Gate line edge roughness amplitude and frequency variation effects on intra die MOS device characteristics

Random fluctuations in fabrication process outcomes such as gate line edge roughness (LER) give rise to corresponding fluctuations in scaled down MOS device characteristics. A thermodynamic-variational model is presented to study the effects of LER on threshold voltage and capacitance of sub-50 nm MOS devices. Conceptually, we treat the geometric definition of the MOS devices on a die as consisting of a collection of gates. In turn, each of these gates has an area, A, and a perimeter, P, defined by nominally straight lines subject to random process outcomes producing roughness. We treat roughness as being deviations from straightness consisting of both transverse amplitude and longitudinal wavelength each having lognormal distribution.We obtain closed-form expressions for variance of threshold voltage (Vth), and device capacitance (C  ) at Onset of Strong Inversion (OSI) for a small device. Using our variational model, we characterized the device electrical properties such as σVthσVth and σC in terms of the statistical parameters of the roughness amplitude and spatial frequency, i.e., inverse roughness wavelength.We then verified our model with numerical analysis of Vth roll-off for small devices and σVthσVth due to dopant fluctuation. Our model was also benchmarked against TCAD of σVthσVth as a function of LER. We then extended our analysis to predict variations in σVthσVth and σC versus average LER spatial frequency and amplitude, and oxide-thickness. Given the intuitive expectation that LER of very short wavelengths must also have small amplitude, we have investigated the case in which the amplitude mean is inversely related to the frequency mean. We compare with the situation in which amplitude and frequency mean are unrelated. Given also that the gate perimeter may consist of different LER signature for each side, we have extended our analysis to the case when the LER statistical difference between gate sides is moderate, as well as when it is significantly large.