Using the antenna-transmission acoustic-resonance technique, we measured temperature dependencies of mechanical resonance frequencies and attenuation of an Fe-doped GaN. A strong internalfriction peak appears during temperature change, at which reduction in frequency occurs. The peak temperature rises as frequency increases, indicating the phonon-assisted hopping conduction of carriers between Fe centers. The Arrhenius plot yields the activation energy of the hopping conduction to be 0.23 6 0.05 eV. The frequency reduction of a quasi-plane-shear resonance mode yields the piezoelectric coefficient e 15 ¼ 0.332 6 0.03 C/m 2 . V C 2015 AIP Publishing LLC.Fe ions have been doped in gallium nitride (GaN) as deep acceptors for compensating n-type carriers to achieve a semi-insulating GaN, 1-4 which is a key material in various electric devices such as a high-electron-mobility transistor (HEMT). 1,5-7 The device performances, however, deteriorate with increasing temperature. 8-10 Deeply trapped carriers in the bulk GaN can be thermally activated, causing the hopping conduction, 11,12 which creates the additional electron pass and affects the carrier mobility. 8 It is thus important to understand electron transport behavior at elevated temperatures in the semi-insulating GaN.Equally important issue is the piezoelectricity of GaN. Wurtzite GaN shows five independent elastic constants C ij and three independent piezoelectric coefficients e ij (e 33 , e 31 , and e 15 ). A complete set of C ij was determined with resonant ultrasound spectroscopy (RUS) 13 for bulk GaN specimens, where e ij were deduced as well, but they were significantly underestimated because of high carrier densities of the specimens. A few theoretical 14-17 and experimental 18 studies gave e 33 and e 31 values, but they significantly differ from each other. (The standard deviation of reported values of e 33 exceeds 20% of their averaged value, for example.) Furthermore, few theoretical reports 16 and no direct measurement appear for e 15 , the piezoelectric coefficient related to the shear stress. Thus, the piezoelectricity of GaN still remains unclear despite its crucial contribution to the twodimensional electron gas in HEMT devices. Simultaneous determination of C ij and e ij has been proven to be possible with the RUS method. 19,20 However, it required extraordinarily precise measurements on resonant frequencies, specimen dimensions, and specimen mass density because of small contributions of e ij to frequencies, 19 and is therefore inapplicable to GaN because contributions of e ij are considerably smaller due to high stiffness.In this study, we propose a methodology for evaluating the carrier dynamics and piezoelectricity in Fe-doped GaN with the antenna-transmission resonant ultrasound spectroscopy and determine the activation energy of the hopping conduction and the piezoelectric coefficient e 15 . The freecarrier flow is restricted in an insulated semiconductor, and the conduction principally occurs by hopping of trapped carriers by acceptors betw...