Sequentially Assembled Graphene Layers on Silicon, the Role of Uncertainty Principles in Graphene–Silicon Schottky Junctions

Abstract

Owing to the atomic thickness of graphene, the out‐of‐plane velocity of carriers is entangled with the thickness of graphene layer as well as the quasiparticle lifetime by means of the position–momentum and energy–time uncertainty principles. The out‐of‐plane velocity is vital for thermionic emission of carriers across the Schottky junction at graphene–silicon interface. In this report, the effect of graphene layer thickening on the electronic and optoelectronic processes is studied in hybrid graphene–silicon Schottky junctions. The thickness of graphene layer is systematically increased via sequentially assembling of chemical vapor deposited (CVD‐grown) graphene layers onto silicon. The assembled graphene layers are found to behave as structurally uncoupled layers leading to a universal scaling of in‐plane current with the number of assembled layers. The reverse saturation current of the graphene–silicon junctions strongly correlates with the number of assembled graphene layers indicating the critical influence of graphene layer thickness on the electronic and optoelectronic properties of graphene–silicon junctions. The experimental observations are quantitatively analyzed based on the uncertainty principles. The effect of graphene layer thickening on the concentration and diffusion length of excess photogenerated charge carriers in graphene is investigated through lateral photovoltage spectroscopy. This work sheds light on the fundamental role of uncertainty principles in the hybrid 2D/3D junctions.

Physics of electron emission and injection in two‐dimensional materials: Theory and simulation

“…Interestingly, in the low‐doping and high‐temperature limit where | ε F | ≪ k B T , Equations (25) and (26) jointly reduce to the Liang–Ang model in Equations (20) and (21) with the same characteristic “ T 3 ” scaling in the pre‐exponential term. In the high‐doping limit of | ε F | ≫ k B T , Trushin thermionic emission model has been successfully employed in the analysis of Schottky contact composed of silicon and mono‐and few‐layer graphene 154 . Nonetheless, it should be noted that the verification of Trushin model in the undoped of | ε F | ≪ k B T remains challenging since electrons capable of performing thermionic emission are typically in the high‐energy states high above the Dirac point at which the 2D Dirac liquid theory breaks down.…”

“…In the high-doping limit of jε F j ) k B T, Trushin thermionic emission model has been successfully employed in the analysis of Schottky contact composed of silicon and mono-and few-layer graphene. 154 Nonetheless, it should be noted that the verification of Trushin model in the undoped of jε F j ( k B T remains challenging since electrons capable of performing thermionic emission are typically in the high-energy states high above the Dirac point at which the 2D Dirac liquid theory breaks down. How the thermionic emission under the 2D Dirac liquid regime can be experimentally probed remains an open question.…”

Quantum Hall coherent perfect absorption in graphene

“…This could significantly affect the absorption properties of 2DEG systems with Dirac spectrum. Graphene, a 2D material composed of carbon atoms arranged in a honeycomb pattern, has attracted huge attention due to its exceptional electronic and optical properties 1 , 2 . Interestingly, the non-equidistant and nonlinear properties of LLs of graphene in the presence of a magnetic field which make it a promising material for various optoelectronic applications arises from its linear energy dispersion relation 3 , 4 .…”

Designing few-layer graphene Schottky contact solar cells: Theoretical efficiency limits and parametric optimization

“…Importantly, FLG is known to possess completely different electrical and optical properties when compared to monolayer graphene [25][26][27] . The incorporation of FLG with 3D semiconductors has thus led to myriads of interfacial transport and charge injection phenomena that are distinctive from the monolayer counterpart [28][29][30][31][32] . In relevance to solar cell applications, employing FLG as a top-layer material offers the following advantages.…”

“…The scaling exponent takes the form of β = 2 and A = 120 A/cm 2 K for a classic Schottky contact composed of 3D bulk metals with parabolic energy dispersion. For FLG-based vertical Schottky contact, the electronic properties of the FLG [28][29][30][31][32] , deviates significantly from the parabolic energy dispersion. Furthermore, the electronic properties of FLG exhibit nontrivial dependences on the number of layers and the layer stacking order.…”