We theoretically investigated the surface orientation effects on the complex band structures and performance of a 5-nm ultrathin-body Ge n-channel double gate tunnel field-effect transistor. The Ge is an indirect bandgap material, and the direct band-to-band (BTB) tunneling rate in Ge is not appreciated. We use (001) and (011) Ge thin-body to project the X[001] and X[100] valley to the 2-D Brillouin zone center, and (111) Ge thin-body to project the L[111] valley pair to the zone center. The trajectory of imaginary k is the key factor for direct BTB tunneling, and we find that the imaginary k-axis of the projected L[111] valley of (111) Ge thin-body provides the best BTB tunneling rate among the three orientations. The direct bandgap of (111) orientation is lowest among the three orientations, which results in the thinnest tunnel barrier in (111) device. The drive current of (111) device is 4× higher than (011) device and 15× higher than (001) device. The (001), (011), and (111) devices have subthreshold slope substantially lower than thermal limit, however, only (111) device has an I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60</sub> (current at 60 mV/decade slope) value close to the desired limit. We use lower Gaussian doping in drain region to suppress ambipolar current. A 5× lower doping results in a 2× longer tunnel barrier at the drain-channel interface and more than two orders of magnitude suppression of ambipolar current.