A p-type ZnO-based II-VI compound semiconductor layer has silver, potassium and/or gold dopants therein at a net p-type dopant concentration of greater than about 1×1017 cm−3. A method of forming the layer includes using an atomic layer deposition (ALD) technique. This technique includes exposing a substrate to a combination of gases: a first reaction gas containing zinc at a concentration that is repeatedly transitioned between at least two concentration levels during a processing time interval, a second reaction gas containing oxygen and a p-type dopant gas containing at least one p-type dopant species selected from a group consisting of silver, potassium and gold. A concentration of oxygen in the second reaction gas may also be repeatedly transitioned between at least two concentration levels. The concentration of zinc in the first reaction gas and the concentration of oxygen in the second reaction gas may be transitioned in an alternating sequence, so that relatively high zinc concentrations in the first reaction gas overlap with relatively low oxygen concentrations in the second reaction gas and vice versa.