Quantum point contacts (QPCs) are nanoscale constrictions that are realized in a high-mobility two-dimensional electron gas by applying negative bias to split Schottky gates on top of a semiconductor. Here, we explore the suitability of these nanodevices to THz detection, by making use of their ability to rectify THz signals via the strong nonlinearities that exist in their conductance. In addition to demonstrating the configuration of these devices that provides optimal THz sensitivity, we also determine their noise equivalent power and responsivity. Our studies suggest that, with further optimization, QPCs can provide a viable approach to broadband THz sensing in the range above 1 THz.
© 2010 OSA
Semiconductor nanostructures, such as quantum wires and dots, offer many attractive features for use as terahertz (THz) sensors. These include: their compact size; the presence of quantized energy levels well-matched to the THz region of the electromagnetic spectrum ; the ability to provide electrical readout, and; compatibility with CMOS circuitry. Among current attempts to utilize these structures for THz sensing, much effort is focused on resonant plasmon excitation in high-mobility two-dimensional electron gas (2DEG) systems [2–10]. Other approaches make use of direct bolometric detection, in which the small thermal capacity of nanostructures is exploited to achieve broadband photon sensing [11–13]. In other work yet, counting of single THz photons has been achieved with high accuracy, by inducing internal transitions between the levels of semiconductor quantum dots [14–16].
Recently, we demonstrated THz detection in quantum point contacts (QPCs), realized by applying negative bias (Vg) to Schottky gates on a semiconductor mesa . The depletion fields due to these gates restrict current in an underlying 2DEG to a nanoconstriction, which can respond sensitively to THz radiation [17–22]. We  showed a clear THz response in such QPCs below 10 K, where, in the linear-transport regime, the conductance exhibits a step-like dependence on Vg, with quantized steps in units of 2e 2/h . Because of this behavior, which is the signature of ballistic transport via one-dimensional “subbands”, the conductance varies in a highly nonlinear manner as a function of Vg. In Ref. 17, it was shown that the large transconductance (∂Id/∂Vg, where Id is the drain current) associated with this nonlinearity is the cause of the pronounced QPC photoresponse. Specifically, using a relatively simple linear-transport model, we were able to attribute this response to rectification of the THz field that yields additional contributions to the source (Vsd) and gate voltages. Essentially, when ∂Id/∂Vg is large, the rectification induces a significant photocurrent that enables THz detection.
There are several features of the rectification mechanism described above that make it of potential interest for THz sensing. The rectification is a classical effect, in which the gates experience a THz-induced time-dependent modulation, causing a similar modulation of the QPC current. (In this sense, the QPC is just a readout device that detects changes in gate potential, with high sensitivity when the nonlinearity in transconductance is pronounced.) Consequently, we expect that the rectification should provide broadband THz response, evidence of which was found in experiments performed up to 2.5 THz . The planar nature of these devices should moreover ensure that parasitic capacitances are small, allowing the QPC to quickly respond to the THz excitation. Finally, while we have studied the rectification at low temperatures, where the step-like variation of the conductance provides the nonlinearity required for rectification, detection should be possible at higher temperatures, provided that other suitable nonlinearities can be identified.
While in Ref . we focused on the physical mechanism of the THz photoresponse, here we present results of further experiments that have specifically been undertaken to establish the suitability of QPCs to THz detection. The new results presented here include: establishing how to configure the QPC to achieve optimal sensitivity in THz detection; demonstrating well-behaved sensor response while varying the incident THz power over more than two orders of magnitude; clarifying the influence of the QPC source-drain on the THz photoresponse, and; providing quantitative estimates for key sensor parameters, namely responsivity and noise equivalent power. Based on these results, we suggest that QPCs can provide a viable approach to broadband THz sensing in the range above 1 THz.
QPCs were realized in high-mobility GaAs/AlGaAs quantum wells, and we focus here on results from the device of Ref. 17 (Sandia sample EA1278, see Fig. 1(a) & Fig. 1(b), inset), whose 2DEG had a density of 3.4 × 1011 cm−2 and a mobility of 400,000 cm2/Vs (both at 2.5 K). THz radiation was directed onto this device, and was collected by an on-chip, broadband bow-tie antenna (“BT” in Fig. 1(a)) with the QPC gates located between its poles (Fig. 1(b), inset). THz was generated by using a CO2 laser to pump a second laser, which used CH2F2 and CH3OH, respectively, to generate radiation at 1.4- & 2.5-THz. The spot size of the THz beam was ~10 mm2 and its polarization was aligned parallel to the bow-tie axis (i.e. along the x-axis). The DC conductance of the QPC was measured in a two-probe configuration at 2.5 K, with small Vsd = 0.5 mV (unless stated otherwise) to ensure that QPC transport was in the linear regime.
Figure 1(b) shows some of the key features of the QPC THz response studied in Ref , plotting the variation of conductance (G QPC = Id/Vsd) with Vg at 2.5 K, in the absence and in the presence of THz radiation. The curves show the well-known step-like variation in units of 2e 2/h, although, due to the relatively high temperature of the measurements, the conductance plateaus have non-zero, rather than zero-, slope . The figure clearly shows that the THz radiation shifts the conductance characteristic to more-negative Vg, implying it has the effect of inducing an effective Vg offset. In the same figure, we also plot the difference between the two conductance curves, expressing the result instead as the THz-induced photocurrent ΔI THz(Vg). This current is clearly peaked between successive conductance plateaus, where ∂Id/∂Vg, is large. In Ref , we developed a rectification model which includes the modulations of both the source-drain and gate voltages by the THz radiation. and obtained excellent quantitative agreement with experiment. While the results of Fig. 1 were obtained at 1.4 THz, in Ref . we showed no quantitative difference in behavior on increasing frequency to 2.5-THz (see Fig. 2(a) ). Such invariance is consistent with the classical origins of the detection mechanism (rectification), and suggests the potential of utilizing this for broadband detection beyond 1 THz.
ΔI THz in Fig. 1(b) was obtained in a “dynamic-sampling” mode, by sweeping Vg, with and without THz present, and subtracting the resulting current variations. For sensing applications, however, “static sampling”, in which Vg is fixed and QPC conductance (current) is monitored to probe for radiation, is more desirable. The results of such sampling are shown in Fig. 1(c), in which we compare the THz response for three different initial conductance values (cases I – III in Fig. 1(b)). In each case, the time-dependent evolution of G QPC was measured while turning the laser on for 60 s. The data clearly confirm the strong Vg dependence of the THz response found for dynamic sampling. To further illustrate this point, in Fig. 2(a) we plot the variation of ΔI THz as a function of the QPC conductance, showing results for both dynamic and static sampling. These measurements were obtained for a radiation frequency of 2.5 THz, the resulting behavior is similar for both the dynamic and static sampling. Local maxima are seen in ΔI THz each time G QPC approaches an integer value, and the transconductance increases. Although the results of the static sampling systematically yield smaller values for ΔI THz, this likely reflects differences in the laser output power between the different measurements. Important is that both types of measurement confirm the correlation of enhanced THz photoresponse to regions of large ∂Id/∂Vg.
For sensing applications it is important to configure any sensor to achieve maximum sensitivity. To study this issue we consider the relative photoresponse ΔI THz/Id = ΔG THz/GQPC, where ΔG THz is the conductance change induced by THz radiation. In Fig. 2(b), we compare the Vg dependence of ΔG THz/GQPC and ΔG THz, and see that the maximum sensitivity of 60% does not occur at the same Vg for which ΔG THz itself is maximal. In fact, with ΔG THz maximal, ΔG THz/GQPC is approximately 30%, around half of the maximum sensitivity. In the inset to Fig. 2(b), we indicate the connection of these different conditions to the QPC conductance. While the maximum of ΔG THz occurs when ∂GQPC/∂Vg is maximal, optimal sensitivity is achieved for more-negative Vg, where G QPC is just increasing from zero. These observations emphasize the need to properly configure the QPC gate voltage in order to achieve optimal sensitivity.
To explore the power dependence of the QPC photoresponse, we studied the influence of the laser intensity on ΔI THz. In this experiment, GQPC was set to ~0.01 × 2e 2/h, and different polyethylene attenuators were used to modify the incident laser power. In Fig. 3(a) , we indicate these power levels, and show the time-dependent change of the QPC current that they produce. The inset to this figure plots the power dependence of ΔI THz and shows a clear linear variation over two orders of magnitude. To estimate the sensor responsivity (the ratio of ΔI THz to the incident optical power that yields it), we note that, for the maximum laser power of 60 mW, ΔI THz ~0.7 nA. To determine the actual laser power incident on the sample, we take the beam size (~10 mm2) and consider a transmission loss  of −15 dB, so that the incident laser power delivered by the beam is 0.2 mW/mm2. If we assume that the active sensor area is equal to that of the entire antenna (0.05 mm2) we compute a responsivity of ~0.1mA/W, too small for practical sensor applications. However, in these experiments the antenna size and geometry were not optimized. Recent work  suggests that the antenna dimensions can actually be significantly reduced, while nonetheless increasing the coupling of the THz field. As an upper bound for the responsivity, we therefore take an active area equal to that of the QPC (~1 μm2), which yields ~3.5 A/W. Responsivities larger than 1 A/W should allow a variety of different THz-sensor applications. The above considerations suggest that such levels of responsivity can be achieved, although this will require further optimization of the integrated-antenna design.
We can also use the data of Fig. 3(a) to estimate the sensor NEP, the laser power that gives a signal-to-noise ratio of one. For this purpose, we calculate the noise in the dark current to be 10 pA (rms, for a bandwidth of ~1 Hz). From the data in Fig. 3, we then infer that ΔI THz is equal to this noise value for a laser output power of 0.7 mW, corresponding to a delivered power of 2.2 × 10−6 W/mm2. In this way, we finally obtain upper and lower bounds on the NEP of 10−7 & 2.2 × 10−12 W/Hz1/2, by taking, respectively, the antenna and QPC areas. As for the factors that limit the NEP, the dark conductance can show significant time-dependent fluctuations, making it problematic to resolve the THz response. This intrinsic device noise is common to split-gate devices, and has been attributed to gate leakage that arises from tunneling of electrons through the Schottky barrier to the 2DEG . It has also been suggested that the noise can be suppressed by utilizing optimized heterostructures , which would lead to further improvement in the NEP figures.
To improve the responsivity of THz detection, larger photocurrents should be generated. One way in which this can be achieved is by increasing Vsd, and, in Fig. 3(b), we show the results of measurements of the QPC current as a function of Vg for different values of Vsd. The bias has clear tendency to wash out the steps in the quantized conductance, as demonstrated by the results of the upper panel of Fig. 3(b). As shown in the lower panel, the modulation of the photocurrent that arises from the conductance steps is simultaneously smeared out. However, overall, ∂Id/∂Vg increases with Vsd at low temperatures giving rise to larger rectified photocurrents in the lower panel of Fig. 3(b).
We conclude by considering the prospects of using QPCs as practical THz sensors. At the low temperatures on which we have thus far focused, we have shown the ability of QPCs to serve as sensitive THz detectors, by exploiting their large transconductance. This large ∂Id/∂Vg arises from the quantized steps in the conductance, which are due to the ballistic transport of carriers via one-dimensional subbands . Since this behavior washes out with increasing temperature  the rectification-based detection is similarly suppressed. In spite of this, due to the classical nature of the rectification, we believe it should be possible to extend its use to much higher temperatures, provided significant conductance nonlinearities can be identified. One potential approach is to initially pinch-off the QPC completely, under conditions of linear transport, and to then induce a current flow by applying a large Vsd. In this situation, highly nonlinear Id-Vsd curves can be obtained, particularly for values of Vsd where current flow through the QPC initially onsets . Such nonlinearities can survive to much higher temperatures than the step-like quantum conductance, and we are currently exploring their suitability for application to THz detection. Finally, a common problem for bolometric detectors at frequencies above 1 THz is increased blackbody radiation noise at elevated temperatures. In the temperature interval from 80 to 150 K, where THz detectors are expected to operate, the maximum in the spectral density of the blackbody radiation ranges from 4.7 to 8.8 THz. The increased blackbody noise in the 1 to10 THz interval sets a natural limit on the NEP achievable with such detectors. An advantage of the rectification mechanism that we have discussed, however, is that it should be largely unaffected by the blackbody background, since it is not based on the direct absorption of the energy of the THz electromagnetic field, but rather on the rectification of the AC voltage that this field induces. Equilibrium blackbody electromagnetic radiation does not induce net voltages. Based on these considerations, we believe that QPC devices have significant potential for application to THz detection.
This work was supported by NSF (ECS-0609146), DoE (DE-FG03-01ER45920), and PSC-CUNY (62040-00 40), and was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. DoE Office of Basic Energy Sciences nanoscale science research center. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the U.S. DoE (Contract No. DE-AC04-94AL85000).
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