1. Theory

  • Definition: A graphene or two-dimensional (2D) material photodetector uses a single layer or a few layers of a van der Waals crystal as the absorber or the channel: graphene, a metal with no gap, the transition-metal dichalcogenides , , and , black phosphorus, and the chalcogenides InSe, GaS, GaSe and , alone or in a hybrid with quantum dots, perovskites, silicon or a waveguide.
  • Graphene: A single layer absorbs of the light from the visible to the infrared, with a Fermi velocity of about , a mobility above (up to in a free sheet), a recombination time of tens of picoseconds and no gap, so that there is no cutoff wavelength and the dark current is large.
  • 2D semiconductors: Monolayer has a direct gap with a response up to 680 nm, few-layer black phosphorus responds to 940 nm and a lateral photodiode of it to 1500 nm, and the gaps and mobilities depend on the number of layers, the substrate and the contacts.
  • Mechanisms: The photovoltaic effect in a built-in field, the photothermoelectric (PTE) effect, the bolometric effect, the photoconductive effect and photogating; the first two give no gain, and the last two can give a gain of to at the cost of speed.
  • Seebeck coefficients: Graphene has ±4 to ±100 , black phosphorus 60 to 335 and monolayer to in depletion, against about 1 of a metal.
  • Device types: The metal-graphene-metal detector with the photocurrent generated at the contacts, the graphene-semiconductor Schottky junction (0.2 A/W, 5 ns), the graphene or phototransistor sensitized by quantum dots, perovskites or other 2D layers, the van der Waals heterostructure photodiode, and the detector integrated on a silicon waveguide.
  • Contacts and substrate: The traps of the substrate, the adsorbates of the ambient air, the contact metal and the edge or phase-engineered contacts decide the gain, the response time and the mobility.
  • Figures of merit: The responsivity, the EQE, the gain, , the noise equivalent power, the linear dynamic range, the bandwidth and the response time.

2. Working Principle

  • Contact photocurrent: A photon absorbed in graphene creates carriers that recombine within tens of picoseconds, and the fields near the metal contacts and at the gate-induced p-n junctions separate them or drive a thermoelectric voltage over a region of 100 nm to 250 nm; the internal efficiency in that region is 6% to 16%.
  • Speed: The carriers leave the high-field region in 0.36 ps and the bandwidth is set by the contact capacitance, 106 GHz for 30 fF with 50 Ω, so that a graphene detector was measured from 10 MHz to 40 GHz, with a loss of at the top that the authors attribute to the probes.
  • Hybrid photogating: A dot or a perovskite layer absorbs the photon, one carrier goes into the graphene and the other stays trapped for the lifetime , so that the mobile carrier circulates times through the channel, with a gain up to and a bandwidth of 10 Hz to 1.5 kHz.
  • 2D semiconductor phototransistor: The trap states of the substrate and the surface hold one carrier for seconds in monolayer , so that the responsivity is 880 A/W while the response is 0.6 s to 9 s, and a gate pulse or a passivation shortens it.
  • Bolometric and PTE sign: A bolometric response in gives a negative photocurrent (-33 nA/K), while the PTE current of graphene changes its sign with the gate and with the position of the spot.

3. Applications

  • High-speed photodetection: A graphene detector of a few square micrometres worked to 40 GHz at 1.55 μm, and graphene on a silicon waveguide gave more than 0.1 A/W above 20 GHz, while a bilayer on a waveguide of 20 μm was simulated to absorb 65% of the TM light.
  • Broadband and SWIR imaging: The graphene-dot phototransistor covers 300 nm to 1800 nm with in an array of 388 × 288 pixels, with a of and a response of 0.1 ms to 1 ms.
  • Flexible detectors: A graphene- device kept 45.5 A/W with a gain of at a bending radius of 1.4 cm.

Graphene Absorption and Photocurrent Mechanisms

NameFormulaRelated FormulaeVariables/Constants
Absorption of graphene layers



Photothermoelectric effect






Bolometric effect





Metal-Graphene-Metal Detector

NameFormulaRelated FormulaeVariables/Constants
Photovoltaic and contact-field photocurrent





Bandwidth of the graphene detector





Photogating and Hybrid Phototransistors

NameFormulaRelated FormulaeVariables/Constants
Photoconductive gain and photogating







Gain-bandwidth product
Noise, detectivity and linear dynamic range






Two-Dimensional Semiconductor Phototransistor

NameFormulaRelated FormulaeVariables/Constants
Responsivity, EQE and cutoff of a 2D semiconductor




Important Questions

Ques: Why is the responsivity of a graphene detector only 0.5 mA/W, and how high can it be?

A layer absorbs , so even with every absorbed photon collected the responsivity at 1.55 μm is mA/W (computed). In the high-field region the internal efficiency is 6% to 16%, which limits a single layer to 1.7 mA/W to 4.6 mA/W, and the measured 0.5 mA/W of a few-layer device, an EQE of (computed), is lower again by a factor 3 to 9. The source does not give the reason; the photodetection region of 100 nm to 250 nm is a small part of the spot of 2 μm and of the channel of 1.2 μm, which is a candidate cause. Without gain graphene is bounded by its absorption, and the larger values of the literature, A/W, come from the gain of hybrids. Reference: Xia et al., Ultrafast graphene photodetector, Nat. Nanotechnol. (2009), arXiv:0912.4794; De Sanctis et al., Graphene-based light sensing: fabrication, characterisation, physical properties and performance, arXiv:1809.04862; Huo and Konstantatos, Recent Progress and Future Prospects of 2D-based Photodetectors, arXiv:1904.10252.

Ques: Is the bandwidth of 40 GHz of the graphene detector a limit of the material?

No. The transit time through a high-field region of 200 nm at the saturation velocity is 0.36 ps, which gives THz (computed, the source gives 1.5 THz), and the RC limit with 50 Ω is 106 GHz for 30 fF and 637 GHz for 5 fF (computed). The measured 40 GHz is therefore set by the instruments and the pads. The source also reports that the S21 sweep reached 26 GHz in the Methods, and attributes a loss of at 40 GHz to the probes, so that the statement of no degradation in the abstract is a statement about the material, and the ‘>500 GHz’ is an estimate from the capacitance of 5 fF to 10 fF, not a measurement. Reference: Xia et al., Ultrafast graphene photodetector, Nat. Nanotechnol. (2009), arXiv:0912.4794.

Ques: Does the Seebeck coefficient of graphene follow the Mott formula, and is in physical?

For graphene with the formula gives 147 μV/K at 0.1 eV and 300 K (computed), consistent with the ‘about 0.1 mV/K’ of the source and with the range ±4 to ±100 μV/K. The other form with gives half of it, 73 μV/K, so the dependence of the conductivity on the energy must be stated. For monolayer the value is 100 mV/K, and a nondegenerate semiconductor has , which requires eV (computed), more than the gap. The value comes from dividing the photovoltage by an estimated temperature rise, and is not a transport coefficient in the sense of the formula. Reference: De Sanctis et al., Graphene-based light sensing: fabrication, characterisation, physical properties and performance, arXiv:1809.04862; Buscema et al., Photocurrent generation with two-dimensional van der Waals semiconductors, arXiv:1506.00679; Huo and Konstantatos, Recent Progress and Future Prospects of 2D-based Photodetectors, arXiv:1904.10252.

Ques: How can the PTE, bolometric and photovoltaic contributions be told apart?

The photovoltaic and PTE currents have no gain and are generated near the contacts or junctions, but the PTE voltage changes its sign with the gate, following the sign of the difference of the Seebeck coefficients, and one source gives , a sublinear dependence on the power. The bolometric effect follows and with the time constant , and gives a negative photocurrent in (-33 nA/K, 2.3 A/W at 980 nm, 50 ms). The photogating effect shows as a shift of the transfer curve along the gate axis with gain and a slow response. A single measurement rarely separates them, and the sources do not give a criterion based on numbers beyond these. Reference: Buscema et al., Photocurrent generation with two-dimensional van der Waals semiconductors, arXiv:1506.00679; De Sanctis et al., Graphene-based light sensing: fabrication, characterisation, physical properties and performance, arXiv:1809.04862; Huo and Konstantatos, Recent Progress and Future Prospects of 2D-based Photodetectors, arXiv:1904.10252.

Ques: What do the gain and the bandwidth of the graphene-quantum-dot phototransistors imply about the physics?

A responsivity of A/W and a gain of at 600 nm give (computed), a plausible absorbed and transferred fraction, and a bandwidth of 10 Hz gives a gain-bandwidth product of Hz. For , and 1 V (assumed) the product is 1.6 GHz (computed), the same order, so the gain is bought with the lifetime and the speed is paid for it, as in any photoconductor. The device with at 1.5 kHz has Hz, which needs a larger voltage or a shorter channel. The EQE of 25% listed next to A/W in the same summary cannot be the same quantity, since A/W at 600 nm is an EQE of (computed), and the review does not say to which device it belongs. Reference: Huo and Konstantatos, Recent Progress and Future Prospects of 2D-based Photodetectors, arXiv:1904.10252; De Sanctis et al., Graphene-based light sensing: fabrication, characterisation, physical properties and performance, arXiv:1809.04862.

Ques: Is the detectivity of the high-gain graphene hybrids comparable between papers?

Not without the bandwidth and the frequency. The graphene- device had at 150 Hz and a bandwidth of 1.5 kHz. If the noise is flicker noise, , and the responsivity is constant, rises as , a factor 3.2 from 150 Hz to 1.5 kHz (computed, an assumption), so the figure at 150 Hz understates the value at the cutoff. The graphene-PbS family is quoted at , and in different sections of the same review, two of them for the same reference, and another review puts the NEP of graphene at , two orders above that of silicon, . Reference: Huo and Konstantatos, Recent Progress and Future Prospects of 2D-based Photodetectors, arXiv:1904.10252; Buscema et al., Photocurrent generation with two-dimensional van der Waals semiconductors, arXiv:1506.00679.

Ques: Why is the monolayer phototransistor so sensitive and so slow?

The 880 A/W at 561 nm is an EQE of (computed), a gain of more than 1900 for an absorbed fraction of at most 1, with a cutoff at 680 nm (1.82 eV, computed). The response was about 4 s in one source and 0.6 s to 9 s in another, and a gate pulse reduced it to 600 ms, the time that the trapped carrier takes to leave. With taken as the EQE and 0.35/4 s as the bandwidth, Hz (computed), against Hz for the graphene hybrids, so the transport and the traps of the monolayer limit it, not the transit time. The 880 A/W is a lower bound, and the area of the device is not given, so cannot be recomputed from the NEP of . Reference: Lopez-Sanchez et al., Ultrasensitive photodetectors based on monolayer MoS2, Nat. Nanotechnol. 8, 497 (2013); Buscema et al., Photocurrent generation with two-dimensional van der Waals semiconductors, arXiv:1506.00679; Huo and Konstantatos, Recent Progress and Future Prospects of 2D-based Photodetectors, arXiv:1904.10252.

Ques: Why do the reported responsivities of differ by six orders of magnitude?

A CVD device measured in vacuum had about 2200 A/W and 780 A/W in air, a factor 2.8 (computed) that points to the adsorbates, while another CVD device had 1.1 mA/W, a ratio of (computed). The first had a resistance of 20 kΩ and a spot of about 1 mm, the second a resistance of 2 GΩ and a spot of 2 μm. A gain from traps, the contacts and the gate voltage act on the first, and the area used for the incident power, the whole spot or the device, changes the responsivity by the ratio of the areas. The source speaks of five orders, and the numbers give six, and the conditions are not equal enough for a comparison. Reference: Buscema et al., Photocurrent generation with two-dimensional van der Waals semiconductors, arXiv:1506.00679.

Ques: Does a graphene or 2D photodetector beat silicon?

A silicon photodiode has 0.5 A/W at 880 nm, an EQE of 70% (computed; the review prints , which is not consistent with its own equation), a response of about 50 ps and a NEP near , while graphene without gain has about 10 mA/W, a response of hundreds of picoseconds and . The gain of hybrids reaches A/W and of against of silicon, but at a bandwidth of 10 Hz to 1.5 kHz. The advantages that the sources support are the absence of a cutoff, the wavelength range from the ultraviolet to the terahertz (the abstract of a review), the integration on silicon waveguides and on flexible substrates, and not the sensitivity at high speed. Reference: Buscema et al., Photocurrent generation with two-dimensional van der Waals semiconductors, arXiv:1506.00679; Huo and Konstantatos, Recent Progress and Future Prospects of 2D-based Photodetectors, arXiv:1904.10252; Koppens et al., Photodetectors based on graphene, other two-dimensional materials and hybrid systems, Nat. Nanotechnol. 9, 780 (2014).

Related pages in this vault: Phototransistor (HPT and Photo-FET), Colloidal Quantum-Dot Photodetector (CQD), Perovskite Photodetector (Photodiode and Photoconductor), Ultraviolet Photodetector (AlGaN, SiC, Ga2O3, Diamond), Photoconductor, Emerging Semiconductor Material’s Values, Graphene Field Effect Transistor.