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When a Electron gets promoted to the conduction band from valence band (In generation) lets say for example in Silicon at room temperature.

Is there any way to determine (on average) how long it will last before falling back down in the hole it just left.

What about with a Voltage Applied?

Thanks

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  • $\begingroup$ Do you mean generation due to absorption of light, or random thermal generation. There are equations which give the radiative recombination rate would that help? $\endgroup$
    – boyfarrell
    Commented Feb 14, 2013 at 12:14
  • $\begingroup$ Random Thermal Gen. $\endgroup$
    – user20118
    Commented Feb 14, 2013 at 19:44

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I think you can get a estimate like this.

For a semiconductor with no split in the quasi-Fermi levels, the electrons and holes take their intrinsic values (carrier density) $n_0$ and $p_0$ ($cm^{-3}$). The charge carriers are in equilibrium with the thermal photons being absorbed and emitted inside the material. So if we calculate the emission rate of thermal photons then we know the time constant for how long the thermally generated carriers will last before recombining (because at equilibrium upwards rates and downward rates must balance).

Let's assume perfect bimolecular recombination, then the rate of thermal emission is,

$\frac{\partial n}{\partial t} = Bn_0p_0$,

where $B$ is the bimolecular recombination coefficient, for GaAs, $B=7\times10^{-10}$$cm^{6}s^{-1}$, and the intrinsic carrier density is, $n_i=n_0=p_0=2\times10^{6}$$cm^{-3}$. This gives a transition rate of 2800 $s^{-1}$.

This seems a bit slow. But it's correct for the assumptions, namely because we assumed an un-doped intrinsic semicondutor (the carrier density is very low).

For more information I recommend 'Light-Emitting Diodes by E. Fred Schubert’, search for the vanRoobroeck-Shockley equation.

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  • $\begingroup$ Is this how fast they are generating? or how long it's lasting before falling back into it's own hole. And when it's generated...is it most likely to fall back into the hole its left? or another hole "near" it? $\endgroup$
    – user20118
    Commented Feb 17, 2013 at 9:05
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    $\begingroup$ At equilibrium generation and recombination are the same so this gives the time-constant for both processes. Semiconductors have an effective density of states of ~$10^{17}\textrm{cm}^{\textrm{-3}}$ at the band edges, so it is extremely unlikely that the same atomic orbital will be involved in both the same generation and recombination process. Hope that clears things up. $\endgroup$
    – boyfarrell
    Commented Feb 17, 2013 at 22:29
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    $\begingroup$ It's nice to read some semiconductor questions on this site, it's mostly heavy on the theory. $\endgroup$
    – boyfarrell
    Commented Feb 18, 2013 at 8:08