  The breakdown behaviour of SiPMs (Silicon PhotoMultiplier) with pixel sizes
of 15$\times $15, 25$\times $25, 50$\times $50, and 100$\times $100 $\mu
$m$^2$, manufactured by KETEK, has been investigated. From the current-voltage
characteristics measured with and without illumination by LED light of 470 nm
wavelength, the current-breakdown voltage, $V_I$, and from linear fits of the
voltage dependence of the SiPM gain, measured by recording pulse-area spectra,
the gain-breakdown voltage, $V_G$, have been obtained. The voltage dependence
of the Geiger-breakdown probability was determined from the fraction of zero
photoelectron events with LED illumination. By comparing the results to a model
calculation, the photodetection-breakdown voltage, $V_{PD}$, has been
determined. Within experimental uncertainties, $V_I$ and $V_{PD}$ are equal and
independent of pixel size. For $V_G$, a dependence on pixel size is observed.
The difference $V_I - V_G$ is about 1 V for the SiPM with 15 $\mu $m pixels,
decreases with pixel size and is compatible with zero for the SiPM with 100
$\mu $m pixels.
