Analysis of rates of tunneling across self-assembled monolayers (SAMs) of n-alkanethiolates SCn (with n = number of carbon atoms) incorporated in junctions having structure Ag-TS-SAM//Ga2O3/EGaIn leads to a value for the injection tunnel current density J(0) (i.e., the current flowing through an ideal junction with n = 0) of 10(3.6 +/- 0.3) A.cm(-2) (V = +0.5 V). This estimation of J(0) does not involve an extrapolation in length, because it was possible to measure current densities across SAMs over the range of lengths n = 1-18. This value of J(0) is estimated under the assumption that values of the geometrical contact area equal the values of the effective electrical contact area. Detailed experimental analysis, however, indicates that the roughness of the Ga2O3 layer, and that of the Ag-TS-SAM, determine values of the effective electrical contact area that are similar to 10(-4) the corresponding values of the geometrical contact area. Conversion of the values of geometrical contact area into the corresponding values of effective electrical contact area results in J(0)(+0.5 V) = 10(7.6 +/- 0.8) A.cm(-2), which is compatible with values reported for junctions using top-electrodes of evaporated Au, and graphene, and also comparable with values of J(0) estimated from tunneling through single molecules. For these EGaIn-based junctions, the value of the tunneling decay factor beta (beta = 0.75 +/- 0.02 angstrom(-1); beta = 0.92 +/- 0.02 nC(-1)) falls within the consensus range across different types of junctions (beta = 0.73-0.89 angstrom(-1); beta = 0.9-1.1 nC(-1)). A comparison of the characteristics of conical Ga2O3/EGaIn tips with the characteristics of other top-electrodes suggests that the EGaIn-based electrodes provide a particularly attractive technology for physical-organic studies of charge transport across SAMs.