Fractals and device performance variability: The key role of roughness in micro and nanofabrication

Nano and micro-fabrication processes generate patterns with rough surfaces. This roughness becomes a significant fraction of pattern dimensions as feature size scales down and starts to affect surface properties and device performance. It has been shown that in most times surface roughness exhibits scale-limited fractal behavior which is characterized by the fractal dimension. Up to now, fractal dimension has been related to the physicochemical properties of open surfaces. Here, we examine its effects on the performance variability of devices incorporating features with rough surfaces. It is shown that when the feature dimension which is parallel to rough surface becomes lower than about 10 times the surface correlation length then the decrease of rms roughness is followed by an increase in the variability of feature dimension perpendicular to rough surface. Both dependencies are determined by the value of the fractal dimension, which means that fractal dimension controls the impact of roughness on the variability of device dimensions and hence performance. We demonstrate the role of fractal dimension in device variability, by examining the impact of the gate sidewall roughness on the leakage current of planar MOSFET devices.