  Sub-gap conductance at a large area junction with a rough interface of a
ferromagnet and a high-T$_{C}$ superconductor is superimposed by multiple peaks
which is not expected from an ideal point contact Andreev reflection process.
We demonstrate this phenomenon by measuring resistance as a function of bias
voltage of a Co/Y$_{1}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ junction with contact
area 50 x 70 $\mu$ $m^{2}$ at various temperatures. In order to analyze such
Andreev reflection data, the interface is assumed to have random potentials
which can create local electric fields. The Blonder-Tinkham-Klapwijk theory is
modified with the inclusion of a broadening parameter due to finite life time
effects of quasi particles. An additional voltage drop due to local electric
fields at the rough interface has been included in terms of an extra energy
shift which may be related to the asymmetry of normalized resistance data. Spin
polarization has been introduced for the ferromagnet. The presented model
explains the multi-peak nature and asymmetry of Andreev reflection data
experimentally observed at large area junctions. Extension of the model also
interprets the experimentally observed anomalous enhancement of resistance
peaks in the sub-gap region which may result from crossing the critical current
limit across the junction.
