# Why the direct band gap semiconductor get higher optical absorption coefficient than indirect band gap semiconductor

I can understand that direct band gap semiconductor doesn't need phonon to absorb light. But in the following formula:

The optical absorption coefficient is proportional to the square of $h\nu$ in the indirect band gap and to the square root of $hv$ in the direct band gap.

Doesn't it means that optical absorption coefficient gets a larger derivative in indirect band gap than in that of the direct band gap?

Why does the direct band gap semiconductor get higher optical absorption coefficient than an indirect band gap semiconductor?

• I think you're trying to say that for a given gap of energy $E$ to be considered "indirect", the momentum offset $p$ is larger than the momentum of a photon of energy $E$. In other words, $p \gg E/c$. – DanielSank Sep 15 '16 at 3:13
• Ok now ask yourself what happens if the bulges are offset in momentum by less than $E/c$ where $E$ is the energy gap. – DanielSank Sep 17 '16 at 13:12