Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion

We propose a simple theory for the $I-V$ curves of normal-superconducting microconstriction contacts which describes the crossover from metallic to tunnel junction behavior. The detailed calculations are performed within a generalized semiconductor model, with the use of the Bogoliubov equations to treat the transmission and reflection of particles at the $N-S$ interface. By including a barrier of arbitrary strength at the interface, we have computed a family of $I-V$ curves ranging from the tunnel junction to the metallic limit. Excess current, generated by Andreev reflection, is found to vary smoothly from $\frac{4\Delta }{3e{R}_N}$ in the metallic case to zero for the tunnel junction. Charge-imbalance generation, previously calculated only for tunnel barriers, has been recalculated for an arbitrary barrier strength, and detailed insight into the conversion of normal current to supercurrent at the interface is obtained. We emphasize that the calculated differential conductance offers a particularly direct experimental test of the predictions of the model.