  It has been recently pointed out that the use of a superconducting (SC) lead
instead of a normal metal lead can suppress the thermal broadening effects in
tunneling conductance from Majorana fermions, helping reveal the quantized
conductance of $2e^2/h$. In this paper we discuss the specific case of
tunneling conductance with SC leads of spin-orbit coupled
semiconductor-superconductor (SM-SC) heterostructures in the presence of a
Zeeman field, a system which has been extensively studied both theoretically
and experimentally using a metallic lead. We examine the $dI/dV$ spectra using
a SC lead for different sets of physical parameters including temperature,
tunneling strength, wire length, magnetic field, and induced SC pairing
potential in the SM nanowire. We conclude that in a finite wire the Majorana
splitting energy $\Delta E$, which has non-trivial dependence on these physical
parameters, remains responsible for the $dI/dV$ peak broadening, even when the
temperature broadening is suppressed by the SC gap in the lead. In a finite
wire the signatures of Majorana fermions with a SC lead are oscillations of
quasi-Majorana peaks about bias $V=\pm\Delta_{\text{lead}}$, in contrast to the
case of metallic leads where such oscillations are about zero bias. Our results
will be useful for analysis of future experiments on SM-SC heterostructures
using SC leads.
