Electric field dependence of optical phonon frequencies in wurtzite GaN observed in GaN high electron mobility transistors

Due to the high dissipated power densities in gallium nitride (GaN) high electron mobility transistors (HEMTs), temperature measurement techniques with high spatial resolution, such as micro-Raman thermography, are critical for ensuring device reliability. However, accurately determining the temperature rise in the ON state of a transistor from shifts in the Raman peak positions requires careful decoupling of the simultaneous effects of temperature, stress, strain, and electric field on the optical phonon frequencies. Although it is well-known that the vertical electric field in the GaN epilayers can shift the Raman peak positions through the strain and/or stress induced by the inverse piezoelectric (IPE) effect, previous studies have not shown quantitative agreement between the strain and/or stress components derived from micro-Raman measurements and those predicted by electro-mechanical models. We attribute this discrepancy to the fact that previous studies have not considered the impact of the electric field on the optical phonon frequencies of wurtzite GaN apart from the IPE effect, which results from changes in the atomic coordinates within the crystal basis and in the electronic configuration. Using density functional theory, we calculated the zone center E2 (high), A1 (LO), and E2 (low) modes to shift by −1.39 cm⁻¹/(MV/cm), 2.16 cm⁻¹/(MV/cm), and −0.36 cm⁻¹/(MV/cm), respectively, due to an electric field component along the c-axis, which are an order of magnitude larger than the shifts associated with the IPE effect. Then, we measured changes in the E₂ (high) and A₁ (LO) Raman peak positions with ≈1 μm spatial resolution in GaN HEMTs biased in the pinched OFF state and showed good agreement between the strain, stress, and electric field components derived from the measurements and our 3D electro-mechanical model. This study helps to explain the reason the pinched OFF state is a suitable reference for removing the contributions of the electric field and the IPE-induced stress from the temperature rise in the ON state and suggests that the IPE-induced stress in the GaN buffer is an order of magnitude smaller than previously believed. Our analysis and experimental results support previous theoretical studies discussing the electric field dependence of optical phonon frequencies apart from the IPE effect and suggest that this is a general phenomenon occurring in all wurtzite and zincblende crystals. The total electric field dependence of the optical phonon frequencies in piezoelectric crystals is a critical consideration in accurately characterizing the stress, strain, electric field, and temperature distributions in microelectronic devices via micro-Raman spectroscopy