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We present a comprehensive investigation of low-frequency noise behavior in complementary (n-p-n + p-n-p) SiGe heterojunction bipolar transistors (HBTs). The low-frequency noise of p-n-p devices is higher than that of n-p-n devices. Noise data from different geometry devices show that n-p-n transistors have an increased size dependence when compared with p-n-p transistors. The 1/f noise of p-n-p SiGe HBTs was found to have an exponential dependence on the (intentionally introduced) interfacial oxide (IFO) thickness at the polysilicon-to-monosilicon interface. Temperature measurements as well as ionizing radiation were used to probe the physics of 1/f noise in n-p-n and p-n-p SiGe HBTs. A weak temperature dependence (nearly a 1/T dependence) of 1/f noise is found in both n-p-n and p-n-p devices with cooling. In most cases, the magnitude of 1/f noise is proportional to IB2. The only exception in our study is for noise in the post-radiation n-p-n transistor biased at a low base current, which exhibits a near-linear dependence on IB. In addition, in proton radiation experiments, the 1/f noise of p-n-p devices was found to have higher radiation tolerance than that of n-p-n devices. A two-step tunneling model and a carrier random-walk model are both used to explain the observed behavior. The first model suggests that 1/f noise may be caused by a trapping-detrapping process occurring at traps located inside IFO, while the second one indicates that noise may be originating from the emitting-recapturing process occurring in states located at the monosilicon-IFO interface.