Deriving electrical conduction in 2d crystal

In summary, the conversation discusses the derivation of the conductivity of graphene. The formula mentioned includes parameters such as electron velocity, density of states, applied voltage, free electron density, current density, and electron charge. The topic of transport is also mentioned, with the suggestion to use the Boltzmann semi-classical theory. However, the individual is looking for a simpler formula for 2D crystals like graphene. The response recommends working out the equivalent of the Drude formula but cautions that it may not work well for graphene. The individual expresses gratitude and plans to work on it independently.
  • #1
steenreem
4
0
Hey.

I want to derive the conductivity of graphene.
I'm looking for a formula of the sort:

[tex]J = \frac{e}{\hbar} n \frac{dE}{dk} D(E) \Delta E[/tex]
where
[tex]\frac{1}{\hbar} \frac{dE}{dk}[/tex]
is the electron velocity,
[tex]D(E) = \frac{dN}{dE}[/tex]
is the density of states,
[tex]\Delta E[/tex]
might be the applied voltage.
[tex]n[/tex]
is the free electron density,
[tex]J[/tex]
is the current density and
[tex]e[/tex] is the electron charge.

Thanks,
Remy.
 
Last edited:
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  • #2
Have you looked at the Boltzmann semi-classical theory of transport?
 
  • #3
Well I just did but it's a but too much for me. I just want a simple formula for 2D crystals like graphene.
 
  • #4
Well, transport is a difficult topic. You could try working out the equivalent of the Drude formula for 2D, which shouldn't be hard, but you are going to need a value for the mean free path or time, which is not trivial to compute. And it may not work well for graphene.
 
  • #5
Okay thanks. I'll try working it out on my own now.
 

1. How is electrical conduction derived in 2D crystals?

Electrical conduction in 2D crystals is derived through a combination of theoretical models and experimental studies. The first step is to understand the electronic band structure of the 2D crystal, which can be done using techniques such as density functional theory (DFT). From this, the density of states and electron scattering mechanisms can be determined to calculate the electrical conductivity.

2. What is the role of defects in electrical conduction of 2D crystals?

Defects play a crucial role in determining the electrical conduction of 2D crystals. They can act as scattering centers for electrons, leading to a decrease in electrical conductivity. However, certain defects can also introduce localized states in the band structure, which can enhance the conductivity. Therefore, understanding the type and concentration of defects is essential in deriving the electrical conduction in 2D crystals.

3. How does the thickness of a 2D crystal affect its electrical conductivity?

The thickness of a 2D crystal can significantly impact its electrical conduction. As the thickness decreases, the electronic band structure changes, and the electron scattering mechanisms become more complex. This can lead to a decrease in conductivity in thinner layers due to increased scattering. However, in certain cases, a thickness-dependent increase in conductivity can also be observed due to quantum confinement effects.

4. Can the electrical conductivity of a 2D crystal be tuned?

Yes, the electrical conductivity of a 2D crystal can be tuned by various methods. One way is by applying an external electric field, which can modify the band structure and alter the electron scattering mechanisms. Another method is by doping the 2D crystal with impurities, which can introduce additional charge carriers and change the conductivity. Additionally, strain engineering and surface functionalization can also be used to tune the conductivity of 2D crystals.

5. What are the potential applications of understanding electrical conduction in 2D crystals?

Understanding electrical conduction in 2D crystals has significant implications in the development of advanced electronic devices. 2D crystals have unique properties, such as high carrier mobility and flexibility, which make them promising candidates for next-generation electronics. They can be used in various applications such as transistors, sensors, and energy storage devices. Additionally, the ability to tune their conductivity opens up opportunities for designing novel devices with tailored electrical properties.

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