Sandwich-type MgB$_{2}$ tunnel junctions*

Properties of superconductors, such as band gap, density of states (DOS) of quasiparticles, and effective phonon spectra, can be studied by electrical tunneling with a high energy resolution of several $k_{B}T$. Sandwich-type MgB$_{2}$ tunnel junctions with Pb or Ag as the counter-electrodes were made on Hybrid Physical-Chemical Vapor Deposition MgB$_{2}$ films with thermal oxide tunnel barrier. The tunnel junctions exhibit very small subgap current at 4.2 K. Fit to the BCS DOS relation, the $\pi $-band and $\sigma $-band gaps of MgB$_{2}$ are found to be 2.3 and 7.4 meV at 4.2 K respectively. Josephson tunneling was observed with $I_{c}R_{n}$ product following the BCS temperature dependence relation, and the critical current showing a Fraunhofer pattern modulated by the applied magnetic field. Effective phonon modes are revealed at 42, 61, and 74 meV. These superb tunnel junctions give us deep insights into the properties of MgB$_{2}$.