A graded composition, high dielectric constant gate insulator is formed between a substrate and floating gate in a flash memory cell transistor. The gate insulator is comprised of amorphous germanium or a graded composition of germanium carbide and silicon carbide. If the composition of the gate insulator is closer to silicon carbide near the substrate, the electron barrier for hot electron injection will be lower. If the gate insulator is closer to the silicon carbide near the floating gate, the tunnel barrier can be lower at the floating gate.