A comparison of MOS inversion layer charge and capacitance formulas

A test is made of a recent proposal by Lewyn and Meindl for approximation of MOS inversion layer charge and substrate capacitance. Included in the test are the charge sheet formula and a new formula derived here which includes the pinning of the depletion layer width in strong inversion. Comparison with numerical calculation shows the Lewyn-Meindl result for charge density is less accurate than the charge sheet result over the entire subthreshold region. Similar inaccuracy is expected in MOS current-voltage curves in the subthreshold region and near pinch-off. The new formula is better than the other two over the entire bias range. A comparison of dc and ac substrate capacitances shows the new result to be better than both of the other formulas. In inversion, however, the percent error in dc capacitance is large. This large percent error corresponds to a small absolute error because the dc capacitance goes to zero in strong inversion. The ac capacitance error in strong inversion is ∼5 percent because of neglect of the ac inversion layer redistribution. Percent error curves for all three formulas are presented as a function of band bending and reverse bias.