Graphene-based Field-effect Transistor Structures for Terahertz
Applications
Ahmad Abbas*a, Mustafa Karabiyika and Nezih Palaa
a
Florida International University, Department of Electrical and Computer Engineering, 10555 West
Flagler Street, Miami, FL 33174
ABSTRACT
We propose Terahertz (THz) plasmonic devices based on linearly integrated FETs (LFETs) on Graphene. LFET
structures are advantageous for (THz) detection since the coupling between the THz radiation and the plasma wave is
strongly enhanced over the single gate devices and accordingly higher-order plasma resonances become possible.
AlGaN/GaN heterostructure LFETs with their high sheet carrier concentration and high electron mobility are promising
for plasmonic THz detection. Nevertheless, our numerical studies show that room temperature resonant absorption of
THz radiation by the plasmons in AlGaN/GaN LFETs is very weak even if the integration density is sufficiently large.
Our simulations also demonstrate that similar LFETs on Graphene, which has very large electron mobility, can
resonantly absorb THz radiation up to 5th harmonic at room temperature. Additionally, we investigated LFETs with
integrated cavities on Graphene. Such Periodic Cavity LFETs substantially enhance the quality factor of the resonant
modes.
Keywords: Terahertz, THz, Graphene, Detector, Plasma, FET
1. INTRODUCTION
Terahertz technologies utilize electromagnetic radiation in the frequency range between 300 GHz and 10 THz
and their potential applications in biology, chemistry, medicine, astronomy and security are wide ranging. THz
wavelengths have several properties that could promote their use as sensing and imaging tools. The envisioned prospect
for THz applications fueled intense research in the last decade leading impressive advancements in emission and
detection of THz radiation. Plasma wave propagation in two-dimensions (2D) has contributed to advancements in
detection and control in THz spectral region1. Because of the nature of plasma wave propagation, device response that
surpasses the electronic drift cutoff frequency limit was possible 1- 11. Plasmonic THz detection devices with Si 2, 3, III-V
compounds 5-14 and GaN 13 based semiconductor structures were observed. These devices include single gate high
electron mobility (HEMT) structures 7,9,10,11,13 , grating gate devices 5,6,12 and arrays of field effect transistors (FET) 14.
Single Gate devices were studied extensively for the detection of THz frequency 5,6,12 but the coupling efficiency to the
THz wave is weak due to small power incident on the device. Accordingly, higher integration density of FETs with a
cumulative effect led to the use of arrays.
In all the previous THz plasmonic detectors, very weak or no response in room temperature due to higher
electron scattering rates was observed. Lately the high mobility properties of Graphene in room temperature was utilized
in a THz detector as a 2D channel 15 but the THz absorption modes had very low quality factors.
Plasma waves in FET structures are governed by two different dispersion relations (i.e. gated and ungated
plasmons). If an infinite perfectly conductive plane is located at distance d from the infinite 2D electron, then the
dispersion relation for the gated plasmons is given by (equation 1) below 24
* ahmad.nabil.abbas@gmail.com
Terahertz Physics, Devices, and Systems VI: Advanced Applications in Industry and Defense,
edited by A. F. Mehdi Anwar, Nibir K. Dhar, Thomas W. Crowe, Proc. of SPIE Vol. 8363, 83630S
© 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.919460
Proc. of SPIE Vol. 8363 83630S-1
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ωp
2
e2 N
k
= *
m ε 0 [ε 1 + ε 2 coth( kd )]
(1)
where ωp and k are the frequency and wave vector of plasma wave, respectively, N is the sheet electron density, e and m*
are the charge and effective mass of electron, ε0 is the dielectric permittivity of air ε1 is the dielectric constant of the
substrate and ε1 is the dielectric constant of the insulator separating the 2D electron layer from the perfectly conductive
plane (i.e. top gate). However, response of a single FET plasma detector is limited by its small area compared to the
beam cross-section. Also, gated plasmons in a single-gate FET are weakly coupled to terahertz radiation because of the
strong screening of the gate plasmons by the metal gate electrode and their vanishingly small net dipole moment due to
their acoustic nature. Use of multiple gates (grating gates) or linearly integrated FETs (LFETs) could circumvent this
problem 23
In LFETs, plasma waves oscillate in phases because of the highly conductive ungated parts of the two
dimensional channel (i.e. Graphene in this study). Plasma oscillations in a LFET structure behave as a single mode and it
is synchronized by the metallic contacts between array elements.
We report on numerical investigation of resonant absorption of THz radiation by LFETs based on large area
Graphene layers. Additionally, we propose a novel structure of Periodic Cavity LFETs (PC-LFET) which is based on the
LFET array where higher confinement and a higher modulation depth of the plasma wave is achieved for lower order
modes. A commercial simulation package of finite-difference time-domain (FDTD) method with a 3D Maxwell equation
solver was used to calculate absorption and transmission spectra of the proposed devices. The simulation was carried out
using periodic boundary conditions for the arrays. Furthermore, real experimental data for dispersion relations and
different loss mechanisms for materials were used in the simulation. The mesh size was sufficiently small to match
experimental data for structures with small features. In order to insure the validity of our results, we have simulated
experimentally measured grating gate GaN/AlGaN devices 16 and compared the results with the simulated results. The
simulation showed good agreement with the results and parameters values of the experiment.
Figure 1. A) Resonant absorption modes in LFET GaN/AlGaN devices with gate width of 1µm and variable source-drain
width values at room temperature. B) Cross sectional view of the LFET GaN/AlGaN structure.
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For all the studied devices, we observed well defined resonant modes in the 1-8 THz spectral range at room
temperature. The resonant absorption modes change with the gate width (LG), periodicity (LG + source and drain metallic
separation Lsd) and gate voltage. The observed resonant frequencies are in good agreement with the analytical results 16
for plasmonic modes in periodically patterned structures. The proposed PC- LFETs demonstrated an improvement of up
to 57% in the modulation depth of the first mode compared to conventional LFETs.
Room temperature operation is a crucial aspect for the practicality of the THz detectors in applications like
medical imaging, security and sensing. The modulation depth in the absorption spectrum of the periodic LFET structures
is controlled by the scattering rate of the two-dimensional channel (2DEG). For GaN/AlGaN heterostructure devices the
scattering rate increases by an order of magnitude from 77K to 295K. Subsequently, the resonant absorption modes at
room temperature have very low modulation depth (i.e. 2-5 %) as shown in figure 1.
2. GRAPHENE-BASED THz PLASMONIC LFETs
Graphene has attracted a lot of attention in the optoelectronic applications industry. Extremely high mobility in
room temperature, low scattering and transparency are some of the important properties of Graphene in optical devices.
Plasmonic devices require a channel with low scattering in order for the resonant modes to have deeper modulation
depth. As a result, Graphene is a perfect candidate for a plasmonic detector at room temperature.
In this section, LFET devices with Graphene as the two-dimensional channel are analyzed. The LFET array is
composed of a periodic gate structure on top of Graphene which allows tunable detection under applied bias. In the
structure, the periodic source and drain patterns make ohmic contacts with the Graphene sheet while the gate is separated
from Graphene by SiO2 for plasma wave propagation confinement between the metal gate and Graphene.
In the analysis, A Graphene sheet is placed on a SiO2 substrate with periodic palladium (Pd) gratings on top of
Graphene. A 50 nm Silicon Dioxide (SiO2) layer is placed on top of Graphene to create the cavity for plasma wave
propagation. Additionally, periodic gate fingers of Titanium (Ti) are placed on top of Sio2. Figure 2 shows the cross
sectional views of the investigated device.
Figure 2. Graphene based LFET THz detector. A) Three-dimensional view. B) Cross-sectional view of a single FET
element of the array.
Because of the long momentum relaxation time of Graphene and high mobility in room temperature (300 K)
compared to GaN/AlGaN 2DEG, very clear resonant modes appear in the absorption spectrum. Figure 3 shows the
Graphene THz plasmonic detector with different gate dimensions and a source-drain size of 0.1 µm. Looking at the
figure, the size of the cavity under the gate with length LG changes the resonant modes and the smaller LG the higher the
frequency of the first mode. Figure 4 shows the electric field profile of two FET elements of the Graphene LFET device
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with the plasma wave of the first mode propagating under the gate. It is apparent that the relatively long SiO2 side airinterface in the FET elements allows the energy of the plasma wave to reradiate and accordingly lower the modulation
depth of the resonant modes.
The results of the simulation were compared to the analytical results using (equation 1) for the resonant
frequencies. For the LFET devices under consideration, the wavelength λ=2LG and the wave vector k= 2π/ LG. This
means that the first mode has a propagating plasma wave of a half wavelength under the gate contact. The simulated
results matched the analytical equation with an error reaching 22 % for higher order modes in small gate dimensions.
These errors are caused by the simplification of the plasma equation used and other non-ideal effects (e.g. fringing fields,
dielectric losses and dielectric properties variations with different wavelengths).
Figure 3. Absorption spectrum of the LFET array Graphene based device for different Gate widths at room temperature.
Figure 4. simulation result of the Graphene LFET device showing two FET elements and the propagation of the first mode
where the high electric field intensity is shown in (white), zero electric field intensity is shown in (dark gray) and the
transition between high and zero intensities in (light gray).
It is noted that the Graphene under analysis has a mobility of 2390 cm2/V.s, carrier concentration of 1.5x1013
cm-2 and a momentum relaxation time of 25x10-14 sec. This is a reasonable practical value corresponding to defects in
the Graphene sheet 19. To ensure validity of those parameters, our simulation results with these values are in agreement
with the Graphene used in 15 with experimental results matching our analysis of Graphene devices in 15. Higher quality
and less defective Graphene with higher mobility values would result in a deeper modulation depth of the modes in the
absorption spectrum. In order to show the effects of the mobility on the operation of the device, higher mobility values of
10000 and 40000 cm2/V.s 21,22, which were previously measured, will be used. Figure 5 shows the change in the
Graphene LFET device response with mobility. Increasing the mobility significantly enhances the quality factor of the
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resonant absorption modes and increases the modulation depth because of the lower value of energy loss, caused by
scattering effects, in the Graphene channel.
Figure 5. Graphene Based devices Absorption spectrum change with Mobility
3. PERIODIC CAVITY LFET ARRAYS
We propose a new structure for the further enhancement of the THz plasmonic detection. The structure, shown
in figure 6, is a periodic LFET structure where the gates completely enclose the cavity and a coupling opening of 100 nm
is placed in the middle point of the gates. Additionally, the top metallic gates are separated from the source-drain fingers
with a 5 nm oxide. This structure further enhances the quality factor of the lower order resonant modes because of the
significant decrease of reradiation effects in the propagation plain of the metallically enclosed cavity. Furthermore, the
slit in the middle of the gate doesn't cause significant radiative losses because it is located on top of the plasma wave
propagation plane. On the other hand, higher order modes suffer from greater losses than traditional LFET array devices
(figure 7 (a)). The reason for this phenomenon is the distribution of electric field intensities under the metal. In lower
order modes, the opening in the metallic top gate (figure 6) doesn’t have any high electric field intensities propagating
under it. For example, the first mode corresponding to half a wavelength has two electric field maxima with one zero
under the opening of the metallic gate. On the other hand, because of the finite length of the metallic gate opening,
higher order modes stack in a more dense way under the metallic gate which makes part of the high electric field
intensity decouple from the plasma wave and accordingly drops the modulation depth of that particular mode.
Figure 6. Periodic Cavity LFET device structure
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To demonstrate the advantages of this structure, the structure is simulated using GaN/AlGaN devices at
temperatures of 77K and 300K and Graphene at 300K. Figure 7 shows the resonant absorption modes of a LFET
structure and Periodic Cavity LFET with (Sio2) as the oxide layer. For all devices, there is a significant improvement in
the first modes. This improvement is apparent in the enhancement of the modulation depth for both Graphene
GaN/AlGaN devices. Alternatively, higher order modes have lower modulation depth than conventional LFET devices
while the small shift in the resonant absorption modes in the periodic cavity LFET is due to the change in the electric
field intensity profile in the cavity due to the opening in the middle of the gate.
Figure 7. Comparison of THz absorption modes in LFET and Periodic cavity LFET structures with LG= 1 µm: of
GaN/AlGaN at 77K (A), GaN/AlGaN at 300 K (B) and Graphene devices at 300K (c)
In this letter, we have demonstrated a novel device showing the viability of using Graphene as a twodimensional channel in THz plasmonic detectors, we showed the device dependence on temperature changes, quality of
Graphene (i.e. mobility) and the changes in the resonant absorption modes with the device dimension LG. Significant
improvement in the device’s response in room temperature over GaN/AlGaN LFET arrays was observed. Additionally,
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we have proposed a novel periodic cavity LFET structure to enhance the absorption response of the resonant modes. A
57% improvement in the modulation depth over LFET array structures was demonstrated in some devices.
Future work should investigate the fabrication of such devices and other issues concerning the choice of oxide
in the periodic cavities LFET, the utilization of bi-layer and few-layer Graphene as 2D channels and other structures to
further enhance the quality factor and modulation depth in different spectral ranges.
References
[1] M. S. Shur and J.-Q. Lü, “Terahertz sources and detectors using two-dimensional electronic fluid in high electronmobility transistors” IEEE Trans. Microwave Theory Tech. 48,750 (2000).
[2] S. J. Allen, D. C. Tsui, and R. A. Logan, “Observation of the two-dimensional plasmon in silicon inversion layers”
Phys. Rev. Lett. 38,980 (1977).
[3] D. C. Tsui, E. Gornik, and R. A. Logan, “Far infrared emission from plasma oscillations of Si inversion layers” Solid
State Commun. 35,875 (1980).
[4] M. Dyakonov and M. S. Shur, “Shallow water analogy for a ballistic field effect transistor: New mechanism of
plasma wave generation by dc current” Phys. Rev. Lett. 71, 2465 (1993).
[5] X. G. Peralta, S. J. Allen, M. C. Wanke, N. E. Harff, J. A. Simmons, M. P.Lilly, J. L. Reno, P. J. Burke, and J. P.
Eisenstein, “Terahertz photoconductivity and plasmon modes in double-quantum-well field-effect transistors” Appl.
Phys. Lett. 81,1627 (2002).
[6] E. A. Shaner, M. Lee, M. C. Wanke, A. D. Grine, J. L. Reno, and S. J.Allen, “Single-quantum-well grating-gated
terahertz plasmon detectors” Appl. Phys. Lett. 87, 193507 (2005).
[7] F. Teppe, D. Veksler, A. P. Dmitriev, V. Yu. Kachorovskii, S. Rumyantsev, W. Knap, and M. S. Shur, “Plasma wave
resonant detection of femtosecond pulsed terahertz radiation by a nanometer field-effect transistor” Appl. Phys. Lett. 87,
052107 (2005).
[8] W. J. Stillman and M. S. Shur, “Closing the gap: plasma wave electronic terahertz detectors” J. Nanoelectron.
Optoelectron. 2,209 (2007).
[9] A. El Fatimy, F. Teppe, N. Dyakonova, W. Knap, D. Seliuta, G. Valušis, A. Shchepetov, Y. Roelens, S. Bollaert, A.
Cappy, and S. Rumyantsev, “Resonant and voltage-tunable terahertz detection in InGaAs⁄ InP nanometer transistors”
Appl. Phys. Lett. 89, 131926 (2006).
[10] A. Shchepetov, C. Gardès, Y. Roelens, A. Cappy, S. Bollaert, S.Boubanga-Tombet, F. Teppe,D.Coquillat, S. Nadar,
N. Dyakonova, H.Videlier, W. Knap, D. Seliuta, R. Vadoclis, and G. Valušis, “Oblique modes effect on terahertz plasma
wave resonant detection in InGaAs⁄ InAlAs multichannel transistors” Appl. Phys.Lett. 92, 242105 (2008).
[11] S. Boubanga-Tombet, F. Teppe, D. Coquillat, S. Nadar, N. Dyakonova, H.Videlier, W. Knap, A.Shchepetov, C.
Gardès, Y. Roelens, S. Bollaert, D.Seliuta, R. Vadoclis, and G. Valušis, “Current driven resonant plasma wave detection
of terahertz radiation: Toward the Dyakonov–Shur instability” Appl. Phys. Lett. 92, 212101 (2008).
[12] H. Saxena, R. E. Peale, and W. R. Buchwald, “Tunable two-dimensional plasmon resonances in an InGaAs/InP high
electron mobility transistor” J. Appl. Phys. 105, 113101 (2009).
[13] A. El Fatimy, S. Boubanga Tombet, F. Teppe, W. Knap, D. B. Veksler, S.Rumyantsev, M. S. Shur, N.Pala, R.
Gaska, Q. Fareed, X. Hu, D. Seliuta, G. Valusis, C. Gaquiere, D. Theron, and A. Cappy, “Terahertz detection by
GaN/AlGaN transistors” Electron. Lett. 42, 1342 (2006).
[14] V. V. Popov, D. M. Ermolaev, K. V. Maremyanin, N. A. Maleev, V. E. Zemlyakov, V. I. Gavrilenko and S. Yu.
Shapoval . “High-responsivity terahertz detection by on-chip InGaAs/GaAs field-effect-transistor array” Appl. Phys.
Lett. 98, 153504 (2011).
Proc. of SPIE Vol. 8363 83630S-7
Downloaded from SPIE Digital Library on 19 Jun 2012 to 139.179.10.194. Terms of Use: http://spiedl.org/terms
[15] Long Ju, Baisong Geng, Jason Horng, Caglar Girit, Michael Martin, Zhao Hao, Hans A. Bechtel, Xiaogan Liang,
Alex Zettl, Y. Ron Shen and Feng Wang . “Graphene plasmonics for tunable terahertz metamaterials” Nature
Nanotechnology 10.1038/NNANO.2011.146.
[16] A.V. Muravoj, D. B. Veksler, V. V. Popov, O. V. Polischuk, N. Pala, X. Hu, R. Gaska, H. Saxena, R. E. Peale and
M. S. Shur. “Temperature dependence of plasmonic terahertz absorption in grating-gate gallium-nitride transistor
structures” Appl. Phys. Lett. 96, 042105 (2010).
[17] G. R. Aizin, V. V. Popov and O. V. Polischuk. “Plasmon enhanced electron drag and terahertz photoconductance in
a grating-gated field-effect transistor with two-dimensional electron channel” Appl. Phys. Lett. 89, 143512 (2006).
[18] V.V. Popov, D.V. Fateev and M. S. Shur. “Plasma oscillations in field-effect transistor arrays” 12th International
Conference on Mathematical Methods in Electromagnetic theory (2008).
[19] Yinxiao Yang and Raghunath Murali. “Impact of size effect on graphene nanoribbon transport” IEEE Electron Dev.
Lett. Vol. 31, No. 3 (2010)
[20] Y. W. Tan, Y. Zhang, H.L. Stormer, and P. Kim. “Temperature dependent electron transport in graphene” Eu. Phys.
J. Special Topics 148, 15-18 (2007)
[21] K. S. Novoselov, A. K. Geim, S. V. Moozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov.
“Electric field effect in atomically thin carbon films” Science Vol. 306, 666 (2004); DOI: 10.1126
[22] Jian-Hao Chen, Chaun Jang, Shudong Xiao, Masa Ishigami and Michael S. Fuhrer. “Intrinsic and extrinsic
performance limits of graphene devices on SiO2” Nature Nanotech. Doi: 10.1038/nnano. 2008.58 (2008)
[23] V. V. Popov, G. M. Tsymbalov, D. V. Fateev, M. S. Shur, “Cooperative absorption of terahertz radiation by
plasmon modes in an array of field-effect transistors with two-dimensional electron channel” Applied Physics Letters,
89, 123504 (2006)
[24] V. V. Popov, M. S. Shur, “Higher-Order Plasmon Resonances in GaN-Based Field-Effect
Transistor Arrays” International Journal of High Speed Electronics and Systems, Vol 17, No.3 (2007)
Proc. of SPIE Vol. 8363 83630S-8
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