Contributed Review: Experimental characterization of inverse piezoelectric strain in GaN HEMTs via micro-Raman spectroscopy

Abstract

Micro-Raman thermography is one of the most popular techniques for measuring local temperature rise in gallium nitride (GaN) high electron mobility transistors (HEMTs) with high spatial and temporal resolution. However, accurate temperature measurements based on changes in the Stokes peak positions of the GaN epitaxial layers requires properly accounting for the stress and/or strain induced by the inverse piezoelectric effect. It is common practice to use the pinched OFF state as the unpowered reference for temperature measurements because the vertical electric field in the GaN buffer that induces inverse piezoelectric stress/strain is relatively independent of the gate bias. Although this approach has yielded temperature measurements that agree with those derived from the Stokes/anti-Stokes ratio and thermal models, there has been significant difficulty in quantifying the mechanical state of the GaN buffer in the pinched OFF state from changes in the Raman spectra. In this paper, we review the experimental technique of micro-Raman thermography and derive expressions for the detailed dependence of the Raman peak positions on strain, stress, and electric field components in wurtzite GaN. We also use a combination of semiconductor device modeling and electro-mechanical modeling to predict the stress and strain induced by the inverse piezoelectric effect. Based on the insights gained from our electromechanical model and the best values of material properties in the literature, we analyze changes in the E2 high and A1 (LO) Raman peaks and demonstrate that there are major quantitative discrepancies between measured and modeled values of inverse piezoelectric stress and strain. We examine many of the hypotheses offered in the literature for these discrepancies but conclude that 2 none of them satisfactorily resolves these discrepancies. Further research is needed to determine whether the electric field along the -axis could be affecting the phonon frequencies apart from the inverse piezoelectric effect in wurtzite GaN, which has been predicted theoretically in zinc blende gallium arsenide (GaAs).

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

“…The strain induced by the IPE effect changes the interatomic distances and force constants, resulting in changes in the optical phonon frequencies of the crystal. By probing the optical phonon frequencies near the Γ-point, micro-Raman spectroscopy can be used to experimentally measure this IPE-induced strain in GaN HEMTs with ≈1 µm spatial resolution from changes in the Raman peak positions [8]- [10].…”

“…Several hypotheses, such as uncertainties in the piezoelectric properties or phonon deformation potentials of GaN, have been suggested to explain the significant disagreement between measured and modeled values of strain, stress, and electric field [8]- [10], [11]. Our recent review [10] investigated many of these hypotheses in detail and concluded that none of them can satisfactorily resolve this disagreement.…”

“…Because the temperature rise in the pinched OFF state is negligible and the average electric field component along the -axis in the GaN buffer is primarily a function of the drain bias, the difference in Raman peak position between the pinched OFF state and the ON state should not include the contributions of the IPE-induced stress and the vertical electric field [8], [10]. Thus, the temperature rise and thermoelastic stress can be simultaneously determined from changes in the positions of two Raman peaks between these two bias conditions [5]- [6].…”

“…Despite the success of using the pinched OFF state as the unpowered reference for micro-Raman temperature measurements that agree with thermal models and micro-Raman measurements based on the Stokes/anti-Stokes ratio (which should not be affected by strain, stress, and electric field), there has been considerable difficulty in deriving quantitative values of the IPE-induced strain and stress components from micro-Raman measurements that agree with electro-mechanical models [8]- [10]. Analysis of the Raman peak shifts of the E2 (high) and A1 (LO) modes between the zero bias state ( = 0 and = 0) and the pinched OFF state based on potential deformation theory and linear piezoelasticity leads to contradictions in the sign and order of magnitude of the strain, stress, and electric field components predicted by simple physical arguments and rigorous electromechanical modeling [8]- [10].…”

“…Our recent review [10] investigated many of these hypotheses in detail and concluded that none of them can satisfactorily resolve this disagreement. In this work, we show that the source of the discrepancy is the fact that the electric field also affects the internal structural parameters of wurtzite GaN beyond the macroscopic strain induced by the IPE effect.…”