Error analysis and frequency selection guidelines for three-frequency correction in MOS capacitors

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/ZrO 2 /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 for most MOS capacitors, e.g. this sample Al/ZrO 2 /IL/n-Si capacitor. The three-frequency correction method together with error analysis is effective in extracting accurate accumulation capacitance.