Unusually efficient photocurrent extraction in monolayer van der Waals heterostructure by tunnelling through discretized barriers

Two-dimensional layered transition-metal dichalcogenides have attracted considerable interest for their unique layer-number-dependent properties. In particular, vertical integration of these two-dimensional crystals to form van der Waals heterostructures can open up a new dimension for the design of functional electronic and optoelectronic devices. Here we report the layer-number-dependent photocurrent generation in graphene/MoS2/graphene heterostructures by creating a device with two distinct regions containing one-layer and seven-layer MoS2 to exclude other extrinsic factors. Photoresponse studies reveal that photoresponsivity in one-layer MoS2 is surprisingly higher than that in seven-layer MoS2 by seven times. Spectral-dependent studies further show that the internal quantum efficiency in one-layer MoS2 can reach a maximum of 65%, far higher than the 7% in seven-layer MoS2. Our theoretical modelling shows that asymmetric potential barriers in the top and bottom interfaces of the graphene/one-layer MoS2/graphene heterojunction enable asymmetric carrier tunnelling, to generate usually high photoresponsivity in one-layer MoS2 device.


Supplementary
Raman spectra of the Figure 1B at the 1L-MoS 2 area (black line) and 7L-MoS 2 area (red line). In the analysis of the Raman spectra of 1L-MoS 2 , the peak at ∼384 cm −1 corresponds to the in-plane (E 1 2g ) mode, while that at ∼403 cm −1 is attributed to the out of plane (A 1g ) mode 1,2 . The frequency difference bsetween these two modes of 19 cm −1 observed in the Raman spectrum in Figure S1 can be used as a measure of 1L-MoS 2 1 . The E 1 2g mode softens, and A 1g mode stiffens with increasing layer thickness, similar to other layered materials, where the bond distance changes with the number of layers 3

Supplementary Note 1
The absorption spectra of MoS 2 was determined from the reflectance measurements 4,5 .
To obtain the absorption spectrum, the reflectance spectrum from the 1L and 6L-MoS 2 flake on a glass substrate (R m+s ) and that from the same bare glass substrate (R s ) were measured using an optical microscope coupled with a spectrometer and CCD camera.
The fractional change in the reflectance, δ R , can be determined as the difference of these two quantities divided by the reflectance from the bare glass substrate ( ). The absorbance of MoS 2 (A) can then be determined by using the relation: , where n sub is the refractive index of the glass substrate.

Supplementary Note 2
The dielectric constant of graphene is determined by the standard approximation 6,7 of ε Gr = (ε below + ε above )/2, where ε below is the dielectric constant of the material below graphene and ε avobe is the dielectric constant of the material above graphene. If the device is in the vacuum (condition for DFT), the dielectric constant for 1L-MoS 2 heterostructure is ε Gr = (ε 1L-MoS2 + ε vacuum )/2 = 2.7, where ε 1L-MoS2 = 4.5 8 . Figure S6b shows calculated electrostatic potential of van der Waals heterostructure device in the vacuum environment, which is highly convinced to the DFT calculated electrostatic potential (Fig. 1E).

Supplementary Note 3
2D peaks are observed at ∼2700 in Gr B and ∼2716 cm -1 in Gr T . The 2D band shift is the evidence of the charge doping in graphene from due to the phonon stiffening 9 . With n-/p-type doping, 2D peak of the graphene shifts in the downward/upward directions, respectively. Top graphene is more p-type doped than bottom graphene caused by different environmental reasons 10  where r is the distance between the electron, Z is atomic number, and is the permittivity of free space. Because the force F on a particle is equal to minus the gradient of the potential energy, the potential energy for the one electron is simply The excited electron is further from the nucleus than the core electrons in the valence band. In effect, the negatively charged core electrons "screen" the excited electron from the full +Ze charge of the nucleus. The excited electron would see only a net   Where g s is spin degeneracy, g v is valley degeneracy, n is electron concentration, e is the elementary charge, k is dielectric constant, is plank constant, v F is Fermi velocity, and m is electron mass, which can deform the Coulomb potential by limits the screening length (or, equivalently, the Debye length of ) 12 . The equations indicates that the Coulomb potential can be deformed depend on carrier concentration (n) in 3 dimentional materials (thick multi-layer materials), while the Coulomb potential is independent on carrier concentration (n) in 2 dimentional materials (thin few-layer materials).

Supplementary Note 5
The excited carrier continuity equation is Where δn is excited carrier density in unit volume (cm 3 ), D is the diffusion coefficient, μ is the mobility,  is the built-in internal electric field, τ is the excited carrier lifetime, and g is the generation rate of carriers 13 . In steady state, the equation is where the k B is the boltzmann constant, T is the temperature, and μ is electron mobility of MoS 2 along the vertical direction.

Supplementary Note 6
The configurations of graphene/MoS 2 /graphene (GMG) is considered in our simulation work. We adapt the depletion approximation, which means MoS 2 is uniformly charged, and the charge density equals its doping level. Therefore, bands of MoS 2 are parabolic instead of linear. This model is reasonable when the device channel is short, as in our cases.
For the simulation of GMG, we consider the electric field induced by gate as E g , and then we have where V g is the gate voltage and D is the thickness of SiO 2 dielectric. Then we consider electric fields in the two grapheme-MoS 2 interfaces as E 1 and E 2 . The carrier density n 1 and n 2 for bottom graphene and top graphene, respectively, can be given by: where h is the plank constant and v F is the Fermi velocity, n 0 is the fixed charge graphene.