This article reports a 12-/13.56-MHz fast-Andenergy-efficient startup crystal oscillator (XO) featuring a binary-search-Assisted two-step injection technique for ultralowpower duty-cycled radios. Specifically, after the first injection, a calibration module refines the auxiliary oscillator's frequency toward the crystal's resonant frequency in a binary-search fashion with a sub-500-ppm error for the second injection. This calibration method eliminates the closed-loop phase-locked loop (PLL) and shortens the calibration period into 48 clock cycles. Prototyped in a 65-nm CMOS process, the XO occupies an active area of 0.134 mm2. The 13.56-MHz XO can achieve a startup time (ts) of 45.8 us with a VDD of 0.7 V, while consuming 5.0 nJ of energy.Ts varies by-2.2% amid temperature variations (-40 C to 85 C). Its steady-state power consumption is 28.4 uW, with an output phase noise of-143.7 dBc/Hz at 1-kHz offset (FoM: 241.8 dBc/Hz), manifesting its state-of-The-Art performance.