  Local current-voltage characteristics for low-dimensional transition metal
dichalcogenides (LD-TMD), as well as the reconstruction of their local density
of states (LDOS) from scanning tunneling microscopy (STM) experiments is of
fundamental interest and can be useful for advanced applications. Most of
existing models are either hardly applicable for the LD-TMD of complex shape
(e.g., those based on Simmons approach), or necessary for solving an
ill-defined integral equation to deconvolute the unknown LDOS (e.g., those
based on Tersoff approach). Using a serial expansion of Tersoff formulae, we
propose a flexible method how to reconstruct the LDOS from local
current-voltage characteristics measured in STM experiments. We established a
set of key physical parameters, which characterize the tunneling current of a
STM probe - sample contact and the sample LDOS expanded in Gaussian functions.
Using a direct variational method coupled with a probabilistic analysis, we
determine these parameters from the STM experiments for MoS2 nanoflakes with
different number of layers. The main result is the reconstruction of the LDOS
in a relatively wide energy range around a Fermi level, which allows insight in
the local band structure of LD-TMDs. The reconstructed LDOS reveals pronounced
size effects for the single-layer, bi-layer and three-layer MoS$_2$ nanoflakes,
which we relate with low dimensionality and strong bending/corrugation of the
nanoflakes. We hope that the proposed elaboration of the Tersoff approach
allowing LDOS reconstruction will be of urgent interest for quantitative
description of STM experiments, as well as useful for the microscopic physical
understanding of the surface, strain and bending contribution to LD-TMDs
electronic properties.
