Report

Hot Carrier–Assisted Intrinsic Photoresponse in Graphene

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Science  04 Nov 2011:
Vol. 334, Issue 6056, pp. 648-652
DOI: 10.1126/science.1211384

Abstract

We report on the intrinsic optoelectronic response of high-quality dual-gated monolayer and bilayer graphene p-n junction devices. Local laser excitation (of wavelength 850 nanometers) at the p-n interface leads to striking six-fold photovoltage patterns as a function of bottom- and top-gate voltages. These patterns, together with the measured spatial and density dependence of the photoresponse, provide strong evidence that nonlocal hot carrier transport, rather than the photovoltaic effect, dominates the intrinsic photoresponse in graphene. This regime, which features a long-lived and spatially distributed hot carrier population, may offer a path to hot carrier–assisted thermoelectric technologies for efficient solar energy harvesting.

The photoresponse of semiconductors, which determines the performance of optoelectronic devices, is governed by energy relaxation pathways of photoexcited electron-hole pairs: Energy transferred to the lattice is lost as heat, while energy transported through charge carriers may be used to drive an optoelectronic circuit (1). Nanoscale systems can offer various ways to control energy relaxation pathways, potentially resulting in more efficient device operation. Novel relaxation pathways that result from electron confinement have been demonstrated in nanocrystal quantum dots and carbon nanotubes (2, 3). In graphene, energy relaxation pathways are strongly altered by the vanishing electronic density of states (46). After initial relaxation of photoexcited carriers (as a result of electron-electron scattering and optical phonon emission), electron-lattice energy relaxation can be quenched (4), which creates a bottleneck that limits further energy redistribution into the lattice. With electron-to-lattice energy relaxation quenched, a novel transport regime is reached in which thermal energy is redistributed solely among electronic charge carriers. The photogenerated carrier population remains hot while the lattice stays cool.

In graphene, hot carriers should play a key role in optoelectronic response (6), yet measurements have not clearly determined the photocurrent generation mechanism. Numerous initial studies suggested that photocurrent generated at graphene-metal contacts (711) results from the photovoltaic (PV) effect, in which a built-in electric field accelerates photogenerated charge carriers to the electronic contacts. More recent studies have looked at monolayer-bilayer interfaces (12) and highly controlled chemical potential gradients at gate voltage–controlled p-n interfaces (13), and their results indicate that photothermoelectric (PTE) effects may play an important role. The PTE effect arises from a light-induced temperature difference resulting in a thermoelectric voltage. Although PTE physics has been invoked to explain photocurrent measured in graphene (12, 13), an experimental proof of its role in determining the intrinsic photoresponse has been lacking.

We report optoelectronic measurements of dual gate voltage–controlled graphene p-n junction devices in the presence of local laser excitation. Dual gate control allows us to explore the rich structure of photoresponse as a function of carrier polarity, varied independently in two adjacent regions. Our measurements indicate that hot electronic carriers dominate graphene’s intrinsic optoelectronic response at temperatures ranging from room temperature down to 10 K and in the linear optical power regime. The hot carrier regime manifests as a strong PTE effect that results in a striking six-fold photovoltage pattern as a function of gate voltages. Additionally, the spatial and charge density dependence of the photoresponse establishes a strong connection between thermal energy transport and electronic charge carriers.

We studied p-n junctions in both monolayer and bilayer graphene devices integrated with global bottom gates and local top gates, as shown in Fig. 1A and described in (14). Tuning the bottom- and top-gate voltages, VBG and VTG respectively, allows independent control of carrier density of electrons (n-type carriers) and holes (p-type carriers) in each region (1517). By applying voltages of opposite polarity on VBG and VTG, we formed a p-n junction at the interface of p- and n-type regions in a single graphene sample (Fig. 1C, bottom). The gate configurations in our devices are similar to those in (1517), with p-n junctions estimated to be narrower than ~80 nm.

Fig. 1

Device geometry, band structure, and optoelectronic characteristics of the graphene p-n junction. (A) Optical microscope image of the dual-gated device incorporating boron nitride top-gate dielectric. The current I is measured at fixed bias voltage VSD. Dashed white lines mark the boundaries of graphene. MLG, monolayer graphene; VTG, top-gate voltage. (B) Resistance (in kilohms) versus VBG and VTG at VSD = 1.4 mV and T = 175 K. Four regions are labeled according to carrier doping, p-type or n-type, in the bottom- and top-gated regions, respectively. CNP, charge neutrality point. (C) Experimental schematic (top) and schematic of monolayer graphene’s band structure in the p-n junction (bottom), showing electron bands (blue) and hole bands (red). The dashed line represents the electron chemical potential (or Fermi energy) EF. (D) Spatially resolved photocurrent map at T = 40 K with laser wavelength λ = 850 nm and optical power = 50 μW (VBG = –5 V, VTG = 2 V, VSD = 0 V). White lines mark location of gold contact and gate electrodes; white triangle is measurement point for Fig. 2A. (E) Photocurrent line trace taken at dashed line in (D). Laser position = 0 corresponds to the edge of the top-gate electrode; the dashed line is a fit to the data (see text).

We first characterized our devices via electronic transport measurements of resistance R as a function of VBG and VTG. Figure 1B shows R versus VBG and VTG for a monolayer graphene (MLG) p-n junction. The resistance exhibited four characteristic regions, a distinctive behavior that reflects gate voltage–tunable charge density and a sharp density gradient at the p-n interface (1517). When the charge density nc was tuned near the neutrality point in each gated region, R increased because of the low density of conduction carriers. When two gates were present, this resulted in two intersecting lines of relatively high resistance, and a maximum resistance Rmax at their intersection, the global charge neutrality point (CNP). The two lines divided the resistance map into four regions: p-n, n-n, n-p, and p-p, labeled according to the carrier doping induced in the bottom-gated and dual-gated regions (regions 1 and 2, respectively). As the carrier density increased away from the CNP, the resistance decreased monotonically from Rmax.

Devices were placed in a low-temperature optical cryostat that combined electronic transport with mirror-controlled scanning laser excitation (Fig. 1C and fig. S1). Figure 1D shows a photocurrent image obtained by scanning a focused laser spot 1 μm in diameter (λ = 850 nm) over the device at VSD = 0 V while measuring the current I. At the sharply defined junction, we observed a strong photocurrent that was an order of magnitude greater than the photocurrent at the contacts and increased linearly with optical power. The maximum photocurrent responsivity reached 5 mA/W at low temperatures, which is greater than previously reported values of 1 mA/W at room temperature (10, 13). As a function of distance, the photocurrent exhibited a triangular shape centered at the junction and extending several micrometers to the contacts (solid line in Fig. 1E). A triangular profile indicates that the charge carriers remained hot throughout the device and contributed to photocurrent (see below).

Unlike the resistance measurements, in which we observed four gate voltage regions, optoelectronic measurements with the laser fixed at the junction exhibited a striking photovoltage pattern, with six regions of alternating photovoltage sign as a function of VBG and VTG (Fig. 2). Because the photoconductance in graphene is negligible (9), the photovoltage established across the device can be determined from the measured IPH according to the relation VPH = IPHR. If the photocurrent originates from the PV effect, in which the photovoltage is proportional to the electric field induced at the junction, then we would expect only a single photovoltage sign change and a monotonic dependence on increasing charge density. However, VPH as a function of VBG and VTG (Fig. 2A) exhibited multiple sign changes (6). Moreover, the photovoltage line traces extracted along the high-resistance ridges (gray lines), along which charge density increases away from the CNP, exhibited strong nonmonotonic gate voltage dependence (Fig. 2A, left and bottom).

Fig. 2

Photovoltage and thermoelectric response of the graphene p-n junction. (A) Photovoltage (VPH) versus VBG and VTG at T = 40 K, measured at the location marked by the triangle in Fig. 1D. Gray dashed lines are lines of high resistance from transport characteristics. The white dashed line is described in the text. Photovoltage line traces were taken along the vertical (left) and diagonal (bottom) gray dashed lines. (B) Absolute value of photovoltage near the CNP. (C) Resistance and thermovoltage versus VBG at VSD = 0 V, VTG = 2.0 V, and T = 40 K (optical power = 1 mW, laser at triangle in Fig. 1D). (D) Schematic of the Seebeck coefficient as a function of Fermi energy for typical resistance characteristics of graphene (inset).

The shape of the photovoltage node lines (i.e., lines at VPH = 0) indicates that whereas R decreased monotonically away from Rmax at the CNP, the photovoltage showed nonmonotonic dependence on gate voltages. In the PV effect, changing the direction of the electric field as the relative carrier densities are changed in regions 1 and 2 would change the sign of the photovoltage across a single nodal line. This line, along which the carrier density in the two regions is equal (white dashed line in Fig. 2A), divides the p-p and n-n regions (6). Figure 2B shows the photovoltage nodes determined by plotting the absolute value of photovoltage |VPH| versus VBG and VTG. We observed three photovoltage nodes that deviated substantially from lines of high resistance. Near the CNP, where R decreased monotonically away from Rmax, the photovoltage displayed a vertically oriented Z-shaped nodal line and two points toward which the three nodal lines converged (arrows in Fig. 2B).

Such nonmonotonic behavior of transport properties is reminiscent of the sign change and nonmonotonic charge density dependence of thermoelectric voltage in graphene (1821). Thermoelectric transport measurements on the same sample showed that the thermovoltage VT measured as a function of VBG exhibited features similar to the photovoltage nodes along the high-resistance ridges. By laser-heating the gold contact far from the graphene-metal junction (triangle in Fig. 1D), we introduced a fixed uncalibrated temperature gradient across the device and measured the resulting thermovoltage (fig. S2). Figure 2C shows VT and R as a function of VBG. Whereas R decreased monotonically away from the CNP, VT exhibited a nonmonotonic gate voltage dependence with peaks that corresponded closely to the gate voltages at which the three nodal lines of the photovoltage converged near the CNP (arrows in Fig. 2B).

We attribute the intricate photovoltage pattern in graphene to the PTE effect. After optical excitation, electron-hole pairs decay rapidly (~10 to 150 fs) into a thermal distribution of electronic carriers (22, 23) with a local effective temperature Tel that remains out of equilibrium with the lattice. The difference in temperature with its surroundings results in a thermal current that is accompanied by a charge current, the magnitude and sign of which is sensitive to carrier type and density (i.e., a p-type sample exhibits charge current with an opposite sign to that of an n-type sample). In unbiased homogeneous graphene, an isotropic thermal current flowing away from the excitation spot is not accompanied by a similar isotropic charge current.

However, in a p-n junction this symmetry is broken, and photoexcitation can result in nonzero net PTE current. The sign and magnitude of PTE voltage resulting from this current depends on the Seebeck coefficient (12, 24) in each region and can be written asVPTE=(S2S1)ΔT(1)where S is thermoelectric power (Seebeck coefficient) in the bottom- and dual-gated regions, and ΔT taken at the junction is proportional to the electron temperature difference between the area of optical excitation and its surroundings (6). From the Mott formula (24), we can write S asS=π2kB2T3e1RdRdVGdVGdE|E=EF(2)where T is the sample temperature, kB is the Boltzmann constant, and EF is the Fermi energy (12, 1821). Whereas R decreased monotonically with VG away from the CNP, S changed nonmonotonically (Fig. 2D). The nonmonotonic dependence of S1 and S2 resulted in multiple sign reversals for the quantity (S1S2), which occurred along three nodal lines and gave rise to the six-fold pattern (Fig. 2A) (6), characteristic of a PTE effect in graphene.

We obtained more direct insight into the origin of the six-fold photovoltage patterns by extracting the two components of the PTE voltage individually. A Fourier analysis technique (14) can extract S1 and S2 because they depend on different combinations of VBG and VTG. The Fourier transform of the data (Fig. 3A), exhibited a pair of streaks. The orientations of these streaks, horizontal (NB) and diagonal (NT), are described by the capacitance matrix of regions 1 and 2 [see (25)]. The relations between these streaks and the individual properties of the two regions are clarified by masking one of the streaks and performing an inverse Fourier transform of the other streak. This procedure revealed two contributions, each behaving as a function of density in the corresponding regions, VPH[NB] and VPH[NT] (Fig. 3B, top). Furthermore, the nonmonotonic density dependence of each contribution was similar to the behavior of the Seebeck coefficient given by the Mott formula (Fig. 3B, bottom). The sum VPH[NB] + VPH[NT] reproduces the photovoltage pattern (Fig. 3A, lower inset). The nonmonotonic behavior of each term produced polarity reversal on three nodal lines and gave rise to a six-fold pattern.

Fig. 3

Fourier analysis of the photovoltage response. (A) Fourier transform |F{VPH}| of photovoltage versus VBG and VTG from Fig. 2A. NB and NT label two components of the Fourier transform masked to extract the bottom- and top-gated photovoltage components. Upper inset: Photovoltage map from Fig. 2A. Lower inset: Sum of the individual Fourier components of the photovoltage. (B) Bottom- and top-gated photovoltage components VPH[NT] and VPH[NB] as a function of VBG and VTG calculated by inverse Fourier transforming along the masked directions NT and NB. Lower panel: Photovoltage line traces from VPH[NB] and VPH[NT]. The VBG axis has been shifted by the CNP voltage for VPH[NB]. (C) Ratio of the photovoltage VPH[NB] to the thermovoltage VT, and resistance as a function of VBG measured along the white dashed line in Fig. 2A.

Six-fold patterns were also observed in the bilayer graphene (BLG) photoresponse. Composed of two Bernal-stacked sheets of monolayer graphene, BLG has hyperbolic bands that touch at zero energy, resulting in the absence of a band gap (2628). Figure 4 shows the photoresponse of a BLG p-n junction photodetector. Using a top-gated configuration, two back-to-back junctions could be tuned by gate voltages. The resistance behaves similarly to the MLG junction, showing four gate voltage regions separated by lines of high resistance (gray dashed lines in Fig. 4C) (fig. S3). A strong photoresponse was observed in the p-n-p configuration, with photocurrent that peaked at the p-n junctions formed near the top-gate edge (Fig. 4B). The six-fold pattern in photovoltage versus VBG and VTG indicates the presence of a strong PTE effect (Fig. 4C).

Fig. 4

Photoresponse in the bilayer graphene p-n-p photodetector. (A) Optical microscope image of the BLG device. The current I is measured at fixed bias voltage VSD. White dashed line marks the boundary of BLG. (B) Photocurrent map at T = 40 K, λ = 850 nm, and optical power = 200 μW (VBG = 15 V, VTG = 10 V, VSD = 0 V). White lines indicate location of gold contact electrodes. (C) Photovoltage at the n-p junction [diamond in (B)] versus VBG and VTG at T = 40 K. Gray dashed lines are lines of high resistance taken from transport characteristics. White dashed line is as in Fig. 2A.

The hot carrier–assisted photoresponse in graphene is characterized by a long-lived and spatially distributed hot electronic population resulting from local excitation. The PTE photoresponse (Eq. 1) depends directly on the electronic temperature, which can be strongly enhanced by long cooling times τ. Because the cooling length ξ ∝ τ½ (24), long cooling times manifest as long cooling lengths. Using solutions to the heat equation (14), we fitted the photocurrent profile (dashed line in Fig. 1E) and obtained excellent fits for ξ > 2 μm (fig. S4). From the cooling length ξ > 2 μm, we estimated a lower bound of the hot carrier cooling time τ ≈ Cel · ξ2/κ ≈ 100 ps, where Cel is the electronic heat capacity and κ is the thermal conductivity of graphene (14). This cooling time is consistent with very slow cooling dynamics recently observed in graphene (23). The dimensions of the device allow us to establish only a lower bound for the cooling length. In contrast, other scattering mechanisms, such as optical phonon scattering, occur on far shorter time scales of ~1 ps (22, 23) and are ineffective at cooling low-energy carriers.

Graphene’s intrinsic photoresponse also exhibits charge density dependence that confirms hot carrier–assisted transport of thermal energy. For excitation fixed at the p-n interface, the steady state value of ΔT (14) at the laser spot is determined (in the limit of long cooling length) byΔT=dQ/dtK1+K2(3)where dQ/dt is the rate of heat entering the system, and K1 and K2 are respectively the electronic contributions to the thermal conductance of regions 1 and 2. Because hot carriers proliferate throughout the system, the Wiedemann-Franz relation, K = π2kB2T/3e2 × (1/R), holds. As a consequence, ΔT ∝ 1/KR (24). To isolate the density dependence of ΔT, we take the ratio of the photovoltage VPH to the thermovoltage VT obtained from a fixed temperature difference (14). This ratio, VPH[NB]/VT ∝ ΔT, is shown in Fig. 3C and clearly exhibits a density dependence that mimics the device resistance. The strong density dependence peaking at the CNP clearly demonstrates the electronic origin of ΔT.

Transport of hot electronic carriers results in a novel nonlocal transport regime that may enable increased power conversion efficiency in energy-harvesting devices. At present, graphene is considered to be an excellent candidate for energy-harvesting optoelectronics, in part because of the presence of high-responsivity photodetection with high internal quantum efficiency (6, 9). Here, we have shown that hot carriers dominate the intrinsic photoresponse and have demonstrated devices with Seebeck coefficients as high as 12 μV/K (at T = 40 K) and high electronic temperature ΔT ~ 4.5 K (14). Hot carrier–assisted photoresponse is predicted to improve the power conversion efficiency of energy-harvesting devices beyond standard limits (29). Our findings, together with new design principles for next-generation solar thermoelectric devices (30), make graphene-based systems viable for energy-harvesting applications.

Supporting Online Material

www.sciencemag.org/cgi/content/full/science.1211384/DC1

Materials and Methods

SOM Text

Figs. S1 to S4

References (3138)

References and Notes

  1. See supporting material on Science Online.
  2. In the top-gated region, both VBG and VTG contribute to nc, resulting in the slope of the diagonal line m = ΔVTGVBG = CBG/CTG ≈ 0.05, where CBG and CTG are respectively the bottom- and top-gate capacitances to graphene. NB and NT in the Fourier transform are perpendicular to the minimum resistance lines (gray dashed lines) in Fig. 2A.
  3. Acknowledgments: We thank M. Baldo, P. McEuen, P. Kim, and A. Yacoby for valuable discussions. Supported by the Air Force Office of Scientific Research, a NSF Early Career Award (P.J.H.), and the Packard Foundation. Sample fabrication was performed at the NSF-funded MIT Center for Materials Science and Engineering and Harvard Center for Nanoscale Science.
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