Programmable resistive memory can be integrated with wide-bandgap semiconductor devices on a wide-bandgap semiconductor, silicon, or insulator substrate. The wide-bandgap semiconductor can be group IV-IV, III-V, or II-VI crystal or compound semiconductor, such as silicon carbide or gallium nitride. The programmable resistive memory can be PCRAM, RRAM, MRAM, or OTP. The OTP element can be a metal, silicon, polysilicon, silicided polysilicon, or thermally insulated wide-bandgap semiconductor. The selector in a programmable resistive memory can be a MOS or diode fabricated by wide-bandgap semiconductor.