We have developed a process for the fabrication of high-quality Nb/AlOx/Nb tunnel junctions with small area and high current densities for the heterodyne mixers at millimeter and submillimeter wavelengths. Their dc I-V curves are numerically studied, including the broadening of quasiparticle density of states resulting from the existence of an imaginary part of the gap energy of Nb. We have found both experimentally and numerically that the subgap current is strongly dependent on bias voltage at temperatures below 4.2K unlike the prediction of the BCS tunneling theory. It is shown that calculated dc I-V curves taking into account the complex number of the gap energy agree well with those of Nb/AlOx/Nb junctions measured at temperatures from 0.4 to 4.2K. We have successfully built receivers at millimeter and submillimeter wavelengths with the noise temperature as low as 4 times the quantum photon noise, employing those high-quality Nb/AlOx/Nb junctions. Those low-noise receivers are to be installed in the ALMA (Atacama Large Millimeter/Submillimeter Array) telescope and they are going into series production now.