Stable threshold voltage extraction using Tikhonov´s regularization theory

We propose a new threshold voltage extraction with stability based on Tikhonov´s regularization theory. It suppresses the instability of the transconductance change method and gives mathematically exact solution. Following the mathematical derivation, we convert the procedure into the MATLAB programming for users´ convenience. Finally, the proposed method extracts the threshold voltage close to the physically meaningful one which means the gate-to-source voltage where φ_s=2φ_f+V_SB. To confirm the proposed one, we compare it with others such as the linear extraction and the normalized mutual integral difference method. It was found that the proposed one extracted the physically meaningful threshold voltage very closely. Moreover, it is also observed that there is a high correlation between the proposed and the normalized mutual integral difference method.