Infrared photodetection in graphene-based heterostructures: bolometric and thermoelectric effects at the tunneling barrier

Mid-infrared photodetectors are crucial for astronomy, medical imaging, nondestructive testing, and environmental monitoring because mid-IR light probes thermal radiation and molecular vibrations. Van der Waals tunneling devices are attractive for IR detection due to strong phonon-polariton absorption in layered dielectrics such as hBN and their intrinsically fast response governed by nanometer-scale vertical transport. However, multiple mechanisms—carrier heating, charge accumulation, nonlinearity-driven rectification, and photon-assisted tunneling—can contribute to photoresponse, making the dominant mechanism unclear, especially in the infrared where experiments are scarce. Prior studies largely focused on the visible/THz ranges with mixed evidence for photon-assisted tunneling. This work addresses the unresolved mechanism of photocurrent generation in graphene/hBN/graphene vertical tunnel structures under mid-IR illumination, testing whether photothermal (bolometric/thermoelectric) effects or photon-assisted tunneling dominate, and exploring the utility of photocurrent as an electron thermometry probe.

The paper situates the work within several strands: (1) Mid-IR detection platforms including phonon polariton-based enhancement in van der Waals materials (e.g., hBN hyperbolic modes) that offer strong absorption and fast response. (2) Known nonlinearity in tunneling devices suggesting rectification at classical frequencies and photon-assisted tunneling at quantum frequencies; superlattice detectors and quantum cascade lasers exploit joint density of states singularities. (3) Prior graphene-based vertical heterostructure studies in the visible reported heating-induced currents, photothermionic effects, and light emission from tunneling. (4) Infrared and THz tunneling photodetection studies exist but with limited direct evidence for photon-assisted mechanisms; the dominant IR mechanism in graphene-based vertical tunneling structures remained unresolved. (5) Twist-controlled resonant tunneling and defect/phonon-assisted tunneling in graphene/hBN devices establish that impurity levels in hBN can mediate resonant transport, providing a context for resonant features expected in photoresponse.

Experimental: Devices were fabricated by dry transfer. The studied structure comprises two single-layer graphene (SLG) electrodes separated by ~3-layer hBN (~1 nm) on an hBN/graphite back-gated substrate. The overlap (tunnel junction) area is ~2.3 µm^2. Metal contacts: Ti (3 nm)/Au (70 nm). A cutout was etched to prevent shorting due to thin hBN displacement. AFM measured layer thicknesses; e-beam lithography and reactive ion etching (SF6) defined contacts and regions. Measurements were conducted in a 7 K closed-cycle cryostat. I–V characteristics were recorded via a Keithley 2636B. Differential conductance dI/dV was obtained by numerical differentiation. The second derivative d^2I/dV^2 was measured via AC-DC mixing: a small AC voltage (VAC ≈ 4.8 mV rms at 4 Hz) added to DC bias; the second harmonic current I2 at +90° phase gives d^2I/dV^2 ≈ √2 I2 / VAC. Photocurrent Iph was measured using a lock-in at 8 Hz chopping of a linearly polarized quantum cascade laser (QCL) at λ = 8.6 µm (ħω ≈ 144 meV), with a ZnSe lens focusing the beam to near diffraction-limited spot; a motorized XY stage enabled mapping. Gate- and bias-resolved maps of Iph, dI/dV, and d^2I/dV^2 were collected. A second device (device #2) with multilayer graphene (2L top, 3L bottom), the same ~1 nm hBN barrier, a larger junction area, and a Si back gate was tested at λ = 6.0 µm. Analysis and modeling: Differential conductance maps revealed resonant tunneling via hBN impurity levels. A model relating impurity alignment to gate and bias (P_n(Vb − Vgate) = Ein + e F(Vb − Vgate) x_in) reproduced the positions of conductance spikes, yielding two main impurity levels E1 = +100 meV and E2 = −70 meV (from the Dirac points) and their positions within the barrier (impurity #1 near mid-barrier; impurity #2 between the second and third hBN layers from the bottom graphene). Photocurrent generation mechanisms were examined: photon-assisted tunneling (PAT) vs thermal (hot-carrier) tunneling. Absence of Iph features shifted by ħω from impurity resonance lines ruled out PAT. A photothermal model based on the Bardeen transfer Hamiltonian was developed:

• DC tunneling current: I(Tt,Tb) = ∫ dE [ft(E) − fb(E)] D(E), where ft,b are Fermi-Dirac distributions in top/bottom graphene with temperatures Tt,Tb and D(E) is the energy-dependent tunneling probability with sharp resonances at E = Ein.
• Photocurrent under illumination: Iph = I(T0 + ΔTt, T0 + ΔTb) − I(T0), with T0 the cryostat temperature and ΔTt, ΔTb the radiation-induced electron heating in each layer. In linear approximation: Iph ≈ (∂I/∂Tt) ΔTt + (∂I/∂Tb) ΔTb. The model predicts, and experiments confirm, that at finite bias Iph is proportional to dI/dT and correlates with d^2I/dV^2 near impurity resonances; at zero bias, Iph is proportional to the temperature difference ΔTt − ΔTb (Seebeck-like across the tunnel barrier). Temperature-dependent DC I–V curves were measured to extract dI/dT and compare with Iph to estimate electron overheating.

• Photocurrent maps under λ = 8.6 µm illumination show extrema that closely track the resonant lines in dI/dV and, in detail, the features of d^2I/dV^2 as functions of gate and bias. At small |Vb| and |Vgate| (|Vb| < 0.25 V, Vgate < 3 V), Iph is directly proportional to d^2I/dV^2; correlations persist at higher biases but with an added positive background.
• Around impurity resonance, Iph exhibits a characteristic double-spike of opposite signs as the Fermi level crosses the impurity level at finite bias, consistent with hot-carrier (thermal) tunneling. Near zero bias, a three-spike pattern appears due to superposition from both layers; exactly at zero bias, Iph is proportional to ΔTt − ΔTb (Seebeck-like across the barrier).
• Absence of photocurrent features shifted by the photon energy relative to impurity lines excludes photon-assisted tunneling as the dominant mechanism at mid-IR frequencies used here.
• The impurity-assisted resonant transport model reproduces the positions of conductance spikes and yields impurity energies E1 ≈ +100 meV and E2 ≈ −70 meV from the graphene Dirac points, with impurity #1 near the barrier center and impurity #2 between the second and third hBN layers from the bottom graphene.
• Additional bias-dependent features in Iph and d^2I/dV^2 at Vb ≈ ±18–20 mV and 175–200 mV are attributed to graphene phonon modes; the high-energy feature exceeds the photon energy and coincides with optical phonon energies.
• Quantitative thermometry via comparison of Iph to dI/dT yields an average electron overheating ΔT ≈ 8 K in each graphene layer at incident power P = 7.2 mW (λ = 8.6 µm). The interlayer temperature difference is estimated to be ≤ 1.5 K from fitting near-zero-bias gate sweeps.
• Temperature dependence (31–100 K) shows decreasing Iph with increasing T, consistent with the expected 1/T decrease of dI/dT due to Fermi function broadening.
• Device performance: the presented device achieved photocurrent up to ~120 pA. A larger-area device (#2) with multilayer graphene produced up to ~5 nA photocurrent at λ = 6.0 µm, with responsivity ~0.8 mA W^-1 and NEP ≈ 830 pW Hz^-1/2.
• Timescale analysis supports thermal origin: estimated electron thermalization time τ_th ~ 80 fs (for ε_F ~ 200 meV, ħω ~ 144 meV) is much shorter than tunneling time τ_tun ~ 40 ps for ~1 nm hBN barrier, suppressing PAT at mid-IR; PAT may emerge at lower frequencies (≤ 1 THz) where thermalization is slower.

The experiments and modeling resolve the dominant mechanism of mid-IR photocurrent in graphene/hBN/graphene tunneling devices with defect-mediated resonances: illumination heats electrons in the graphene layers, modifying their Fermi distributions and, through the strong energy dependence of D(E), modulating the tunneling probability. At finite bias, this yields a bolometric effect across the tunnel barrier, with Iph tracking dI/dT and correlating with d^2I/dV^2. At zero bias, asymmetric heating between layers produces a Seebeck-like tunneling current proportional to ΔTt − ΔTb. These barrier-transverse bolometric and thermoelectric effects are maximized when a graphene Fermi level aligns with an hBN impurity state, where small temperature changes produce large variations in energy-averaged tunneling probability. The absence of photon-energy-shifted resonance features in Iph maps excludes photon-assisted tunneling under the present conditions; a timescale comparison indicates rapid electron thermalization outpaces interlayer tunneling, naturally suppressing PAT for mid-IR photons. The close agreement between the photothermal tunneling model and experiment across bias and gate confirms the interpretation and enables using Iph as a quantitative probe of electron temperature in 2D materials. The approach suggests practical routes to improve detector performance (larger junction area, thinner or less resistive barriers such as WS2) and to deploy vertical tunnel junctions as local electron thermometers under non-equilibrium photoexcitation.

The study identifies radiation-induced electron heating as the primary source of photocurrent in graphene/hBN/graphene tunnel junctions under mid-IR illumination. Photocurrent arises from bolometric modulation of tunneling at finite bias and a Seebeck-like effect across the tunnel barrier at zero bias. Iph correlates with d^2I/dV^2 and with dI/dT, peaking when graphene Fermi levels align with defect states in hBN. A Bardeen transfer Hamiltonian model quantitatively reproduces the gate- and bias-resolved photocurrent maps and enables extraction of electron overheating (ΔT ~ 8 K at 7.2 mW). The absence of photon-assisted tunneling signatures is attributed to ultrafast thermalization relative to tunneling. The results establish vertical tunneling photocurrent as a practical electron thermometry tool and suggest design strategies to enhance sensitivity (larger area, thinner/less resistive barriers such as WS2). Future work could explore operation at higher temperatures where thermoelectric effects extend over larger bias ranges, investigate the transition to photon-assisted regimes at THz frequencies, and integrate arrays of such tunnel micro-detectors for multipixel mid-IR imaging.

• Experiments were conducted primarily at cryogenic temperatures (~7 K); photocurrent magnitude and mechanisms at room temperature require further characterization.
• Precise zero-bias measurements were limited by voltage setting/measurement accuracy, preventing clear isolation of the ideal two-spike thermoelectric profile exactly at Vb = 0.
• The temperature difference between layers (ΔTt − ΔTb) could only be bounded (≤ 1.5 K) rather than directly resolved due to limited sensitivity and near-zero-bias artifacts.
• The dominant mechanism is tied to impurity-assisted resonant tunneling; devices lacking suitable defect states may exhibit different behaviors or reduced sensitivity.
• Background photocurrent at large biases complicates direct proportionality to d^2I/dV^2 outside the low-bias regime.
• Generalization to other barrier materials and thicknesses, or to room-temperature operation, was not exhaustively tested within this study.