Error analysis and frequency selection guidelines for three-frequency correction in MOS capacitors. (10th October 2018) - Zhang, Xizhen; Zhang, Sujuan; Pan, Xiuyu; Zhu, Huichao; Cheng, Chuanhui; Cheng, Yi; Yu, Tao; Xing, Guichao; Zhang, Daming; Bai, Mindi; Luo, Xixian; Chen, Baojiu
Abstract: The three-frequency correction method is used to extract the model parameters in a five-element model which includes MOS capacitance C, parallel resistance R p, interface layer (IL) capacitance C i, IL resistance R i, and series resistance R s . A method for the error analysis of these model parameters has been developed, using error propagation of measured capacitance C m and resistance R m . We have applied this error analysis method to a 0.3 mm × 0.3 mm Al/ZrO2 /IL/n-Si MOS capacitor with dielectric thickness 35.9 nm. Accumulation capacitances and their errors at various frequency combinations have been calculated to study suitable frequency selection. The errors in the three-frequency correction method depend on selection of the three frequencies ( f 1 > f 2 > f 3 ) and dissipation factor D m . For large differences between frequencies f 1 and f 3 ( f 3 / f 1 ∼ 0.05– 0.2), the f 2 value should be equal to or a little larger than the average value ( f 3 + f 1 )/2 to ensure a small error (less than 4%) in spite of large D m ∼ 0.20–0.31 at f 1 = 1.0–1.6 MHz. For three close f 1 and f 3 ( f 3 / f 1 ∼ 0.25–0.6), small ratios for f 2 / f 1 < ∼ 2/3 and f 3 / f 2 < ∼ 2/3 ( f 3 / f 1 < 0.44), f 2 = ( f 3 + f 1 )/2 and small D m less than ∼0.20 have been suggested to ensure error less than 4%. Considering the error and possible dispersion, the difference between f 1 and f 3 should be moderate, i.e. f 3 / f 1 = 0.05 ∼ 0.44. For optimal frequency selection, we suggest f 3 / f 1 = ∼0.10 and f 2 = ( f 3 + f 1 )/2. The frequency selection is not critical f or most MOS capacitors, e.g. this sample Al/ZrO2 /IL/n-Si capacitor. The three-frequency correction method together with error analysis is effective in extracting accurate accumulation capacitance.