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We report the fabrication and electrical characteristics of self-shunted Josephson junctions consisting of NbN electrodes, an AlN barrier, and an NbNx normal layer for an SFQ circuit application. To fabricate such junctions with a high characteristic voltage V c, we have studied their preparation conditions including the surface treatments of MgO substrates. Junction characteristics at 4 K were dependent on the electrical properties and film thickness of the NbNx layer; the underdamped junctions changed into overdamped ones with an increase in the film thickness. The overdamped junctions showed a characteristic voltage Vc of 0.8 mV and a critical current density Jc of 22 A/cm2 at 4.2 K.