Multi-Band Model Hamiltonian for Tunnel Devices with Van Der Waals Heterojunctions

We study the electronic properties of a van der Waals (vdW) heterostructure made of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{SnSe}_{2}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{WSe}_{2}$</tex> by abinitio methods in order to simulate an Esaki diode built with these materials. We use Density Functional Theory (DFT) to parametrize a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k} \cdot \mathrm{p}$</tex> model in order to achieve the transport calculations. Furthermore we introduce a tunneling coefficient parametrized by DFT. This coefficient depends on the electric field in the device in order to precisely describe the quantum tunneling happening in the heterostructure. This model Hamiltonian is then used to compute current-voltage characteristics for our Esaki diode via Non-Equilibrium Green's Functions (NEGF) calculations.