Nature of carrier injection in metal/2D-semiconductor interface and its implications for the limits of contact resistance

Monolayers of transition metal dichalcogenides (TMDCs) exhibit excellent electronic and optical properties. However, the performance of these two-dimensional (2D) devices are often limited by the large resistance offered by the metal contact interface. To date, the carrier injection mechanism from metal to 2D TMDC layers remains unclear, with widely varying reports of Schottky barrier height (SBH) and contact resistance ($R_{\mathrm{c}}$), particularly in the monolayer limit. In this paper, we use a combination of theory and experiments in Au and Ni contacted monolayer $\mathrm{Mo}{\mathrm{S}}_2$ device to elucidate the following points: (i) the carriers are injected at the source contact through a cascade of two potential barriers—the barrier heights being determined by the degree of interaction between the metal and the TMDC layer; (ii) the conventional Richardson equation becomes invalid due to the multidimensional nature of the injection barriers, and using Bardeen-Tersoff theory, we derive the appropriate form of the Richardson equation that describes such a composite barrier; (iii) we propose a novel transfer length method (TLM) based SBH extraction methodology, to reliably extract SBH by eliminating any confounding effect of temperature dependent channel resistance variation; (iv) we derive the Landauer limit of the contact resistance achievable in such devices. A comparison of the limits with the experimentally achieved contact resistance reveals plenty of room for technological improvements.

Figure 1

Schematic diagram showing possible carrier injection process from metal to monolayer $\mathrm{Mo}{\mathrm{S}}_2$. This is modeled as a series connection of back-to-back diodes and resistor in a backgated device. The arrows indicate the direction of electron flow (opposite of current flow).

Figure 2

Electronic structure of monolayer $\mathrm{Mo}{\mathrm{S}}_2$ under monolayer metal. (a) The LPDOS and OPDOS for (a) pristine $1\mathrm{H}\text{−}\mathrm{Mo}{\mathrm{S}}_2$, (b) Au/$\mathrm{Mo}{\mathrm{S}}_2$ interface, (c) Au/$\mathrm{Mo}{\mathrm{S}}_2$ interface with interfacial SV, (d) Ni/$\mathrm{Mo}{\mathrm{S}}_2$ interface, (e) Ni/$\mathrm{Mo}{\mathrm{S}}_2$ interface with interfacial SV. (f) Charge density plots for Au/$\mathrm{Mo}{\mathrm{S}}_2$ interface, (g) Au/$\mathrm{Mo}{\mathrm{S}}_2$ interface with interfacial SV, (h) Ni/$\mathrm{Mo}{\mathrm{S}}_2$ interface, and (i) Ni/$\mathrm{Mo}{\mathrm{S}}_2$ interface with interfacial SV.

Figure 3

Electronic structure of monolayer $\mathrm{Mo}{\mathrm{S}}_2$ under bilayer metal. (a) $\mathrm{Monolayer}\text{−}\mathrm{Mo}{\mathrm{S}}_2$/bilayer-Au DOS, (b) $\mathrm{monolayer}\text{−}\mathrm{Mo}{\mathrm{S}}_2$/bilayer-Ni DOS, (c) $\mathrm{Mo}{\mathrm{S}}_2$/Au charge density plot, (d) $\mathrm{Mo}{\mathrm{S}}_2$/Ni charge density plot.

Figure 4

Characterization of monolayer (1L) $\mathrm{Mo}{\mathrm{S}}_2$ on metal and on $\mathrm{Si}{\mathrm{O}}_2$. (a) Raman intensity of 1L $\mathrm{Mo}{\mathrm{S}}_2$ on various substrates. (b) The FWHM of Raman peaks as a function of substrate. (c) The PL spectra of 1L $\mathrm{Mo}{\mathrm{S}}_2$ as a function of substrate, showing strong suppression on metal. (d) The CPD image of 1L $\mathrm{Mo}{\mathrm{S}}_2$ on Au and $\mathrm{Si}{\mathrm{O}}_2$ lines showing strong work function differences. Inset. A 2D AFM image of the flake. (e) Corresponding AFM image of Au lines and triangular 1L flake. (f) Values of CPD along scan line 1 ($\mathrm{Mo}{\mathrm{S}}_2$/Au-Au) and scan line 2 ($\mathrm{Mo}{\mathrm{S}}_2$/$\mathrm{Au}\text{−}\mathrm{Mo}{\mathrm{S}}_2$/$\mathrm{Si}{\mathrm{O}}_2\text{−}\mathrm{Mo}{\mathrm{S}}_2$/Au). (g) The CPD image of 1L/multilayer (ML) $\mathrm{Mo}{\mathrm{S}}_2$ on Ni and $\mathrm{Si}{\mathrm{O}}_2$ lines. (h) Corresponding AFM image of Ni lines and $\mathrm{Mo}{\mathrm{S}}_2$ flake. (i) Values of CPD along scan line 1 (Ni-1L $\mathrm{Mo}{\mathrm{S}}_2$/Ni-ML $\mathrm{Mo}{\mathrm{S}}_2$/Ni-Ni) and scan line 2 (1L $\mathrm{Mo}{\mathrm{S}}_2$/Ni-1L $\mathrm{Mo}{\mathrm{S}}_2$/$\mathrm{Si}{\mathrm{O}}_2$).

Figure 5

Individual processes in cascade during carrier injection at the source junction. (a) The origin of the vertical diode ${\mathrm{D}}_{\mathrm{V}}$ (with barrier ${\varphi }_V$) between the metal and the monolayer underneath the contact, through a tunneling vdW gap. (b) The variation of potential in the monolayer underneath the contact (current crowding regime) with $V_0=V\left(x=0\right)$. Red curves correspond to ten times better conductivity in the 2D film, compared with the blue curves. Inset: schematic of the calculation method in the current crowding regime. (c) Two possible origins of potential barrier ${\varphi }_H$ in horizontal diode ${\mathrm{D}}_{\mathrm{H}}$ at contact edge. Left panel: doping difference induced built-in barrier (weak interaction with contact). Right panel: Fermi level pinning induced Schottky barrier (strong interaction with contact). (d) A schematic 3D diagram depicting the different barriers encountered by the electron injected from the metal at the source end: the two barriers (${\varphi }_V$ and ${\varphi }_H$) with a sandwiched current crowding region in between.

Figure 6

Dimensionality of different metal/semiconductor contact topologies. (a) The 3D metal contacted with 3D semiconductor. (b) Edge contact between 3D metal and 2D semiconductor. (c) Top contact between 3D metal and 2D semiconductor.

Figure 7

Electrical extraction of effective barrier height. (a) Optical image and the corresponding Raman mapping of a typical TLM device. In the Raman map, red patch corresponds to the monolayer $\mathrm{Mo}{\mathrm{S}}_2$ and the green signal is from Si. Inset. A scanning electron microscopy image of the device. (b) $I_{\mathrm{ds}}\text{−}{V}_{\mathrm{g}}$ plot of Au and Ni contacted device at multiple temperatures. Ni devices show lower threshold voltage. (c) Forward and reverse $I_{\mathrm{ds}}\text{−}{V}_{\mathrm{ds}}$ sweep of a backgated monolayer transistor with a 300-nm channel length, showing 52 μA/μm drive current at $V_{\mathrm{ds}}=2\mathrm{V}$ and $V_{\mathrm{g}}=80\mathrm{V}$.

Figure 8

Barrier height extraction methodology. (a) A typical TLM fit for Au and Ni devices with intercept at $L=0$ corresponding to $R_{\mathrm{cT}}$. (b) Method of calculation of $I_{\mathrm{c}}=V_{\mathrm{ds}}/R_{\mathrm{cS}}$, which is the hypothetical current obtained when $V_{\mathrm{ds}}$ is applied across the source contact diode. (c) $I_{\mathrm{c}}$ is used in a Richardson plot at different biasing conditions. The slopes of the linear fits correspond to the effective barrier height.

Figure 9

Device operating condition dependent extracted barrier height. (a) The effective barrier height for $\mathrm{Au}\text{−}\mathrm{Mo}{\mathrm{S}}_2$ contact, as extracted from TLM, is plotted as a function of $V_{\mathrm{ds}}$ and gate electric field. (b) Horizontal slices of (a) at different gate electric field. (c) and (d) The effective barrier height for $\mathrm{Ni}\text{−}\mathrm{Mo}{\mathrm{S}}_2$ contact.

Figure 10

Experimental validation of thermionic model. Comparison of coupled Poisson Schrödinger (CPS) solution predicted ${\varphi }_{B,\mathrm{eff}}$ (shown in red solid line for Au and red broken lines for Ni) and the corresponding TLM extracted value (golden circle for Au and blue triangle for Ni), at small $V_{\mathrm{ds}}$ using channel doping ($6.3\times {10}^9\mathrm{c}{\mathrm{m}}^{-2}$ for Au and $2.24\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$ for Ni) as fitting parameter. The star symbols indicate ${\varphi }_V$ at $V_{\mathrm{g}}=0$, which is obtained by subtracting the KPFM extracted ${\varphi }_H$ from simulated ${\varphi }_{B,\mathrm{eff}}$. The blue lines (solid for Au and broken for Ni) correspond to ${\varphi }_V$ at nonzero $V_{\mathrm{g}}$ and are obtained by fitting a doping concentration ($7.0\times {10}^{11}\mathrm{c}{\mathrm{m}}^{-2}$ for Au and $4.76\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$ for Ni) underneath the contact corresponding to the star.

Figure 11

Limits of contact resistance. The extracted total contact resistance $R_{\mathrm{cT}}=R_{\mathrm{cS}}+R_{\mathrm{cD}}$ for Au and Ni at different temperatures (215 to 290 K) are shown as a function of the 2D sheet carrier density. Annealed Ni contact is also shown at 290 K. The corresponding lower limits achievable for Au ($d=3\AA$, $W_{\mathrm{m}}=5.3\mathrm{eV}$), Ni ($d=2.2\AA$, $W_{\mathrm{m}}=5.06\mathrm{eV}$), and an ideal contact ($d=0$) are shown for comparison. For monolayer (1L) and multilayer (ML), $g_{\mathrm{v}}=2$ and $g_{\mathrm{v}}=6$ are used, respectively. Tunneling vdW gap ($d$) values are obtained from DFT calculation, and metal work function ($W_{\mathrm{m}}$) are obtained from KPFM results.