3D Time-of-flight distance measurement with custom - Universität ...
3D Time-of-flight distance measurement with custom - Universität ...
3D Time-of-flight distance measurement with custom - Universität ...
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64 CHAPTER 3<br />
1<br />
kT<br />
Dn = ⋅ vth<br />
⋅ ldiff<br />
= µ n ⋅<br />
3<br />
q<br />
Equation 3.8<br />
Equivalently the electron needs a mean time tdiff to travel the <strong>distance</strong> ldiff by thermal<br />
diffusion:<br />
2<br />
l<br />
t<br />
diff<br />
diff = Equation 3.9<br />
Dn<br />
In Equation 3.8 ldiff is the mean free path between collisions <strong>of</strong> the charge carrier<br />
<strong>with</strong> the lattice or other carriers. Carrier diffusivity, mobility and lifetime depend on<br />
the state <strong>of</strong> the charge carrier, whether they are the majority carriers or the minority<br />
carriers. Generally, in photo elements, the minority carriers contribute to the<br />
photocurrent and are therefore <strong>of</strong> interest. In the case <strong>of</strong> the p-type process we<br />
used, electrons are the minority carriers. Therefore, we only gave the equations for<br />
electron diffusivity and diffusion length above.<br />
Figure 3.12 shows the dependency <strong>of</strong> mobility, lifetime and diffusion length as a<br />
function <strong>of</strong> the doping concentration for both electrons and holes in silicon at<br />
300° K.
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