Hole-tunneling Si0.82Ge0.18/Si asymmetric triple-barrier (TB) resonant tunneling diodes (p-RTDs) were created by sputter epitaxy instead of conventional chemical vapor phase epitaxy. As a result, a peak current density (PCD) of 297 kA/cm2 with a peak-to-valley current ratio of 7.3 was recorded at room temperature. The observed high planarity of the films grown by sputter epitaxy is also considered one of the factors behind the high PCD. From the results of self-consistent theoretical calculations of current–voltage characteristics using box-shaped potentials as a first approximation and considering space charge effects of quantum wells, heavy-hole-to-heavy-hole and light-hole-to-light-hole state transitions under the tunneling conditions of the TB potential structure applied in this study were found to be inherent current paths. Moreover, the light and heavy hole currents contribute almost equally to the overall device current, resulting in a theoretical PCD of 637 kA/cm2, which is close to the experimental result. Further analytical simulations with adjusted series resistance and thickness of the nondoped layer allowed the alignment of the theoretically obtained PCD voltage position with the experimentally obtained one. Thus, the theoretical and analytical calculations explain the operation mechanisms of SiGe/Si p-RTDs, and the proposed fabrication method using our sputter epitaxy method is very useful for the actual production of high-PCD SiGe/Si p-RTDs operating at room temperature.