We theoretically study the performance limits of current-gain cutoff frequency, ƒ
T, for the HEMTs with InAs or In
0.70Ga
0.30As middle layers in the multi-quantum-well (MQW) channels by means of the quantum-corrected Monte Carlo (MC) method. We calculate the distribution of the delay time along the channel, τ(x), and define the effective gate length,
Lg, eff, as the corresponding length to (x). By extrapolating
Lg, eff to
Lg = 0nm, we estimate the lower limit of
Lg, eff,
Lg, eff(0). Then we estimate the performance limit of ƒ
T, ƒ
T(0), by extrapolating ƒ
T to
Lg, eff(0). The estimated ƒ
T(0) are about 3.6 and 3.7THz for the HEMTs with InAs middle layers of 5 and 8nm in thickness, and about 3.0THz for the HEMT with In
0.70Ga
0.30As middle layer of 8nm in thickness, respectively. The higher ƒ
T(0) in the HEMTs with InAs middle layers are attributed to the increased average electron velocity,
vd, in the channel. These results indicate the superior potential of the HEMTs using InAs in the channels. The HEMT with InAs middle layer of 8nm in thickness shows the highest ƒ
T on condition of the same
Lg because of its highest
vd. However, the increased total channel thickness results in the longer
Lg, eff(0), which leads to the restriction of ƒ
T(0). Therefore, in order to increase ƒ
T(0), it is essential to make
Lg, eff short in addition to making
vd high. Our results strongly encourage in making an effort to develop the HEMTs that operate in the terahertz region.
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