I'm trying to understand recombination in semiconductors from a wave perspective. I'm considering the wave vector $k$ not just as momentum, but as a descriptor of the wave function's phase. In direct semiconductors, the electron and hole wave functions overlap at $k=0$, facilitating recombination. In indirect semiconductors, they're in different $k$-spaces and need to align for recombination. This alignment is achieved through phonon interactions, which I'm interpreting as interference between the electron's wave function and the lattice's vibrational waves. Does this wave-based view hold up? How can it account for wave function localization and energy conservation?
$\begingroup$
$\endgroup$
2
-
3$\begingroup$ ‘Distant’ does not make much sense when wave functions extend throughout the crystal. $\endgroup$– Jon CusterCommented Sep 23, 2023 at 17:34
-
$\begingroup$ Yes,I do understand that. Which is why I decided to look at recombination as wave functions rather than looking at it as particles. $\endgroup$– VarshaCommented Sep 24, 2023 at 2:16
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
No, this interference idea between electron and phonon wave is not correct. Interference occurs only between the same type of wave at the same frequency. For the recombination in an indirect semiconductor, for conservation of crystal momentum, you need the difference in k-space of the minimum of the conduction band and the maximum of the valence band (und thus difference in crystal momentum) compensated by a suitable phonon crystal momentum. The frequency and thus energy of such a phonon is usually much smaller than the electron Bloch wave frequency.
