Acoustoelectric photoresponse of graphene nanoribbons

The acoustoelectric current in graphene nanoribbons, with widths ranging between 350 nm and 600 nm, has been investigated as a function of illumination. For all nanoribbon widths, the acoustoelectric current was observed to decrease on illumination, in contrast to the increase in acoustoelectric current measured in unpatterned graphene sheet devices. This is thought to be due to the higher initial conductivities of the nanoribbons compared to unpatterned devices.


Introduction
2D materials [1], such as graphene and molybdenum disulphide, naturally lend themselves to integration with surface acoustic wave (SAW) devices. The electric fields associated with a SAW propagating on a piezoelectric substrate can be used to transport charge carriers in these materials, at the speed of sound, over macroscopic distances. This leads to an acoustoelectric (AE) current, an effect that has been extensively studied in other nanostructures [2,3] for applications such as metrology [4][5][6] and quantum information [7][8][9][10][11][12][13]. AE currents have been measured in both uncoated [14][15][16] and coated [17,18] graphene devices, and also in molybdenum disulphide [19]. We have also have previously studied the AE response of large-area graphene sheets produced by chemical vapour deposition (CVD) transferred to LiNbO 3 SAW devices at room temperature [20], low temperature [21], and under illumination [22]. There have also been experimental [23] and theoretical studies [24,25] of the use of external fields applied to the carrier system amplify the acoustic waves.
One of the unique electronic properties of graphene, the ability to tune its conductivity over orders of magnitude, also allows the AE current to be tuned dynamically [26][27][28][29][30], where the ambipolar nature of graphene allows the sign of the AE current to be reversed [26][27][28][29]. In addition, using an ion gel gate to modulate the conductivity of graphene, Bandhu and Nash [30] not only reversed the direction of the current, but also demonstrated that graphene can be used to control the SAW amplitude and velocity. Optimization of this approach could lead to a practical, cost-effective voltage-controlled velocity shifter suitable for use in wireless sensor applications [30].
We have recently investigated the AE effect in graphene nanoribbons (GNRs) [31], and showed that an AE current can be generated in GNRs with physical widths as small as 200 nm at room temperature (note that the ribbons studied in this work are much larger than those in which a bandgap can be created [32]). The positive current in the direction of the SAWs, which corresponds to the transportation of holes, exhibited a linear dependence on SAW intensity and frequency. This is consistent with the interaction between the charge carriers in the GNRs and the piezoelectric fields associated with the SAWs being described by a relatively simple classical relaxation model. Somewhat counter-intuitively, as the GNR width is decreased, the measured AE current increases. This was thought to be caused by an increase of the carrier mobility due to increased doping arising from damage to the GNR edges. In this paper, we study the effect of illumination on GNRs, and show that the ribbons of widths of 350 nm to 650 nm show a clear photoresponse in the AE current.
(Some figures may appear in colour only in the online journal) Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Method
To study the AE photoresponse of GNRs monolayer graphene, grown by CVD on ~5 mm × ~5 mm copper foils (Graphene Supermarket), was transferred between the opposing interdigital transducers (IDTs) of a commercially available 128° YX LiNbO 3 SAW delay line with a centre-to-centre IDT separation distance of 5.4 mm, and IDT aperture of 3.25 mm. The IDTs had a double-digit geometry, allowing the efficient excitation of SAWs at a number of resonant frequencies. The graphene was patterned into arrays of parallel nanoribbons with a 50% fill factor, using electron beam lithography and reactive ion etching, with the GNRs oriented such that their long-axis was parallel to the SAW propagation direction. Note that each array consists of many hundreds of nanoribbons, and that individual nanoribbons within an array are connected by a 500 nm-wide perpendicular bridge of graphene every 10 µm to help maintain electrical conductivity [33], as shown schematically in the magnified region of figure 1. To enable the channel width dependence of the AE photoresponse to be studied, neighbouring arrays of GNRs with different nanoribbon widths were fabricated on the same SAW device, as shown schematically in figure 1. This device geometry enables a better comparison of the electronic properties of the GNR arrays, since each nanoribbon experiences the same SAW intensity and has undergone an identical fabrication process. Nanoribbon widths of 350, 400, 500 and 600 nm were characterised, with measured sheet resistances of 3.7, 3.8, 5.4, and 7.0 kΩ/□ respectively [31], so that the widest ribbons have the smallest electrical conductivity. Further details of the device layout and fabrication process can be found in [31].
All measurements were made under vacuum (chamber pres sure approximately 6 × 10 −6 mbar) with continuous pumping to reduce the accumulation of dopants, at room temper ature. Continuous wave SAWs were excited at the input transducer using a Hewlett-Packard 8648C RF signal generator, with the RF power set to +20.0 dBm, The AE current, Iae, was measured using a Keithley K2400 source-measurement unit. Two-terminal current-voltage measurements were used to determine the GNR array conductivities, and arrays that were not being characterised were electrically grounded to reduce interference. The SAW amplitude at the output IDT was measured using a LeCroy WaveRunner 204Xi-A digital oscilloscope, and used to estimate SAW intensity.
A Thorlabs MCWHL2 LED (peak emission wavelength of 450 nm) was used to study the AE photoresponse. LED drive currents of 0.2 A and 1.4 A were used, producing an incident light intensity on the sample of 0.24 mW mm −2 and 1.20 mW mm −2 respectively after correcting for the measurement geometry. A motorised shutter was used to control the exposure of the sample to the LED.

Results and discussion
The measured AE current, for a nanoribbon width of 500 nm, is plotted as a function of time for SAW frequencies of 33 MHz and 355 MHz in figures 2(a) and (b) respectively. The vertical dashed lines indicate the time at which the motorised shutter was opened after 1 h, allowing illumination by the LED (with an intensity of 1.20 mW mm −2 ) for a period of 1 h, before the shutter was then closed again. Although only results from 500 nm wide nanoribbons are presented here, similar results were obtained in all the nanoribbons. A negative current in the direction of SAW propagation was observed in all, corresponding to n-type doping of the nanoribbons, in contrast to the p-doping observed previously in these nanoribbon arrays [31]. This most likely reflects the increased vacuum pump-out time before these new measurements were undertaken, leading to the removal of surface adsorbates that p-dope graphene, such as molecular water. The magnitude of the AE current was largest for a SAW frequency of 355 MHz in each nanoribbon array. This is thought to arise from an enhanced piezoelectric interaction between the GNRs and the SAWs when the SAW wavelength (approximately 11 µm at 355 MHz) is equal to the periodicity (10 µm) of the perpendicular graphene bridges in the array [31].
Upon illumination, a rapid decrease in the magnitude of the AE current was observed at both SAW frequencies in all GNR arrays. The fast initial change in the current is followed by a much slower decrease in current over the timescale of an hour or so. This effect was also observed in unpatterned graphene [22] and is broadly the same for different SAW frequencies. Unfortunately, the origin of this slow relaxation is unknown, and will be explored in future work. Closing the shutter again causes the current to quickly approach its original value. The decrease in the measured AE current under illumination contrasts with the AE photoresponse of continuous graphene sheets [22], where the magnitude of the current increased upon exposure to light. A larger change in AE current due to illumination was measured at the higher incident light intensity, and at the higher SAW frequency, as seen previously in graphene sheets. The conductivity of the GNRs (σ 2D ) was also recorded as a function of time and is plotted as the solid blue line in figure 2(c) for an illumination intensity of 1.20 mW mm −2 . Upon exposure to the light, the conductivity quickly decreases, by as much as ~5% in the case of the array of 600 nm-wide GNRs. This compares to a decrease of up to 6% measured in the conductivity of an unpatterned graphene sample under the same illumination [22]. When the shutter is closed, the conductivity increases again towards its value prior to illumination.
The decrease in conductivity under illumination gives rise to an increase in the SAW attenuation per unit length, which can be calculated from the conductivity utilising the classical relaxation model widely used to describe the AE interaction between the SAWs and charge carriers in low dimensional systems [34,35]: where K 2 is the piezoelectric coupling coefficient (0.056 in 128° YX LiNbO 3 ), λ is the SAW wavelength, and the attenuation is maximum at a characteristic conductivity, σ M, . In this work, a value of σ M = 10 −7 Ω −1 was taken, which was extracted from previous measurements where we used an ion gel top gate [30] to modify the conductivity of unpatterned graphene on lithium niobate. The characteristic conductivity σ M, was extracted from the measurement of SAW attenuation as a function of gate bias, with the value of σ M taken as the value of σ 2D when the SAW attenuation was at a maximum (equation (1)). This value is likely to be sensitive to any nonuniformity of the graphene [30], and could vary from sample to sample due to differences in doping. However, as σ 2D is much, much greater than σ M , for all the ribbon widths and in unpatterned graphene, small variations in the characteristic conductivity are unlikely to alter the interpretation of the results obtained here. Future work will include the simultaneous measurement of the SAW attenuation, as a function of illumination, to probe this further. The calculated attenuation coefficient is plotted for 500 nm ribbons in figure 2(c), showing how a decrease in conductivity under illumination leads to an increase in the attenuation coefficient. In figure 3(a) the decrease in measured conductivity under illumination, for intensities 0.24 mW mm −2 and 1.20 mW mm −2 , is plotted as a function of nanoribbon width. A similar trend is observed for both illumination levels, with the largest change in conductivity observed for the widest ribbons. In figure 3(b), the corresponding change in attenuation coefficient, calculated from the measured conductivity using equation (1)   . The dashed red line shows the corresponding attenuation coefficient, which was calculated from the measured conductivity using equation (1). occurs in the widest ribbons. We believe that this is because the widest ribbons have the smallest initial conductivity [31].
The AE current density, j, is determined both by the attenuation, but also by the charge carrier mobility µ: where I is the SAW intensity and v is the velocity of the SAW (3979 m s −1 in 128° YX LiNbO 3 ). In unpatterned graphene sheets, the increase in AE current under illumination was attributed to the generation of a hot carrier distribution [22]. Although this hot carrier distribution leads to a decrease in the charge carrier mobility µ, the corresponding decrease in conductivity led to a much larger increase in the attenuation coefficient, due to the non-monotonic behaviour described by equation (1), resulting in an overall increase in the measured AE current. The contrasting decrease of the measured AE current, under illumination, of the nanoribbons studied here is therefore likely due to the large difference in the initial conductivity of the unpatterned and nanoribbon graphene. The arrays of the 600 nm-wide and 350 nm-wide GNRs have conductivities ~11× and 21× greater [31] respectively than that of a typical unpatterned device [20][21][22]. Therefore, a decrease in the conductivity of the nanoribbons under illumination leads to a smaller change in the attenuation coefficient than that seen in the continuous graphene. This is shown schematically in figure 4, where the calculated attenuation coefficient (equation (1)) is plotted as a function of σ 2D /σ M . Under illumination, the conductivity of the nanoribbons decreases, but this only leads to a relatively small increase in the attenuation coefficient as compared to that observed in unpatterned graphene. This relatively small increase in the attenuation coefficient cannot therefore be large enough to compensate for the decrease in mobility, which overall leads to a decrease in the AE current under illumination.

Conclusion
In conclusion, we have investigated the AE cur rent in arrays of monolayer CVD GNRs with widths in the range 350-600 nm, as a function of illumination. Under illumination, both the AE current and the conductivity were observed to decrease, where the decrease in conductivity is consistent with the generation of a hot carrier distribution. The decrease in AE current contrasts with the increase in current observed in unpatterned graphene devices under illumination, even though the conductivity of these devices was also observed to decrease under illumination. This difference in observed behaviour is thought to be due to the very high conductivity of the nanoribbons compared to unpatterned graphene. A decrease of the conductivity of the ribbons under illumination only therefore leads to a small increase in the attenuation coefficient of the SAW, and is not enough to compensate for the reduction in mobility due to increased carrier-carrier scattering. Overall, the AE current therefore decreases on illumination.