A method for producing a p-type ZnO based compound semiconductor layer comprising the steps of (a) preparing an n-type single crystal ZnO based compound semiconductor structure containing a Group 11 element which is Cu and/or Ag and at least one Group 13 element selected from the group consisting of B, Ga, and Al, by supplying (i) Zn, or Zn and Mg, (ii) O, and (iii) the at least one Group 13 element selected from the group consisting of B, Ga, and Al to form a Mg x Zn 1-x O (0 ≤ x ≤ 0.6) single crystal film doped with the Group 13 element; and supplying the Group 11 element which is Cu and/or Ag on the Mg x Zn 1-x O (0 ≤ x ≤ 0.6) single crystal film; wherein supplying Zn is carried out in an open period of a Zn cell shutter, supplying O is carried out in an open period of an O cell shutter, supplying at least one of B, Ga, or Al is carried out in a open period of at least one of B, Ga or Al cell shutter, and supplying Cu and/or Ag is carried out in an open period of a Cu and/or Ag cell shutter; wherein the open period of the Zn cell shutter includes the open period of the O cell shutter and the open period of the Cu and/or Ag cell shutter, and does not include the open period of the at least one of the B, Ga, or Al cell shutter; wherein the open period of the O cell shutter or the open period of the Cu and/or Ag cell shutter does not coincide with a beginning of the open period of the Zn cell shutter and does not coincide with an ending of the open period of the Zn cell shutter; and (b) annealing the n-type single crystal ZnO based compound semiconductor structure to form a p-type ZnO based compound semiconductor layer co-doped with the Group 11 element and the Group 13 element. (a) preparing an n-type single crystal ZnO based compound semiconductor structure containing a Group 11 element which is Cu and/or Ag and at least one Group 13 element selected from the group consisting of B, Ga, and Al, by supplying (i) Zn, or Zn and Mg, (ii) O, and (iii) the at least one Group 13 element selected from the group consisting of B, Ga, and Al to form a Mg x Zn 1-x O (0 ≤ x ≤ 0.6) single crystal film doped with the Group 13 element; and supplying the Group 11 element which is Cu and/or Ag on the Mg x Zn 1-x O (0 ≤ x ≤ 0.6) single crystal film; wherein supplying Zn is carried out in an open period of a Zn cell shutter, supplying O is carried out in an open period of an O cell shutter, supplying at least one of B, Ga, or Al is carried out in a open period of at least one of B, Ga or Al cell shutter, and supplying Cu and/or Ag is carried out in an open period of a Cu and/or Ag cell shutter; wherein the open period of the Zn cell shutter includes the open period of the O cell shutter and the open period of the Cu and/or Ag cell shutter, and does not include the open period of the at least one of the B, Ga, or Al cell shutter; wherein the open period of the O cell shutter or the open period of the Cu and/or Ag cell shutter does not coincide with a beginning of the open period of the Zn cell shutter and does not coincide with an ending of the open period of the Zn cell shutter; and supplying (i) Zn, or Zn and Mg, (ii) O, and (iii) the at least one Group 13 element selected from the group consisting of B, Ga, and Al to form a Mg x Zn 1-x O (0 ≤ x ≤ 0.6) single crystal film doped with the Group 13 element; and supplying the Group 11 element which is Cu and/or Ag on the Mg x Zn 1-x O (0 ≤ x ≤ 0.6) single crystal film; (b) annealing the n-type single crystal ZnO based compound semiconductor structure to form a p-type ZnO based compound semiconductor layer co-doped with the Group 11 element and the Group 13 element.