Solving F-N Tunneling Equation Unit Match Problem

The right term is a function of distance and is given in units of A/V^2. In summary, the equation for F-N tunneling in a two-dimensional layered molybdenum disulfide junction can be solved by matching the units of the left and right terms, with the left term being a transcendental function and the right term being a function of distance in A/V^2 units. This can be done by adjusting the parameters in the equation to ensure that both sides have the same units.
  • #1
Ghazanfar
1
0
Hi, Everyone, Hope you are fine and doing great. I am new here and need to ask how can we match both sides of F-N tunneling equation in unit. I am attaching the equation, i am working on but i could not solve the unit match problem.
upload_2017-12-13_11-3-43.png

if the left term has unit A/V2 then how can we solve 2nd term in the right side to have exactly same units. Please help...attached is the link from which i took this equation.
Ultimate thin vertical p–n junction composed of two-dimensional layered molybdenum disulfide (https://www.nature.com/articles/ncomms7564)
 

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  • #2
The term on the left is a transcendental function, and therefore to make sense must have no units.
 

1. What is the F-N Tunneling Equation?

The F-N Tunneling Equation, also known as the Fowler-Nordheim Tunneling Equation, is a mathematical formula used to describe the tunneling of electrons through a potential barrier. It is commonly used in the field of nanotechnology to study the transport of electrons in nanoscale devices.

2. How is the F-N Tunneling Equation derived?

The F-N Tunneling Equation is derived from the Schrödinger equation, which is a fundamental equation in quantum mechanics. It takes into account the energy of the electrons, the potential barrier they are tunneling through, and the distance they are tunneling. The equation was first proposed by Ralph H. Fowler and Lothar Wolfgang Nordheim in 1928.

3. What is the significance of solving the F-N Tunneling Equation?

Solving the F-N Tunneling Equation allows scientists to understand and predict the behavior of electrons in nanoscale devices, which is crucial for the development of new technologies such as transistors and memory devices. It also helps in the study of quantum tunneling phenomena and can provide insights into the properties of materials at the nanoscale.

4. How is the F-N Tunneling Equation used in practical applications?

The F-N Tunneling Equation is used in practical applications such as the design and optimization of nanoscale electronic devices, such as flash memory and quantum dot transistors. It is also used in the development of new materials and technologies for energy harvesting and storage.

5. What are some challenges in solving the F-N Tunneling Equation?

Solving the F-N Tunneling Equation can be a complex task, as it involves solving differential equations and taking into account various factors such as temperature, electric field, and material properties. Additionally, the accuracy of the results can be affected by experimental uncertainties and variations in the material properties. Therefore, it requires advanced mathematical and computational techniques to obtain accurate solutions.

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