  Heterostructures comprising of silicon (Si), molybdenum disulfide (MoS${_2}$)
and graphene are investigated with respect to the vertical current conduction
mechanism. The measured current-voltage (I-V) characteristics exhibit
temperature dependent asymmetric current, indicating thermally activated charge
carrier transport. The data is compared and fitted to a current transport model
that confirms thermionic emission as the responsible transport mechanism across
the devices. Theoretical calculations in combination with the experimental data
suggest that the heterojunction barrier from Si to MoS${_2}$ is linearly
temperature dependent for T = 200 to 300 K with a positive temperature
coefficient. The temperature dependence may be attributed to a change in band
gap difference between Si and MoS${_2}$, strain at the Si/MoS${_2}$ interface
or different electron effective masses in Si and MoS${_2}$, leading to a
possible entropy change stemming from variation in density of states as
electrons move from Si to MoS${_2}$. The low barrier formed between Si and
MoS${_2}$ and the resultant thermionic emission demonstrated here makes the
present devices potential candidates as the emitter diode of graphene-base hot
electron transistors for future high-speed electronics.
