Extraction of the threshold voltage of MOSFETs

Abstract

The threshold voltage VT is an important parameter for MOSFET modeling, simulation and characterization [1, 2], as can be seen clearly from the MOSFET models developed and discussed in Chapter 1. Such a voltage is conventionally defined as the gate voltage that causes the onset of strong inversion in the channel of MOSFETs. Figure 3.1 shows a qualitative plot of the inversion layer charge Q’I vs. the applied gate voltage Vg, which includes the characteristics of depletion, weak inversion, moderate, and strong inversion regions. The point where the Q’ I plot becomes a straight-line is the onset of strong inversion. As seen in Figure 3.1 , the transition of the exact point toward the straight-line region is very gradual, and no clear point can be identified that could conventionally be taken as the onset of strong inversion. Thus a possible definition of the onset point, which yields VT, can be the Vg value for which Q’I is within an acceptable value not much larger than zero. The voltage VMO shown in Figure 3.1 fits into this definition. Alternatively, VT can be determined from the extrapolation of the slope of the linear region, and VTO shown in Figure 3.1 would be the appropriate threshold voltage. The last possible definition of VT is taken at the point where the curve becomes straight-line, which yields VT = VHO, as indicated in Fig 3.1.. It turns out that VHO is about 0.6 V above VMO at room temperature and for practical fabrication processes [3]. Clearly, the first two definitions have defined the voltage for onset of moderate inversion, whereas the last one has defined the onset for strong inversion. In fact, often no distinction is made between VMO, VTO, and VHO in the literature, and all three are taken to be one and the same point called threshold.