# How electrons are excited in direct transitions?

by hokhani
Tags: electrons, transitions
 P: 265 When a photon is radiated to a direct gap semiconductor and an electron is excited from valence band minimum to conduction band maximum, the applied force on the electron is zero (because k isn't changed) but the electron acquires energy. What is the source of the energy obtained by the electron in this transition?
 P: 101 it's from valence band "max" to conduction band min. Think of it in terms of excitation in an atom. You're going from quantum number n to n+1. There's an increase in energy associated with that. It corresponds with being "further" away from the nucleus. This is the same story in bands. The valence band is "closer" to the nucleus and the conduction band is "farther" from the nucleus.
P: 3,564
 Quote by hokhani the applied force on the electron is zero (because k isn't changed) but the electron acquires energy. What is the source of the energy obtained by the electron in this transition?
The energy stems from the photon. I wouldn't say that the applied force is zero, as k isn't true momentum. The momentum of the photon is taken up by the lattice as a hole.

P: 265
How electrons are excited in direct transitions?

 Quote by DrDu I wouldn't say that the applied force is zero, as k isn't true momentum.
I can not give exactly any idea about photon force, But I know that in an electric field:
$Fexternal=d(\hbar k)/dt$
Emeritus
PF Gold
P: 29,239
 Quote by hokhani I can not give exactly any idea about photon force, But I know that in an electric field: $Fexternal=d(\hbar k)/dt$
Not sure what that has anything to do with this. We clearly know that a photon has momentum, so when it is absorbed, there has to be a momentum transfer. But as DrDu has stated, this is taken up by the lattice of the solids as a whole, and it is not manifested in the energy transition of the electron. This is not just an isolated electron encountering a photon.

The reverse is also true. An electron in the conduction band decaying back to the valence band can emit a photon. While the electron may not have change any of its crystal momentum, clearly a photon that is emitted has a momentum. The recoil momentum is once again taken up by the crystal lattice.

Zz.
PF Gold
P: 1,466
 Quote by hokhani $Fexternal=d(\hbar k)/dt$
You can't use BBcodes inside latex, you should use " _ " for the sub scripts.
P: 265
 Quote by adjacent You can't use BBcodes inside latex, you should use " _ " for the sub scripts.
Thank you. But using "_" I can only write one letter (for example: e) in the subscript and not more than one (for example: external).
PF Gold
P: 1,466
 Quote by hokhani Thank you. But using "_" I can only write one letter (for example: e) in the subscript and not more than one (for example: external).
Use _{Whatever you want} .
See,
$F_{external}=\frac{\text{d}(\hbar k)}{\text{d}t}$

What I wrote is:
$F_{external}=\frac{\text{d}(\hbar k)}{\text{d}t}$
You can also right-click on my latex> show math as> Tex commands
P: 3,564
 Quote by hokhani Thank you. But using "_" I can only write one letter (for example: e) in the subscript and not more than one (for example: external).
Enclose them in curly brackets or use _\mathrm{ext} if you want them roman style.
 Emeritus Sci Advisor PF Gold P: 29,239 I assume that your question has been satisfactorily answered (please acknowledge if it is, rather than let it hang) considering that we are now discussing how to do LaTex in this thread. Zz.
P: 3,564
 Quote by hokhani I can not give exactly any idea about photon force, But I know that in an electric field: $F_\mathrm{external}=d(\hbar k)/dt$
This holds for the motion of wavepackets in one band, not for interband transitions.
 HW Helper Thanks P: 10,383 You can imagine the interband transition like an elastic collision, for example, with a photon and the electron. As the photon has momentum p=h/λ, the momentum of the electron also has to change. But the momentum of the photon is much less than that of the crystal momentum at the Brillouin zone boundary so the transition looks almost vertical. Exactly vertical transition can happen by the assistance of an other particle, with a phonon. ehild

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