Narrow-band radiation sensing in the terahertz and microwave bands using the radiation-induced magnetoresistance oscillations R. G. Mani Citation: Appl. Phys. Lett. 92, 102107 (2008); doi: 10.1063/1.2896614 View online: http://dx.doi.org/10.1063/1.2896614 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v92/i10 Published by the American Institute of Physics.
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APPLIED PHYSICS LETTERS 92, 102107 共2008兲
Narrow-band radiation sensing in the terahertz and microwave bands using the radiation-induced magnetoresistance oscillations R. G. Mania兲 Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA
共Received 17 October 2007; accepted 22 February 2008; published online 13 March 2008兲 Tuned narrow-band sensing of microwave and terahertz radiation can be realized by subjecting an irradiated two-dimensional electron system to both a static and a time varying magnetic field, and detecting at the harmonics of the modulation. A third harmonic sensor is considered here in conjunction with periodic-in-the-inverse-magnetic-field radiation-induced magnetoresistance oscillations. © 2008 American Institute of Physics. 关DOI: 10.1063/1.2896614兴 Experiments suggest that microwave and terahertz photoexcitation of GaAs/ AlGaAs specimens produces “1 / 4-cycle shifted” periodic-in-the-inverse-magnetic-field magneto-resistance oscillations, and further, a vanishing dissipative electrical resistance, at modest radiation intensities.1 The observed phenomena1–3 have seen some theoretical interest4 partly because of the unexpected realization of zeroresistance states through photoexcitation. Here, we examine narrow-band radiation sensing based on the abovementioned phenomena since the experimental results also implied that it should be possible to characterize the frequency f of the radiation, through measurements of the resistance oscillations periodicity B−1 f given the empirical relation B f = 2 fm* / e.1 Radiation sensing in the terahertz band 共0.3– 10 THz兲 and at the upper end of the microwave band 共0.1– 0.3 THz兲 presents unique challenges because these regimes fall between the upper bound in f where electronic approaches continue to operate and the lower limit in f where optical techniques begin to function. In addition, the small photon energy here implies that ambient background thermal noise can easily dominate natural signals. Yet, detectors and compact radiation sources are needed here for applications such as biological agent identification, large informationbandwidth communications, and imaging for security and medical purposes.5–8 Previous work suggests that photoexcitation at f induces periodic-in-the-inverse-magnetic-field magnetoresistance oscillations at liquid helium temperatures with zero-resistance states at the deepest resistance minima.1 Typically, in experiment, a GaAs/ AlGaAs heterostructure specimen was mounted inside a waveguide and irradiated with electromagnetic waves, as electrical measurements were carried out using standard lock-in techniques 共see Ref. 1兲. Figure 1 illustrates radiation-induced oscillations at f = 240 GHz. Such magnetoresistance oscillations normally become weaker with decreasing photoexcitation and they remain observable down to 1 W / cm2. Here, we develop an approach for radiation sensing at low temperatures using these phenomena. At the outset, one might consider radiation detection by examining a B-field sweep of the magnetoresistance under photoexcitation. This approach, which is akin to a single shot experiment, reveals, however, the radiation spectra over the course of the B sweep. In order to keep up to date with a a兲
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changing photoexcitation, it is necessary to periodically repeat the sweep. Yet, from a practical point of view, periodically implementing a full B sweep might be cumbersome and limit the sensing speed. Some questions of interest here are as follows: what is the range of B over which it is necessary to carry out a sweep and how will this span be reflected in the detector spectral sensitivity? Further, is it possible to tune the spectral sensitivity by selecting available parameters? Here, we outline a scenario, where the B field is swept but it is swept over a prescribed window that is determined by the sensing requirement. In order to realize narrow-band sensitivity about a radiation frequency f, the magnetic field is held constant at B0 = B f / n, where n is an integer and n 艌 1. This corresponds to operating at an integral node of the radiation-induced resistance oscillations. However, one might also try to operate at a half-integral node, especially at low radiation intensities. Next, in addition to the static magnetic field, a second sinusoidal component is applied to the specimen, 共see Fig. 2兲. As shown below, when the peak-to-peak amplitude of this oscillating component is close to the period of the radiationinduced resistance oscillations in the B−1 scale, there appears a signal at the third harmonic of the modulation frequency, which is proportional to the radiation intensity in a narrow band about the frequency f. Detection of this third harmonic signal helps to facilitate tuned narrow-band sensing. In this approach, the detector sensitivity may be shifted from the vicinity of one frequency f to another frequency f 1, simply by changing the static magnetic field 共B0兲 and simultaneously adjusting the peak-to-peak amplitude of modulation
FIG. 1. 共Color online兲 共a兲 Radiation-induced magnetoresistance oscillations are exhibited at the frequency f = 240 GHz. Also exhibited is the electron spin resonance 共ESR兲 of diphenylpicrylhydrazil 共DPPH兲, which provides a reference magnetic field marker for these measurements 共see Ref. 1兲.
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© 2008 American Institute of Physics
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FIG. 2. 共Color online兲 共a兲 A sketch of the radiation-induced magnetoresistance Rxx vs the normalized inverse magnetic field. Imagine that 共B / B f 兲−1 = constant= n and consider the superposition of a small oscillatory component. Here, the oscillating component is arbitrarily assumed to have a time period of 100 ms. Panels 共b兲 and 共c兲 show the time variation of the total inverse field when the peak-to-peak modulation amplitudes are 0.5 and 1 times the period of the radiation-induced oscillations.
so that it once again corresponds to just one period of the radiation-induced resistance oscillations at f 1. The underlying mechanism of this approach is summarized in Figs. 2 and 3. In the illustration of Fig. 2共a兲, at 共B / B f 兲−1 = p, with p = n − 1, n − 1 / 2, n , n + 1 / 2, n + 1, Rxx under photoexcitation equals the dark Rxx. Figures 2共b兲 and 2共c兲 convey the magnetic field on the specimen, as a function of time 共shown on the ordinate兲, when an oscillating component is superimposed on the static field. We next examined the response of the specimen to the combined effects of the static
FIG. 3. 共Color online兲 共a兲 The time varying ␦Rxx appears similar to the modulation, within a phase factor, when the peak-to-peak sinusoidal modulation is 1 / 2 of the characteristic period 关see 共b兲兴. In this situation, the Fourier transform 关see the inset of 共a兲 and 共b兲兴 shows that the dominant component is the −1 component. 共c兲 The ␦Rxx signal develops a third harmonic component when the sinusoidal modulation is increased to match the period of the radiation-induced oscillations 关see 共d兲兴. This is confirmed by the 3−1 peak in the Fourier transform 关see the inset of 共c兲 and 共d兲兴.
Appl. Phys. Lett. 92, 102107 共2008兲
FIG. 4. 共Color online兲 The simulated detector response at the third harmonic −1 and the working point as a function of f 共top abscissa兲, when B−1 0 =1 T corresponds to n = 2.
magnetic field, the oscillatory component, and the photoexcitation in Fig. 3. When the peak-to-peak amplitude of modulation is relatively small, i.e., ⌬共B / B f 兲−1 艋 1 / 2 关see Fig. 3共b兲兴, the time dependent change in the resistance ␦Rxx under photoexcitation at frequency f, shown in Fig. 3共a兲, reflects mostly the time variation of the magnetic field within a phase factor. This situation changes dramatically, however, when the peak-to-peak modulation amplitude matches the period of the radiation-induced resistance oscillations 关see Fig. 2共c兲兴 and compare Figs. 3共c兲 and 3共d兲. In Fig. 3共c兲, the time response of the specimen, i.e., ␦Rxx共t兲, exhibits a strong third harmonic component, which is evident both in the Fourier transform 关inset of Figs. 3共c兲 and 3共d兲兴 and the third harmonic bandpass filtered ␦Rxx共t兲 关see Fig. 3共c兲兴. A further increase in the modulation amplitude such that it corresponds to two periods of the radiation-induced resistance oscillations 共not shown兲 reduces the third harmonic component, as the fifth harmonic component takes its place. Simulation results are exhibited in Fig. 4, which shows the Fourier amplitude of the detector response at the third harmonic when the static field was held constant at the set point, i.e., B f / n, with n = 2, and the modulation amplitude was selected for the third harmonic sensor, as in Fig. 2共c兲. We assumed the oscillatory resistance response of the device at a given f to be an exponentially damped sinusoid, i.e., osc = A⬘ exp共− / B兲sin共2B f / B − 兲.1 The radiation freRxx quency was stepped over the interval shown in Fig. 4 共top abscissa兲. At each f, ␦Rxx was evaluated for a long time interval compared to the modulation period and Fourier transformed. For a center frequency of nearly 400 GHz, the results for the third harmonics sensor suggest enhanced sensitivity between roughly 200 and 800 GHz. This bandwidth can be reduced further in this approach, however, by utilizing higher, e.g., fifth or seventh, harmonic detection. Although Fourier transforms have been utilized here to present the concept, they are not necessary for the operation of the actual sensor. The real-time radiation sensing occurs simply through the continuous detection of the desired harmonic. Although the static field has been held constant at the nodes here, one might also analogously hold it constant at a maximum or a minimum of the resistance oscillations and utilize modulation to realize an even-harmonic sensor. A similar approach may also be applied supplementarily in the case of periodic-in-B radiation-induced resistance and photovoltage oscillations.9
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Appl. Phys. Lett. 92, 102107 共2008兲
R. G. Mani
Next, we address the question of how to realize modulation that spans the desired interval in B−1. If a solenoidal coil provides the magnetic field and modulation, then the coil excitation current will determine the field and modulation. Thus, the problem reduces to provide the correct driving signal to the coil. For this purpose, we recall the so-called reciprocal circuits which help satisfy the condition VinVout = constant= k, implying Vout = kV−1 in , where Vin and Vout are the input and output of the circuit, respectively.10 We imagine exciting the input of a reciprocal circuit with Vin = V0 + A sin共t兲, where is the modulation frequency and A is the amplitude of modulation. The coil current could then satisfy I ⬀ Vout = k关V0 + A sin共t兲兴−1, as a result B−1 ⬀ V0 + A sin共t兲. Here, V0 will serve to set the operating point in B−1, while A will help to set the modulation amplitude in B−1. In summary, we have suggested that tuned narrow-band sensing of the terahertz and microwave radiation can be realized at low temperatures by superimposing a static and a time varying magnetic field and detecting at the harmonics of the modulation, on a device that exhibits radiation-induced magnetoresistance oscillations.1–3 Special thanks to V. Umansky for the high quality MBE specimens. R.G.M. is supported by the Army Research Office under W911NF-07-01-0158.
1
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