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Nanoscience andNanotechnology LettersVol. 5, 754–757, 2013

Graphene-Based Periodic Gate Field EffectTransistor Structures for Terahertz Applications

Mustafa Karabiyik, Chowdhury Al-Amin, and Nezih Pala∗

Electrical and Computer Engineering, Florida International University,EC 3910, Miami, FL 33174, USA

We report on theoretical investigation of graphene based Field Effect Transistor (FET) structuresfor resonant absorption of terahertz (THz) radiation by the plasmons excited in the high sheetconcentration and high carrier mobility active layers. Metallic grating gates with varying periodswere used to couple the THz radiation into the plasmons in the active region of the devices. Suchgrating gates not only improve the coupling by providing momentum match between the incidentradiation and the plasmons but also allows the control of carrier concentration in the channel byexternal bias. Our studies demonstrate that the proposed periodic gate FET structures of Graphenecan resonantly absorb THz radiation up to 6th harmonic at room temperature. Moreover, thesestructures have the advantage of tunability since the resonant absorption modes strongly dependon the sheet carrier concentration in the channel which could be controlled by gate bias.

Keywords: THz, Graphene, Plasmons, Two Dimensional Electron Gas, 2DEG.

1. INTRODUCTION

Terahertz technologies utilize electromagnetic (EM) radia-tion in the frequency range between 300 GHz and 10 THzand their potential applications in biology, chemistry,medicine, astronomy and security are wide ranging. Theabundance of potential THz applications fuelled intenseresearch in the last decade leading impressive advance-ments in emission and detection of THz radiation. Plasmawave propagation in two-dimensions (2D) has contributedto advancements in detection and control in THz spec-tral region.1 Large propagation velocity of plasma wavescompared to electron drift velocities allows plasmonicdevice to exceed electron drift limited cut off frequencies.Plasmonic THz detection has been demonstrated usingSilicon,2–4 III–V compounds5–8 and III-N9–11 based semi-conductor devices. III-N devices have been particularly ofinterest due to their high sheet carrier concentration. Thecoupling efficiency of single gate plasmonic devices toTHz radiation is weak due to small active region of thesedevices. To mitigate this problem, grating gate couplers ona large active region and linearly integrated Field EffectTransistor (FET) arrays with high integration density areproposed.12 Device geometry has not been the only lim-itation for the response of THz plasmonic devices. Mostof the previously observed THz plasmonic detectors have

∗Author to whom correspondence should be addressed.

demonstrated very weak response at room temperaturedue to high electron scattering rates.13–15 Graphene withremarkably high electron mobility at room temperature,with reported values in excess of 15,000 cm2/V · s16 hasstrong potential for THz plasmonic devices. Recently, thehigh mobility properties of Graphene at room temperaturewas exploited to demonstrate graphene plasmonic THzmetamaterials.17 However, the reported structures werebased on graphene nanoribbons which were fabricated byplasma etching presented low quality factors. The lowquality factor could be ascribed to the high carrier scatter-ing rate and limited mobility due to the plasma damagesinduced during the etching process.18 Recently large areagraphene samples with good electrical characteristics havebeen grown.19 Intense research in the field is expected tomake mass production of large area high quality graphenewidely available in near future for various applications.20

True capabilities of graphene grating gate structures needto be explored to design and fabricate graphene plasmonicTHz devices. In this letter, we report on theoretical andnumerical analysis of THz plasmonic behaviour in largearea graphene FET structures with grating gate couplers.

2. DESIGN AND METHOD

The structures investigated in this study consist ofgraphene layers on sapphire substrates (see Fig. 1).Titanium grating gates are placed on 17 nm thick SiO2

754 Nanosci. Nanotechnol. Lett. 2013, Vol. 5, No. 7 1941-4900/2013/5/754/004 doi:10.1166/nnl.2013.1622

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Karabiyik et al. Graphene-Based Periodic Gate FET Structures for Terahertz Applications

Fig. 1. Cross section of the studied structures (not to scale).

layer deposited on graphene. Different gate period, L,and gate finger length, w, combinations were studied.A commercial simulation package of finite-differencetime-domain (FDTD) method with a 3D Maxwell equa-tion solver and a custom code for data analysis were usedto calculate absorption and transmission spectra of thestructures. FDTD tool allowed both time domain and fre-quency domain information. A broadband pulse was sentfrom the source and EM field propagation through thestructure was calculated until there was no electromagneticfield left in the entire devices. Frequency domain informa-tion at the spatial points of interest were obtained throughFourier transform of the time domain information. Fre-quency dependence of power flow and modal profiles wereobtained in the frequency range of 1–8 THz. The simula-tions were carried out using periodic boundary conditionsfor the grating gate arrays. Furthermore, real experimen-tal data for dispersion relations and different loss mecha-nisms for materials were used in the simulation. The meshsize was sufficiently small to match experimental data forstructures with small features. We validated our simulationmethod by comparing the numerical results with the exper-imental results reported in the literature for GaN-basedgrating gate devices10 and graphene nanoribbon metama-terial structures.17

3. RESULTS AND DISCUSSION

A short channel with high sheet carrier concentration actsas a resonant cavity for the plasma waves with the funda-mental frequency of �0 and its harmonics. An incomingelectromagnetic radiation excites plasma waves in such achannel. When �0� � 1 (� is the momentum relaxationtime) the resonant condition is satisfied. Sheet electrondensity in a graphene layer can be estimated by

Ns =�

ed�Vg −Vd� (1)

Where � is the permittivity, d is the dielectric thickness,e is the unit charge, Vg is the gate voltage and Vd is thevoltage corresponding to Dirac point at which the graphenesheet has charge neutrality. The electron energy disper-sion in undoped graphene is linear E = �VF · k with kbeing the electron momentum and VF being the 2D Fermivelocity, which is a constant for graphene (VF = 106 m/s).

The linear electron energy spectrum implies zero effec-tive electron mass in graphene. The electron “inertia” inmassless graphene is described by a fictitious “relativis-tic” effective mass mF = EF /V

2F , where EF is the Fermi

energy. The relation between the Fermi energy and sheetcarrier density can be given as

EF = �VF

√2�NS (2)

Using Eqs. (1) and (2) one can obtain

mF = �

VF

√2��ed

V0 (3)

where V0 = Vg −Vd. For a typical value of V0 = 1 Eq. (3)yields mF = 0�03 m0 where m0 is the free electron mass.It should be noted that mF decreases to zero with the gatevoltage Vg approaches to the Dirac voltage. Electron relax-ation rate in graphene with electron mobility can beestimated as 1/� = e/mF . Therefore, �0� � 1 is satis-fied for frequencies above 2 THz even for low mobilitygraphene with = 1600 cm2/Vs.Coupling of EM radiation into 2D electron gas (2DEG)

in high sheet carrier concentration channels via gratinggate couplers was first investigated by Zhent et al.21 andlater applied to III–IV56 and III-N systems.10 Plasmon dis-persion in a gated graphene can be formally written in thesame form as in a conventional semiconductor structurewith substituting the effective electron mass by the “rela-tivistic” effective mass mF :

�= q

√eV0

mF

(4)

where q is the plasmon wavevector, which is determinedby the grating gate period L, q = 2�n/L (n= 123 � � �).Substituting Eqs. (3) into (4) results in22

�= q4

√Ns

V 2F e

4d2

2��2�2(5)

which gives the plasmon resonant modes in graphene.Room temperature operation is a crucial aspect for the

practicality of the THz devices for many practical applica-tions like medical imaging, security and sensing. Plasmaresonances in a grating gate device can be best excitedwhen the radiative damping �rad is equal to the dissipa-tive damping �dis caused by the carrier scattering.11 In thiscase the maximum absorbance is given by 0.5 (1−√

R0)where R0 is the reflectivity when there is no resonant sur-face layer. Dissipative damping �dis of a plasmon modeincreases with temperature. Therefore, matching conditionof �dis = �rad requires strong radiative broadening at roomtemperatures. Since the radiative broadening is directlyproportional to the conductivity of the channel, graphenelayers are especially promising for room temperature res-onant absorption of THz radiation. Radiative dampening

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Graphene-Based Periodic Gate FET Structures for Terahertz Applications Karabiyik et al.

is also directly proportional to the strength of couplingbetween the plasmon modes and the incident THz radi-ation. Strong electric near field induced in narrow slitsbetween the grating gate fingers greatly enhances the cou-pling and hence the radiative dampening. Slit width w inthe investigated devices was chosen to be about 10% ofthe gate finger width to achieve the maximum resonantabsorbance.Resonant absorption of THz radiation by the plasmons

induces an oscillating current and creates nonuniformimpedance distribution in the active layer which lead toan electrical response depending on incident power, polar-ization and frequency. In the photovoltaic (PV) detectionscheme when asymmetric boundary conditions (i.e., shortcircuit boundary condition at the source side of the chan-nel and open circuit boundary condition at the drain sideof the channel) are applied, nonlinear properties of thetransistor structure rectifies the oscillating current inducedby the incoming radiation and results in a photoresponsein the form of DC voltage between source and drain.1–3

An improved signal can be obtained when a constant cur-rent is applied between the ohmic terminals at the bothends of the channel and drain voltage is monitored whichis referred as the photoconductive (PC) detection mode.56

Analysis of the electrical response at different modalitiesis beyond the scope of this study.In Figure 2 we compare the room temperature absorp-

tion spectra of graphene and GaN grating gate devices withthe same geometrical parameters. Following the experi-mental details reported in Ref. [10], Al0�2Ga0�8N/GaN HighElectron Mobility Transistor (HEMT) epilayer structure onsapphire was used for GaN devices with room temperatureelectron mobility of = 1200 cm2/V · s and sheet carrierdensity of NS = 7�5×1012 cm−2. For the graphene devices,mobility of = 3000 cm2/V was used while the sheet car-rier concentration was kept the same with the one for GaN

0 1 2 3 4 5 6 7 80

10

20

30

40

50

iiAbs

orpt

ion

(%)

Frequency (THz)

i

Fig. 2. Room temperature absorption spectra of AlGaN/GaN andGraphene grating gate FET structures with L = 1�5 m w = 0�15 m,NS = 7�5×1012 cm−2. (i) Graphene (ii) Al0�2Ga0�8N/GaN. Curve (ii) is inwell agreement with the experimental data reported in Ref. [10].

Fig. 3. Electric field distribution for the first mode (top) and secondmode (bottom) of plasmon resonances in graphene grating gate devices.Light coloured boxes representing gate metals and dashed lines repre-senting graphene layers are added for the clarity.

devices. The graphene devices present well pronouncedresonant absorption peaks corresponding to the fundamen-tal mode and first two harmonics in the 1–8 THz range.The resonant frequencies are in agreement with the calcu-lated values using the Eq. (5). Electric field distributionsfor the first two resonant modes of the plasmons are shownin Figure 3. Resonant absorption for GaN-based deviceson the other hand is not observable due to higher scatteringrates at room temperature. The absorption characteristicsfor GaN devices is in good agreement with theoretical andexperimental ones reported in Ref. [10] which validatesour simulation method.The modulation depth in the absorption spectrum of the

periodic gated FET structures is also controlled by the car-rier scattering rate in the channel. The lower scattering ratein graphene compared to GaN HEMT devices allows clearabsorption peaks with large modulation depth. Effect ofthe scattering rate in graphene is presented in Figure 4. Forlower mobilities (curve i) contribution of Drude absorptionwhich monotonically decreases with frequency is visibleat the background. As the mobility increases, modulationdepth increases especially at higher frequency modes. Thisis in agreement with the fact that Drude absorption alsodecreases with increasing mobility.23

An important advantage of the grating gate devices istunability of the resonant absorption frequencies thoughcontrolling the charge concentration by the applied gate

0 1 2 3 4 5 6 7 80

10

20

30

40

50

i

iii

ii

Abs

orpt

ion

(%)

Frequency (THz)

Fig. 4. Absorption spectra of graphene with different mobilities. L =1�5 m w = 0�15 m, NS = 7�5× 1012 cm−2. (i) = 3000 cm2/V · s(ii) = 15000 cm2/V · s (iii) = 40000 cm2/V · s.

756 Nanosci. Nanotechnol. Lett. 5, 754–757, 2013

Delivered by Publishing Technology to: Nezih PalaIP: 88.241.32.108 On: Fri, 28 Jun 2013 20:01:37

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Karabiyik et al. Graphene-Based Periodic Gate FET Structures for Terahertz Applications

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

Abs

orpt

ion

(%)

Frequency (THz)

iii

ii

i

Fig. 5. Absorption spectra of graphene grating gate FET structurewith different carrier concentrations. L = 1�5 m w = 0�15 m, =15000 cm2/V · s (i) Ns = 3�6× 1012 cm−2 (ii) Ns = 8�3× 1012 cm−2

(iii) Ns = 1�5×1013 cm−2.

voltage. Figure 5 clearly shows the shift of the resonantfrequencies by the charge carrier concentration as expectedfrom the Eq. (5). It should be noted that the plasmon fre-quency in graphene exhibits different dependence on thegate voltage (∼N 1/4

s ) as compared with gated plasmons inconventional semiconductor structures (∼N 1/2

s ). The datain Figure 5 also shows that, it is possible to reduce spec-tral separation of modes (increase the spectral density) byslightly decreasing the carrier concentration and to observehigher order modes in a selected spectral range.

4. CONCLUSION

We investigated the plasmonic absorption characteristics ofGraphene grating gate FET structures at THz frequencies.FDTD simulations and analytic calculations showed thatthe investigated devices could present well pronouncedresonant absorption peaks up to 6th harmonic even at roomtemperature in 1–8 THz. The large modulation depth ofhigher order modes hints that it is possible to observe evenhigher modes beyond 10 THz which was the spectral limitin this study. Moreover, the resonant frequencies can betuned by modulating the channel carrier concentration bygate bias. The results are important to design graphenebased plasmonic THz devices operating at ambient tem-perature for wide range of applications.

Acknowledgments: This work is supported by NSFCAREER program (Program manager: Samir El-Ghazaly)and Qatar National Research Fund National PrioritiesResearch Program (NPRP) (NPRP No. 09-1211-2-475).

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Received: 14 January 2013. Accepted: 16 February 2013.

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