# Extraction of the Effective Length and Width of Submicron MOS Transistors

**Introduction**

The accurate extraction of the effective length and width of submicron MOS transistors is very important for analog circuit design. A number of methodologies have been developed in the past to extract the effective length and width parameters with varying success. This article describes new BETA routine that can be used for DL and DW parameter extraction. The parameter BETA is extracted using the traditional methods briefly described in this article.

**Extraction**

The extraction of parameters DL and DW is performed in two steps. The first step consists of extracting the parameter BETA for each single device. The second step consists of the geometry processing. In this step, the effective length and width parameters are extracted by linear regression covering the results from all geometries measured.

Figure 1. Extraction of BETA0 parameter
from GDS versus VGS curve using maximum slope method.

Figure 2. Extraction of BETA0 parameter
from IDS versus VGS curve using maximum slope method.

BETA Extraction for Single device

The parameter BETA can be extracted from the transfer characteristics Ids versus Vgs (Vds= const, Vbs = 0V) using three different methods. The "model_sel" fitting variable enables selection of one among these methods. Selecting 0 or 1 for this fitting variable correspond to take the maximum slope from respectively GDS/VGS (Figure 1) or IDS/VGS (Figure 2) curves. If "model_sel" is set to 2 then the so called Hamer method is used to extract the device parameter BETA, VTH and THETA (see IEEE Proceedings, Vol 133, Pt. 1, No. 2, April 1986). The accuracy of this extraction depends of the selection of the three (ids,vgs) points. The simulated drain current computed with the extracted parameters and plotted with the measured data for the strong inversion region enables control of the extraction quality (Figure 3).

Geometry processing

The single device parameter BETA is taken from different geometries and the effective length and width are extracted by applying linear regression.

Extraction of DW parameter is accomplished by linear regression on BETA distribution from devices with various channel widths Wdraw and a long common channel length Ldraw ( Figure 4):

`BETA = BETA0 (Wdraw - DW) / Ldraw`

After the extraction DW is converted to the model parameter depending on the selected SPICE model.

Figure 3. Extraction of BETA0 parameter
using Hamer method.

Figure 4. Extraction of WD parameter.

Extraction of DL parameter is accomplished by linear regression on 1/BETA distribution from devices with various channel lengths Ldraw and a large common channel width Wdraw ( Figure 5):

`BETA = (Ldraw - DL) / (Wdraw * BETA0)`

After the extraction DL is converted to the model parameter depending on the selected SPICE model.

This routine has been adapted for all supported
MOSFET models: ```
LEVEL1, LEVEL2, LEVEL3, BSIM1, BSIM2, BSIM3V2,
BSIM3V3, LEVEL9, EKV
```

and `MASTAR.`

Figure 5. Extraction of LD parameter.

Summary

A new routine BETA is available for extraction
of the effective channel length and channel width of submicron MOS
transistors. The routine has been tested on a large number of submicron
technologies and has demonstrated superior performance against other
extraction methodologies.