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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 16771–16776
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Enhanced electromagnetic coupling between terahertz radiation and plasmons in a grating-gate transistor structure on membrane substrate

Vyacheslav V. Popov, Denis V. Fateev, Olga V. Polischuk, and Michael S. Shur  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 16771-16776 (2010)
http://dx.doi.org/10.1364/OE.18.016771


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Abstract

We have shown that the electromagnetic coupling of a grating-gate plasmonic detector to terahertz radiation can be considerably enhanced by placing the detector onto a membrane substrate and using a narrow-slit grating-gate. The responsivity of the membrane detector can be enhanced by a factor of 50 as compared to a conventional grating-gate plasmonic detector on a bulk substrate due to enhanced electromagnetic coupling between the plasmons and terahertz radiation.

© 2010 OSA

1. Introduction

In this paper, we show that the responsivity of the grating-gate plasmonic THz detector can be considerably enhanced due to increased electromagnetic coupling between plasmons and THz radiation in the grating-gate structure on a membrane substrate. The strength of electromagnetic coupling between plasmons in 2DEC and THz radiation depends on both the geometry of the grating-gate coupler and the substrate thickness. We show that the strength of the higher-order plasmon resonances in the grating-gate structure on a membrane substrate is at least four times higher than that for a conventional grating-gate plasmonic detector on a bulk substrate for typical parameters of the grating-gate structure. The coupling strength can be further enhanced by an order of magnitude with a proper design of the grating-gate coupler.

2. Model of the resonant surface layer

To examine the essential physics of the electromagnetic coupling in the grating-gated 2DEC structures schematically shown in the insets in Figs. 1(a)
Fig. 1 Calculated terahertz absorption spectra of the grating-gated 2DEC on (a) a bulk substrate and on (b) the membrane substrate for the gate voltage value – 1 V for L = 4 µm, h = 4 µm, d = 0.4 μm, ε = 12.8, m* = 0.069m 0, and τ = 8.5×10−12 s. The insets in panels (a) and (b) show schematic views of the grating-gate structures on bulk and membrane substrates, respectively.
and 1(b), we employ the simplest phenomenological model of the resonant surface layer. Since the both gate-to-channel separation d and the grating gate period L are much smaller than THz radiation wavelength, the response of the grating-gated 2DEC to external in-plane electric field E=E0exp(iωt) can be described by the surface admittance [24

24. D. S. Tsui, S. J. Allen Jr, R. A. Logan, A. Kamgar, and S. N. Coppersmith, “High-frequency conductivity ijn silicon inversion layers: Drude relaxation, 2D plasmons and minigaps in a surface superlattice,” Surf. Sci. 73, 419–433 (1978). [CrossRef]

,25

25. V. V. Popov, O. V. Polischuk, T. V. Teperik, X. G. Peralta, S. J. Allen, N. J. M. Horing, and M. C. Wanke, “Absorption of terahertz radiation by plasmon modes in a grid-gated double-quantum-well field-effect transistor,” J. Appl. Phys. 94(5), 3556–3562 (2003). [CrossRef]

]
Y(ω)=n=0Yn(ω)=iσ¯0n=02βn2ωγeω2ωpn2+2iγeω,
(1)
where σ¯0=e2N¯sτ/m, is the sheet dc conductivity of the 2DEG with N¯s being the equilibrium sheet electron density averaged over the period of the structure, and e and m being the electron charge and effective mass, respectively, ωpn is the frequency of the nth plasma resonance, γe=1/2τ is the plasmon dissipative damping caused by electron scattering in the 2DEC with the characteristic relaxation time τ, and βn2 is a phenomenological coefficient of coupling between the incident THz electromagnetic wave of frequency ω and the nth plasmon mode. Assuming ω0=0 and β02=1 we have the zeroth term in series Eq. (1) as the Drude background admittance,

Y0(ω)=iσ¯02γeω+2iγe.

If γe<<ωpn and ωωpn, the nth term dominates in series Eq. (1). Then, in the vicinity of the nth plasma resonance, one has

Y(ω)Yn(ω)iσ¯0βn2γeωωpn+iγe.
(2)

Using conventional Fresnel formulas, we can calculate the reflectivity, transmittivity, and absorbance of the entire structure comprising the grating-gated 2DEC with the surface admittance defined by Eq. (1) [or Eq. (2) if γe<<ωpn and ωωpn] on the front surface of the substrate slab of thickness h.

If the grating-gated 2DEC lies on the surface of the a semi-infinite bulk substrate [see the inset in Fig. 1(a)], we obtain the absorbance in the neighborhood of the nth plasma resonance as [25

25. V. V. Popov, O. V. Polischuk, T. V. Teperik, X. G. Peralta, S. J. Allen, N. J. M. Horing, and M. C. Wanke, “Absorption of terahertz radiation by plasmon modes in a grid-gated double-quantum-well field-effect transistor,” J. Appl. Phys. 94(5), 3556–3562 (2003). [CrossRef]

,26

26. Equation (3) is approximately valid also for a bulk substrate of finite thickness with a bevel back surface, in which the interference effects in the substrate are eliminated.

]
An(ω)=2γeγrn(1R0)(ωωpn)2+(γe+γrn)2,
(3)
where
R0=(ε1)2(ε+1)2
(4)
is the reflectivity of a bare surface of the semi-infinite bulk substrate (with no resonant surface layer) with ε being the substrate dielectric constant (the ambient media is assumed to be vacuum) and
γrn=e2N¯s2mZ0βn2(ε+1)
(5)
is the radiative damping the nth plasmon mode with Z 0 being the free space impedance. The radiative damping can be viewed as a measure of the coupling strength between the incident THz wave and the nth plasmon mode [25

25. V. V. Popov, O. V. Polischuk, T. V. Teperik, X. G. Peralta, S. J. Allen, N. J. M. Horing, and M. C. Wanke, “Absorption of terahertz radiation by plasmon modes in a grid-gated double-quantum-well field-effect transistor,” J. Appl. Phys. 94(5), 3556–3562 (2003). [CrossRef]

].

At the resonance, ω=ωpn, Eq. (3) yields
Ares=2γeγrn(γe+γrn)2(1R0)
(6)
with the maximum absorbance Aresmax=0.5(1R0) for γe=γrn. For example, for a GaAs substrate (ε=12.8), one has Aresmax0.22. The condition γe=γrn can be re-written in the form of the matching condition for the surface admittance of the resonant layer at the nth plasmon resonance as Y(ωpn)=(ε+1)/Z0. Notice the inverted dependencies of Areson the ratio γe/γrn in two different casesγe<γrn and γe>γrn. The value γrn can be close to γe at the fundamental plasmon resonance in the grating-gate structure [19

19. V. V. Popov, M. S. Shur, G. M. Tsymbalov, and D. V. Fateev, “Higher-order plasmon resonances in GaN-based field-effect transistor arrays,” Int. J. High Speed Electron. Syst. 17(3), 557–566 (2007). [CrossRef]

]. However, the inequality γrn<γe is typically valid for higher-order plasmon resonances (because of a small net dipole moment of a higher-order plasmon mode). In this case, Eq. (6) becomes

Ares2γrnγe(1R0).
(7)

Now, let us consider the structure with a thin membrane-like substrate with thickness h<<λε, where λε is the THz wavelength in the substrate material [see the inset in Fig. 1(b)]. To the first-order approximation in respect to a small ratio between the substrate thickness and THz wavelength, the electromagnetic problem is equivalent to that considering the resonant layer with effective admittance
Yeff(ω)=Y(ω)iZ0k0h(ε1),
(8)
where k0=ω/c with c being the speed of light, suspended in the free space (ε=1). The effective admittance given by Eq. (8) is the sum of the resonant layer admittance Y(ω) and the sheet admittance of a thin dielectric substrate slab (the latter has a purely capacitive nature [27

27. E. H. Newman and J. L. Blanchard, “TM scattering by an impedance sheet extension of a parabolic cylinder,” IEEE Trans. Antenn. Propag. 36(4), 527–534 (1988). [CrossRef]

]). It means that the problem can be described by an equivalent transmission line of the characteristic impedance Z 0, which is shunted in the middle by a load with the effective admittance Eq. (8).

The absorption resonance lineshape in the membrane structure described by the sheet admittance Eq. (8) is formally defined by the same Eq. (3) with R 0 = 0 and ωpn and γrn replaced by ωpn(M)=ωpn[1γek0h(ε1)/(2ωpn)] and γrn(M)e2N¯sZ0βn2/4m, where ωpn(M) and γrn(M) are the frequency and radiative damping of the nth plasmon mode in the grating-gate structure on a thin membrane substrate, respectively. Since the second term in the square brackets in the right-hand side of the expression for ωpn(M) is the product of two small factors γe/ωpn and k 0 h, one has ωpn(M)ωpn (the same approximation was used when obtaining the expression for γrn(M)). Then Eq. (6) with R 0 = 0 yields the maximum absorbance Aresmax=0.5 for γe=γrn(M) [i .e ., Y(ωpn)2/Z0]in the structure with a membrane-like substrate. Notice that this value of the maximum absorption is twice as high as that for the structure with a bulk GaAs substrate. The plasmon radiative damping (or, which is the same, the coupling strength between the plasmon modes and THz radiation) also doubles in the membrane structure (γrn(M)2γrn) for ε10. Therefore, the absorption at higher-order plasmon resonances given by Eq. (7) increases fourfold due to the cumulative effect of reduced reflection (R00) and enhanced coupling between plasmons and THz radiation in the membrane structure.

3. Self-consistent electromagnetic modeling

Within the framework of a simple model of the surface resonant layer described in Section 2, the plasmon-resonance frequencies ωpn (or ωpn(M)) and radiative damping γrn (or γrn(M)) are phenomenological parameters, which are to be extracted from the measured plasmon absorption spectrum or calculated using a first-principle electromagnetic approach. We calculated the THz absorption spectra using a self-consistent electromagnetic approach described in detail in Ref. 28

28. V. V. Popov, G. M. Tsymbalov, and M. S. Shur, “Plasma wave instability and amplification of terahertz radiation in field-effect-transistor arrays,” J. Phys. Condens. Matter 20(38), 384208 (2008). [CrossRef] [PubMed]

. Figures 1(a) and 1(b) show the calculated spectra of plasmon resonances in the grating-gated 2DEC on the bulk and membrane substrates, respectively, for different values of the grating-gate aspect ratio w/L, where w is the width of the grating-gate finger. Other parameters are characteristic of AlGaAs/GaAs structures studied in experiments [14

14. 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(9), 1627–1629 (2002). [CrossRef]

,16

16. 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(19), 193507 (2005). [CrossRef]

]: L = 4 µm, h = 4 µm, τ = 8.5×10−12 s, homogeneous electron density in the channel at zero gate voltage is N s = 4.14×1011 cm–2, and d = 0.4 μm, which yields the channel pinch-off voltage of –2.3 V (as calculated in the parallel-plate capacitor model). The barrier-layer and substrate dielectric constants are 12.8 each, and m* = 0.069m 0 with m 0 being the free electron mass.

In accordance with Eq. (6) obtained in the framework of a simple model of the surface resonance layer, the maximum absorbance at the plasmon resonance reaches 0.5(1R0)0.22 in the structure with a bulk GaAs substrate [see Fig. 1(a)] and 0.5 in the structure with a membrane substrate [Fig. 1(b)]. As follows from Fig. 1, the absorbance at the second-order plasmon resonance increases roughly by a factor of 5 in the structure on the membrane substrate compared to the structure on a bulk substrate for the same grating aspect ratio 0.5 in accordance with Eq. (7). Absorbance at the higher-order plasmon resonances increases by more than an order of magnitude for narrow slits of the grating gate due to enhanced electromagnetic coupling between the plasmons and THz radiation [19

19. V. V. Popov, M. S. Shur, G. M. Tsymbalov, and D. V. Fateev, “Higher-order plasmon resonances in GaN-based field-effect transistor arrays,” Int. J. High Speed Electron. Syst. 17(3), 557–566 (2007). [CrossRef]

]. The photoresponse of the grating-gate plasmonic detector is linear in respect to the incoming THz power [14

14. 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(9), 1627–1629 (2002). [CrossRef]

]. This means that the responsivity of the slit-grating-gate plasmonic THz detector on a membrane substrate exceeds that of a conventional detector with 0.5-duty-cycle grating gate on a bulk substrate by a factor of 50 at the higher-order plasmon resonances.

4. Conclusions

In conclusion, we have shown that the responsivity of a grating-gate plasmonic detector can be dramatically enhanced by placing the detector onto a membrane substrate and using narrow-slit grating gate due to considerable enhancement of the electromagnetic coupling between the plasmons and THz radiation. Because the electromagnetic coupling is extremely fast process, such enhancement in the responsivity would not deteriorate the detector operation speed as opposed, e.g., to the bolometric enhancement of detector responsivity studied in Ref. 23

23. E. A. Shaner, M. C. Wanke, A. D. Grine, S. K. Lyo, J. L. Reno, and S. J. Allen, “‘Enhanced responsivity in membrane isolated split-grating-gate plasmonic terahertz detectors,” Appl. Phys. Lett. 90(18), 181127 (2007). [CrossRef]

. These results open up possibilities for improving performance of the grating-gate plasmonic THz detectors.

Acknowledgments

We thank Professor V. Ryzhii for useful discussions. This work at RPI was supported by the National Science Foundation under the auspices of the I/UCRC “Connection One”. The work at the Kotelnikov Institute was supported by the RFBR (Grant No. 09-02-00395) and by the Russian Academy of Sciences Program “Fundamentals of Nanotechnologies and Nanomaterials.”

References and links

1.

M. Dyakonov and M. Shur, “Detection, mixing, and frequency multiplication of terahertz radiation by two-dimensional electron fluid,” IEEE Trans. on Electron, Devices 43(3), 380–387 (1996). [CrossRef]

2.

W. Knap, J. Lusakowski, T. Parenty, S. Bollaert, A. Cappy, V. V. Popov, and M. S. Shur, “Terahertz emission by plasma waves in 60 nm gate high electron mobility transistors,” Appl. Phys. Lett. 84(13), 2331–2333 (2004). [CrossRef]

3.

A. Satou, V. Ryzhii, I. Khmyrova, M. Ryzhii, and M. S. Shur, “Characteristics of a terahertz photomixer based on a high-electron mobility transistor structure with optical input through the ungated regions,” J. Appl. Phys. 95(4), 2084–2089 (2004). [CrossRef]

4.

F. Teppe, W. Knap, D. Veksler, M. S. Shur, A. P. Dmitriev, V. Yu. Kachorovskii, and S. Rumyantsev, “Room-temperature plasma waves resonant detection of sub-terahertz radiation by nanometer field-effect transistor,” Appl. Phys. Lett. 87(5), 052107 (2005). [CrossRef]

5.

N. Pala, F. Teppe, D. Veksler, Y. Deng, M. S. Shur, and R. Gaska, “Nonresonant detection of terahertz radiation by silicon-on-insulator MOSFETs,” Electron. Lett. 41(7), 447–448 (2005). [CrossRef]

6.

A. El Fatimy, F. Teppe, N. Dyakonova, W. Knap, D. Seliuta, G. Valusis, A. Shcherepetov, Y. Roelens, S. Bollaert, A. Cappy, and S. Rumyantsev, “Resonant and voltage-tunable terahertz detection in InGaAs/InP nanometer transistors,” Appl. Phys. Lett. 89(13), 131926 (2006). [CrossRef]

7.

W. J. Stillman and M. S. Shur, “Closing the gap: Plasma wave electronic terahertz detectors,” J. Nanoelectron. Optoelectron. 2(3), 209–221 (2007). [CrossRef]

8.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Théron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys. 107(2), 024504 (2010). [CrossRef]

9.

A. Lisauskas, W. von Spiegel, S. Boubanga-Tombet, A. El Fatimy, D. Coquillat, F. Teppe, N. Dyakonova, W. Knap, and H. G. Roskos, “Terahertz imaging with GaAs field-effect transistors,” Electron. Lett. 44(6), 408–409 (2008). [CrossRef]

10.

A. El Fatimy, J. C. Delagnes, A. Younus, E. Nguema, F. Teppe, W. Knap, E. Abraham, and P. Mounaix, “Plasma wave field effect transistor as a resonant detector for 1 terahertz imaging applications,” Opt. Commun. 282(15), 3055–3058 (2009). [CrossRef]

11.

W. Knap, M. Dyakonov, D. Coquillat, F. Teppe, N. Dyakonova, J. Łusakowski, K. Karpierz, M. Sakowicz, G. Valusis, D. Seliuta, I. Kasalynas, A. El Fatimy, Y. M. Meziani, and T. Otsuji, “Field effect transistors for terahertz detection: Physics and first imaging applications,” J. Infrared Millim. Terahertz Waves 30(12), 1319–1337 (2009).

12.

S. J. Allen Jr, D. C. Tsui, and R. A. Logan, “Observation of the two-dimensional plasmon in silicon inversion layers,” Phys. Rev. Lett. 38(17), 980–983 (1977). [CrossRef]

13.

T. N. Theis, J. P. Kotthaus, and P. J. Stiles, “Two-dimensional magnetoplasmon in the silicon inversion layer,” Solid State Commun. 24(4), 273–277 (1977). [CrossRef]

14.

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(9), 1627–1629 (2002). [CrossRef]

15.

T. Otsuji, M. Hanabe, and O. Ogawara, “Terahertz plasma wave resonance of two-dimensional electrons in InGaP/InGaAs/GaAs high-electron-mobility transistors,” Appl. Phys. Lett. 85(11), 2119–2121 (2004). [CrossRef]

16.

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(19), 193507 (2005). [CrossRef]

17.

A. V. Muravjov, 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(4), 042105 (2010). [CrossRef]

18.

D. Coquillat, S. Nadar, F. Teppe, N. Dyakonova, S. Boubanga-Tombet, W. Knap, T. Nishimura, T. Otsuji, Y. M. Meziani, G. M. Tsymbalov, and V. V. Popov, “Room temperature detection of sub-terahertz radiation in double-grating-gate transistors,” Opt. Express 18(6), 6024–6032 (2010). [CrossRef] [PubMed]

19.

V. V. Popov, M. S. Shur, G. M. Tsymbalov, and D. V. Fateev, “Higher-order plasmon resonances in GaN-based field-effect transistor arrays,” Int. J. High Speed Electron. Syst. 17(3), 557–566 (2007). [CrossRef]

20.

E. A. Shaner, A. D. Grine, M. C. Wanke, M. Lee, J. L. Reno, and S. J. Allen, “Far-infrared spectrum analysis using plasmon modes in a quantum-well transistor,” IEEE Photon. Technol. Lett. 18(18), 1925–1927 (2006). [CrossRef]

21.

G. C. Dyer, J. D. Crossno, G. R. Aizin, E. A. Shaner, M. C. Wanke, J. L. Reno, and S. J. Allen, “A plasmonic terahertz detector with a monolithic hot electron bolometer,” J. Phys. Condens. Matter 21(19), 195803 (2009). [CrossRef] [PubMed]

22.

V. Ryzhii, A. Satou, T. Otsuji, and M. S. Shur, “Plasma mechanisms of resonant terahertz detection in a two-dimensional electron channel with split gates,” J. Appl. Phys. 103(1), 014504 (2008). [CrossRef]

23.

E. A. Shaner, M. C. Wanke, A. D. Grine, S. K. Lyo, J. L. Reno, and S. J. Allen, “‘Enhanced responsivity in membrane isolated split-grating-gate plasmonic terahertz detectors,” Appl. Phys. Lett. 90(18), 181127 (2007). [CrossRef]

24.

D. S. Tsui, S. J. Allen Jr, R. A. Logan, A. Kamgar, and S. N. Coppersmith, “High-frequency conductivity ijn silicon inversion layers: Drude relaxation, 2D plasmons and minigaps in a surface superlattice,” Surf. Sci. 73, 419–433 (1978). [CrossRef]

25.

V. V. Popov, O. V. Polischuk, T. V. Teperik, X. G. Peralta, S. J. Allen, N. J. M. Horing, and M. C. Wanke, “Absorption of terahertz radiation by plasmon modes in a grid-gated double-quantum-well field-effect transistor,” J. Appl. Phys. 94(5), 3556–3562 (2003). [CrossRef]

26.

Equation (3) is approximately valid also for a bulk substrate of finite thickness with a bevel back surface, in which the interference effects in the substrate are eliminated.

27.

E. H. Newman and J. L. Blanchard, “TM scattering by an impedance sheet extension of a parabolic cylinder,” IEEE Trans. Antenn. Propag. 36(4), 527–534 (1988). [CrossRef]

28.

V. V. Popov, G. M. Tsymbalov, and M. S. Shur, “Plasma wave instability and amplification of terahertz radiation in field-effect-transistor arrays,” J. Phys. Condens. Matter 20(38), 384208 (2008). [CrossRef] [PubMed]

OCIS Codes
(040.0040) Detectors : Detectors
(050.2770) Diffraction and gratings : Gratings
(040.2235) Detectors : Far infrared or terahertz
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Detectors

History
Original Manuscript: June 7, 2010
Revised Manuscript: July 7, 2010
Manuscript Accepted: July 7, 2010
Published: July 23, 2010

Citation
Vyacheslav V. Popov, Denis V. Fateev, Olga V. Polischuk, and Michael S. Shur, "Enhanced electromagnetic coupling between terahertz radiation and plasmons in a grating-gate transistor structure on membrane substrate," Opt. Express 18, 16771-16776 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16771


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References

  1. M. Dyakonov and M. Shur, “Detection, mixing, and frequency multiplication of terahertz radiation by two-dimensional electron fluid,” IEEE Trans. on Electron, Devices 43(3), 380–387 (1996). [CrossRef]
  2. W. Knap, J. Lusakowski, T. Parenty, S. Bollaert, A. Cappy, V. V. Popov, and M. S. Shur, “Terahertz emission by plasma waves in 60 nm gate high electron mobility transistors,” Appl. Phys. Lett. 84(13), 2331–2333 (2004). [CrossRef]
  3. A. Satou, V. Ryzhii, I. Khmyrova, M. Ryzhii, and M. S. Shur, “Characteristics of a terahertz photomixer based on a high-electron mobility transistor structure with optical input through the ungated regions,” J. Appl. Phys. 95(4), 2084–2089 (2004). [CrossRef]
  4. F. Teppe, W. Knap, D. Veksler, M. S. Shur, A. P. Dmitriev, V. Yu. Kachorovskii, and S. Rumyantsev, “Room-temperature plasma waves resonant detection of sub-terahertz radiation by nanometer field-effect transistor,” Appl. Phys. Lett. 87(5), 052107 (2005). [CrossRef]
  5. N. Pala, F. Teppe, D. Veksler, Y. Deng, M. S. Shur, and R. Gaska, “Nonresonant detection of terahertz radiation by silicon-on-insulator MOSFETs,” Electron. Lett. 41(7), 447–448 (2005). [CrossRef]
  6. A. El Fatimy, F. Teppe, N. Dyakonova, W. Knap, D. Seliuta, G. Valusis, A. Shcherepetov, Y. Roelens, S. Bollaert, A. Cappy, and S. Rumyantsev, “Resonant and voltage-tunable terahertz detection in InGaAs/InP nanometer transistors,” Appl. Phys. Lett. 89(13), 131926 (2006). [CrossRef]
  7. W. J. Stillman and M. S. Shur, “Closing the gap: Plasma wave electronic terahertz detectors,” J. Nanoelectron. Optoelectron. 2(3), 209–221 (2007). [CrossRef]
  8. A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Théron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys. 107(2), 024504 (2010). [CrossRef]
  9. A. Lisauskas, W. von Spiegel, S. Boubanga-Tombet, A. El Fatimy, D. Coquillat, F. Teppe, N. Dyakonova, W. Knap, and H. G. Roskos, “Terahertz imaging with GaAs field-effect transistors,” Electron. Lett. 44(6), 408–409 (2008). [CrossRef]
  10. A. El Fatimy, J. C. Delagnes, A. Younus, E. Nguema, F. Teppe, W. Knap, E. Abraham, and P. Mounaix, “Plasma wave field effect transistor as a resonant detector for 1 terahertz imaging applications,” Opt. Commun. 282(15), 3055–3058 (2009). [CrossRef]
  11. W. Knap, M. Dyakonov, D. Coquillat, F. Teppe, N. Dyakonova, J. Łusakowski, K. Karpierz, M. Sakowicz, G. Valusis, D. Seliuta, I. Kasalynas, A. El Fatimy, Y. M. Meziani, and T. Otsuji, “Field effect transistors for terahertz detection: Physics and first imaging applications,” J. Infrared Millim. Terahertz Waves 30(12), 1319–1337 (2009).
  12. S. J. Allen, D. C. Tsui, and R. A. Logan, “Observation of the two-dimensional plasmon in silicon inversion layers,” Phys. Rev. Lett. 38(17), 980–983 (1977). [CrossRef]
  13. T. N. Theis, J. P. Kotthaus, and P. J. Stiles, “Two-dimensional magnetoplasmon in the silicon inversion layer,” Solid State Commun. 24(4), 273–277 (1977). [CrossRef]
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  26. Equation (3) is approximately valid also for a bulk substrate of finite thickness with a bevel back surface, in which the interference effects in the substrate are eliminated.
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