Several methods have been found to make p-type gallium nitride. P-type gallium nitride has long been sought for electronic devices. N-type gallium nitride is readily available. Discovery of p-type gallium nitride and the methods for making it will enable its use in ultraviolet and blue light-emitting diodes and lasers. pGaN will further enable blue photocathode elements to be made. Molecular beam epitaxy on substrates held at the proper temperatures, assisted by a nitrogen beam of the proper energy produced several types of p-type GaN with hole concentrations of about 5.times.10.sup.11 /cm.sup.3 and hole mobilities of about 500 cm.sup.2 /V-sec, measured at 250.degree. K. P-type GaN can be formed of unintentionally-doped material or can be doped with magnesium by diffusion, ion implantation, or co-evaporation. When applicable, the nitrogen can be substituted with other group III elements such as Al.