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We present an optically-detected time-of-flight technique with femtosecond resolution that monitors the change in the electroabsorption due to charge transport in a p-i-n diode, and show how it may be used to determine the electron transit time, velocity-field characteristic, and transient electron velocity overshoot in GaN at room temperature. In a GaN homojunction p-i-n diode, the peak electron velocity of 1.9x107 cm/s , corresponding to a transit time of ~2.5 ps across the 0.53 micrometers depletion region, is attained at ~ 225 kV/cm. The steady-state velocity-field characteristic is in qualitative agreement with theoretical calculations. A measurement of the high field transient electron velocity overshoot was also performed using a semi-transparent p-contact AlGaN/GaN heterojunction p-i-n diode. Transient electron velocity overshoot is observed at fields as low as ~100 kV/cm, with the peak transient electron velocity becoming larger with increasing electric field until a maximum of 7.25x107 cm/s is observed within the first 200 fs after photoexcitation at a field of 320 kV/cm. At higher fields, the measurement of the peak velocity is limited by the 80 fs duration of the pulses, but the increase in transit time with increasing field suggests the onset of negative differential resistance. Theoretical Monte Carlo calculations incorporating a GaN full-zone band structure show that although the peak steady-state velocity occurs at ~200 kV/cm, the ensuing negative differential resistance region of the velocity-field curve is not initially associated with intervalley transfer, as the majority of electrons do not attain sufficient energy to effect this transfer until they are subjected to much higher fields (>325kV/cm). Insight into this behavior can be gleaned from the band nonparabolicity deduced from the constant energy surfaces in the (Gamma) valley, which shows that the effective mass in the c-direction can be viewed as becoming larger at high k-values. This larger effective mass may play a role in velocity overshoot by reducing the velocity and momentum relaxation time at high k-values in the (Gamma) valley. Theoretical calculations employing a semiclassical transport model in the collisionless regime confirm the importance of this nonparabolicity for the determination of the temporal shape of the transient velocity overshoot curves.
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