This work presents the first demonstration of the transistor-free memory-diode (MD) array fabricated on Ge-on-Insulator (GeOI), which can work as an ultra-compact <inline-formula> <tex-math notation="LaTeX">8{F}^{{2}} </tex-math></inline-formula> ternary content addressable memory (TCAM). Through the wafer bonding and thinning techniques, the Ge layer in the GeOI structure maintains the monocrystalline quality originated from bulk Ge to ensure the Fermi-level pinning effect, forming an effective Schottky barrier with low reverse-bias leakage currents. Furthermore, an ultra-thin Y-doped GeOx layer is introduced to suppress the surface-state current, enabling a higher rectifying ratio. Thanks to the ultra-high rectifying (<inline-formula> <tex-math notation="LaTeX">>\,\,2\times 10^{{5}}{)} </tex-math></inline-formula> and sufficient on/off ratios (> 500), the 4-bits MD-TCAM array shows over 2 orders differences between the match and mismatch currents, which experimentally verifies the feasibility and accuracy of parallel data search.