In general for crystal growth, material should deposit on the seed crystal and not on any adjacent supporting structures. This efficiently uses the source material and avoids the possibility of spurious polycrystals encroaching on, and interfering with the single crystal growth. In this paper, a new crucible design with a cooling fin in contact with the seed was simulated and experimentally demonstrated on the physical vapor transport (PVT) crystal growth of scandium nitride (ScN). The heat transfer of the growth cavity for a conventional crucible and a modified crucible with the cooling fin were modeled theoretically via computational fluid dynamics (CFD) with FLUENT. The CFD results showed that the seed in the modified crucible was approximately 10 °C cooler than the crucible lid, while in the conventional crucible the temperature of the seed and lid were uniform. The experimental results showed that increasing the temperature gradient between the source and the seed by employing the cooling fin led to a dramatic increase in the growth rate of ScN on the seed and reduced growth on the lid. The relative growth rates were 80% and 20% on the seed and lid respectively, in the modified crucible, compared to 25% and 75% with the conventional crucible. Thus, the modified crucible improved the process by increasing the growth rate of single crystals grown by sublimation.