A fast, voltage-tunable terahertz mixer based on the intersubband transition of a high-mobility 2-dimensional electron gas has been fabricated from a single 40 nm GaAs-AlGaAs square quantum well heterostructure. The device is called a Tunable Antenna-Coupled Intersubband Terahertz mixer and shows tunability of the detection frequency from 2.52 to 3.11 THz with small (<1 V) top gate and bottom gate voltage biases. Mixing at 2.52 THz has been observed at 60 K with a −3dB intermediate frequency bandwidth exceeding 6 GHz.

Terahertz (THz) heterodyne receivers are widely used for high-resolution THz spectroscopy in space and are important for applications in bio-medical imaging and future THz wireless communications.1,2 In a THz heterodyne system, a nonlinear element referred to as a mixer down-converts an incoming THz signal (RF) into an intermediate-frequency (IF) signal at a much lower frequency (usually at several GHz) using a THz local-oscillator (LO) source with known frequency and power. For a low-noise, high-resolution THz heterodyne system, a sensitive, broadband mixer is essential. Above 1 THz, superconducting hot-electron bolometers (HEBs) are current state-of-the-art mixers that offer low noise temperature (within an order of magnitude of the quantum limit), wide IF bandwidth (∼3 GHz), and small required LO power (∼1 μW).2 However, cryogenic operating temperature less than or equal to 4 K limits the use of superconducting HEBs in certain applications such as deep-space missions to planets and comets that cannot afford the power and mass required for active cryogenic cooling. For such applications, Schottky diode mixers that work at ambient temperature are the only option so far, but with the cost of higher noise and higher required LO power (∼1 mW). The latter especially limits the use of Schottky mixers in heterodyne array applications.

In this Letter, we demonstrate a Tunable Antenna-Coupled Intersubband Terahertz (TACIT) mixer, which is a type of HEB mixer based on a high-mobility 2-dimensional electron gas (2DEG) in a GaAs-AlGaAs quantum well that uses an intersubband transition for efficient absorption of THz radiation.3 TACIT mixers operate at relatively high temperatures (50–70 K), which are accessible with passive cooling for deep-space missions and with compact, light-weight cryocoolers for other applications, and are predicted to offer low single-sideband (SSB) noise temperature (∼1000 K), a wide IF bandwidth (>10 GHz), and low required LO power (<1 μW).4 The prototype TACIT mixer described in this Letter demonstrates tunability in the detection frequency between 2.52 THz and 3.11 THz with small top and bottom gate biases (<1 V) and THz mixing at 2.52 THz at 60 K with an IF bandwidth exceeding 6 GHz. The noise temperature, the conversion loss, and the required LO power of the prototype device have not been measured for the current nonoptimized device. However, a bolometric mixer analysis based on the current-voltage (IV) curve for a model device indicates that a further optimized TACIT device can offer impressive mixer characteristics at 60 K, making TACIT mixers a viable, alternative mixer technology for low-noise, high-resolution THz spectroscopy with possible array applications in deep space and for other applications in which relaxed cryogenic and LO power requirements are advantageous.

Since the early 1990s, two-terminal versions of 2DEG-based HEB mixers have been proposed5 and have demonstrated mixing in the millimeter-wave range with wide IF bandwidths ranging from 3 GHz for phonon-cooled devices6,7 to 20 GHz for diffusion-cooled devices8 and even to 40 GHz for ballistically cooled devices.9 Like a superconducting HEB, a 2DEG HEB has an antenna coupled to two ohmic contacts (source and drain) that orients RF and LO electric fields along the 2DEG plane, and the radiation is absorbed through ohmic losses in the electrons. Because of the large kinetic inductance of high-mobility 2DEGs,10 however, the RF coupling efficiency in these two-terminal devices significantly degrades at THz frequencies. As a result, the conversion loss greatly increases above the practical upper frequency limit of 500 GHz,9 limiting the application of the two-terminal 2DEG HEB mixers at THz frequencies.

TACIT mixers overcome the frequency limit in two-terminal 2DEG HEB mixers by using two additional gates to achieve a high THz coupling efficiency through the intersubband transition of a 2DEG confined in a quantum well. In this four-terminal device scheme [see Fig. 1(a)], two ohmic contacts (source and drain) are used to apply a DC bias current and measure the IF response in the device resistance and two additional gates (top gate and bottom gate) are used to couple THz RF and LO into the active region of the device in which THz radiation is resonantly absorbed by the 2DEG through an intersubband transition. The absorbed THz energy promotes the electrons from the ground subband to the first excited subband. The electrons thermalize in less than 10 ps above 50 K11 and heat up the active region, resulting in a fast bolometric response in the device resistance that follows the IF at GHz frequencies. To satisfy the selection rule for an intersubband transition in a confined 2DEG,12 a planar antenna structure is integrated in the bottom gate metallization to orient the THz electric fields perpendicular to the 2DEG plane.

FIG. 1.

(a) Schematic for the vertical profile of a TACIT mixer with equivalent circuits for the device impedance seen by the IF chain and by the THz antenna on resonance. A single GaAs-AlGaAs quantum well membrane (brown) contains a high-mobility 2DEG (color with gradation) with two ohmic contacts (source and drain) to measure the IF response. Two additional gates (top and bottom gates) are used to couple THz radiation into the active region of the device. (b) Optical microscope image of a fabricated TACIT mixer showing the semi-transparent GaAs-AlGaAs quantum well membrane on a Si substrate that has Au bonding pads for electrical access to the four terminals. (c) Optical microscope image of the active region covered by the top gate metallization with an RF stub and choke filter.

FIG. 1.

(a) Schematic for the vertical profile of a TACIT mixer with equivalent circuits for the device impedance seen by the IF chain and by the THz antenna on resonance. A single GaAs-AlGaAs quantum well membrane (brown) contains a high-mobility 2DEG (color with gradation) with two ohmic contacts (source and drain) to measure the IF response. Two additional gates (top and bottom gates) are used to couple THz radiation into the active region of the device. (b) Optical microscope image of a fabricated TACIT mixer showing the semi-transparent GaAs-AlGaAs quantum well membrane on a Si substrate that has Au bonding pads for electrical access to the four terminals. (c) Optical microscope image of the active region covered by the top gate metallization with an RF stub and choke filter.

Close modal

With a top gate and a bottom gate that couple the THz radiation separately from the IF readout, the impedance seen by a THz antenna (RF impedance) and the impedance seen by the IF chain (IF impedance) of a TACIT mixer can be optimized separately. In two-terminal 2DEG HEB mixers, both the RF impedance and the IF impedance are modeled by an inductor with the kinetic inductance of a 2DEG, Lk, in series with a resistor with the source-drain resistance RSD(Te) that depends on electron temperature Te [see the equivalent circuit for the IF chain in Fig. 1(a)]. In TACIT mixers, however, the THz absorption occurs between the top gate and the bottom gate, and the RF impedance is now modeled by a capacitor with the geometric capacitance CG, formed by the top and the bottom gate, in series with an effective resonator circuit that represents the intersubband transition.4 On resonance, the impedance of the effective resonator becomes purely resistive and is modeled by a resistor with the resistance Rzz presented to a current oscillating between the top gate and the bottom gate. It is important to note that the resistance Rzz is different from the source-drain resistance RSD(Te), which is responsible for the IF response. The antenna structure is designed in a way that the real part of the antenna impedance roughly matches Rzz and the reactive part tunes out CG. In a fabricated device, Rzz can be further tuned by varying the charge density with voltage biases on the top and bottom gates, and the RF impedance can be matched closely to the antenna impedance, yielding a high RF coupling efficiency in a TACIT mixer.

The detection frequency of a TACIT mixer is determined by the intersubband absorption frequency for the transition between the ground and the first excited subbands for a 2DEG confined in a GaAs-AlGaAs quantum well. The absorption frequency can be tuned by applying an external electric field perpendicular to the 2DEG plane (along the growth direction of the quantum well) and by varying the charge density in the well. The electric field tilts the potential profile of the well along the growth direction (see schematics below Fig. 3) and increases the energy spacing between the subbands via the DC Stark effect, resulting in a roughly parabolic tuning curve for the absorption frequency as a function of the field at a given charge density. At a fixed electric field, the electron-electron interaction causes the intersubband absorption frequency to shift with increasing charge density.13,14 The intersubband absorption frequency for a given electric field, charge density, and temperature can be calculated by self-consistently solving the Schrödinger equation and Poisson's equation, taking into account Fermi-Dirac statistics, and including the effect of the electrostatic potential from the charge density (self-consistent Hartree potential), many-body effects on the energy of the 2DEG (the exchange and correlation energies), and collective effects on the absorption (depolarization and exciton shifts).12 

In a TACIT mixer, the electric field and the charge density are independently tuned by applying voltage biases to the top and the bottom gates. While voltage-tunable direct detection via intersubband absorption has already been demonstrated in devices based on various 2DEG systems including a Si inversion layer15 and coupled GaAs-AlGaAs quantum well structures,16,17 the symmetric dual gate structure in a TACIT mixer offers independent control of the electric field and the charge density and allows more precise tuning of the absorption frequency and the device impedance by varying either the electric field or the charge density while fixing the other. Assuming that the top and the bottom gates form parallel-plate capacitors with the 2DEG, the electric field E and the charge density ns are tuned by the top and bottom gate biases VT(B) through the following simple relations:

E=1d(VTVB)
(1)

and

ns=n0+ce(VT+VB),
(2)

where d is the distance between the top and the bottom gates, n0 is the intrinsic charge density in the well, c is the capacitance per unit area between each gate and the 2DEG, and e is the elementary charge.

A prototype TACIT mixer was fabricated from a modulation-doped 40 nm GaAs-AlGaAs square quantum well heterostructure [see Figs. 1(b) and 1(c)] where a wide tunability in the intersubband absorption frequency (2.5–4 THz) has been observed previously.18 The sample was grown by Molecular Beam Epitaxy (MBE) and contains a high-mobility 2DEG with mobility μ=9.4×106 cm2 V−1 s−1 and charge density n0=2.2×1011cm2 at 2 K. To process both sides of the quantum well sample, a modified version of the EBASE flip-chip process19 with UV contact lithography was used. For the prototype device, a single-slot antenna [see Fig. 1(c)] was chosen for its simplicity in design and capability of providing sufficient THz coupling to linearly polarized sources despite the asymmetric beam pattern in horizontal and vertical polarizations.

After the fabrication, current-voltage (IV) curves were measured to check the bolometric nature of the detection mechanism and the gating of the fabricated device, and both direct detection and heterodyne detection were performed to verify the tunability in the THz response and the capability of THz mixing, respectively. For each IV curve measurement, the source was biased with the drain being grounded, and the top gate and the bottom gate were biased to a fixed voltage to avoid floating gates that would otherwise make the charge density in the active region fluctuate during the measurement. For direct and heterodyne detection measurements, a hyperhemispherical Si lens was used to quasioptically focus THz radiation onto the slot antenna coupled to the active region of the device. The device was bonded on the back side of the Si lens, and the mixer block that contains the Si lens was thermally anchored to a cold plate in a liquid helium cryostat that could be warmed up to 60 K. A bandwidth limiting filter was mounted on the LN2 (77 K) thermal shield of the cryostat to filter any unwanted thermal radiation coupling to the device. For direct detection, a CO2-pumped molecular gas far-infrared (FIR) laser provided THz signals at 2.52 THz and 3.11 THz. The device response was measured using a lock-in amplifier while chopping the THz signal with a mechanical chopper. For heterodyne detection, THz RF was provided by a custom tunable solid-state frequency multiplier built at Jet Propulsion Laboratory, and THz LO was provided by the FIR laser. A bias-tee was used to apply DC bias to the source-drain channel and to couple out the IF response, which was amplified with a low-noise microwave amplifier and detected by a spectrum analyzer. For both THz heterodyne and direct detection measurements, the source was biased to 50 mV with the drain being grounded.

Figure 2 shows IV curves of the TACIT mixer at 50 K with different charge densities in the active region. The top gate voltage was varied from −2 V to 1 V with the bottom gate fixed to 0 V to effectively vary the charge density set by the voltage sum [VT+VB; see Eq. (2)]. We observed that the IV curve was tunable from being completely flat (when the active region is depleted of electrons) to being linear (when there are excess electrons). At VT=0V, the IV curve showed a nonlinear bolometric response due to the hot-electron effect. The temperature coefficient of resistance α (α=1RdRdT) was measured to be 0.02 K−1. We observed similar tunability in the IV curve with voltage biases on the bottom gate, confirming the normal operation of both gates within the tested range of the voltage biases. The device resistance at the source-drain bias of 50 mV was ∼500 Ω at VT = 1 V. Compared with the 2DEG sheet resistance of 75 Ω/ measured at 50 K in a Hall bar sample, the high device resistance at VT=1 V was expected due to the nonsquare 2DEG mesa geometry and the corresponding current-crowding effect that occurs when current flows from the 1 mm wide 2DEG connected to the contacts to the 5 μm wide active region of the device. With optimal mesa design and proper tuning of the charge density, we expect that the device resistance can be lowered to better match the 50 Ω impedance of the IF chain.

FIG. 2.

Current-voltage (IV) curves of the fabricated TACIT mixer at 50 K with different charge densities in the active region. The IV curves show the tunable bolometric response of the fabricated TACIT device depending on the charge density.

FIG. 2.

Current-voltage (IV) curves of the fabricated TACIT mixer at 50 K with different charge densities in the active region. The IV curves show the tunable bolometric response of the fabricated TACIT device depending on the charge density.

Close modal

Figure 3 shows the direct detection results at 2.52 THz and 3.11 THz at 36 K [Figs. 3(a) and 3(b)] along with the calculated absorption frequency at the same temperature [Fig. 3(c)]. Figures 3(a) and 3(b) show the device responsivities at 2.52 THz and 3.11 THz at 36 K as a function of the effective DC electric field, which was converted from the top and bottom gate biases (VTVB; marked on the top of the plot) using Eq. (1). The curves were shifted horizontally with an offset of −0.98 mV/nm to cancel out a built-in electric field in the quantum well. Each curve in the plot corresponds to a different charge density in the active region set by the sum of the top and bottom gate biases (VT+VB). The voltage sum was not converted to a charge density as the charge density estimated from Eq. (2) was too high, possibly because of an asymmetry in the gate structure or the diffusion of the electrons out of the active region, which will be further investigated in future devices. While we observed similar responsivity behavior at 60 K including the double-peak behavior at 3.11 THz [see the inset in Fig. 3(b)], we present the result at 36 K at which we acquired the cleanest curves and thus investigated most extensively. The tuning curves shown in Fig. 3(c) were calculated by self-consistently solving the Schrödinger equation to calculate the energy spacing between the ground and the first excited subbands in a 40 nm GaAs-AlGaAs square quantum well.

FIG. 3.

(a) Responsivity at 2.52 THz at 36 K as a function of the electric field applied along the growth direction of the quantum well. Each curve corresponds to a different charge density set by the voltage sum (VT+VB). (b) Responsivity at 3.11 THz at 36 K as a function of the applied electric field with the inset showing the similar double-peak behavior at 60 K. (c) Calculated absorption frequency as a function of the electric field at 36 K at estimated charge densities in the active region of the device. The diagrams below the x-axis represent the potential energy experienced by an electron in a quantum well with negative, zero, and positive electric fields. The spacing between the dashed lines representing the subband energies increases with either a positive or negative electric field.

FIG. 3.

(a) Responsivity at 2.52 THz at 36 K as a function of the electric field applied along the growth direction of the quantum well. Each curve corresponds to a different charge density set by the voltage sum (VT+VB). (b) Responsivity at 3.11 THz at 36 K as a function of the applied electric field with the inset showing the similar double-peak behavior at 60 K. (c) Calculated absorption frequency as a function of the electric field at 36 K at estimated charge densities in the active region of the device. The diagrams below the x-axis represent the potential energy experienced by an electron in a quantum well with negative, zero, and positive electric fields. The spacing between the dashed lines representing the subband energies increases with either a positive or negative electric field.

Close modal

The observed device responses at 2.52 THz and 3.11 THz [Figs. 3(a) and 3(b)] show tunability in the detection frequency consistent with the absorption behavior predicted by the calculation [Fig. 3(c)]. At 2.52 THz, we observed single peaks in the responsivity curves with the width of the peak increasing with a higher charge density. This behavior is consistent with the theoretical model shown in Fig. 3(c); the bottom dashed line at 2.52 THz intersects the tuning curves near the bottom where there is a range of the field values at which the incoming THz radiation matches the absorption frequency. The range of these field values broadens with increasing charge density. At 3.11 THz, we observed double peaks with the position of the peak shifting outward in the electric field over increasing charge density. These shifts in the peak position are consistent with the tuning curves in Fig. 3(c) as the top dashed line at 3.11 THz intersects the curves at more negative and more positive electric fields for a higher charge density.

We also observed side peaks at high field biases (± ∼2 mV/nm) at 2.52 THz and asymmetry in the amplitude of the two peaks at 3.11 THz. The side peak at the positive field bias above 1 mV/nm at 2.52 THz and the asymmetry in the two peaks at 3.11 THz may be associated with the leakage at the top gate. In the fabricated device, the top gate metal was directly deposited on the semi-insulating GaAs cap layer shortly after removing the native oxide layer and forms a Schottky gate that has a threshold voltage of ∼1 V. Above the field value of 1 mV/nm, the top gate bias starts to exceed the threshold voltage, resulting in the gate leakage that leads to small artifacts in the responsivity amplitude. In future devices, we can avoid the breakdown of the gate by having a thin oxide layer between the gate metal and the GaAs cap layer. In addition to the side peaks at 2.52 THz and the asymmetry at 3.11 THz, we observed negative values in the responsivity curves for 3.11 THz at negative field biases. While we do not know at the moment what causes the negative values in the device response, it is likely that the negative signal is an experimental artifact due to the phase shift arising from the unfavorable combination of the device impedance and the capacitance of the bandwidth limiting filter as only the in-phase component of the response was recorded using the lock-in amplifier. Both the negative responses at 3.11 THz and the side peaks at the positive and negative field biases at 2.52 THz will be more thoroughly investigated in future experiment.

In the current measurements, the range of experimentally accessible THz frequencies was limited by the available lines in the CO2-pumped molecular gas laser. In the future, the device response beyond 3.11 THz will be investigated with other THz sources such as a quantum cascade laser (QCL) to verify the full tunable range for the detection frequency expected in the current design of the quantum well (2.5–4 THz).

Figure 4 shows the result of the heterodyne detection at 2.52 THz at 60 K. We observed IF signals in the GHz range, confirming the THz mixing capability of TACIT mixers at 60 K. The frequency dependence of the IF response shows that the −3dB bandwidth exceeds 6 GHz. The frequency spectrum was not fitted with the single-pole Lorentzian because of the 12dB/octave roll-off that suggests the existence of higher-order filtering possibly due to parasitic reactance of the on-chip IF circuitry. This essentially limits the observed IF bandwidth of the fabricated TACIT mixer, which we expect to be ∼10 GHz otherwise based on the previous work by Lee et al.8 in which an IF bandwidth of ∼ 10 GHz was observed at 77 K in a GaAs-AlGaAs 2DEG HEB device that has a device length similar to the length of the active region (5μm) in the TACIT mixer. The −3dB bandwidth exceeding 6 GHz suggests that the fabricated TACIT mixer might be a diffusion-cooled device rather than a phonon-cooled device, in which the typical value of the −3dB bandwidth is ∼3 GHz in GaAs-AlGaAs 2DEG devices.6,7

FIG. 4.

Normalized IF response at 2.52 THz at 60 K as a function of the IF frequency. The dashed line indicates the −3dB point.

FIG. 4.

Normalized IF response at 2.52 THz at 60 K as a function of the IF frequency. The dashed line indicates the −3dB point.

Close modal

Finally, we estimate the noise temperature, the conversion loss, and the required LO power for an optimized TACIT mixer at 60 K by applying bolometric mixer theory20–22 to the IV curve for the active region of a model device. The IV curve for the active region was scaled from the IV curve measured in a Hall bar sample to make the device resistance ∼50 Ω at the bias point. For the modeling, we assumed the optimal bias, perfectly matched IF channel, and the RF coupling efficiency of 70%, which is a typical value for hot-electron bolometers coupled with planar antenna structures (see, for example, Ref. 23). At 60 K, the conversion loss is estimated to be ∼7.5 dB at a DC bias of ∼2.5 mV at which the dissipated DC power is ∼0.15 μW. For the noise temperature, we consider the contributions from Johnson noise and from thermal energy fluctuation. At the LO power of ∼0.2 μW, the Johnson mixer noise temperature and the thermal fluctuation mixer noise temperature are estimated to be ∼400 K and ∼300 K, respectively, yielding the total single-sideband (SSB) mixer noise temperature of ∼700 K.

In summary, we have achieved a THz 2DEG-HEB mixer based on the intersubband transition of a high-mobility 2DEG confined in a 40 nm GaAs-AlGaAs square quantum well. The fabricated device shows tunability in the detection frequency between 2.52 THz and 3.11 THz consistent with theoretical calculation. Heterodyne detection at 2.52 THz was observed at 60 K with an IF bandwidth exceeding 6 GHz, showing the THz mixing capability of the TACIT mixer with a wide IF bandwidth.

See the supplementary material for more details on the impedance matching in a TACIT mixer as well as the sample growth and the device fabrication. Also, the temperature dependence of the bolometric response of the fabricated TACIT mixer and the quantitative details on the mixer modeling are provided.

This research was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. A portion of this work was performed in the UCSB Nanofabrication Facility, an open access laboratory. We thank Karl Unterrainer and Michael Krall for early help with ohmic contacts and Dr. Brian Thibeault and Dr. Demis D. John for their help in discussing the flip-chip processing steps. The C++ codes for calculating the detection frequency of TACIT mixers were written by Dr. Bryan Galdrikian and modified by Dr. Chris Morris. We are grateful for early leadership by W. R. McGrath (deceased). The work at UCSB was supported by the NASA PICASSO program via a contract with JPL.

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Supplementary Material