Analysis of the stress distribution in the nonuniformly bent GaN thin film grown on a sapphire substrate

We analyze the stress distribution in the nonuniformly bent GaN epilayers grown on a sapphire substrate. By using theoretical analysis combined with an analytical formula describing the realistic shape for the wafer bending of GaN epiwafers, we examine the effect of nonuniformity in the wafer bending on the stress-value variation over the entire wafer. We show that the stress on the GaN thin film can deviate by ∼1 MPa from the value obtained by the simple Stoney’s formula that is typically used for the uniformly bent wafer. We also show that the maximum value of the stress linearly increases with the bow difference along the horizontal and vertical directions.