Extremely low-dislocation density in GaN crystal was realized by a new method taking advantage of a polarity difference. Dot patterned layer and stripe patterned layer with periodicity were formed on GaAs initial substrates, respectively. Thick GaN crystals were grown on them by hydride vapor phase epitaxy (HVPE). In most area GaN was grown with Ga-polarity but only on the patterned layer GaN with N-polarity was grown. We call this area with N-polarity a core. At the core the GaN crystal always forms concave shape because of lower growth rate of N-polarity. So, inverse pyramidal pits or V-shaped valleys were formed placing cores at the bottom. The position of the pits and valleys was fixed by the cores during the growth. As the growth proceeds, dislocations existing on the facet plane of pit or V-shaped valley propagate to the core. Thus, dislocation density was drastically reduced. Treading dislocation density lower than 6 x 103 cm(-2) was obtained between the cores. This process is improved process of dislocation elimination by the epitaxial-growth with inverse-pyramidal pits (DEEP) already we have proposed, so we call this new process as advanced-DEEP (A-DEEP). (c) 2007 Elsevier B.V. All rights reserved.