Numerical Simulation of RF Noise in Si Devices

Abstract

The workhorse of today's TCAD is the drift-diffusion (DD) model, which in the special formulation of the impedance field method has been used for a long time for noise calculation, but there has been much debate over its noise source. The derivation of the DD noise model from the Langevin-type Boltzmann equation (LBE) is discussed in detail and it is shown that the DD noise source should be local in the real space, white and given by the power spectral density (PSD) of the velocity fluctuations at zero frequency calculated under homogeneous bulk conditions in analogy to the mobility. The white noise source and frequency independent mobility of the DD model reflect the neglect of certain acceleration terms in the LBE. By comparison of solutions of the LBE with and without these terms it is found that the DD model works well up to frequencies of about 100 GHz in silicon devices. Comparison of solutions of the LBE and DD model for different definitions of the noise source shows that the best device results are obtained with the PSD of the velocity fluctuations calculated under bulk conditions. Use of the Einstein relation to calculate the noise source for nonequilibrium, as is often done, leads to an underestimation of noise. While the DD model delivers good results in sub-micron devices, it fails in very small devices resulting in spurious super shot noise. Based on the LBE it is found that excess noise in devices is mostly due to scattering of cold or warm electrons, whereas hot electrons contribute little in the absence of electron-hole pair generation