp angle edges is not possible due to charge accumulation on the corners. This high charge density results into high electric field values which can end up to the silicon breakdown. Employing rounded metal edges allow the designer to apply very high reverse voltages up to −80 V before reaching the breakdown condition. In the design with curved edges, the breakdown limit will not reach unless Va becomes less than 90 V.

Figure 6
Fig. 6 S21 of the plasmonic switch versus frequency as the device is operating in different modes at THz frequency range.
presents the transmission coefficient S21 of the plasmonic THz switch implemented inside the doped silicon as different bias voltages are applied onto the Schottky contact. As illustrated, the insertion loss of the proposed device is less than 1dB in a wide frequency range. Moreover, the switch offers signal isolations (S21ON – S21OFF) up to 13 dB at 320GHz. On the other hand, the isolation reduces down to 1.5 dB in the first portion of the simulated frequency range. The signal isolation offered by the plasmonic switch can impose another criterion on the minimum operating frequency of the switch. Here, at least 3 dB signal isolation is expected from a single Schottky-diode-based switch. Therefore, it is concluded that the operating bandwidth of the first design is 60 GHz from 260 GHz to 320 GHz.

In Fig. 7
Fig. 7 S11 of the plasmonic switch versus frequency as the device is operating in different modes at THz frequency range.
, the return loss of the plasmonic THz switch is depicted. As presented, the return loss of the device is better than −30 dB as operating in the ON mode. The small amount of the input signal reflection is very attractive especially as connecting several components in a complex photonic system.

As shown, it is possible to achieve high levels of signal isolation by extending the length of the active device. However, the large reverse voltages required to achieve an acceptable level of insertion losses make the device application in modern compact photonic systems unfeasible. To address this problem, an optimized plasmonic switch is proposed in the following section.

5. Optimization: plasmonic switch using a PIN diode

Here, the simulation results of the optimized device with the length ld2 = 5 × d are reported. Figures 10(a)
Fig. 10 The hole and electron density distributions, and the magnitude of the electric field at f = 300 GHz as: (a), (b), (c) Va = 5 V and (d), (e), (f) Va = 0 V, respectively.
and 10(b) respectively depict the distributions of the hole and electron density logarithm (log10 p and log10 n) inside the intrinsic silicon wafer as the applied voltage is 5V. As shown in Figs. 10(a)-10(b), the PIN diode operates in the high-level-injection mode with very high level of electron and hole densities as Va = 5 V. Figure 10(c) depicts the magnitude of the ac electric field inside the plasmonic switch as the PIN diode is forward-biased. As expected, the presence of the high electron and hole densities in the forward bias condition causes large wave attenuations as the SPPs are passing through the device. In Figs. 10(d)-10(e), the distributions of the electron and hole density logarithm inside the device with Va = 0 V are presented, respectively. As the diode is reverse-biased, the electron and hole densities are respectively less than or equal to 5 × 1013 (cm−3) and 107 (cm−3). This is true throughout the silicon wafer except at the locations of the Ohmic contacts. The small numbers of free carriers in the reverse-biased diode guarantee negligible insertion losses as the switch is operating in the ON mode. This is confirmed by the magnitude of the ac electric field inside the active device presented in Fig. 10(f). Comparing the field distribution inside the plasmonic switch in the ON and OFF mode (Figs. 10(c) and 10(f)) at a single frequency, it is concluded that the field profile is largest at the proximity of the indentation edges and it decreases exponentially as moving to the perpendicular direction (y axis).

Figure 11
Fig. 11 Insertion losses of the optimized plasmonic switch versus frequency under different bias conditions
presents the transmission coefficient S21 of the optimized plasmonic switch as different voltages are applied between the p++ and n++-type doped Ohmic contacts. The PIN diode is forward-biased as Va rises above the threshold voltage Vth = 5 V. As illustrated in Fig. 11, the signal isolations can be further improved by increasing the applied voltage above Vth. This is due the increase of the carrier densities compared to the ones depicted in Figs. 10(a)-10(b). As illustrated in Fig. 11, the difference between the power of the transmitted signal in the ON (Va-ON = 0 V) and the OFF (Va-OFF = 7 V) modes can reach up to 14 dB at 320GHz, and the minimum expected isolation in the frequency range is about 7 dB. The insertion loss of the proposed device is less than 2dB in a wide frequency range.

In Fig. 12
Fig. 12 Return losses of the optimized plasmonic switch (with the PIN diode) versus frequency as the device is operating in THz frequency range.
, the return losses of the THz plasmonic switch with the PIN diode under different bias voltages are shown. As illustrated, the return loss of the switch operating in the ON mode (Va = 0 V) is better than −20 dB.

6. Conclusion

In this paper, a THz plasmonic switch inside a silicon wafer is proposed and simulated. The results are presented using the scattering parameters of the active device. Due to the maturity of the semiconductor device fabrication techniques, it is anticipated that the proposed design can be implemented easily compared to the previously proposed plasmonic switches. However, the developed device suffers from high required control voltages. To address this challenge, an optimized design with an integrated PIN diode is suggested. As illustrated, the optimized switch provides comparatively high signal isolations and acceptable level of insertion losses. Moreover, it is shown that the device can operate in a wide THz frequency range. Additionally, it is expected that this design can be further improved by incorporating a variety of doped areas inside the device. For instance, this may be possible by increasing the number of the p++-doped wells. Small input reflection coefficients of the designed switches suggest that they can be cascaded to achieve high signal isolations. We envision that the proposed switches may be useful in future all-integrated silicon-based THz plasmonic devices and communication systems.

References and links

1.

C. M. Armstrong, “The truth about terahertz,” IEEE Spectr. 49(9), 36–41 (2012). [CrossRef]

2.

C. W. Berry, N. Wang, M. R. Hashemi, M. Unlu, and M. Jarrahi, “Significant performance enhancement in photoconductive terahertz optoelectronics by incorporating plasmonic contact electrodes,” Nat Commun 4, 1622 (2013). [CrossRef] [PubMed]

3.

W. F. Andress, H. Yoon, K. Y. M. Yeung, L. Qin, K. West, L. Pfeiffer, and D. Ham, “Ultra-subwavelength two-dimensional plasmonic circuits,” Nano Lett. 12(5), 2272–2277 (2012). [CrossRef] [PubMed]

4.

T. Otsuji, T. Watanabe, S. A. B. Tombet, A. Satou, W. M. Kanp, V. V. Popov, M. Ryzhii, and V. Ryzhii, “Emission and detaction of terahertz radiation using two-dimensional electrons in III-V semiconductors and graphene,” IEEE Trans. Terahertz Sci. & Technol. 3(1), 63–71 (2013). [CrossRef]

5.

G. C. Dyer, S. Preu, G. R. Aizin, J. Mikalopas, A. D. Grine, J. L. Reno, J. M. Hensley, N. Q. Vinh, A. C. Gossard, M. S. Sherwin, S. J. Allen, and E. A. Shaner, “Enhanced performance of resonant sub-terahertz detection in a plasmonic cavity,” Appl. Phys. Lett. 100(8), 083506 (2012). [CrossRef]

6.

M. A. Khorrami, S. El-Ghazaly, S. Q. Yu, and H. Naseem, “Compact terahertz surface plasmon switch inside a two dimensional electron gas layer,” IEEE MTT-S Int. Microwave Symp. Dig.,Montreal, Canada, (2012). [CrossRef]

7.

M. A. Khorrami, S. El-Ghazaly, S. Q. Yu, and H. Naseem, “Terahertz plasmon amplification using two dimensional electron-gas layers,” J. Appl. Phys. 111(9), 094501 (2012). [CrossRef]

8.

M. A. Khorrami, S. El-Ghazaly, S. Q. Yu, and H. Naseem, “Analytical modeling of THz wave propagation inside ungated two dimensional electron gas layers,” IEEE MTT-S Int. Microwave Symp. Dig.,Baltimore, USA (2011).

9.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

10.

S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007), pp. 93–100.

11.

L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]

12.

B. Wang, L. Liu, and S. He, “Propagation loss of terahertz surface plasmon polaritons on a periodically structured Ag surface,” J. Appl. Phys. 104(10), 103531 (2008). [CrossRef]

13.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010). [CrossRef] [PubMed]

14.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. G. Davies, E. Linfield, D. F. Lim, C. S. Tan, S. F. Yu, H. C. Liu, and Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013). [CrossRef]

15.

V. Konoplev, A. R. Phipps, A. D. R. Pheps, C. W. Robertson, K. Ronald, and A. W. Cross, “Surface field excitation by an obliquely incident wave,” Appl. Phys. Lett. 102(14), 141106 (2013). [CrossRef]

16.

J. Gomez Rivas, J. A. Sanchez-Gil, M. Kuttge, P. H. Bolivar, and H. Kurz, “Optically switchable mirrors for surface plasmon polaritons propagating on semiconductor surfaces,” Phys. Rev. B 74(24), 245324 (2006). [CrossRef]

17.

J. A. Sanchez-Gil and J. G. Rivas, “Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces,” Phys. Rev. B 73(20), 205410 (2006). [CrossRef]

18.

E. Hendry, M. J. Lockyear, J. Gomez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75(23), 235305 (2007). [CrossRef]

19.

K. Song and P. Mazmuder, “Active terahertz spoof surface plasmon polariton switch comprising the perfect conductor metamaterial,” IEEE Trans. on Elect. Devices 56(11), 2792–2799 (2009). [CrossRef]

20.

Z. Xu, K. Song, and P. Mazumder, “Dynamic terahertz spoof surface plasmon-polariton switch based on resonance and absorption,” IEEE Trans. Electron. Dev. 58(7), 2172–2176 (2011). [CrossRef]

21.

A. V. Krasavin and N. Zheludev, “Active plasmonics: Controlling signals in Au/Ga waveguide using nanoscale structural transformations,” Appl. Phys. Lett. 84(8), 1416–1418 (2004).

22.

K. F. MacDoland, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009). [CrossRef]

23.

Y. Urzhumov, J. S. Lee, T. Tyler, S. Dhar, V. Nguyen, N. M. Jokerst, P. Schmalenberg, and D. R. Smith, “Electronically reconfigurable metal-on-silicon metamaterial,” Phys. Rev. B 86(7), 075112 (2012). [CrossRef]

24.

Ansoft HFSS, Ansys Inc., Pittsburg, PA.

25.

C. A. Balanis, Advanced Engineering Electromagnetics, 1rd edition (John Wiley & Sons, 1989).

26.

Atlas User’s Manual, Silvaco, Santa Clara, CA, Jul. 2010.

27.

M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. 56(17), 1694–1696 (1990). [CrossRef]

28.

T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997). [CrossRef]

29.

C. C. Hu, Modern Semiconductor Devices for Integrated Circuits (Prentice Hall, 2010).

30.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008). [CrossRef]

31.

J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Graphene-based plasmonic switches at near infrared frequencies,” Opt. Express 21(13), 15490–15504 (2013). [CrossRef] [PubMed]

32.

P. Chen, C. Argyropoulos, and A. Alu, “Terahertz antenna phase shifters using integrally-gated graphene transmission-lines,” IEEE Trans. Antenn. Propag. 61(4), 1528–1537 (2013). [CrossRef]

33.

D. M. Pozar, Microwave Engineering, 3rd edition (John Wiley & Sons, 2005).

OCIS Codes
(130.2790) Integrated optics : Guided waves
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics
(250.6715) Optoelectronics : Switching

ToC Category:
Plasmonics

History
Original Manuscript: August 19, 2013
Revised Manuscript: September 29, 2013
Manuscript Accepted: October 7, 2013
Published: October 17, 2013

Citation
Mohammad Ali Khorrami and Samir El-Ghazaly, "Design and analysis of a silicon-based terahertz plasmonic switch," Opt. Express 21, 25452-25466 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25452


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References

  1. C. M. Armstrong, “The truth about terahertz,” IEEE Spectr.49(9), 36–41 (2012). [CrossRef]
  2. C. W. Berry, N. Wang, M. R. Hashemi, M. Unlu, and M. Jarrahi, “Significant performance enhancement in photoconductive terahertz optoelectronics by incorporating plasmonic contact electrodes,” Nat Commun4, 1622 (2013). [CrossRef] [PubMed]
  3. W. F. Andress, H. Yoon, K. Y. M. Yeung, L. Qin, K. West, L. Pfeiffer, and D. Ham, “Ultra-subwavelength two-dimensional plasmonic circuits,” Nano Lett.12(5), 2272–2277 (2012). [CrossRef] [PubMed]
  4. T. Otsuji, T. Watanabe, S. A. B. Tombet, A. Satou, W. M. Kanp, V. V. Popov, M. Ryzhii, and V. Ryzhii, “Emission and detaction of terahertz radiation using two-dimensional electrons in III-V semiconductors and graphene,” IEEE Trans. Terahertz Sci. & Technol.3(1), 63–71 (2013). [CrossRef]
  5. G. C. Dyer, S. Preu, G. R. Aizin, J. Mikalopas, A. D. Grine, J. L. Reno, J. M. Hensley, N. Q. Vinh, A. C. Gossard, M. S. Sherwin, S. J. Allen, and E. A. Shaner, “Enhanced performance of resonant sub-terahertz detection in a plasmonic cavity,” Appl. Phys. Lett.100(8), 083506 (2012). [CrossRef]
  6. M. A. Khorrami, S. El-Ghazaly, S. Q. Yu, and H. Naseem, “Compact terahertz surface plasmon switch inside a two dimensional electron gas layer,” IEEE MTT-S Int. Microwave Symp. Dig.,Montreal, Canada, (2012). [CrossRef]
  7. M. A. Khorrami, S. El-Ghazaly, S. Q. Yu, and H. Naseem, “Terahertz plasmon amplification using two dimensional electron-gas layers,” J. Appl. Phys.111(9), 094501 (2012). [CrossRef]
  8. M. A. Khorrami, S. El-Ghazaly, S. Q. Yu, and H. Naseem, “Analytical modeling of THz wave propagation inside ungated two dimensional electron gas layers,” IEEE MTT-S Int. Microwave Symp. Dig.,Baltimore, USA (2011).
  9. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004). [CrossRef] [PubMed]
  10. S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007), pp. 93–100.
  11. L. Shen, X. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express16(5), 3326–3333 (2008). [CrossRef] [PubMed]
  12. B. Wang, L. Liu, and S. He, “Propagation loss of terahertz surface plasmon polaritons on a periodically structured Ag surface,” J. Appl. Phys.104(10), 103531 (2008). [CrossRef]
  13. N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater.9(9), 730–735 (2010). [CrossRef] [PubMed]
  14. G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. G. Davies, E. Linfield, D. F. Lim, C. S. Tan, S. F. Yu, H. C. Liu, and Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett.102(3), 031119 (2013). [CrossRef]
  15. V. Konoplev, A. R. Phipps, A. D. R. Pheps, C. W. Robertson, K. Ronald, and A. W. Cross, “Surface field excitation by an obliquely incident wave,” Appl. Phys. Lett.102(14), 141106 (2013). [CrossRef]
  16. J. Gomez Rivas, J. A. Sanchez-Gil, M. Kuttge, P. H. Bolivar, and H. Kurz, “Optically switchable mirrors for surface plasmon polaritons propagating on semiconductor surfaces,” Phys. Rev. B74(24), 245324 (2006). [CrossRef]
  17. J. A. Sanchez-Gil and J. G. Rivas, “Thermal switching of the scattering coefficients of terahertz surface plasmon polaritons impinging on a finite array of subwavelength grooves on semiconductor surfaces,” Phys. Rev. B73(20), 205410 (2006). [CrossRef]
  18. E. Hendry, M. J. Lockyear, J. Gomez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B75(23), 235305 (2007). [CrossRef]
  19. K. Song and P. Mazmuder, “Active terahertz spoof surface plasmon polariton switch comprising the perfect conductor metamaterial,” IEEE Trans. on Elect. Devices56(11), 2792–2799 (2009). [CrossRef]
  20. Z. Xu, K. Song, and P. Mazumder, “Dynamic terahertz spoof surface plasmon-polariton switch based on resonance and absorption,” IEEE Trans. Electron. Dev.58(7), 2172–2176 (2011). [CrossRef]
  21. A. V. Krasavin and N. Zheludev, “Active plasmonics: Controlling signals in Au/Ga waveguide using nanoscale structural transformations,” Appl. Phys. Lett.84(8), 1416–1418 (2004).
  22. K. F. MacDoland, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3(1), 55–58 (2009). [CrossRef]
  23. Y. Urzhumov, J. S. Lee, T. Tyler, S. Dhar, V. Nguyen, N. M. Jokerst, P. Schmalenberg, and D. R. Smith, “Electronically reconfigurable metal-on-silicon metamaterial,” Phys. Rev. B86(7), 075112 (2012). [CrossRef]
  24. Ansoft HFSS, Ansys Inc., Pittsburg, PA.
  25. C. A. Balanis, Advanced Engineering Electromagnetics, 1rd edition (John Wiley & Sons, 1989).
  26. Atlas User’s Manual, Silvaco, Santa Clara, CA, Jul. 2010.
  27. M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56(17), 1694–1696 (1990). [CrossRef]
  28. T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett.78(6), 1106–1109 (1997). [CrossRef]
  29. C. C. Hu, Modern Semiconductor Devices for Integrated Circuits (Prentice Hall, 2010).
  30. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Transmission line and equivalent circuit models for plasmonic waveguide components,” IEEE J. Sel. Top. Quantum Electron.14(6), 1462–1472 (2008). [CrossRef]
  31. J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Graphene-based plasmonic switches at near infrared frequencies,” Opt. Express21(13), 15490–15504 (2013). [CrossRef] [PubMed]
  32. P. Chen, C. Argyropoulos, and A. Alu, “Terahertz antenna phase shifters using integrally-gated graphene transmission-lines,” IEEE Trans. Antenn. Propag.61(4), 1528–1537 (2013). [CrossRef]
  33. D. M. Pozar, Microwave Engineering, 3rd edition (John Wiley & Sons, 2005).

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