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Nanometer size field effect transistors for terahertz detectors
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
Nanometer size field effect transistors forterahertz detectorsW Knap1,2, S Rumyantsev1,3, M S Vitiello4, D Coquillat1, S Blin5,N Dyakonova1, M Shur3, F Teppe1, A Tredicucci4 and T Nagatsuma6
1 Laboratoire Charles Coulomb, UMR 5221, Universite Montpellier 2 and CNRS, F-34950 Montpellier,France2 Institute of High Pressure Physics UNIPRESS PAN, 02-845 Warsaw, Poland3 Rensselaer Polytechnic Institute, Troy, NY 12180, USA4 NEST, Istituto Nanoscienze—CNR and Scuola Normale Superiore, I-56127 Pisa, Italy5 Institute Electronique du Sud, UMR 5214, Universite Montpellier 2 and CNRS, F-34950 Montpellier,France6 Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
Received 5 November 2012, in final form 22 February 2013Published 25 April 2013Online at stacks.iop.org/Nano/24/214002
AbstractNanometer size field effect transistors can operate as efficient resonant or broadband terahertzdetectors, mixers, phase shifters and frequency multipliers at frequencies far beyond theirfundamental cut-off frequency. This work is an overview of some recent results concerning theapplication of nanometer scale field effect transistors for the detection of terahertz radiation.
(Some figures may appear in colour only in the online journal)
1. Introduction
Interest in terahertz (THz) systems and technology has grownsignificantly over the past 10 years. THz rays (T-rays)present an alternative to x-rays for imaging through paper,cloth and many plastic materials. In contrast to x-rays theyare non-ionizing and therefore inherently safe. Applicationsof THz rays range from nondestructive testing to medicalimaging, security screening of objects and persons, andsecure wireless communication. THz imaging and wirelesscommunication applications suffer, however, from the lack oflow-cost detector arrays operating at room temperature.
Existing commercially available detectors of terahertz ra-diation have specific performance and application limitationsarising from their design and principle of operation:
• Bolometers require cryogenic temperatures and are usuallyof high size and weight.• Golay cells, which are simple opto-acoustic detectors
capable of operating in a wide spectrum range (upto 30 THz) are also bulky and have their modulationfrequency limited to a few tens of hertz.• Pyroelectric detectors are characterized by high sensitivity,
high bandwidth (up to 30 THz), and room temperature op-eration. However the modulation frequency of pyroelectricdetectors does not exceed 10 kHz.
• Schottky diode detectors operate in the bandwidth up to2–3 THz and in the gigahertz sampling frequency range.Their responsivity and noise equivalent power ranges from∼100 V W−1 to 1–2 kV W−1 and from 2 to 50 pW Hz−1/2,respectively. (Here, the highest value of responsivity andsmallest value of NEP correspond to the sub-terahertzfrequency range.)
Interest in using nanometer field effect transistors (FETs)for THz applications was initiated in the early 1990s by thetheoretical work of Dyakonov and Shur [1], who predictedthat the channel of a FET could act as a resonator for plasmawaves. These waves have typical velocities s ∼ 106 m s−1.The fundamental frequency f of this resonator depends on itsdimensions and, for nanometer gate lengths (L ≤ 10−6 m), canreach the terahertz (1 THz = 10−12 s−1) range, since f ∼ s/L.A steady current flow in an asymmetric FET channel can leadto the instability and spontaneous generation of plasma waves.This can in turn lead to the emission of electromagneticradiation at the plasma wave frequency and its harmonics.Later, it was also shown [2] that the nonlinear properties ofthe 2D plasma in the transistor channel could be used fordetection and mixing of THz radiation.
Rectification and detection of THz radiation is alsopossible in the non-resonant case (low electron mobility)
when plasma waves decay at a distance smaller than thechannel length. The typical length of this region, whicheffectively rectifies THz radiation, ranges from 30 to300 nm [3]. Therefore, both resonant and non-resonant plasmawave THz detection requires nanometer scale FETs.
Both THz emission [4–7], resonant [8–11] and non-resonant [3, 12–16] detection, were observed at cryogenicand room temperatures, clearly demonstrating effects relatedto the plasma excitations. Currently, the most promisingapplication appears to be the room temperature broadbandTHz detection in the non-resonant regime for imaging andcommunication applications.
The real large-scale interest in using FETs as THzdetectors started around 2004 after the first experimentaldemonstration of sub-THz and THz detection in silicon-CMOS FETs [17]. Soon after (2006) it was shownthat Si-CMOS FETs can reach a noise equivalent powercompetitive with the best conventional room temperatureTHz detectors [18]. Both pioneering works have clearlystated the importance of Si-CMOS FETs, which present theadvantages of room temperature operation, very fast responsetimes, easy on-chip integration with read-out electronicsand high reproducibility, leading to straight-forward arrayfabrication. Recent studies demonstrate the main detectorcharacteristics, responsivity and noise equivalent power,within the same range as Schottky barrier diodes [19, 20,30]. Other existing THz detectors, such as bolometers, Golaycells, and pyroelectric detectors, require specialized andless common fabrication technologies, which do not allowmonolithic integration.
Recently focal plane arrays in silicon technology havebeen designed and used for imaging at frequencies reachingthe 1 THz range [21–25]. Heterodyne detection using SiMOSFETs was also shown [26] and seems to be themost promising approach for THz imaging applications.Improvement of plasmonic terahertz detection by usingdouble-grating-gate field effect transistor structures was alsodemonstrated [27–30].
This paper is a review of recent results on THzdetection using nanometer size FETs. The subjects wereselected in a way to stress some new physical aspectsand developments rather than purely technological orengineering improvements. Sections 2–4 are devoted to basicphysics-related problems such as the power dependence of thephotoresponse, temperature dependence of the response, andhelicity sensitive detection, respectively.
Until now, most work on nanometer FET detectorsconsidered mainly THz imaging applications. In sections 5and 6 we show the progress in overcoming the loadingproblems and demonstrate first results on the application ofnanometer FETs as detectors in wireless communication withsignals modulated in the GHz frequency range.
Finally, in sections 7 and 8 we present results from THzdetection by nanowires and graphene transistors. Possibledevelopments of future THz detectors using these newnanostructures are addressed in section 9.
Figure 1. Transfer current–voltage characteristics measured for adrain voltage of 1 mV (dash-dotted lines, right hand scale) andresponse of 0.13 µm CMOS FET to 0.3 THz radiation at 100 and275 K (solid lines). Upper inset shows the layout of the test structurecontaining transistors with different antenna design. An array of 3by 4 transistors in the lower left corner of the inset represents aprototype of the imaging matrix. Lower inset on the right shows theschematic of the photoresponse measurement circuit [19].
2. Detection of THz radiation by FET in low andhigh power limits
When THz radiation is coupled between the gate and sourceof the FET, the THz ac voltage simultaneously modulatesthe carrier density and the carrier drift velocity. This leadsto nonlinearity and, as a result, the photoresponse appears inthe form of a dc voltage between the source and drain. Forhigh carrier mobility devices (e.g. III–V devices at cryogenictemperatures) the THz field can induce plasma waves thatpropagate in the channel, and resonant plasma modes canbe excited, leading to a resonant narrowband and gate biastunable detection [2, 9–11, 31]. At room temperature, plasmawaves are usually overdamped and the THz radiation causesonly a carrier density perturbation that decays exponentiallywith a distance of the order of a few tens of nanometers.
A more detailed description of the physical mechanismof THz detection by FETs can be found in [3, 32]. In thecase of room temperature broadband detection (overdampedplasma) the detection process can be alternatively explainedby the model of distributed resistive self-mixing. Althoughnot treating all plasma-related physics rigorously, the resistivemixing model allows a rational detector design [33, 34].
A typical schematic of the photoresponse measurementcircuit and a test element layout together with measuredsignal and transfer characteristics are shown in figure 1.Asymmetry between the source and drain is needed toinduce photoresponse. There exist various ways to reachsuch asymmetry. One is the difference in the source anddrain boundary conditions due to external (parasitic) orinternal capacitances. Another is the asymmetry in feedingthe incoming radiation, which can be achieved by specialantenna connections, as shown in the lower inset in figure 1. In
this circuit the radiation predominantly creates an ac voltagebetween the source and the gate [19].
The mechanism of the detection depends on the ω0τ
product, where ω0 = πs/2Lg is the fundamental plasmaharmonic frequency, s is the plasma wave velocity, Lg is thegate length, and τ is the momentum relaxation time (relatedto carrier mobility). At room temperature τ = 10−13–10−14 sdepending on the semiconductor material.
In the regime when ω0τ � 1 (high mobility), the FETcan operate as a resonant detector. When ω0τ � 1 (lowmobility), the plasma oscillations are overdamped, and theFET response is a smooth function of frequency and gatevoltage, representing a non-resonant detection regime.
The dependence of the non-resonant response onthe basic parameters, such as the gate length, channelcapacitance, and frequency, was analyzed in [12]. The set ofequations from [12] allows analysis and optimization of thenon-resonant response as a function of the above-mentionedparameters.
Plasma wave velocity:
s2= s2
0
[1+ exp
(−
qV0
ηkT
)]ln[
1+ exp(
qV0
ηkT
)],
s0 =
√ηkT
m. (1)
Response signal:
1u =qu2
a
4ms2
[1−
1
sh2Q+ cos2Q
], Q =
Lg
l;
l = s
√2τω. (2)
Here ua is the ac THz voltage on the gate relative to thesource, V0 = Vg − Vt,Vg is the dc gate voltage, Vt is thethreshold voltage, m is the effective mass, and η determinesthe sub-threshold slope of the channel conductivity decayσ(V0) ∼ exp(qV0/ηkT). The parameter η is within the rangeη = 1.1–1.5 for well-designed devices; however practically itcan be as high as η = 3–5, especially at low temperatures.
Q = Lg/l is the ratio of the gate length to thecharacteristic length l of the voltage decay from source todrain (see equation (2)). This length is usually somewhatsmaller than the gate length and lies within 30–300 nmdepending on the frequency and momentum relaxation timeτ (carrier mobility).
For low frequencies and a long gate, when distributiveeffects play a minor role, a phenomenological formula [13]relates the expected detector signal to the channel conductiv-ity:
1u =u2
a
4
[1σ
dσdu
]u=V0
. (3)
Equation (3) allows a calculation of the expected pho-toresponse by a simple differentiation of the transfercurrent–voltage characteristic.
In the sub-threshold range the channel conductivitydepends on the gate voltage as σ(V0) ∼ exp(qV0/ηkT). Using
equation (3) one obtains the maximum value of the responsesignal:
1u =qu2
a
4ηkT. (4)
The same result was obtained in [12] using equation (2).Equation (4) allows an estimation of the maximum
responsivity. Assuming that all incident radiation power Pis absorbed by the detector, one can approximate u2
a by theproduct of the input channel impedance ∼l/(σW) and poweru2
a ∼ Pl/(σW). Here W is the gate width, σ is the channelconductivity and l the characteristic length as defined above.In this case the voltage responsivity RV can be approximatedas
RV ∼ ql/(4σWηkT). (5)
A more rigorous derivation of FET detector responsivity canbe found in [35].
Since the conductivity entering the denominator decaysas σ(V0) ∼ exp(qV0/ηkT), it becomes exponentially smallbelow threshold. Therefore RV may become exponentiallylarge below threshold. For example, using equation (5) withη = 2 and an input channel resistance of 500� one gets RV ∼
10 kV W−1. In the real experimental conditions responsivityis limited by antenna coupling and loading effects discussedin sections 5 and 9. A responsivity up to 5 kV W−1 and aNEP in the range of a few pW Hz−1/2 was reported by manyauthors [19, 36]. These values are comparable to the bestresults reported for Schottky diode-based detectors, placingFETs as important competitors with the additional advantageof easy integration into arrays.
For low intensities of THz radiation the photoresponseis proportional to the radiation power (photovoltaic effect)and is described by equation (2). At higher intensities thephotoresponse is no longer proportional to the incomingpower. A sub-linear dependence was observed in experiments(see figure 2). The theoretical model developed in [37]provides analytical expressions:
1u =u2
a
2(√
V20 + u2
a/2+ V0)
. (6)
Below threshold (V0 < 0), the response is given by
1u =ηkT
qln I0
qua
ηkT, (7)
where I0 is the Bessel function.Figure 2 compares experimental results with theory for
the high terahertz power nonlinear regime of operation.InGaAs/GaAs HEMTs with a 0.13 µm gate length were usedas a detector of 1.63 THz radiation produced by an opticallypumped CO2 laser with a maximum power of 160 mW.
Good agreement between experiment and calculations forboth above and below threshold regimes was obtained. Asseen at high ac power, the response increases sub-linearlywith the increase of u2
a , i.e. with the increase of the incomingterahertz power. The linear regime of operation is limitedby u2
a ≈ 1 mV2 (∼30 mW). This is still a rather high
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Nanotechnology 24 (2013) 214002 W Knap et al
Figure 2. Comparison between the analytical calculations usingequations (6) and (7) (solid lines) and measured results (squares andcircles) for V0 = −70 mV and V0 = 100 mV (after [37]). Dashedlines indicate the linear dependence.
Figure 3. Maximum response (at Vg ∼ Vt) of GaAs, GaN HEMTand Si MOSFET to 300 GHz radiation as a function of temperature(after [38]).
power for this frequency range. For detection using typicalsemiconductor THz sources and backward wave oscillators(BWO) we should expect a linear regime of operation.
3. Temperature dependence of the non-resonantdetection
The temperature dependence of non-resonant THz detectionby FETs was investigated in [38]. The experimental resultsin the temperature range 30 K < T < 300 K agree wellwith equation (4), which predicts that the maximal responseis inversely proportional to temperature. At temperaturesfrom 300 to 30 K the photoresponse of GaAs-, GaN-, andSi-based FETs increased with a temperature decrease. Below30 K the photoresponse was temperature independent (seefigure 3). (The difference in the response amplitude fordifferent transistors is explained by the different antennastructures leading to different THz coupling to the devices.)
Figure 4. Polarization dependence of the response, f = 0.8 THz.Ellipses on the top illustrate the polarization states (after [40]).
As shown in [20], the low-temperature saturation is correlatedwith the saturation of the sub-threshold slope observed in thestatic transfer characteristics of the transistors.
Therefore, the physical mechanism of the low-temperature response saturation is attributed to the transportregime change from the collision/diffusion dominated oneto the ballistic or traps dominated one. These results clearlyshow that THz detectors based on field effect transistorsmay significantly improve their responsivity with reducedtemperature. Since noise also decreases with a temperaturedecrease, an even higher improvement in noise equivalentpower can be achieved. However, at low temperatures (below30 K) the change of transport mechanism limits furtherimprovements.
4. Helicity-dependent terahertz detection with FETs
The sensitivity of the terahertz plasmonic broadband detectorsto linear polarization orientation has been relatively wellestablished [39]. However, the photoresponse proportional tothe degree of circular polarization has been only recentlyobserved in GaAs/AlGaAs HEMTs and Si MOSFETs [40].The experiments were performed applying a CW and pulsedTHz radiation in the frequency range 0.6–2.5 THz [40].The important new experimental and theoretical discoveryof [40] was that the photon helicity can be sensed through theinterference of two ac currents generated on opposite sidesof the transistor channel. The coupling of the radiation to thetransistor channel can be modeled by two effective antennas,producing an ac voltage between source and gate, and betweendrain and gate. In the case of long transistors there is nointerference between the currents induced at opposite sidesof the channel, and the corresponding contributions to thetotal photoresponse are independent. For sufficiently shorttransistor channels, the ac currents generated at the source anddrain interfere in the mid-section of the device leading to an
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Nanotechnology 24 (2013) 214002 W Knap et al
ac current component that depends on their phase difference.Such a phase difference appears when the source and thedrain sides are excited by mutually orthogonal components ofcircular (or elliptically) polarized radiation. The interferenceterm in this case is sensitive to the radiation helicity.
Figure 4 shows a polarization behavior of the signalobtained by varying the radiation ellipticity.
It is worth stressing that the observed helicity-dependentresponse in FETs is strictly related to their particular THzrectification physical mechanism. It provides the basis for avery sensitive (more than two orders of magnitude comparedto other known methods), fast and all-electric characterizationof the THz radiation polarization state and, therefore, canbe used for the development of new methods of THzellipsometry.
5. Loading effects
The channel resistance exponentially increases belowthreshold and may become comparable to or even higherthan the input resistance of the measurements system. Atthis point the response signal decreases due to a simplevoltage—dividing effect (loading effect). Due to this loadingeffect, the signal may also depend on the modulationfrequency because even a small capacitance can lead to largeRC constants.
The loading effects related to resistances were firstanalyzed in [41] (see also [42] and references therein). Themost complete approach to the loading effects is presentedin [13]. It was shown that to reproduce the experimentalresults one should divide the photovoltaic signal 1u by afactor (1 + RCH/Z), where RCH is the channel resistance andZ is the complex load impedance of the read-out setup. SinceZ contains not only the load resistance of the preamplifiersbut also all the parasitic capacitances, the amplitude of theresponse depends on the modulation frequency fm.
Figure 5 shows the influence of the modulation frequency,fm and load resistance on the gate voltage dependence of theresponse.
In general, both: (i) an increase of the modulationfrequency fm and (ii) a decrease of the input impedance ofthe read-out circuit lead to a decrease of the signal in thesub-threshold range.
As seen from figure 5(a), an increase of the modulationfrequency up to 10 kHz leads to a decrease of the signal inthe high-resistance range (close to threshold). However, farfrom the threshold when the transistor is in the low-resistancestate, the signal is independent of frequency in the wholeinvestigated frequency range.
In figure 5(b) we show results obtained with themodulation frequencies 133 Hz and 10 kHz for loadresistances decreasing from 10 M� to 1 k�. Similar to theresults from figure 5(a), one can see a gradual decrease ofthe signal in the high-resistance state (close to threshold). Farfrom the threshold, when the transistor is in the low-resistancestate, the signal does not depend on load resistance. For thehigh load resistance of 1 M� there is a difference in theresponse for 133 Hz and 10 kHz modulation. For lower loads,
Figure 5. (a) Gate voltage dependence of the 300 GHzphotoresponse for a constant load resistance 10 M� and differentmodulation frequencies. The modulation frequency was graduallyincreased from 23 Hz, 133 Hz, 1 kHz, 3 kHz to 10 kHz. (b) Gatevoltage dependence of the response for different load resistancesand two modulation frequencies. Results obtained with a constantmodulation frequency 133 Hz (triangles) and load resistancechanging from 10 M� to 1 M�, 10 k� and 1 k�. For a modulationfrequency 10 kHz (squares) the load resistance was 1 M�, 10 k�and 1 k�. Continuous black lines show results of calculations(after [13]).
however, the photoresponse is the same for both frequenciesin the whole range of gate voltages. Results in figure 5 showthe trade-off between bandwidth and response amplitude. Aswill be shown in section 6, the bandwidth up to a gigahertzrange can be achieved by operating the transistor in the openstate.
The experimental results could be very well reproduced(solid lines) without any fitting parameters using aphenomenological approach (equation (3)) and normalizationfactor (1 + RCH/Z), with Z measured by a standard LCRbridge.
As can be seen in figure 5, the bandwidth of detectorsoperated in their high impedance mode (close to the threshold)is limited to a few kHz. The limitation of bandwidth is a resultof three main factors: the output resistance of the detector, theinput resistance of the amplifier and the parasitic capacitances.In the case presented in figure 5, the parasitic capacitancesof the cables between transistor and amplifier were relativelyhigh (of the order of 150 pF), the output resistance close tothe threshold was around 1 M�, and the input resistance ofthe preamplifier was 10 M�.
There are two ways to increase the bandwidth:
(i) Operate the transistor far from the threshold, where thechannel resistance is lower (close to 50 �). In figure 5
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Nanotechnology 24 (2013) 214002 W Knap et al
Figure 6. Detection power as function of the modulation frequency,f = 0.305 THz (after [45]).
it is clear that the bandwidth for higher gate voltages ishigher.
(ii) Integrate the transistor, load and amplifier to decreaseparasitic capacitances.
As shown in section 6, bandwidths up to the GHz rangecan be achieved by combining both methods.
6. Plasma wave detectors for terahertzcommunication
An important application of THz systems is wirelesscommunication. In theory, the modulation bandwidth could bein the sub-THz range, exceeding 100 GHz [43]. For example,for heterodyne detection, the intermediate frequency can beof the order of 50–100 GHz for a 200 nm gate transistoroperating at room temperatures in the above-threshold regime,and of the order of 5–10 GHz in the below thresholdregime [44]. As was demonstrated in [45], modulation up to8 GHz can be reached in wireless communication systemsusing a 250 nm gate-length plasmonic GaAs/AlGaAs fieldeffect transistor as a detector.
Figure 6 presents the amplitude of the detectedmodulation signal measured using a spectrum analyzer. Thedetector was mounted directly on 50 � microstrip lines. Thegate voltage was applied to keep the detector in the open state(far from the threshold) providing its output resistance close to50 �. The signal was amplified using a 50 � 30 dB amplifier.The modulation signal was observed for frequencies between0.3 MHz and 8 GHz.
There is usually a trade-off between bandwidth andresponse amplitude. Far from the threshold this kind ofdetector has a 3 dB bandwidth up to the GHz range, butrelatively low sensitivity (1.3 V W−1) (13.3 nW Hz−1/2), thenoise being the thermal noise of the amplifier. As mentionedabove, an improvement can be obtained by integrating thetransistor with a fast amplifier.
Figure 7. Response of the InAs/InSb nanowire to 0.293 THzradiation. Red solid line shows the measured response, blue dashedline is obtained from transfer current–voltage characteristics usingequation (3). Inset shows the SEM picture of the device activeregion (after [48]).
7. Terahertz detection by nanowire FETs
Nanowire FETs are promising candidates for THz detectors,due to their one dimensionality, which modifies the spectraof allowed plasma modes. Both InAs and heterostructureInAs/InSb nanowire lateral field effect transistors have beenstudied in [46–48].
InAs nanowire FETs detectors were first developed for0.3 THz radiation by the application of both bow-tie and log-periodic antennas between the source and gate electrode [46].The THz response was tested in a top-incidence configurationor through the substrate using a Si lens for improvedcollection. A NEP of a few 10−9 W Hz−1/2 was measuredfor the first devices [46]. The concept was then extended to ahigher frequency range by appropriate scaling of the antennageometry. In this case a NEP of ∼6 × 10−11 W Hz−1/2
was recorded using a 1.5 THz quantum cascade laser as asource [47].
Heterostructured nanowires, consisting of two segments(InAs and InSb forming a heterojunction in the middle)exhibited a peculiar behavior [48]. The gate electrode waslocated on one side of the nanowire, as it was for the InAsdevices, and on both sides of the InAs/InSb heterojunction(see inset in figure 7). In general the devices behaved asn-channel FETs at gate voltages above threshold Vt = −2 Vand up to Vg = (4–5) V. A further increase of the gatevoltage led to a decrease of the current, which is possiblylinked to the electron distribution being pulled towards thenanowire surface. Figure 7 shows (i) the measured responseof the transistors to 0.293 THz radiation (red solid line) and(ii) the shape of the gate voltage dependence of the response,which is predicted based on the numerical differentiation(see equation (3)) of the current–voltage characteristic(blue dashed line). Although the shape obtained from thecurrent–voltage characteristic differs from the experimentalone, the dependence can still be qualitatively explained byequation (3).
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Nanotechnology 24 (2013) 214002 W Knap et al
Figure 8. Response as a function of gate voltage for differentpolarization angles for a top gate graphene transistor, f = 0.3 THzInset shows SEM pictures of the antenna design (a) andconfiguration of the graphene transistor (b) (after [55]).
8. Graphene FETs for terahertz applications
Graphene, a one–three atom-thick planar sheet of ahoneycomb carbon crystal is a unique material with superiorproperties. The unusual gapless band structure of graphenewith a linear energy spectra for electrons and holes may leadto giant carrier mobility at room temperature and a broadbandflat optical response. In combination with extremely highthermal conductivity, these properties make graphene veryappealing for electronics and sensor applications, includingTHz applications.
A number of graphene-based THz devices have beenproposed recently. This includes a graphene tunnelingtransit-time THz oscillator based on electrically inducedp–i–n junctions [49], THz lasers based on optically pumpedmultiple graphene structures [50], double graphene layerplasma resonance THz detectors exploring the tunnelingbetween graphene layers and the resonant excitation ofplasma oscillations [51], THz graphene electro-opticalmodulators [52] and some others. A review of recentachievements on graphene-based THz devices can be foundin [53]. The potential of using graphene transistors operatingin the plasma wave mode was also studied theoretically [54]and experimentally [55].
The use of graphene for THz detection based on plasmaeffects is motivated by its potential to reach very highmobility, which makes graphene a promising candidate forfuture resonant plasma detectors.
In [55], single- and double-layer graphene flakesmechanically exfoliated on Si/SiO2 substrates were used tofabricate top gate transistors. Log-periodic circular-toothedantennas at the source and gate were used to couple 0.3 THzradiation (see figure 8). A 35 nm thick HfO2 layer was usedas the gate dielectric. The channel length was 7–10 µm, whilethe gate length was 200–300 nm. A SEM picture of devices infalse color is shown in the inset in figure 8.
Figure 8 shows the responsivity as a function of gatevoltage for different polarization angles. The specific featureof these dependences is the change of the sign of the response
Figure 9. Response at f = 2.55 THz at zero and 0.1 V drain biasfor graphene back-gate transistor. Inset shows the dependence of theresponse on the polarization angle.
at the charge neutrality (Dirac) voltage. This behavior andoverall shape of these dependences was well described by thephenomenological equation (3).
Similar results were obtained at higher frequencies up to3.11 THz for back-gated graphene transistors [56] (see [57]for the device details).
Figure 9 shows the response at f = 2.55 THz at zero and0.1 V drain bias. As seen, the drain voltage (current) increasesthe amplitude of the response by more than one order ofmagnitude. The inset shows the dependence of the responseat Vd = 0 on the polarization angle.
These experiments were performed using mechanicallyexfoliated graphene with mobility limited to∼(3000–10 000) cm2 V−1 s−1. Much better results, includingplasma wave resonances and resonant detection, are expectedon suspended graphene samples with even higher mobility.
9. Discussion and conclusions
Nanometer size field effect transistors operating as broadbandTHz detectors, mixers, phase shifters and frequencymultipliers at THz frequencies compete with commerciallyavailable Schottky diodes. Recent studies show that FETsreach responsivities, NEPs and speeds of the same order ofmagnitude as Schottky diodes while having advantages inCMOS VLSI compatibility.
Further improvements of the FET THz detectors shouldrelate to (i) improving the coupling with external radiation and(ii) improving the transistor design as well as its integrationwith impedance matching amplifiers.
The typical wavelength of sub-THz or THz radiation isin the range from one mm to hundreds of microns. Withtransistor dimensions on the nanometer scale direct efficientcoupling through antennas is difficult due to (i) the unknowntransistor input impedance in the THz frequency range and(ii) radiation coupling to the substrate instead of the transistoritself.
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Nanotechnology 24 (2013) 214002 W Knap et al
The most spectacular progress can be achieved byimproving the transistor and reaching the resonant detectionregime. Resonant detection can be more sensitive, spectrallyresolved and gate voltage tunable. There are two main waysto reach this goal: (i) increase the carrier mobility and(ii) improve the device geometry. The high mobility can beattained by using InSb—or graphene-based channels with thecarrier mobilities exceeding 8000–10 000 cm2 V−1 s−1.
An improvement of device geometry is necessary toeliminate the existence of oblique plasma modes. Mosttransistors are devices with gate widths much greater thanthe gate length. In such devices, plasma waves propagatingin the oblique directions travel in different directions and for adifferent distances. This leads to the broadening of the plasmawave spectrum [11, 32]. One may decrease the role of obliquemodes using narrow channel transistors or transistors based onnanowires [58, 59]. However, there is a trade-off between thechannel width and carrier mobility because for very narrowchannels additional scattering from the channel borders limitsthe mobility. Therefore, the development of narrow channelnanowires with high carrier mobility for resonant plasma THzdetection is still a future technological challenge.
In conclusion: we have presented an overview of recentexperimental results on the detection of terahertz radiationby nanometer scale FETs. Currently, the most promisingapplication appears to be broadband THz detection in thenon-resonant regime. Different kinds of FETs have exhibitedsuch detection, including Si, GaAs, GaN, nanowires, andgraphene devices.
New applications such as THz ellipsometry andpolarization sensitive imaging have been discussed. We havealso shown that the operation of THz FET detectors atcryogenic temperatures can improve their performance. Animportant achievement is the demonstration of broadbandTHz communications with up to 8 GHz modulation frequency.
Further progress with THz detection by FETs shouldbe related to the improvement of the THz coupling andimprovement of the transistor design. In particular, suspendedgraphene transistors with carrier mobilities exceeding8000–10 000 cm2 V−1 s−1 show promise for resonantdetection. Other promising directions are the development ofgrating gate structures and nanowire transistors. They maylead to efficient, resonant and voltage tunable THz detectors.
Acknowledgments
We thank Professor M Dyakonov and Professor S Ganichevfor many helpful discussions. This work was supported byANR project ‘WITH’ and by CNRS and GDR-I project‘Semiconductor sources and detectors of THz frequencies’and by the US—French initiative ‘PUF’. The Montpellierteam affiliated with the Physics and Electronics departmentswas supported by the Scientifique Interest GroupementGIS—TERALAB. The work at RPI was supported by theUS NSF under the auspices of the NSF EAGER programand by the ARL Cooperative Research Agreement. MSVacknowledges financial support of the Italian Ministry ofEducation, University, and Research (MIUR) through the
program ‘FIRB-Futuro in Ricerca 2010’ RBFR10LULP‘Fundamental research on terahertz photonic devices’.
References
[1] Dyakonov M I and Shur M S 1993 Shallow water analogy fora ballistic field effect transistor: new mechanism of plasmawave generation by dc current Phys. Rev. Lett. 71 2465
[2] Dyakonov M I and Shur M S 1996 Plasma wave electronics:novel terahertz devices using two-dimensional electronfluid IEEE Trans. Electron Devices 43 380
[3] Knap W et al 2009 Field effect transistors for terahertzdetection: physics and first imaging applications J. InfraredMillim. Terahz. Waves 30 1319
[4] Knap W, Łusakowski J, Parenty T, Bollaert S, Cappy A,Popov V V and Shur M S 2004 Terahertz emission byplasma waves in 60 nm gate high electron mobilitytransistors Appl. Phys. Lett. 84 3523
[5] Dyakonova N, Teppe F, Łusakowski J, Knap W,Levinshtein M, Dmitriev A P, Shur M, Bollaert S andCappy A 2005 Magnetic field effect on the terahertzemission from nanometer InGaAs/AlInAs high electronmobility transistors J. Appl. Phys. 97 4313
[6] Dyakonova N et al 2006 Room temperature terahertz emissionfrom nanometer field-effect transistors Appl. Phys. Lett.88 141906
[7] El Fatimy A et al 2010 AlGaN/GaN high electron mobilitytransistors as a voltage-tunable room temperature terahertzsources J. Appl. Phys. 107 024504
[8] Lu J-Q, Shur M S, Hesler J L, Sun L and Weikle R 1998Terahertz detector utilizing two-dimensional electronicfluid IEEE Electron Device Lett. 19 373
[9] Lu J-Q and Shur M S 2001 Terahertz detection byhigh-electron-mobility transistor: enhancement by drainbias Appl. Phys. Lett. 78 2587
[10] Knap W, Deng Y, Rumyantsev S and Shur M S 2002Resonant detection of sub terahertz and terahertz radiationby plasma waves in submicron field-effect transistors Appl.Phys. Lett. 81 4637
[11] El Fatimy A et al 2006 Resonant and voltage-tunable terahertzdetection in InGaAs/InP nanometer transistors Appl. Phys.Lett. 89 131926
[12] Knap W et al 2002 Nonresonant detection of terahertzradiation in field effect transistors J. Appl. Phys. 91 9346
[13] Sakowicz M, Lifshits M B, Klimenko O A, Schuster F,Coquillat D, Teppe F and Knap W 2011 Terahertzresponsivity of field effect transistors versus their staticchannel conductivity and loading effects J. Appl. Phys.110 054512
[14] Lu J-Q and Shur M S 2001 Terahertz detection by highelectron mobility transistor: effect of drain bias Appl. Phys.Lett. 78 2587–8
[15] Veksler D, Teppe F, Dmitriev A P, Kachorovskii V Yu,Knap W and Shur M S 2006 Detection of terahertzradiation in gated two-dimensional structures governed bydc current Phys. Rev. B 73 125328
[16] Elkhatib T A, Kachorovskii V Yu, Stillman W J,Rumyantsev S, Zhang X-C and Shur M S 2011 Terahertzresponse of field-effect transistors in saturation regimeAppl. Phys. Lett. 98 243505
[17] Knap W, Teppe F, Meziani Y, Dyakonova N, Lusakowski J,Boeuf F, Skotnicki T, Maude D, Rumyantsev S andShur M S 2004 Plasma wave detection of sub-terahertz andterahertz radiation by silicon field-effect transistors Appl.Phys. Lett. 85 675
[18] Tauk R et al 2006 Plasma wave detection of terahertz radiationby silicon field effects transistors: responsivity and noiseequivalent power Appl. Phys. Lett. 89 253511
[19] Schuster F, Coquillat D, Videlier H, Sakowicz M, Teppe F,Dussopt L, Giffard B, Skotnicki T and Knap W 2011
[20] Schuster F, Knap W and Nguyen V 2011 Terahertz imagingachieved with low-cost CMOS detectors Laser Focus World47 37
[21] Ojefors E, Pfeiffer U R, Lisauskas A and Roskos H G 2009A 0.65 THz focal-plane array in a quarter-micron CMOSprocess technology IEEE J. Solid-State Circuits 44 1968
[22] Sherry H, Grzyb J, Zhao Y, Al Hadi R, Cathelin A,Kaiser A and Pfeiffer U 2012 ISSCC 2012 IEEE Int.Solid-State Circuits Conf. Digest of Technical Papers
[23] Lisauskas A, Glaab D, Roskos H G, Oejefors E andPfeiffer U R 2009 Terahertz imaging with Si MOSFETfocal-plane arrays Terahertz Technology and Applications II(Proc. SPIE) (San Jose, CA: Jan. 2009) vol 7215
[24] Boppel S, Lisauskas A, Max A, Krozer V andRoskos H G 2012 CMOS detector arrays in a virtual10-kilopixel camera for coherent terahertz real-timeimaging Opt. Lett. 37 536
[25] Boppel S, Lisauskas A, Krozer V and Roskos H G 2011Performance and performance variations of sub-1 THzdetectors fabricated with 0.15 µm CMOS foundry processElectron. Lett. 47 661
[26] Glaab D, Boppel S, Lisauskas A, Pfeiffer U, Ojefors E andRoskos H G 2010 Terahertz heterodyne detection withsilicon field-effect transistors Appl. Phys. Lett. 96 042106
[27] Watanabe T et al 2012 Ultrahigh sensitive plasmonic terahertzdetector based on an asymmetric dual-grating gate HEMTstructure Solid-State Electron. 78 109
[28] Popov V V, Fateev D V, Otsuji T, Meziani Y M,Coquillat D and Knap W 2011 Plasmonic terahertzdetection by a double-grating-gate field-effect transistorstructure with an asymmetric unit cell Appl. Phys. Lett.99 243504
[29] Popov V V, Ermolaev D M, Maremyanin K V, Maleev N A,Zemlyakov V E, Gavrilenko V I and Shapoval S Yu 2011High-responsivity terahertz detection by on-chipInGaAs/GaAs field-effect-transistor array Appl. Phys. Lett.98 153504
[30] Han R N, Zhang Y M, Coquillat D, Videlier H, Knap W,Brown E and Kenneth K O 2011 A 280-GHz Schottkydiode detector in 130-nm digital CMOS IEEE J. Solid-StateCircuits 46 2602
[31] Knap W, Deng Y, Rumyantsev S and Shur M S 2002Resonant detection of subterahertz and terahertz radiationby plasma waves in submicron field-effect transistors Appl.Phys. Lett. 81 4637
Knap W, Deng Y, Rumyantsev S and Shur M S 2002Resonant detection of subterahertz and terahertz radiationby plasma waves in submicron field-effect transistors Appl.Phys. Lett. 80 3434
[32] Knap W and Dyakonov M I 2013 Field effect transistors forterahertz applications Handbook of Terahertz Technology(Cambridge: Woodhead Publishing) pp 121–55
[33] Lisauskas A, Pfeiffer U, Ojefors E, Bolivar P H, Glaab D andRoskos H G 2009 Rational design of high-responsivitydetectors of terahertz radiation based on distributedself-mixing in silicon field-effect transistors J. Appl. Phys.105 114511
[34] Perenzoni D, Perenzoni M, Gonzo L, Capobianco A D andSacchetto F 2010 Analysis and design of a CMOS-basedterahertz sensor and readout Proc. SPIE 7726 772618
[35] Kachorovskii V Yu, Roumyantsev S L, Knap W andShur M 2012 Performance limits for field effect transistorsas terahertz detectors Appl. Phys. Lett. submitted
[36] Ojefors E, Pfeiffer U, Lisauskas A and Roskos H 2009 A0.65 THz focal-plane array in a quarter-micron CMOSprocess technology IEEE J. Solid-State Circuits 44 1968
[37] Gutin A, Kachorovskii V, Muraviev A and Shur M 2012Plasma wave terahertz detector response at high intensitiesJ. Appl. Phys. 112 014508
[38] Klimenko O A et al 2012 Temperature enhancement ofterahertz responsivity of plasma field effect transistorsJ. Appl. Phys. 112 014506
[39] Sakowicz M, Łusakowski J, Karpierz K, Grynberg M,Knap W and Gwarek W 2008 Polarization sensitivedetection of 100 GHz radiation by high mobility field-effecttransistors J. Appl. Phys. 104 024519
[40] Drexler C et al 2012 Helicity sensitive terahertz radiationdetection by field effect transistors J. Appl. Phys.111 124504
Romanov K S and Dyakonov M I 2013 Theory ofhelicity-sensitive terahertz radiation detection by field effecttransistors Appl. Phys. Lett. accepted
[41] Stillman W, Shur M S, Rumyantsev S, Veksler D andGuarin F 2007 Device loading effects on nonresonantdetection of terahertz radiation by silicon MOSFETsElectron. Lett. 43 422
[42] Stillman W, Donais C, Rumyantsev S, Shur M, Veksler D,Hobbs C, Smith C, Bersuker G, Taylor W andJammy R 2011 Silicon FinFETs as detectors of terahertzand sub-terahertz radiation Int. J. High Speed Electron.Syst. 20 27
[43] Kachorovskii V Yu and Shur M S 2008 Field effect transistoras ultrafast tunable detector of terahertz radiation SolidState Electron. 52 182–5
[44] Gershgorin B, Kachorovskii V Yu, Lvov Y V andShur M S 2008 Field effect transistor as heterodyneterahertz detector Electron. Lett. 44 1036–7
[45] Blin S et al 2012 Plasma-wave detectors for terahertz wirelesscommunication IEEE Electron Device Lett. 33 1354
[46] Vitiello M S, Viti L, Romeo L, Ercolani D, Scalari G,Beltram J, Sorba L and Tredicucci A 2012 Semiconductornanowires for highly sensitive, room-temperature detectionof terahertz quantum cascade laser emission Appl. Phys.Lett. 100 241101
[47] Vitiello M S, Coquillat D, Viti L, Ercolani D, Teppe F,Pitanti A, Beltram F, Sorba L, Knap W andTredicucci A 2012 Room-temperature terahertz detectorsbased on semiconductor nanowire field- effect transistorsNano Lett. 12 96
[48] Pitanti A, Coquillat D, Ercolani D, Sorba L, Teppe F, Knap W,De Simoni G, Beltram F, Tredicucci A andVitiello M S 2012 Terahertz detection by heterostructuredInAs/InSb nanowire based field effect transistors Appl.Phys. Lett. 101 141103
[49] Ryzhii V, Ryzhii M, Mitin V and Shur M S 2009 Graphenetunneling transit-time terahertz oscillator based onelectrically induced p–i–n junction Appl. Phys. Express2 034503
[50] Ryzhii V, Dubinov A A, Otsuji T, Mitin V and Shur M S 2010Terahertz lasers based on optically pumped multiplegraphene structures with slot-line and dielectric waveguidesJ. Appl. Phys. 107 054505
[51] Ryzhii V, Otsuji T, Ryzhii M and Shur M S 2012 Doublegraphene-layer plasma resonances terahertz detector J.Phys. D: Appl. Phys. 45 302001
[52] Ryzhii V, Satou A, Otsuji T, Ryzhii M, Ryabova N,Yurchenko S O and Shur M S 2012 Graphene-basedelectro-optical modulator: concept and analysis IMFEDK2012 IEEE Int. Mtg for Future of Electron Devices, Kansaip 2
[53] Otsuji T, Tombet S A B, Satou A, Fukidome H, Suemitsu M,Sano E, Popov V, Ryzhii M and Ryzhii V 2012Graphene-based devices in terahertz science andtechnology J. Phys. D: Appl. Phys. 45 303001
[54] Rudin S 2011 Non-linear plasma oscillations in semiconductorand graphene channels and application to the detection ofterahertz signals Int. J. High Speed Electron. Syst. 20 567
[55] Vicarelli L, Vitiello M S, Coquillat D, Lombardo A,Ferrari A C, Knap W, Polini M, Pellegrini V andTredicucci A 2012 Graphene field-effect transistors asroom-temperature terahertz detectors Nature Mater. 11 865
[56] Muraviev A, Rumyantsev S, Liu G, Shur M S andBalandin A A, unpublished
[57] Rumyantsev S, Liu G, Stillman W, Shur M andBalandin A A 2010 Electrical and noise characteristics ofgraphene field-effect transistors: ambient effects, noise
sources and physical mechanisms J. Phys.: Condens.Matter 22 395302
[58] Shchepetov A et al 2008 Oblique modes effect on terahertzplasma wave resonant detection in InGaAs/InAlAsmultichannel transistors Appl. Phys. Lett. 92 242105
[59] Boubanga-Tombet S et al 2008 Current driven resonantplasma wave detection of terahertz radiation: toward theDyakonov–Shur instability Appl. Phys. Lett. 92 212101
