  Charge multiplication (CM) in p$^+$n epitaxial silicon pad diodes of 75, 100
and 150 $\upmu$m thickness at high voltages after proton irradiation with 1 MeV
neutron equivalent fluences in the order of $10^{16}$ cm$^{-2}$ was studied as
an option to overcome the strong trapping of charge carriers in the innermost
tracking region of future Super-LHC detectors. Charge collection efficiency
(CCE) measurements using the Transient Current Technique (TCT) with radiation
of different penetration (670, 830, 1060 nm laser light and $\alpha$-particles
with optional absorbers) were used to locate the CM region close to the
p$^+$-implantation. The dependence of CM on material, thickness of the
epitaxial layer, annealing and temperature was studied. The collected charge in
the CM regime was found to be proportional to the deposited charge, uniform
over the diode area and stable over a period of several days. Randomly
occurring micro discharges at high voltages turned out to be the largest
challenge for operation of the diodes in the CM regime. Although at high
voltages an increase of the TCT baseline noise was observed, the
signal-to-noise ratio was found to improve due to CM for laser light. Possible
effects on the charge spectra measured with laser light due to statistical
fluctuations in the CM process were not observed. In contrast, the relative
width of the spectra increased in the case of $\alpha$-particles, probably due
to varying charge deposited in the CM region.
