Calculation of the band structure of Si

In summary: OK, so you don't need to calculate the band structure, you only need to calculate the transport coefficients. I understand. Thanks for clarifying that for me.
  • #1
Dmitry
4
0
Please, help me to calculate the band structure of Si using the pseudopotential method. I will appreciate if you send me a simple program of calculation in any programming language very much and will be very grateful for any link or reference. The problem is than I've read the pile of books and haven't found anything concrete, everyting is too vague. Thanks!
 
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  • #2
Try this:

http://www.research.ibm.com/DAMOCLES/html_files/numerics.html#compbnd [Broken]

and

M Elices et al., J. Phys. C: Solid State Phys. v.7, p.3020 (1974).

Zz.
 
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  • #3
Thanks, ZapperZ!

Thanks, ZapperZ, but this page is not exactly what I need. For now it would be enough for me to calculate without nonlocal contribution and spin-orbit interaction. I am looking for something more simple. Anyway, you are right, I need this calculation for Monte-Carlo simulation. And again, I need something more specific.
As for the Solid State Phys. article, I don't have the opportunity to get it. Maybe, if you have the electronic copy of it, you can help me a lot by sending it to me by e-mail: dima_r@pisem.net. Thank you!
 
  • #4
Just what are you needing the full band structure calculation for? I have some expertise in this area and find that method of calculating the band structure depends on the calculation to be performed later.

dt
 
  • #5
Thanks for your interest!
I need the full band structure calculation for Monte Carlo simulation of transport process.
For the beginning I need something simple enough, and then I will improve the calculation.
 
  • #6
Dmitry said:
Thanks for your interest!
I need the full band structure calculation for Monte Carlo simulation of transport process.
For the beginning I need something simple enough, and then I will improve the calculation.

OK, so now *I* am confused.

If all you wanted to do is to simulate the transport process, then why can't you just USE the already available band structure for Si rather than actually calculating it? I initially thought that this is your whole project since this is already a daunting task by itself. But if you really have to do this, and then in turn, use Monte Carlo to solve something like the Boltzman transport equation, I want to know who is the sadist who is forcing you to do all this!

:)

Zz.
 
  • #7
Well, you are right - he is a sadist! He is my supervisor of studies. There is a project to create a Monte-Carlo device simulation program. We were using the quadratic energy-wavevector relation with nonparabolicity and decided to improve the accuracy. My task is to write a module for the full band structure calculation. I think my supervisor has underestimated the difficulty of this task and overestimated my abilities.
 
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  • #8
You do not need the full band structure calculation to calculate the transport coefficients in Si, believe me I know. You only need to do a [tex] \vec{k} * \vec{p} [/tex] calculation. Include the nonparbolicity of the bands by including the off diagonal terms in the matrix. My advisor and his collaborators calculated the Hall and conductivity mobilities in Si about 20 years ago, look for papers by Frank L (F.L.) Madarasz or Frank Szmulowicsz in the 1983-86 timeframe. I extended this framework to anisotropic semiconductors for my dissertation, although money and time kept me from finishing the complete study.

The long and short of it is that the Boltzmann equation should mot be solved using Monte Carlo, but using the methods in my advisors papers. They have been quoted in the open literature as "definitive", the problem is that no one wants to do the problems correctly. Send me a private message and we can discuss it offline if you wish.

dt
 

1. How is the band structure of Si calculated?

The band structure of Si is typically calculated using a combination of first principles methods, such as density functional theory (DFT), and empirical models. DFT calculates the electronic structure of a material by solving the Schrödinger equation for a system of interacting electrons. Empirical models, such as the tight-binding model, are then used to refine the results and account for additional factors such as electron-electron interactions.

2. What is the significance of the band structure of Si?

The band structure of Si is important because it provides information about the energy levels and electronic properties of the material. This information is crucial in understanding the behavior of Si in various applications, such as in electronic devices. The band structure also reveals the band gap, which is the energy range where no electron states exist, and is a key factor in determining the material's conductivity and other properties.

3. How does the band structure of Si differ from other materials?

The band structure of Si differs from other materials due to its unique crystal structure and electronic properties. Si has a diamond lattice structure, which leads to a specific band structure with distinct energy levels and band gaps. Additionally, the electronic properties of Si, such as its electron affinity and effective mass, are different from other materials, which can affect its band structure.

4. Can the band structure of Si be experimentally measured?

Yes, the band structure of Si can be experimentally measured using techniques such as angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). These methods allow for the direct observation of the energy levels and band gaps in Si, providing valuable data for validating theoretical calculations and understanding the material's electronic properties.

5. How does the band structure of Si change under different conditions?

The band structure of Si can change under different conditions, such as temperature, pressure, and doping. For example, increasing the temperature can cause the band gap in Si to decrease, while applying pressure can alter the energy levels and band gaps. Doping Si with impurities can also significantly affect its band structure, leading to changes in its electronic properties and potential applications.

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