Micro-Raman thermography is one of the most popular techniques for measuring local temperature rise in gallium nitride (GaN) high electron mobility transistors with high spatial and temporal resolution. However, accurate temperature measurements based on changes in the Stokes peak positions of the GaN epitaxial layers require 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 electro-mechanical 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 none of them satisfactorily resolves these discrepancies. Further research is needed to determine whether the electric field components 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).
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