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Heterostructures comprising of silicon (Si), molybdenum disulfide (MoS${_2}$)and graphene are investigated with respect to the vertical current conductionmechanism. The measured current-voltage (I-V) characteristics exhibittemperature dependent asymmetric current, indicating thermally activated chargecarrier transport. The data is compared and fitted to a current transport modelthat confirms thermionic emission as the responsible transport mechanism acrossthe devices. Theoretical calculations in combination with the experimental datasuggest that the heterojunction barrier from Si to MoS${_2}$ is linearlytemperature dependent for T = 200 to 300 K with a positive temperaturecoefficient. The temperature dependence may be attributed to a change in bandgap difference between Si and MoS${_2}$, strain at the Si/MoS${_2}$ interfaceor different electron effective masses in Si and MoS${_2}$, leading to apossible entropy change stemming from variation in density of states aselectrons move from Si to MoS${_2}$. The low barrier formed between Si andMoS${_2}$ and the resultant thermionic emission demonstrated here makes thepresent devices potential candidates as the emitter diode of graphene-base hotelectron transistors for future high-speed electronics.

Electron Transport across Vertical Silicon / MoS${_2}$ / Graphene  Heterostructures: Towards Efficient Emitter Diodes for Graphene-Base Hot  Electron Transistors