APPLIED PHYSICS LETTERS
VOLUME 80, NUMBER 18
6 MAY 2002
Resonant detection of subterahertz radiation by plasma waves
in a submicron field-effect transistor
W. Knap,a) Y. Deng, S. Rumyantsev,b) J.-Q. Lü, and M. S. Shur
Department of ECSE and CIEEM, Rensselaer Polytechnic Institute, Troy, New York 12180
C. A. Saylor and L. C. Brunel
Center for Interdisciplinary Magnetic Resonance, NHMFL, Florida State University, Tallahassee,
Florida 32310
共Received 22 August 2001; accepted for publication 26 February 2002兲
The resonant detection of subterahertz radiation by two-dimensional electron plasma confined in a
submicron gate GaAs/AlGaAs field-effect transistor is demonstrated. The results show that the
critical parameter that governs the sensitivity of the resonant detection is ␻␶, where ␻ is the
radiation frequency and ␶ is the momentum scattering time. By lowering the temperature and hence
increasing ␶ and increasing the detection frequency ␻, we reached ␻ ␶ ⬃1 and observed resonant
detection of 600 GHz radiation in a 0.15 ␮m gate length GaAs field-effect transistor. The evolution
of the observed photoresponse signal with temperature and frequency is reproduced well within the
framework of a theoretical model. © 2002 American Institute of Physics.
关DOI: 10.1063/1.1473685兴
Nowadays, the most frequently used detectors of terahertz radiation are Schottky diodes. They are broadband detectors that rely on the nonlinearity of the current versus
voltage characteristics of a metal–semiconductor junction.1
There is great interest in new solid state devices that
could detect and emit terahertz radiation in a selective and
tunable way. The difficulty in detecting and generating terahertz radiation using solid state devices is related to two
factors: 共i兲 the transit times in the devices are typically much
longer than the period of the terahertz oscillations and 共ii兲 the
quanta of terahertz radiation are much smaller than room or
even liquid nitrogen thermal energy. However, plasma waves
in a gated two-dimensional electron gas can propagate with
much faster velocity than the electron drift velocity and their
excitation is not linked to any type of electronic transition.
Hence, they can be excited even at elevated temperatures.2
Allen et al. observed infrared absorption,3 and Tsui et al. reported weak infrared emission related to plasma waves in
silicon inversion layers.4 Burke et al. showed that the impedance of a high mobility transistor exhibits maxima at the
fundamental plasma frequency and its harmonics.5
The theory given in Ref. 6 predicted that a constant
drain-to-source voltage might be induced by electromagnetic
radiation coupled into the channel of a field-effect transistor
共FET兲. In a high mobility channel, this constant drain-tosource voltage should have resonant dependence on the radiation frequency, with the resonant frequency being proportional to the square root of the surface carrier density and
inversely proportional to the gate length. With carrier densities on the order of 1012 cm⫺2 and gate length dimensions
less than 1 ␮m the FET plasma frequency can reach the THz
range.2 The carrier density can be tuned by the gate-to-source
a兲
Also with GES CNRS–Université Montpellier 2, 34950 Montpellier,
France; electronic mail: knap@rpi.edu
b兲
On leave from the Ioffe Institute of the Russian Academy of Sciences,
194021 St. Petersburg, Russia.
voltage. This implies that a FET may be used as a resonant
tunable detector of THz radiation.
The dimensionless parameter that determines detector
behavior is ␻␶, where ␻ ⫽2 ␲ f and f is the radiation frequency. Two opposite cases 共␻ ␶ Ⰷ1 and ␻ ␶ Ⰶ1兲 are discussed in Ref. 6. When ␻ ␶ Ⰷ1, the FET can operate as a
resonant detector. When ␻ ␶ Ⰶ1, the plasma oscillations are
overdamped and the detector response is a smooth function
of ␻ as well as of the gate voltage 共broadband detector兲.
There have been a few experimental observations of nonresonant detection.7 However, until now, final experimental
confirmation of the possibility of resonant detection of THz
radiation by submicron FETs has not been reported.
In this letter we present investigations of the photoresponse of a GaAs/AlGaAs field-effect transistor for two subTHz frequencies, 200 and 600 GHz, in the temperature range
of 8 –300 K. We observed resonant detection when ␻␶ was
increased by increasing the frequency ␻ or by increasing the
scattering time ␶ 共mobility兲.
The FETs used in the experiments were commercial
GaAs/AlGaAs field-effect transistors 共Fujitsu FHR20X兲 with
gate length L⫽0.15 ␮ m. They were removed from their
packages and mounted on a quartz plate in order to avoid any
parasitic interference and reflections, like in Ref. 7. A complete set of current–voltage characteristics was measured for
each temperature 共see the inset of Fig. 1 for a representative
example兲. The transistor parameters were extracted using the
AIM-Spice model.8 A comparison between the measured
data and the FET model is shown in the inset of Fig. 1. One
can see that a good description of the current–voltage characteristics was obtained.
The change in source–drain resistance, with the magnetic field applied perpendicular to the conducting twodimensional plane, was measured up to 13 T. The result for
temperature of 10 K is shown in Fig. 1. The resistance increases with the magnetic field. At higher magnetic fields,
characteristic Shubnikov–de Haas oscillations are superim-
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© 2002 American Institute of Physics
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Appl. Phys. Lett., Vol. 80, No. 18, 6 May 2002
Knap et al.
FIG. 1. Relative source–drain resistance R sd /R 0 as a function of the magnetic field at 10 K. The dashed line is the parabolic fit. The inset shows I ds
vs U ds for different gate voltages at T⫽296 K. Points correspond to the
experimental results.
posed on the positive magnetoresistance background. The
oscillations confirm the existence of mobile two-dimensional
electrons in the transistor channel. The maximum carrier
density determined from the 1/B period of the oscillations for
zero gate voltage (U g ⫽0) was n s ⬃2⫻1012 cm⫺2 . The
parabolic-like change in background source–drain resistance
is due to the geometric magnetoresistance effect9 and is proportional to the (1⫹ ␮ 2 B 2 ) factor. Therefore, by fitting the
experimental data with a parabolic dependence 共dashed line兲
we determined mobility of ␮ ⬃7000 cm2 /V s at T⫽10 K.
The mobility values used in AIM-Spice simulations were
consistent with the magnetoresistance measurements.
Photoresponse measurements were performed with 200
and 600 GHz radiation systems based on a 100 GHz Gunn
diode with a frequency doubler 共for the 200 GHz system兲 or
doubler and tripler 共for the 600 GHz system兲. The maximum
output power was about 3 mW for the 200 GHz system and
0.3 mW for the 600 GHz system, respectively. Attenuators
were used in order to limit the power at the focused spot to
about 0.1 mW to avoid heating effects. A waveguide with a
cylindrical cone was connected to the output of the Gunn
diode to couple out the radiation. The radiation beam was
then focused by a parabolic mirror and led through the cryostat window to the sample, which was placed on a quartz
substrate glued to the cold finger of the closed cycle cryostat.
The radiation beam diameter at the sample holder was ⬃1
mm, a dimension that was much larger than the device size.
No special coupling antennas were used and the terahertz
radiation was coupled to the device through metallization
pads. In each measurement, we tested a few parabolic mirror
orientations and a few incident angles in order to determine
possible interference effects. We found that different beam
geometry/incidence angles changed only the amplitude of the
signal not its spectral shape.
The radiation intensity was modulated with a mechanical
chopper 共30–300 Hz range兲 and the open-circuit source–
drain voltage was measured by a voltage preamplifier 共1 M⍀
input resistance兲 followed by a lock-in amplifier. A regulated
temperature system allowed temperature stabilization to
within 1 K over a range of 8 –300 K. The results of measurements for a few temperatures are shown in Fig. 2共a兲. We
observed a typical 1/⫻-like background signal, which diverged for gate voltage that approached threshold voltage. At
the lowest temperatures 共below 30 K兲 a very reproducible
maximum superimposed on the background was observed.
FIG. 2. 共a兲 Experimental drain response U ds for different temperatures. The
results for temperatures of 296 共the lowest curve兲, 200, 150, 80, 12, and 8 K
共the highest curve兲 are shown. The inset shows the resonant signal ⌬U ds at
8 K obtained after subtraction of the 1/U 0 -like background from the experimental result. 共b兲 Resonant plasma frequency as a function of the gate voltage. The vertical arrow shows the crossing point with the 600 GHz horizontal line, the voltage of expected resonant detection.
The inset of Fig. 2共a兲 shows the shape of the maximum after
subtraction of the nonresonant background signal.
The theory predicts that a constant drain-to-source voltage might be induced by electromagnetic radiation coupled
into the channel of a field-effect transistor.2,6 As mentioned
above, this constant drain-to-source voltage can have resonant dependence on the radiation frequency, f, with a
maxima at plasma oscillation frequency of f 0 ⫽ ␣ s/L and its
odd harmonics 共␣ is the numerical constant that depends on
the boundary conditions and is equal to ␣ ⫽1/4 for the ac
short circuit at the source and the ac open circuit at the drain
conditions2兲. Here L is the channel length and s is the plasma
wave velocity that can be expressed as s⫽(eU 0 /m * ) 1/2
where m * is the effective mass of carriers. U 0 is the swing
voltage that controls the carrier density n s . In the gradual
channel approximation, U 0 is related to the carrier density by
the simple relation U 0 ⫽n s e/C and can be expressed as U 0
⫽(U g – U th) where U g is the gate-to-source voltage, U th is
the threshold voltage, and C is the gate to channel capacitance per unit area. In Fig. 2共b兲, we plot the plasma frequency versus gate voltage dependence for ␣ ⫽1/4 and U th
⫽0.47. As can be seen, the resonant frequency of the transistor decreases with the applied gate voltage from its maximum value of ⬃1.8 THz 共at zero gate bias兲 to zero, which is
reached when the gate voltage is equal to the threshold voltage. The fact that the maximum plasma wave frequency of
the device is 1.8 THz explains why detection of the first
plasma harmonics could not be observed in earlier experiments performed at 2.5 THz.7 The horizontal line in Fig. 2共b兲
corresponds to 600 GHz, which is the measurement frequency used in this work. One can see that the expected
position of the resonance 共marked by an arrow兲 is close to
the one observed in the experiment. In order to get a more
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Knap et al.
Appl. Phys. Lett., Vol. 80, No. 18, 6 May 2002
FIG. 3. Drain–source voltage U ds for different temperatures calculated according to Eq. 共1兲. The results are normalized to the U ds value at U g
⫽0.47 V for 8 K. The results for temperatures of 296 共the lowest solid
curve兲, 200, 150, 80, 12, and 8 K 共the highest solid curve兲 are shown. The
expected increase in detector response when ␻␶ slightly increases to 1.5 is
shown by a dashed line. The inset shows the change in electron mobility ␮
and ␻␶ for 600 GHz with a decrease in temperature, and the dashed line is
a guide for the eye.
quantitative description of the results we use the following
expressions for the drain response derived from Ref. 6:
U ds⫽
1 U 2a
f 共 ␻ 兲,
4 U0
共1兲
where
f 共 ␻ 兲 ⫽1⫹ ␤ ⫺
␤⫽
1⫹ ␤ cos共 2k 0⬘ L 兲
sinh2 共 k 0⬙ L 兲 ⫹cos2 共 k 0⬘ L 兲
2␻␶
冑1⫹ 共 ␻ ␶ 兲 2
,
,
␻
␻
k 0⬘ ⫽ 共 1/␤ ⫹1/2兲 1/2, k 0⬙ ⫽ 共 1/␤ ⫺1/2兲 1/2.
s
s
Here U a is the ac gate-to-drain voltage induced by external
illumination. Using Eq. 共1兲, we calculated the detector response expected using the device parameters determined
from I – V and magnetoresistance measurements for different
temperatures. The results are shown in Fig. 3. As can be seen
from a comparison of Figs. 2共a兲 and 3 good overall agreement between measured and calculated spectra was obtained.
The temperature evolution of the background, as well as of
the position and the width of the resonant signal seen in the
experiment 关Fig. 2共a兲兴, are reproduced well in the calculated
spectra 共Fig. 3兲.
In order to understand the temperature evolution of the
spectra one has to consider the change in the ␻␶ parameter.
The measured mobility ␮ versus the temperature dependence
is plotted in the inset of Fig. 3. As can be seen 共right-hand
scale兲, the mobility increases with a decrease in temperature.
The momentum scattering time was calculated as ␶
⫽ ␮ m * /e. For the scale on the left-hand side of the inset, we
show the value of ␻␶ for frequency of 600 GHz. One can see
that at temperatures above 50 K ␻ ␶ Ⰶ1. At temperatures be-
3435
low 30 K, one approaches the condition of resonant detection
( ␻ ␶ ⫽1). This explains why at higher temperatures only the
1/U 0 -like nonresonant background is observed10 but, at low
temperatures, a resonant feature is superimposed on this
background. This behavior is seen in the experimental data
关Fig. 2共a兲兴 and in the theoretical calculations 共Fig. 3兲. The
value of the ␻␶ parameter also determines the sensitivity of
detection. 共The expected increase in detector response when
␻␶ slightly increases to 1.5 is shown by a dashed line in Fig.
3兲. One expects very high sensitivity of such detectors for
high mobility GaAs FETs.6
We also compared the detector response at the same temperature 共8 K兲 but for two different frequencies, 200 and 600
GHz. We observed that, with an increase in frequency, a
resonant detection structure appeared. This is due to the fact
that ␻␶ increases by a factor of 3 between 200 and 600 GHz.
In summary, our results clearly demonstrate resonant detection by two-dimensional electron plasma confined in submicron field-effect transistors. The critical parameter that
governs the physics of the detection problem is ␻␶. We demonstrated that by increasing ␶ 共by lowering the temperature兲
or increasing the detection frequency ␻, one can reach resonant detection of sub-THz radiation in a 0.15 ␮m gate length
GaAs field-effect transistor. Both the resonant and nonresonant parts of the photoresponse signal observed, as well as
their evolution with the temperature and frequency, were explained within the framework of a theoretical model developed earlier. Theoretical estimates point to the possibility of
achieving, in high mobility GaAs FETs, resonant detection
up to several orders of magnitude more sensitive than that of
conventional Schottky diodes.6
The authors would like to thank Professor M. Dyakonov
and Professor B. Shklovskii for useful discussions. This
work was partially supported by the National Science Foundation under Grant No. 0080509 and by DARPA 共project
monitors E. Martinez and D. Woolard兲.
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M. Dyakonov and M. S. Shur, in Terahertz Sources and Systems, edited by
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共1977兲.
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J.-Q. Lü, M. S. Shur, J. L. Hesler, L. Sun, and R. Weikle, IEEE Electron
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Silicon and Beyond: Advanced Device Models and Circuit Simulators,
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W. Knap, V. Kachorovskii, Y. Deng, S. Rumyantsev, J.-Q. Lü, R. Gaska,
M. S. Shur, G. Simin, X. Hu, M. Asif Khan, C. A. Saylor, and L. C.
Brunel, J. Appl. Phys. 共to be published兲.
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