As momentum is conserved, the transfer of momentum occurs to crystal momentum.
2.
This tensor expresses the change in group velocity due to a change in crystal momentum.
3.
Where is the del operator in reciprocal space, and force gives a rate of change in crystal momentum:
4.
When "'k "'is multiplied by the reduced Planck's constant, it equals the electron's crystal momentum.
5.
Here perhaps the analogy between crystal momentum and true momentum is at its most powerful, for these are precisely the equations that a free space electron obeys in the absence of any crystal structure.
6.
Related to this, the group velocity of an electron can be calculated based on how the energy of a Bloch state varies with "'k "'; for more details see crystal momentum.
7.
Where, " k " is the crystal momentum, V is the classical potential, the term on the RHS is the effect of collision, the fourth term on the LHS represents non-local quantum mechanical effects.
8.
In regions where the band is approximately parabolic the crystal momentum is equal to the momentum of a free particle with momentum \ hbar k if we assign the particle an effective mass that's related to the curvature of the parabola.
9.
Thin-films of amorphous silicon, which due to a relaxed requirement in crystal momentum preservation can achieve direct bandgaps and intermixing of carbon, can tune the bandgap, but other issues have prevented these from matching the performance of traditional cells.
10.
Due to this coupling among the excitations for all values of the crystal momentum \ hbar { \ mathbf k }, the optical excitations in semiconductor cannot be described on the level of isolated optical transitions but have to be treated as an interacting many-body quantum system.
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