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

Abstract

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 -axis, which are an order of magnitude larger than the shifts associated with 2 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 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 microRaman spectroscopy.

Simultaneous measurement of temperature, stress, and electric field in GaN HEMTs with micro-Raman spectroscopy

“…This technique overcomes the limitation of previous approaches that measure temperature rise in GaN HEMTs in the ON state by using the pinched OFF state as the unpowered reference and assuming that the pinched OFF state removes the effects of IPE stress on the Raman spectrum. We show that micro-Raman measurements in the pinched OFF state with the three-peak fit method exhibit the same vertical electric field and in-plane stress validated in our previous work with two peaks 17 yet with zero temperature rise. Measurements in the ON state using our three-peak fit method yield the same vertical electric field as in the pinched OFF state at the same drain bias and approximately the same temperature rise and in-plane stress as the two-peak fit method with the pinched OFF state as the unpowered reference.…”

“…11,15,16 In a recent study, we proposed that the vertical electric field along the c-axis strongly affects the Stokes peak positions of wurtzite GaN independently of the IPE strain and needs to be accounted for with a term depending on the electric field apart from that of the stress in the c-plane. 17 We also validated our hypothesis with measurements of the vertical electric field and in-plane IPE stress in GaN HEMTs using the simultaneous change in the Stokes peak position of two phonon modes.…”

Experimental Characterization of the Thermal Time Constants of GaN HEMTs Via Micro-Raman Thermometry

“…Analyzing the shifts of both the E2 (high) and A1 (LO) peaks properly decouples the temperature rise from the induced thermoelastic stress without the need for calibration of each sample while additionally providing measurements of the thermoelastic stress. However, (2a) and (2b) cannot capture the effect of the inverse piezoelectric stress and electric field along the -axis due to the inability of cut off the current in an ungated HEMT [28]. The 100×, NA = 0.8 microscope objective used in our measurements resulted in a laser spot size of ≈0.8 µm with a depth of field of ≈3.3 µm [25] such that the temperature and thermoelastic stress values represent the volumetric average value of these quantities over a ≈0.8 µm cylinder through the depth of the GaN buffer.…”

Thermal Management and Characterization of High-Power Wide-Bandgap Semiconductor Electronic and Photonic Devices in Automotive Applications

“…This procedure is advantageous because it does not require calibration to determine the peak position-temperature relationship. Bagnall et al performed an in-depth theoretical analysis coupled with experimental results to demonstrate that there is an additional electric field component that contributes to the phonon frequency shift of Raman-active optical phonon modes, in addition to temperature, mechanical stress, and IPE stress [33,34]. A complete explanation was provided as to why the reference condition suggested by Beechem et al is the proper method for Raman thermometry as it removes both the IPE stress and electric field contributions from the phonon frequency shift.…”

“…A complete explanation was provided as to why the reference condition suggested by Beechem et al is the proper method for Raman thermometry as it removes both the IPE stress and electric field contributions from the phonon frequency shift. This leaves only the temperature and biaxial thermoelastic stress components, which can be determined using the multispectral analysis established by Choi et al [25,[32][33][34]. Typical steady-state measurement capabilities were extended to monitor the transient evolution of the thermal response of operating GaN devices by using a variable-delay laser pulse with locked-in device electrical excitation [35][36][37].…”