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Tunneling through the space-charge region of a uniformly doped semiconductor has been calculated in the effective-mass approximation. The exact solutions of the one-dimensional Schrodinger equation for a parabolic potential are used to determine the transparency of the barrier. Numerical results are presented for parameters appropriate to indium and w-type germanium. An example of experimental results typical of this system is quoted to illustrate qualitative agreement.

The electrical characteristics of diodes made from degenerate n-type Ge with either Au or In as the metallic element are reported. The results support a previously published calculation [Phys. Rev. 150, 466 (1966)]. It is significant that the observation can be interpreted quantitatively. Data are presented in terms of the dependence of incremental resistance dv/di or conductance di/dv on applied voltage. Maxima in the incremental resistance predicted to occur at an applied voltage which corresponds to the Fermi degeneracy of the n-type Ge are observed. Data for several values of impurity, density, and temperature are shown to correspond quantitatively with the prediction. However, evidence suggests the importance of band tailing, a feature not included in the calculation. Observation of several additional effects is also reported. Pronounced structure near zero bias appears when the metallic element is in the superconducting state. This is well described by the BCS theory. The threshold for tunneling into the conduction-band minimum Γ2′ was also observed. From this the separation in energy with respect to the L-band minima is determined to be Γ2′−L=0.154±0.003 eV. Anomalous structure at zero bias similar to that observed by others in p-n junctions and metal-oxide-metal structures is reported but not interpreted.

A new method is suggested for analyzing the tunneling data from metal-semiconductor (Schottky) junctions, and the method is appled to p-type GaAs. The method allows a determination of the argument of the tunneling integral. The results indicate that the tunneling current depends upon the density of states of the semiconductor. This disagrees with Harrison's WKBJ results, but does agree with the recent exact solution of tunneling in Schottky junctions.

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