# Calculation of the band structure of Si

1. Apr 25, 2004

### Dmitry

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!

2. Apr 25, 2004

### ZapperZ

Staff Emeritus
3. Apr 25, 2004

### Dmitry

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. Apr 26, 2004

### Dr Transport

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. Apr 26, 2004

### Dmitry

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. Apr 26, 2004

### ZapperZ

Staff Emeritus
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. Apr 26, 2004

### Dmitry

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.

Last edited: Apr 26, 2004
8. Apr 27, 2004

### Dr Transport

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 $$\vec{k} * \vec{p}$$ 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