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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SOLID-STATE IMAGE SENSING 59<br />
<strong>with</strong> the channel potential ΦS:<br />
⎧<br />
⎛<br />
⎞⎫<br />
⎪<br />
⎜<br />
2 ⎛<br />
Q ⎞<br />
2⋅<br />
C ⋅<br />
⎟⎪<br />
⎪<br />
⎜<br />
⎜ − + n<br />
ox VG<br />
VFB<br />
⎟<br />
Q ε ⋅ ε ⋅ ⋅<br />
⎝<br />
⎠ ⎟⎪<br />
Φ = − + n + 0 Si q NA<br />
Cox<br />
s V G VFB<br />
⎨<br />
⋅⎜1<br />
− 1+<br />
2<br />
⎟⎬<br />
Cox<br />
⎪ C ⎜<br />
ε0<br />
⋅ εSi<br />
⋅ q⋅<br />
N<br />
ox<br />
A ⎟⎪<br />
⎪<br />
⎜<br />
⎟⎪<br />
⎩<br />
⎝<br />
⎠⎭<br />
Equation 3.4<br />
In this equation Qn is the charge <strong>of</strong> integrated electrons per unit area. (This charge<br />
is <strong>of</strong> negative polarity, because electrons are collected. q, the elementary charge, is<br />
<strong>of</strong> positive polarity � Qn = -ne·q). VG is the gate voltage, VFB is the flatband voltage<br />
and (VG - VFB) is the effective gate voltage. (See [TEU] for more details). The oxide<br />
capacitance per unit area Cox is given by:<br />
ε0<br />
⋅ ε<br />
C<br />
ox<br />
ox =<br />
t<br />
Equation 3.5<br />
ox<br />
In Figure 3.8 the depletion width is shown as a function <strong>of</strong> typical doping<br />
concentrations and gate voltages. The higher the gate voltage and the lower the<br />
substrate doping, the deeper the depletion region is. For CCD applications the<br />
depletion region should usually be as deep as possible in order to directly capture<br />
as many optically generated charge carriers as possible.
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