In a process of reducing a resistivity of a polymer film for carbonization in a surface conduction electron-emitting device, by irradiating an energy beam onto the polymer film, when an energy intensity of the beam given in a unit area in a unit time is assumed to be W W/m2, W satisfies a formula W≧2×T×(ρsub·Csub·λsub/τ)1/2, where T is defined as a temperature ° C. at which the polymer film is heated for one hour in a vacuum degree of 1×10−4 Pa to reduce a resistivity of the polymer film to 0.1 Ω·cm, Csub is a specific heat J/kg·K of the substrate, ρsub is a specific gravity kg/m3 of the substrate, λsub is a heat conductivity W/m·K of the substrate, and τ is an irradiation time in the range of 10−9 sec to 10 sec.