Transport and other measurements have been made on CuInSe2+x samples obtained from Bridgman ingots grown from melts containing controlled amounts of elemental sodium, where x represents the excess of Se over stoichiometry. Thermoelectric power and Hall coefficient at room temperature show a conductivity sign change horn p- to n-type in otherwise stoichiometric CuInSe2 (x=0), with added Na between 02 and 0.3 at%. It is further found that the critical amount of Na required to change the conductivity type, denoted by [Na](crit), increases with x, almost linearly, with an initial slope of 2, corresponding to an approximate formula of [Na](crit)=2x+delta, where delta is found to be 025 at% Na. This behavior can be accounted for quantitatively using a 'selenium starvation' model, whereby at the p-to-n type change, two atoms of sodium have reacted with one atom of Se to form a molecule like Na2Se, with an atom-to-atom ratio [Na]/[Se]=2. Such molecules were detected in growth run residues. However, no Na or Na compounds were detected in the interior of bulk crystals. In stoichiometric material (x=0), the crystal structure remained chalcopyrite with up to at least 3 at Na in the melt, despite the conductivity type changes. Further, no beta-phase was detected in the bulk material by XRD but it was found at the surface of samples by XPS. (C) 2013 Elsevier B.V. All rights reserved.