How Does Optical Absorption Threshold Measure the Band Gap in Semiconductors?

[ehrenfest]

[SOLVED] direct absorption proces

Homework Statement

My solid-state physics book (Kittel) says the following in the chapter about semiconductors:

"In a direct absorption process the threshold of continuous optical absorption at frequency $\omega_g$ measure the band gap $E_g = \hbar \omega_g$",

Apparently this is a definition, so it is hard to argue with it, but can someone explain what the "threshold of continuous optical absorption" means and how that could measure the band gap?

Homework Equations

The Attempt at a Solution

 

[olgranpappy]

Homework Statement

My solid-state physics book (Kittel) says the following in the chapter about semiconductors:

"In a direct absorption process the threshold of continuous optical absorption at frequency $\omega_g$ measure the band gap $E_g = \hbar \omega_g$",

Apparently this is a definition, so it is hard to argue with it, but can someone explain what the "threshold of continuous optical absorption" means and how that could measure the band gap?

by "threshold" of absorption he means the lowest (incoming beam) energy at which you measure absorption. below this energy there will be no absorption and the incoming beam will simply pass through the material as if it were completely transpartent.

I.e., the absorption spectrum should look something like a theta function
$$\theta(\hbar \omega - E_g)$$
times some other smooth function

in real life the absorption spectrum is not a perfect step function, but it does "turn on" fairly sharply at "threshold" (sharply enough so that we can tell what the threshold incoming energy is).

The reason he uses the word "continuous" is that there actually can be some absorption "below threshold" due to bound states, but that absorption shows up in the spectrum as discrete little peaks (like delta function, but not infinity sharp), not as a continuous spectrum.

 

[ehrenfest]

by "threshold" of absorption he means the lowest (incoming beam) energy at which you measure absorption. below this energy there will be no absorption and the incoming beam will simply pass through the material as if it were completely transpartent.

I.e., the absorption spectrum should look something like a theta function
$$\theta(\hbar \omega - E_g)$$
times some other smooth function

in real life the absorption spectrum is not a perfect step function, but it does "turn on" fairly sharply at "threshold" (sharply enough so that we can tell what the threshold incoming energy is).

The reason he uses the word "continuous" is that there actually can be some absorption "below threshold" due to bound states, but that absorption shows up in the spectrum as discrete little peaks (like delta function, but not infinity sharp), not as a continuous spectrum.

I see, thanks.