Assessment of the Impact of Inelastic Tunneling on the Frequency-Depth Conversion from Low-Frequency Noise Spectra

An expression is derived for the conversion of the frequency axis of a low-frequency noise spectrum into a depth axis, based on the capture and emission time constant of a random telegraph signal. By connecting the corner frequency of the corresponding Lorentzian spectrum to the measured trapping time constant, the effect of multiphonon relaxation upon tunneling into an oxide trap can be included in a natural way. With this expression, one can derive in a straightforward manner some important trends with respect to the impact of several trap and material parameters on the tunneling depth, both for SiO₂ and high- κ gate dielectrics.