Room temperature detection of sub-terahertz radiation in double-grating-gate transistors

: Room temperature photovoltaic non-resonant detection by large area double-grating-gate InGaP/InGaAs/GaAs heterostructures was investigated in sub-THz range (0.24 THz). Semi-quantitative estimation of the characteristic detection length combined with self-consistent calculations of the electric fields excited in the structure by incoming terahertz radiation allowed us to interpret quantitatively the results and conclude that this detection takes place mainly in the regions of strong oscillating electric field excited in depleted portions of the channel.


Introduction
It is known that hydrodynamic nonlinearities in two-dimensional (2D) electron channels can be used for detection of terahertz (THz) radiation [1]. Resonant THz detection is related to the excitation of high quality plasma waves (plasmons) in 2D electron channel, whereas a broadband non-resonant THz detection is related to overdamped plasmons in depleted regions of the channel. In the both resonant and non-resonant cases, THz photoresponse originates from the nonlinear dynamics of 2D electron fluid described by the hydrodynamic equations [1] 0, where ( , ) E x t is the in-plane electric field depending on the time t and coordinate x in 2D electron system, τ is the electron momentum relaxation time, ( , ) ( , ) ( , ) is the density of induced electric current, N(x,t) and V(x,t) are hydrodynamic electron density and velocity in 2D electron channel, and e and m* are the electron charge and effective mass, respectively. There are two different nonlinear terms in the system Eqs. (1) and (2): the second term in the Euler equation Eq. (1) describing the nonlinear electron convection in 2D electron fluid and the product ( , ) ( , ) N x t V x t defining the current density in the continuity equation Eq. (2). Time average of the nonlinear current yields the detection signal. It should be noted that either of the two nonlinear terms vanishes in the case of uniform oscillating currents flowing in 2D system. Hence, those nonlinearities are related to non-uniform currents inherent in the plasmon mode. In principle, both nonlinear terms can contribute to the detection signal depending on the geometry of the structure and the length of 2D electron channel. However, for symmetry reasons, the detection response must be zero in 2D electron channel with identical boundary conditions at its opposite ends if there is no bias DC current flowing in the channel. As shown in [1,2], the nonlinear electron convection does not contribute to a non-resonant detection signal for relatively long 2D electron channel (when the length of the sample is much longer than the plasmon correlation length). Both the nonresonant [2][3][4] and resonant [5][6][7] plasmon detection have been observed experimentally in single-unit field-effect transistors with 2D electron channels.
It can be anticipated that high net detectivity can be obtained if a high-quality plasmon resonance is excited in the resonant plasmonic THz detector, while high net detectivity of the non-resonant THz detector can be obtained if strong THz electric fields are induced in depleted regions of the channel. Therefore, the problem of effective coupling between THz radiation and 2D electron system is of crucial importance. The metal grating coupler is a conventional tool that can ensure strong coupling between the plasmons in 2D electron channel and THz radiation [8][9][10][11][12]. Resonant plasmon THz detection based on the photoconductive and photovoltaic response of the grating-gated field-effect-transistor structures was reported in [13,14].
In this paper, we report on the room temperature non-resonant THz detection in large area double-grating-gate InGaP/InGaAs/GaAs transistors and interpret this detection as coming from the regions of strong oscillating electric field excited in depleted portions of the channel.

Experimental
The device structure is based on InGaP/InGaAs/GaAs high-electron mobility transistor (HEMT) and incorporates doubly interdigitated grating gates (G1 and G2) [15,16] (see Fig.  1). The 2D electron channel is formed in a quantum well at the heterointerface between a 15nm-thick undoped InGaAs channel layer and a 60-nm-thick, Si-δ doped InGaP carriersupplying layer. The electron density in the channel is 2.5×10 12 cm −2 with the electron effective mass and room temperature mobility m*= 0.04m 0 where m 0 is the free-electron mass, and µ = 7000 cm 2 /V·s, respectively. The grating gate is formed with 65-nm-thick Ti/Au/Ti by a standard lift-off process. Four different structures with a double-grating-gate were fabricated. The metal fingers of one grating gate G1 are of the same length L G1 = 100 nm in all structures, while grating gate G2 was designed to have fingers of different lengths L G2 = 300, 800, 1300, and 1800 nm for different structures. The spacing between the grating-gate fingers is 100 nm for all four structures. We estimated the gate-to-channel separation as d = 65 nm. Side (source and drain) ohmic contacts of the device were fabricated which allowed us to apply DC drain bias voltage and to measure THz photoresponse. The whole length of the channel between the source and drain contacts covered by the double-grating gate is about 80 µm with the channel width of 30 µm in each structure. In different structures, double-grating gates have from 40 to 150 periods depending on the length of the period in a particular structure. The transfer characteristics of the structure with L G2 = 300 nm are shown in the inset of Fig. 2 for drain-to-source voltage 0.5 V. For these measurements, the source contact of the device was grounded and the 2D electron channel was depleted by applying negative voltage to either grating gate while leaving the other unbiased (grounded). The channel depletion threshold voltages estimated from Fig. 2 are U thG1 ≈-3.5 V and U thG2 ≈-3.0 V for biased gratings G1 and G2, respectively.
Each double-grating-gate structure was irradiated at normal incidence by THz beam at frequency 0.24 THz. We measured a photovoltaic DC response between the source and drain contacts (the source contact was grounded and no drain bias DC voltage was applied) at room temperature. The electron momentum relaxation time in 2D electron channel at T = 300 K is m µm e τ * = = 0.17 ps, which yields the quality factor smaller than unity, ωτ = 0.25, for the incident radiation frequency ω/2π = 0.24 THz. Therefore, the non-resonant detection should be expected in our experiments at room temperature. Terahertz radiation was generated by a Backward Wave Oscillator (BWO) with maximum output power of 5 mW. The radiation was linearly polarized and chopped at 170 Hz. The radiation-induced photovoltage ∆U was measured as a function of the gate voltage U G1 or/and U G2 as 170 Hz ac voltage component of the source-to-drain voltage using the standard lock-in technique. No special antenna was used to couple THz radiation to the device. The sample holder was mounted on a rotary stage so that dependence of the signal on the polarization of the electric field of the incident THz wave in the sample plane could be measured. Figure 2 demonstrates the photoresponse measured as a function of the gate voltage U G1 (for U G2 = 0) and that as a function of the gate voltage U G2 (for U G1 = 0) for the structure with L G2 = 300 nm when the THz electric field was directed across the grating-gate fingers (i.e., in the source-to-drain direction). The photoresponse grows when one of the grating gates, either G1 or G2, is biased to the threshold voltage. The strongest photoresponse in all structures was observed when the electric-field vector of the incident THz wave was directed across the grating-gate fingers (i.e., in the source-todrain direction). Figure 3 shows the dependence of the photoresponse on the azimuthal angle φ between the THz electric field and the source-to-drain direction for the structure with L G2 = 1300 nm. A two-lobe-shape angle dependence that relatively well follows the cos 2 φ law, was obtained with the maximal photoresponse for φ = 0. This demonstrates that the coupling between THz radiation and 2D electron channel is ensured by the double-grating gate. Measured photoresponse per period of the structure for φ = 0 is documented in Table 1 for all four structures under two different biasing conditions. Within the measurement uncertainty, the photoresponse grows with decreasing the length of undepleted portion of the channel per the structure period (under unbiased grating-gate finger) for samples # 1-4, while it grows with increasing the length of a depleted portion of the channel per the structure period (under a biased grating-gate finger) for samples # 5-8. Note that an absolute value of the photoresponse is relatively small because fabrication arrangements were not undertaken to bring designed asymmetry into the structure unit cell, which is required for ensuring the photovoltaic response. (For a device having a vertical plane of the mirror symmetry, the photovoltaic response is zero for symmetry reasons.) However, measured dependence of the photoresponse on the structure geometry suggests that there is some systematic, though small, asymmetry in the double-grating gate in all four structures.

Theoretical consideration and discussion
The theory of non-resonant terahertz detection due to hydrodynamic nonlinearity of the 2D electron fluid was initially proposed in [1] and then developed in more advanced form in [2] taking into account a finite electron temperature. However, this theory assumes asymmetric excitation of the channel, where a predefined THz electric field is applied at one end of the channel, and then it describes how this field propagates along the channel producing a photoresponse. Therefore, such theory cannot be used directly for quantitative analysis of the periodic structure under study, where the oscillating currents are excited in every point of the channel simultaneously by normally incident THz wave. Because of that in this paper we use a semi-quantitative approach for describing the THz photoresponse in the double-grating-gate structure.
In a periodic structure, the electron convection term in the Euler equation [the second term in Eq. (1)] does not contribute to the photoresponse of the entire structure incorporating many dozens of periods because the spatial average of this term over the structure period is zero. Therefore, the only source of hydrodynamic nonlinearity in the periodic structure is the product ( , ) ( , ) N x t V x t defining the current density in 2D electron fluid. Then, for relatively small perturbations N(x,t) and V(x,t), the time-independent photoresponse current density is where N(x) and V(x) are the amplitudes of the linear perturbations of the oscillating electron density and velocity, respectively, (i.e., those proportional to the first power of the electric field in 2D channel) and the angular brackets denote the spatial averaging over the period of the structure. As mentioned in section 2, the photocurrent will be zero in the structure with symmetric unit cell (having a vertical plane of the mirror symmetry) for symmetry reasons even if this type of nonlinearity works. Therefore, a specific asymmetry of the structure unit cell should be considered in order to calculate the THz photovoltaic response. However, we can evaluate the strength of the nonlinearity in a semi-quantitative way even without considering a particular asymmetry of the structure. The where |E x /E 0 | is the electric-field enhancement factor (the ratio between the amplitudes of the induced in-plane electric field E x in 2D electron channel and the electric field E 0 in the incident THz wave) and ∆ is the spatial period of the induced electric field variation along the x-coordinate in 2D electron channel. As shown in Refs [1,2]. and clearly demonstrated in Fig.  2, the non-resonant detection response originates predominantly in depleted parts of the channel. Then we can describe the net effect of detection coming from a depleted portion of the channel (per the structure period) by the characteristic detection length where w is the length of the depleted part of the channel within the strong electric field region per the structure period. The value of L D exhibits maximum for w = ∆/4 when the maximal asymmetry of the electric-field distribution over the depleted portion of 2D electron channel takes place. We calculated the normal and in-plane electric field distributions over the period of the structure in a first-principle electromagnetic approach described in Ref [17]. for all eight samples specified in Table 1. Distributions of the oscillating electric-field amplitudes over the structure period for samples # 1 and 8 are shown in Fig. 4. Naturally, nodes of the in-plane component of the electric field coincide with antinodes of the normal component of the electric field. Strong electric field with the electric-field-enhancement factor |E x /E 0 | ≈5 is excited in the channel under the entire gate G1 when it is biased down to the threshold voltage U thG1 while U thG2 = 0. However, strong electric field with the electric-field-enhancement factor |E x /E 0 | ≈2.5 is excited only near the edges of gate G2 when it is biased down to the threshold voltage U thG2 while U thG2 = 0 because a long gate finger G2 effectively screens the central part of the gated channel. The regions with strong electric field can be thought as having the length of ∆/2. It means that each region of strong electric field can be viewed as two oppositely-connected channels of length ∆/4, which are short-circuited at the center of this region but open-circuited at the ends of this region. The widths of the regions with strong electric field, ∆/2, were estimated as 165 nm, 110 nm, 100 nm, 65 nm, 180 nm, 245 nm, 280 nm, and 330 nm for samples # 1 to 8, respectively. Within a similar electrostatic approach (assuming zero electron temperature in the channel), we also calculated the equilibrium electron density in 2D channel over the structure period when one or the other grating gate is biased to its threshold voltage (see Fig. 5). It is seen in Fig. 5 that the channel can be depleted under almost entire gate finger G2 while only small portion of the channel is depleted under gate finger G1. If we assume that the photovoltaic response is caused by slight lateral shift between the two different grating gates G1 and G2, the electric field at opposite ends of the depleted region of the channel would be also slightly different. Then we can characterize the photoresponse for different samples by estimating the detection length in the region of strong electric field having length ∆/4 at one end of the depleted part of the channel. Because of a very short depleted region under gate G1, one has w ≪ ∆/4 for samples # 1-4 and, hence, Eq.
for those samples. In the last formula the ratio w/∆ is the form-factor describing a fraction of ∆ occupied by the depleted portion of the channel. For samples # 5-8, the whole region of strong electric field is depleted so that one has w ≈ ∆/4 and, hence, in this case. Calculated detection lengths for all eight different samples shown in Fig. 6 demonstrate good agreement with the measured photoresponse for all samples. The only fitting parameter to match the detection length dependencies for samples # 1-4 and those for samples # 5-8 is the length of the depleted region of 2D channel in samples # 1-4, which was assumed to be 2w ≈25 nm. This is a reasonable value taking into consideration extremely short depleted region of the channel under gate finger G1 that is demonstrated in Fig. 5.

Conclusions
We have measured a room temperature THz photovoltaic response in double-grating-gate InGaP/InGaAs/GaAs transistors and clearly show that the photoresponse is due to hydrodynamic nonlinearity of 2D electron fluid in the channel and that the main part this photoresponse is coming from depleted regions of the channel. Strong THz-electric-field enhancement factor achieved in the double-grating-gate structure was demonstrated. Our results allow us to predict the high responsisivity of the double gate grating structures with a designed asymmetric unit cell.