Schottky barrier lowering due to interface states in 2D heterophase devices

The Schottky barrier of a metal–semiconductor junction is one of the key quantities affecting the charge transport in a transistor. The Schottky barrier height depends on several factors, such as work function difference, local atomic configuration in the interface, and impurity doping. We show that also the presence of interface states at 2D metal–semiconductor junctions can give rise to a large renormalization of the effective Schottky barrier determined from the temperature dependence of the current. We investigate the charge transport in n- and p-doped monolayer MoTe2 1T′–1H junctions using ab initio quantum transport calculations. The Schottky barriers are extracted both from the projected density of states and the transmission spectrum, and by simulating the IT-characteristic and applying the thermionic emission model. We find interface states originating from the metallic 1T′ phase rather than the semiconducting 1H phase in contrast to the phenomenon of Fermi level pinning. Furthermore, we find that these interface states mediate large tunneling currents which dominates the charge transport and can lower the effective barrier to a value of only 55 meV.


A nanoribbon of this interface is created with 18 atomic layers of each phase and 20Å
of vacuum between periodic images in the x-direction. The 6 atomic layers closest to the interface are allowed to relax and the remaining 1T' phase is fixed while the remaining 1H phase is kept rigid to allow for a compression or elongation of the interface region. 4. The relaxed interface is converted to a device configuration in order to perform the NEGF calculations. The central region is composed of about 6 nm's of 1T' phase and 19 nm's of 1H phase. For these calculation we use Dirichlet boundary conditions between the central region and electrodes, periodic boundary conditions in the y-direction and Neumann boundary conditions in the z-direction to avoid electrostatic interactions between neighbouring interface dipoles. The cell height is 15 nm's which ensures that the out-of-plane fields due to the 2D interface are properly accounted for and that their effect on the size of the barrier is minimized. [6,7,8]   All the structure relaxations use a force tolerance of 0.02 eV/Å and the k-point grid for the isolated 1H phase is (7, 7, 1) while it is (5, 11, 1) for the isolated 1T' phase and (k x , 6, 1) for the remaining calculations. k x = 1 for the nanoribbon calculation and k x = 401 for the NEGF calculation. The occupations are described by using a Fermi-Dirac occupation function with an electronic temperature of 300 K.

B Bandstructures
The band diagrams of the 1T' and 1H phase of MoTe 2 can be seen in Figure 2 including the relative placement of the Fermi level for a n-or p-doping of N D/A = 4.9 × 10 11 cm −2 .

C Substrate effect
The depletion width scales with the effective dielectric constant of the 2D material which is modified by the surrounding dielectric subtrate. [9,10] We therefore investigate the effect of scaling the depletion width.
Using the Wentzel-Kramers-Brillouin (WKB) approximation and atomic units, the tunneling through an exponential barrier placed at x = 0 with height Φ SB and depletion width x D is given by, Where x cl is the classical turning point of the barrier. We make the substitution z = e −x/xD resulting in, Scaling the depletion width by s, x D → s x D , will therefore result in a transmission,  We have scaled the tunneling part of the transmission of the n-doped device with N D = 4.6×10 12 cm −2 using s = 0.5, s = 1.5 and s = 2 to investigate the effect of including a substrate. This results in a shift of the two regimes in Figure 4g in the main text. In Table 1, we list the temperature at which the thermionic current becomes larger than the tunneling current, T I T E >I T U N . This shows that the tunneling current remains non-negligible for a depletion width up to twice the size of the calculated width.
D WKB model to evaluate the effect of the interface states.
The conduction band bending of the device with doping N D = 4.6 × 10 12 cm −2 is fitted to an exponential function which yields, when the unit of energy is eV and the unit of x is Angstrom. The fit can be seen on Figure  3. From this potential barrier, we can calculate the corresponding transmission using the WKB approximation as explained in section C. This transmission is seen together with the result of the calculation in the middle part of Figure 3. We have scaled the WKB transmission to reach the same value as the calculated transmission at the top of the barrier. Above the barrier, we set the WKB transmission to be constant at this value. This is a way of including that the availability of states for transport limits the transmission. As it can be seen on the figure, the WKB model show a very similar transmission except that the peak caused by the interface states is absent.
The current is now calculated using equation (2) in the main text and an Arrhenius plot is used to find the TE barrier. The result can be seen in the right part of figure 3 and show a large difference between the tunneling current from the calculation and the tunneling current from the WKB model. This results in very different TE barrier heights between 300 and 450 K; 55 meV from the calculation and 0.18 eV from the WKB model. We believe this strongly supports our claim, that it is the interface states which are responsible for the very low barrier. Note, that the thermionic current of the two models are almost identical between 300 and 450 K which justifies that we have chosen the transmission of the WKB model to be constant above the barrier.
E Transmission eigenstates of the highly p-doped device.
The transmission eigenstates of the p-doped device at 0.16 eV below the Fermi level and at the k y -value of -0.27, indicated by the white star on Figure 4f in the main text, are shown on Figure 4a and 4b. Figure 4c show the norm of the two transmission eigenstates. The behavior is generally the same as observed in the n-doped device.