  We study gated field effect transistors (FETs) with fractal geometries under
Dyakonov and Shur asymmetric boundary conditions, where the source and drain
span the left and right edges of the device respectively. An AC THz potential
difference is applied between source and gate while a static source-drain
voltage, rectified by the nonlinearities of FET electrons, is measured. We
find, for a recursion depth, n, that resonant peaks in the potential integrated
along the drain at ${\omega}_n = 3n{\omega}_0$ are amplified while all other
are diminished. Additionally, we find the presence of peaks with frequencies
dependent on the fractal dimensions of both the Sierpinski carpet and a similar
alternative fractal. We then show the advantage of employing the alternative
fractal as a superior geometry for the photodetector when compared to the
Sierpinski carpet.
