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How can I calculate the effective mass of electron in the conduction band of silicon with the approximation that they are free, from its energy band diagram by my hand - not software or something else?

Ecem
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    You may want to try asking in https://physics.stackexchange.com/ – Rodo Jan 08 '21 at 18:05
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    Don't all electrons have the same mass? – Andy aka Jan 08 '21 at 18:15
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    @Andyaka no! There's an effective electron mass dependent on the energy of that electron; that's a shortcut to make a few density calculations easier. Also, remember that we sometimes meet electrons at slightly unhealthy speeds, at which special relativity actually does mean they have a different mass. – Marcus Müller Jan 08 '21 at 18:48
  • @MarcusMüller So how can I calculate it only from energy band diagram? – Ecem Jan 08 '21 at 18:51
  • @Ecem by doing all that you've learned in your solid state/semiconductor course! Honestly, your question requires us to write a chapter in a book about semiconductor physics. Can you try to narrow it down? – Marcus Müller Jan 08 '21 at 19:14
  • Use the formulae https://ecee.colorado.edu/~bart/book/book/chapter2/gif/tab2_3_2.gif – Tony Stewart EE75 Jan 08 '21 at 19:16
  • Duplicate question posted on Physics.SE: https://physics.stackexchange.com/q/606225/22927 – The Photon Jan 08 '21 at 19:33
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    @Andyaka What Marcus said, but really the effective mass depends on the curvature of the energy bands when the electron is moving in a periodic potential (i.e. in a semiconductor crystal). – The Photon Jan 08 '21 at 19:37
  • I’m sure all of electronics can be derived using Newtonian physics hehe – Andy aka Jan 08 '21 at 20:06
  • @Ecem There are at least two commonly found definitions for the mass of an electron in semiconductors. One is the *conductivity* mass and the other is the *density of states* mass. Which one are you considering? (And by the way, you can just go look those up and find much of what you want to know.) – jonk Jan 08 '21 at 20:43
  • @jonk Thank jonk. Actually I also found density of states mass and conductivity mass but I could not understand what is the difference between them. I also found their formulas but I am not sure which one is proper for my question. – Ecem Jan 08 '21 at 20:48
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    @Ecem But how would I know which meaning is ***proper*** for your question??? Cripes. I'm not psychic and my crystal ball never really did work right! Am I supposed to just guess and hope I'm right? Perhaps if you review [this page](https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_3.htm#2_3_6) where the author goes into some effort to delineate the differences? You have to judge this, not me. – jonk Jan 08 '21 at 20:50
  • @jonk Hahah sorry jonk. Actually my professor asked us to find the effective mass of electron in the conduction band of silicon from the energy band diagram of silicon, that's why I really do not know which one is proper. – Ecem Jan 08 '21 at 20:54
  • @Ecem Then it's probably (but again, what do I know?) *density of states* case. Please refer to the page I linked and read forward. I suspect you'll agree. The approach using the energy diagram is discussed there. You should be able to take what you find there and ferret out whatever else you feel you need, afterwards. – jonk Jan 08 '21 at 21:01
  • @jonk also remembering our discussion on influence of temperature on diode current, *the formulas different people know and have learned* differ across backgrounds, and I wouldn't bet on the formula on bart's website that you've linked to being the same as I'd find in the *Halbleiterbauelemente* scriptum I've been given in my fifth or sixth semester. So, Ecem, might really be hard for us to give you an intro that is 100% compatible with what your prof teaches, anyway. – Marcus Müller Jan 09 '21 at 15:13

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