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Device Modeling 101 - How to Extract Threshold Voltage of MOSFETs

Blog Post created by MALong Employee on Nov 17, 2016

Threshold voltage (Vth) is one of the most important electrical parameters in MOSFET modeling. There are many existing methods for Vth 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 Vth as the gate voltage (Vg) required to achieve a chosen drain current (Id) in the device's linear region of operation. Usually drain voltage (Vd) is less than 100mV to bias transistor at linear region and both source and body nodes are connected to ground. Id is determined by (Wm/Lm) x Icon, where Wm and Lm are the mask channel width and length respectively, Icon is the arbitrary value assigned by users. Typical value of Icon is 1e-7. Icon may be different for different process nodes. CC method is widely adopted because of its simplicity. Drawback of CC method is that extracted Vth strongly depends on Icon. The procedure of CC method is shown as Figure 1.

Figure 1: Procedure of Constant Current Method

 

The ELR method evaluates Vth by finding the intercept at Vg axis of the linear extrapolation of “Id vs. Vg“ curve at the point of maximum trans-conductance (gm). The value of Vth is calculated by subtracting Vd/2 to Vg intercept point to minimize the effect of different value of Vd. 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:

 

 Algorithm Class in MBP

 Vth Calculation Method

VTH_CON (x, y, icon)

VTH_CON_LogId (x, y, icon)

VTH_CONW (x, y, icon)

VTH_CONW_LogId (x, y, icon)

VTH_CON_ABS (x, y, icon)

VTH_CON_XWXL (x, y, icon)

VTH_CON_LogId_XWXL (x, y, icon)

 

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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