Shockley-Ramo theorem and long-range photocurrent response in gapless materials

Song, Justin C. W.; Levitov, L. S.

doi:10.1103/physrevb.90.075415

Cited by 65 publications

(80 citation statements)

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“…1 shows that at V BG = V D , the charge density is non-uniform in graphene, and a p-n junction exists near and roughly parallel to the graphene edge. Such a p-n junction will give rise to a local photocurrent due to PTE when illuminated by light, and this in turn drives a global current, independent of distance to the collecting electrodes, according to the Shockley-Ramo framework developed in [2]. Since the p-n junction closely follows the graphene edges ( Fig.…”

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Dirac-point photocurrents due to the photothermoelectric effect in non-uniform graphene devices

Fuhrer

Medhekar

2020

Nat. Nanotechnol.

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Q. Ma et al. [1] recently reported a strong photocurrent associated with charge neutrality in graphene devices with non-uniform geometries, which they interpreted as an intrinsic photoresponse enhanced by the momentum non-relaxing nature of electron-electron collisions at charge neutrality. Here we argue that gradients in charge carrier density give rise to a photothermoelectric effect (PTE) which is strongly peaked around charge neutrality, i.e. at p-n junctions, and such p-n junctions naturally arise at the edges of graphene devices due to fringing capacitance. Using known parameters, the PTE effect in the presence of charge density gradients predicts the sign, spatial distribution, gate voltage dependence, and temperature dependence of the photoresponse in non-uniform graphene devices, including predicting the observed sign change of the signal away from charge neutrality, and the non-monotonic temperature dependence, neither of which is explained by the intrinsic photocurrents in graphene. We propose future experiments which may disentangle the contributions of PTE and intrinsic photocurrent in graphene devices.Q. Ma et al. [1] show that the PTE is zero in the case of uniform carrier density n in graphene. However, if n is non-uniform, a local PTE arises, proportional to the gradient in the local thermopower:. One known source of such non-uniformity is the variation in the local backgate capacitance to the graphene. The effect of geometry on capacitance is significant; for example, the capacitance per area for a 1 micron strip of graphene on 300 nm SiO 2 is ~40% larger than for a 10 micron strip of graphene[3] largely due to fringing capacitance at the strip edges. Fig. 1 models the non-uniform carrier density in a graphene device of geometry similar to Fig. 2 in [1]. As-fabricated graphene devices often have a uniform background carrier density -n D without application of a gate voltage, and require a finite backgate voltage V BG = V D = n D e/c g , where c g is the average capacitance per unit area and e the elementary charge, to tune to charge neutrality. Fig. 1 shows that at V BG = V D , the charge density is non-uniform in graphene, and a p-n junction exists near and roughly parallel to the graphene edge. Such a p-n junction will give rise to a local photocurrent due to PTE when illuminated by light, and this in turn drives a global current, independent of distance to the collecting electrodes, according to the Shockley-Ramo framework developed in [2]. Since the p-n junction closely follows the graphene edges (Fig. 1) the spatial dependence of the photocurrent is indistinguishable from the model in [1]. Other sources of non-uniform doping, such as chemical termination of edges, treatment of the oxide near the edge during plasma etching, or self-doping from edge states could also give rise to p-n junctions at graphene edges independent of the gating effect, but will not be discussed here.We now discuss the sign of the photocurrent. For the device in Fig. 2 of [1], R(V BG ) is shown, indicating V D is posi...

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Dirac-point photocurrents due to the photothermoelectric effect in non-uniform graphene devices

Fuhrer

Medhekar

2020

Nat. Nanotechnol.

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“…Rather, in such a gapless material the localized current density source j loc produces a global photocurrent I ph by setting up an electric field that drives ambient carriers outside the excitation region and into the contacts, as recently discussed by Song and Levitov 5 . These authors derived an expression giving I ph as an integral over j loc , analogous to the Shockley-Ramo theorem that gives the current generated between two conducting plates when a charge moves in the insulating space between them 27,28 .…”

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“…The gate-voltage dependence is produced by the dependence of the thermoelectric coefficients on carrier density. We can model the results quantitatively by applying Song and Levitov's theorem 5 to the extrinsic thermoelectric current j th = − ↔ α ∇T , with ↔ α the 2D thermoelectric tensor. Use of this local relationship is justified as the momentum relaxation length is less than 29 ∼1 µm.…”

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Photo-Nernst current in graphene

et al. 2015

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Photocurrent measurements provide a powerful means of studying the spatially resolved optoelectronic and electrical properties of a material or device [1][2][3][4][5][6][7] . Generally speaking there are two classes of mechanism for photocurrent generation: those involving separation of electrons and holes, and thermoelectric e ects driven by electron temperature gradients. Here we introduce a new member in the latter class: the photo-Nernst e ect. In graphene devices in a perpendicular magnetic field we observe photocurrent generated uniformly along the free edges, with opposite sign at opposite edges. The signal is antisymmetric in field, shows a peak versus gate voltage at the neutrality point flanked by wings of opposite sign at low fields, and exhibits quantum oscillations at higher fields. These features are all explained by the Nernst e ect In a semiconductor, electrons and holes generated by photons can live long enough to be spatially separated by an electric field and diffuse to the contacts. This is the basis of photovoltaic cell operation. In contrast, in a gapless material such as graphene the full electron distribution rapidly thermalizes, eliminating the distinction between electrons and holes. Nevertheless, photocurrent is readily produced when light is focused on inhomogeneous regions or junctions in graphene devices 6,7,[13][14][15][16][17][18][19][20] . Detailed measurements of the dependence on gate voltage and time delay have shown that it is primarily of a thermoelectric nature 6,11,13,17,19 , and that the heating of the electrons is sometimes enhanced by slow energy transfer to the lattice due to the large optical phonon energy and high electron velocity 14,[21][22][23][24][25][26] . However, the means by which a thermoelectric current near the laser spot results in photocurrent in the contacts, which may be located some distance away, has received much less attention.Unlike in a semiconductor, in graphene one cannot talk about diffusion of majority carriers to the contacts. Rather, in such a gapless material the localized current density source j loc produces a global photocurrent I ph by setting up an electric field that drives ambient carriers outside the excitation region and into the contacts, as recently discussed by Song and Levitov 5 . These authors derived an expression giving I ph as an integral over j loc , analogous to the Shockley-Ramo theorem that gives the current generated between two conducting plates when a charge moves in the insulating space between them 27,28 . Our measurements on graphene devices in a magnetic field demonstrate the existence of the photo-Nernst effect which produces a photocurrent according to this theorem. In the presence of a perpendicular field B a transverse current proportional to B tends to circulate around the laser spot, that is, perpendicular to the electron temperature gradient in the graphene generated by the laser. When the laser is near a free edge, the integral of this chiral j loc points along the edge, producing a photocurrent which is...

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“…It has been predicted that a floating contact would modify the internal potential of graphene in a dipole pattern. 29 It would have been difficult to observe this data without using MPDPM. No single image, or dependence of a single parameter, contains a clear experimental signature of changing electrochemical potential.…”

Section: B Image Analysismentioning

confidence: 99%

Multiple parameter dynamic photoresponse microscopy for data-intensive optoelectronic measurements of van der Waals heterostructures

Arp

Gabor

2019

Review of Scientific Instruments

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Quantum devices made from van der Waals (vdW) heterostructures of two dimensional (2D) materials may herald a new frontier in designer materials that exhibit novel electronic properties and unusual electronic phases. However, due to the complexity of layered atomic structures and the physics that emerges, experimental realization of devices with tailored physical properties will require comprehensive measurements across a large domain of material and device parameters. Such multi-parameter measurements require new strategies that combine data-intensive techniques -often applied in astronomy and high energy physicswith the experimental tools of solid state physics and materials science. We discuss the challenges of comprehensive experimental science and present a technique, called Multi-Parameter Dynamic Photoresponse Microscopy (MPDPM), that utilizes ultrafast lasers, diffraction limited scanning beam optics, and hardware automation to characterize the photoresponse of 2D heterostructures in a time efficient manner. Using comprehensive methods on vdW heterostructures results in large and complicated data sets; in the case of MPDPM, we measure a large set of images requiring advanced image analysis to extract the underlying physics. We discuss how to approach such data sets in general, and in the specific case of a graphene -boron nitride -graphite heterostructure photocell.

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Shockley-Ramo theorem and long-range photocurrent response in gapless materials

Cited by 65 publications

References 21 publications

Dirac-point photocurrents due to the photothermoelectric effect in non-uniform graphene devices

Dirac-point photocurrents due to the photothermoelectric effect in non-uniform graphene devices

Photo-Nernst current in graphene

Multiple parameter dynamic photoresponse microscopy for data-intensive optoelectronic measurements of van der Waals heterostructures

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