3D Time-of-flight distance measurement with custom - Universität ...

68 CHAPTER 3
difference of only 1 V between the gates of 10 µm length, this field is 10 5 V/m, a
value at which the saturation velocity is not yet reached. The drift in such an electric
field would take the electron only about 0.8 nanoseconds. For 30 µm gate length
the traveling time would be 7 nanoseconds for the same potential difference. Also,
for a fixed potential difference, the E-field drift time increases with the square of the
drift length.
In reality the process of carrier movement is a superposition of both cases
discussed above. However, the real potential distribution is also a superposition of
both extreme cases sketched in Figure 3.14 (a+b), we do not have an abrupt
potential step between two gates at different potential nor do we have a linearly
falling potential distribution over the entire gate length. Generally, for typical doping
concentrations, the horizontal electrical field in the semiconductor, caused by a
potential gradient between two neighboring gates, the so-called fringing field, only
extends to a relatively small area between the gates [BEY]. Therefore, for relatively
long gates, the charge transport will be dominated by pure thermal diffusion and
only for very short gates do the fringing fields have an influence. Figure 3.14 (c)
shows a more realistic potential distribution.
The estimation of the fringing field extension is relatively complex and also difficult
to simulate, since it strongly depends on the semiconductor’s doping
concentrations. Unfortunately semiconductor foundries keep these exact doping
profiles secret. At least we know that there are additional impurities and implants,
especially directly beneath the semiconductor surface (e.g. anti-punch through
implants). Due to this lack of process-parameter knowledge and the complexity of
available simulation tools, it appears to be more practical, in the framework of this
dissertation, to measure rather than to simulate the actual speed performance.
3.1.4 Noise sources
The performance of solid-state imagers is limited by several different noise sources.
These can generally be divided into three classes: (1) photon shot noise,
(2) photocharge conversion noise and (3) quantization noise.
Shot noise (or quantum noise) describes the statistical Poisson-distributed nature of
the arrival process of photons and the generation process of electron-hole pairs.