Extraction Algorithms

This section describes the extraction algorithms for the classical, narrow width, short channel, saturation region, and sidewall capacitance extractions.

Classical Parameter Extractions

This extraction calculates the classical model parameters UO, VTO, NSUB, and UEXP from the ID versus Vg measurement at varying bulk voltages on a large device. Select the gate voltage range to cover the cutoff as well as the linear region, including the mobility reduction range. The bulk should be biased at 0V as well as at values that cover the normal operating range of the device.

Parameters UO and VTO are first extracted from the Vb = 0 curve. To calculate these parameters, a least-squares fit is carried out to the maximum slope of the curve in the linear region. The parameter UEXP is calculated to fit the reduction in the slope of the same curve when higher gate voltages are applied. The parameter is calculated based on the specified value of UCRIT.

The combination of UO, UEXP and UCRIT has a redundant parameter. IC-CAP keeps the UCRIT fixed at its specified value and extracts UO and UEXP. An unreasonable value for UCRIT might result in an unexpected value for the mobility UO.

The same curve fitting is carried out on the curve with the largest absolute value of bulk voltage. The threshold voltage at this bias is then calculated from the intersection of this line. The parameter NSUB is calculated from the difference in the two threshold voltages.

Narrow-Width Parameter Extractions

This extraction calculates the narrow device parameters WD and DELTA from the Id versus Vg measurement. The setup and extraction are similar to the classical extraction. The threshold voltage (VTH) and Beta (effective mobility) are calculated using least-squares fitting. The parameter WD is calculated from Beta and UO. The parameter DELTA is calculated from the shift in threshold voltage (the difference of VTH and VTO).

Short-Channel Parameter Extractions

This extraction calculates the short channel parameters LD and XJ from the Id versus Vg measurement. The setup and extraction are similar to the classical and narrow width. The effective Gamma (or effective NSUB) and Beta (effective mobility) are calculated using least-squares fitting. The parameter LD is calculated from Beta and UO. The parameter XJ is calculated from the change in Gamma (or NSUB).

The parameter XJ is the only parameter that controls the effect of channel length on the shift of threshold voltage due to bulk bias. This parameter is extracted by IC-CAP to fit the threshold shift and therefore its extracted value may not correspond to the metallurgical junction depth. In other words, XJ is an empirical (not a physical) parameter in this model.

Saturation Parameter Extractions

This extraction calculates the saturation parameters VMAX and NEFF from the Id versus Vd measurement. The measurement can be taken at a single gate voltage or at various gate voltages. Only the highest gate voltage curve is used in the extraction. Ensure the drain voltage sweep is sufficient to cover both the linear and saturation regions.

In this extraction, first the knee point or the saturation point is found from the shape of the curve for the maximum gate voltage. VMAX is calculated from the saturation point. NEFF is then calculated to fit the saturation portion of the curve.

Sidewall and Junction Capacitance Parameter Extractions

To accomplish total cv extraction (due to both bottom area and sidewall area), measure two DUTs using the same setup specifications. In these extractions, CJ and CJSW are calculated, then PB, MJ and MJSW are extracted.

CJ and CJSW Extractions

The values of CJ and CJSW are extracted from the measured capacitance data from the two different structures. The capacitors should have different ratios of their bottom area to sidewall area for best resolution of the equations.

The areas and perimeters used for the calculations are stored in the Model level variable table. The example MOS Model files provided with IC-CAP use variable names AreaCap1, PerimCap1, AreaCap2, and PerimCap2.

The capacitor in the cjdarea Setup has a capacitance dominated by the bottom area of the device. The capacitor in the cjdperimeter Setup has a capacitance whose perimeter area contribution is significant. The names in the variable table and in the DUT must match for the extraction to perform properly.

PB, MJ and MJSW Extractions

The parameter PB is extracted using the junction capacitance measurement not dominated by the sidewall effect. This is the DUT named cbd1 in the example MOS Model files.

The total capacitance is modeled by two equations that represent the bottom junction area and the sidewall junction area. The values of MJ and MJSW are obtained by simultaneously solving the two equations for total capacitance of each of the measured structures. An iterative method is used to obtain the built-in potential and grading factors.