Threshold voltage (V_{th}) is one of the most important electrical parameters in MOSFET modeling. There are many existing methods for V_{th} extraction. Most of these procedures are based on static drain current versus gate voltage characteristics of single transistor. The most popular methods used in industry are

- Constant Current (CC) method
- Extrapolation in Linear Region (ELR) method.

The CC method defines V_{th} as the gate voltage (V_{g}) required to achieve a chosen drain current (I_{d}) in the device's linear region of operation. Usually drain voltage (V_{d}) is less than 100mV to bias transistor at linear region and both source and body nodes are connected to ground. I_{d} is determined by (W_{m}/L_{m}) x I_{con}, where W_{m} and L_{m} are the mask channel width and length respectively, I_{con} is the arbitrary value assigned by users. Typical value of I_{con} is 1e^{-7}. I_{con} may be different for different process nodes. CC method is widely adopted because of its simplicity. Drawback of CC method is that extracted V_{th} strongly depends on I_{con}. The procedure of CC method is shown as Figure 1.

Figure 1: Procedure of Constant Current Method

The ELR method evaluates V_{th} by finding the intercept at Vg axis of the linear extrapolation of “I_{d }vs. V_{g}“ curve at the point of maximum trans-conductance (gm). The value of Vth is calculated by subtracting V_{d}/2 to V_{g} intercept point to minimize the effect of different value of V_{d}. The bias condition is the same with the CC method. The procedure of ELR method is shown as Figure 2.

Figure 2: Procedure of Extrapolation in Linear Region Method

In Keysight’s MBP, Model Builder Program, both CC and ELR methods are implemented in built-in libraries and can be easily used in IMV (InterMediate Variable) page as shown in Figure 3.

Figure 3: Vth vs. Length in MBP

For the CC method, MBP also provides different algorithms for you to choose directly:

*References:*

*[1] A. Ortiz-Conde et al., “A review of recent MOSFET threshold voltage extraction methods,” Solid-State Electron., vol. 47, no. 4, pp. 677–683, 2003.*

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