A financial support by NATO linkage grant CLG977520 — „Semiconductor Sources for Terahertz Generation“ is highly acknoledged. The work at RPI was supported by the national Science Foundation (Program Monitor Dr. James Mink).
The terahertz part of the electromagnetic spectrum lies A resonant, voltage-tunable detection based on excitation at the border between wavelengths generated by solid of plasmon resonance in a two-dimensional electron gas state electronics and optics. Many excitations observed in (2DEG) confined in a field effect transistor (FET) was condensed matter, liquids, gases and biological substances proposed in the early 90-es [12,13], and reported only correspond to the THz range of frequincies, i. e. to recently [14–16]. A FET, biased by gate-to-source voltage 0.3-30 meV photon energies. Spectral analysis in the Ugs, and subject to and electromagnetic radiation can THz region can be used for studies of these excitations, develop a constant drain-to-source voltage Uds, which has such as phonons, cyclotron or spin resonance, as well as a resonant dependence on the frequency of radiation with for investigations of molecular (rotational and vibrational) maxima at plasma oscillation frequencies , f = N/2.
N excitations in liquids, gases and biological substances. A Resonant plasma frequencies are discrete and given by growing interest in the analysis of signals carried by THz N = 0(1 + 2N), where 0 = s/2L, and N = 0, 1, 2....
radiation is also related to possible applications of THz The plasma wave velocity, s, depends on the carrier spectroscopy for non-destructive sensing and imaging in density in the transistor’s channel, n, and the gate-to-channel medicine, food industry and defence [1,2]. capacitance (C = 0/d) per unit area: s =(e2n/mC)1/2, Terahertz broadband detectors include bolometers [3–5], where e and m are the electron charge and the effective pyroelectric detectors, Schottky diodes [6,7] and photo- mass, respectively, is dielectric constant and d is the gateconductive detectors . An advantage of selective and to-channel distance. In the gradual channel approximation, tuneable detectors is that they require no gratings of moving the carrier density in the channel is related to the gate-tomirrors of perform a spectral analysis. Tuneability was source voltage by a relation n = CU0/e, where U0 is the demonstrated for photoconductive detectors (GaAs , gate-to-channel voltage swing, U0 = Ugs - Uth, and Uth is InP , and InSb ) placed in a magnetic field which the threshold voltage. The fundamental plasma frequency tuned the energy of optical transitions between the levels of can be expressed by an approximate relation shallow donors or cyclotron and impurity shifted cyclotron 1 eUresonance. Such detectors, however, require liquid helium f =. (1) 4L m temperatures and magnetic fields of a few Tesla.
For many applications, tuning a detector’s response with This has two important consequences: i) a sufficiently an applied voltage is much easier than by the magnetic field. short (sub-micron) FET can operate as a THz detector and Magnetotransport characterization of THz detectors based on plasma oscillations in submicron field... The most important parameters related to the resonant detection are the electron scattering time and the electron concentration. The former one, related to the electron mobility, enters into the quality factor 0, which, for given value of, gives a low bound of frequency for which FET can operate as a resonant detector. The electron concentration determines the transistor threshold voltage (which affects the maximum swing voltage, directly related to the frequency of plasmon resonance, as shown in Eq. 1). Therefore, determination of the electron density and mobility in a transistor is a key point in view of its applications as a resonant plasma device. The magnetotransport determination of these parameters is addressed in the present work.
The standard equations for the current density ( j) in the Figure 1. Photoinduced drain-to-source voltage of GaAs/GaAsAs 2DEG in the presence of the magnetic field (perpendicular FET (from group A) as a function of gate-to-source voltage to the 2DEG plane) are and temperature from 8, 20, 60, 100 K to 200 K (from top to bottom). Inset shows the resonant detection of the 0.6, 0.8 and jx = xx Ex + xyEy, 1.2 THz radiation from multiplied Gunn diode source (See  and  for details). Higher Gunn diode harmonics are visible jy = -xyEx + xxEy.
after illumination of FET . The arrows mark positions of Here Ex and Ey are the components of the electric field 2D plasmon resonances — and corresponds to detection of 0.6, 0.8 and 1.2 THz from left to the right correspondingly (See  in the (xy) plane and xx and xy are components of the and  for details).
comductivity tensor. In the Drude–Boltzman theory these components depend on the magnetic field:
xx = 0/(1 + µ2B2), ii) a pesponse frequency of such a detector can be tuned by xy = 0µB/(1 + µ2B2).
The width of a resonant curve is determined by the The boundary conditions for these equations depend on quality factor 0, wher is the electron momentum the sample geometry. Two important limiting cases considrelaxation time. The resonant detection becomes possible ered in this work are the Hall bar geometry and transistor ” if the quality factor reaches and exceeds the value of 1. If geometry“ (with the device width, D, being much larger 0 1, plasma oscillations are over-damped and the FET than the device length, L). For a long Hall bar, L D. In response is a smooth function of as well as of gate-tothis case, there is no current in the y“ direction, jy = 0, ” source voltage (a non-resonant broadband detection ).
and the measured Ex = jx /0. This means that conductivity Resonant and non-resonant detection of THz radiation (and resistivity) does not depend on the magnetic field.
was recently demonstrated in two field-effect devices: a In other words there is no magnetoresistance. This is a commercial FET [14,15,17] and a double quantum well FET general feature of a degenerate two-dimensional gas. On with a periodic grating . In both cases, the frequency of the other hand, in the case of a very short but wide device a standing 2D plasmon wave was tuned to a THz frequency (L D), the Hall voltage is short-circuited by long currentby varying the gate-to-source voltage. In Fig. 1 we show supplying contacts. Then Ey = 0 and jx = xxEx. This an example of the resonant detection of THz radiation geometry is equivalent to that of the Corbino disk. In rerformed using a GaAs/GaAlAs FET.
this case, the measured Ex = jx (1 + µ2B2)/0 and one The temperature evolution of spectra shown in Fig. 1 expects a parabolic increase of the sample resistance and is mainly related to a change in the electron scattering Lorentzian (1/(1 + µ2B2)) decrease of the conductance.
time. A resonant feature (marked by an arrow) starts The coefficient of the parabolic magnetoresistance (or to be visible below about 30 K because only then does halfwidth or Lorentzian magnetoconductivity) is equal to th electron scattering time increases sufficiently for the the mobility. In quantizing magnetic fields (µB 1), the condition 0 1 to be fulfilled. Illumination of the conductivity exhibits Shubnikov–de Hass oscillations. These transistor with visible light leads to an additional increase oscillations are periodic as a function of inverse magnetic of the electron mobility (µ) and, as a result, to an increase field (1/B), the period depending only on the carrier of the quality factor 0. This allowed for better resolution density.
of the main resonance (0.6 THz) and observation of the In this work, different GaAs and GaInAs FETs and Hallresonant detection of higher harmonics (0.8 and 1.2 THz) bar test structures were investigated by magnetotransport of a frequency-multiplied 0.2 THz Gunn diode source — as measurement in high magnetic field (up to 14 T). We show shown in the inset in Fig. 1. how magnetoconductivity data allow evaluating the electron Физика твердого тела, 2004, том 46, вып. 140 J. Lusakowski, W. Knap, N. Dyakonova, E. Kaminska, A. Piotrowska, K. Golaszewska, M.S. Shur, D. Smirnov...
mobility and concentration in a transistor channel even for a non-ideal geometry. The results are then used for the interpretation of the recently observed resonant detection and for the estimation of the parameters relevant to the THz detection in these field effect transistors. The maximun frequency and the quality factor that limit the THz detection in different field effect structures are descussed.
1. Experiment and Results Three groups of devices, named A, B and C, were investigated. The group A included commercially available Fujitsu FX20 FETs with a gate length (L) of 0.15 µm, gate width (D) of 50 µm and the gate to channel separation (d) Figure 3. Example of characteristics of transistor T5 (from of 25 nm. Their threshold voltage varied between –0.group B). Transient characteristics at T = 4.2K as a function and –0.5 V and the electron mobility was estimated to be of the magnetic field, B, equal to (from top to bottom, in Tesla):
0.1–0.2 m2/Vs at 300 K and 0.5–1.0 m2/Vs at 4 K. 0, 0.030, 0.051, 0.068, 0.090, 0.140, 0.260 and 1. The inset shows output characteristics for gate-source voltage equal to (from top to Transistors and Hall-bars of the group B and C were bottom, in volts): 0, –0.1, –0.2, –0.3 and –0.4.
processed out of MBE-grown high electron mobility GaAs/GaAlAs and GaInAs/GaAlAs heterostructures, respectively. The group B transistors had the threshold voltage of –0.2 to –0.5 V and the electron mobility of 5–20 m2/Vs were used for independent measurements of the electron at 4.2 K, while the corresponding values for the group C density and mobility.
transistors were –1 to –2V and 1–2m2/Vs, respectively.
Measurements were carried out at liquid helium temperThe gate to channel distance was d 160 and d 40 nm atures (4.2 or 8 K) after cooling the sample in the dark.
for group B and C transistors, respectively. The same mask A typical set of measurements carried out on transistors was used in the case of B and C (Fig. 2) which defined involved: i) output characteristics (drain current, Id, vs.
transistors with the gate length equal to 0.8, 1.5 and 2.5 µm.
drain-to-source voltage, Uds ) as a function of Ugs voltage The source to drain distance was 10 µm for all transistors and the magnetic field, B; ii) transient characteristics (drain and the gate was placed close to the source contact to ensure current vs. gate-to-source voltage, Ugs ) as a function of B;
asymmetry of the transistor (necessary for the detection).
iii) magnetoconductivity (drain current vs. B) as a function Two gated Hall-bars and a Schottky diode were fabricated of gate-to-source voltage. (Let us note that in the following next to each group of the six transistors. Hall structures the gate-to-sourse voltage is always negative and its increase means an increase of its absolute value.) An example of the experimental data, for one of the group B transistors, is shown in Fig. 3.
In some cases, additional data were taken after illumination of a sample with a red light emitting diode. Output characteristics were used for determination of a range Uds and Ugs which drain current changed linearly with drain-to-source voltage. Transient characteristics allowed determining the threshold voltage, values of which are cited in the preceding paragraph.
An analysis of magnetoconductivity of transistors presented below uses the following scheme. At low magnetic fields one observes a strong decrease of conductivity with an increase of the magnetic field which leads to a Lorentzlike shape of the magnetoconductivity curve. This curve is used for estimation of the electron mobility in the transistor channel. At large magnetic fields, Shubnikov–de Haas oscillations are observed and used for determination of the electron concentration. Measurements were performed for different values of the gate-to-source voltage. Results of Figure 2. A photograph of a dice of the group B and C measurements carried out on transistors are compared with devices with litographically defined six transistors, two Hall-bars and Schottky diode. magnetotransport results obtained for gated Hall-bars.
Физика твердого тела, 2004, том 46, вып. Magnetotransport characterization of THz detectors based on plasma oscillations in submicron field... tance, [R(B) - R(0)]1/2, normalized to its value at 1 T. If the magnetoconductivity were described by a Lorentzian -1 +(B/B1/2)2, then this figure would show a straight line. We found that magnetoresistance for all gate-to-sourse voltages and for both transistors can be described by a Lorentzian-like dependence but with the exponent equal to 1.3 rather than 2. An inverse of the halfwidth of these Lorentzian-like magnetoconductivity curves, B-1, is 1/plotted as a function of a gate-to-source voltage in Fig. 6.
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