The superconducting proximity effect is investigated in the one-dimensional superconductor--normal-material junction model to reveal the mechanism of the recently developed superconducting transistor. Based on the integral kernel which connects the clean and dirty limits, the boundary condition of the pair potential and the behavior of the extrapolation length are clarified by carrying out a numerical solution of Gorkov's integral equation. The result is extended also for the case that the normal substance becomes semiconducting. When the chemical potential is lowered below the conduction-band bottom, the decay length of the integral kernel changes from Pippard's characteristic length to an atomic scale length. The value of the pair potential at the fixed point on the superconductor side is investigated as the function of the chemical potential in the normal region. The result qualitatively explains the change of the pair potential on the superconductor side as the function of the gate voltage by the Hitachi group.